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The central role that Reservoir engineers play in a field's development and planning, cannot be underestimated. Recommending, the most appropriate and most cost effective reservoir depletion schemes has a great impact on a field's and ultimately a company's profitability. If done correctly, it will result in a windfall for the company but if done incorrectly or haphazardly, it will result in financial disaster. Advanced Reservoir Engineering, 2nd Edition provides reservoir engineers with valuable insight into the tools, techniques and science of efficient oil recovery even in the most difficult fields. Reorganized for ease of use and with 40% new information, this new edition represents a 50% update over the previous edition. The main objective of the book is to continue to provide practicing engineers and engineering students with an understanding of day-to-day reservoir engineering operations and problems and how to maintain and solve them. Concise and readable, this new edition begins with the fundaments to provide those new professionals a firm foundation of in the methods and techniques. Chapter one, which once dealt with the theory and practice of transient flow analysis and well testing, is now changed to deal exclusively with well testing. The theory and practice of transient flow analysis moved to a more appropriate section of the book. The author has added five new chapters, Reservoir characterization and Up-scaling, Miscible WAG Flood, Enhance Oil Recovery, Reservoir Management and Optimization, and Reservoir Simulation. In addition, the author has added a simulations code chapter. Assist engineering and other personnel to solve operating problems. Develop plans for oil and gas field drilling, and for product recovery and treatment. Maintain records of drilling and production operations. Confer with scientific, engineering, and technical personnel to resolve design, research, and testing problems. Write technical reports for engineering and management personnel.

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... Coning can seriously impact the well productivity and influence the degree of depletion and the overall recovery efficiency of the oil reservoirs. (2) ...

... The gas-oil and water-oil contacts are prone to deforming into a bell shape due to these counterbalancing forces as shown schematically in Figure 1. (2) There are essential forces that could have an impact on fluid flow patterns around well bores such as capillary forces, gravity forces and viscosity forces. ...

... On the other hand, if the pressure in the system is unstable, an unstable cone will keep moving forward until stable circumstances are achieved. (2) ...

in this report you will find a beneficial information about the methods to diagnose the source of the water production that comes with producing oil reservoirs and how to calculate the water breakthrough time in two correlations and to compare it to a real case data and also how to predict the water cut performance also compared to a real field case .

... This retrograde condensation behaviour continues as pressure decreases until liquid dropout approaches its maximum volume. Pressure reduction beyond the point of maximum liquid dropout initiates the typical vaporization process, which continues until all the condensed liquid has vaporized as the reservoir pressure approaches the lower dew-point pressure where the reservoir system reverts to single phase (vapour) [1][2][3]. ...

... Representative fluid samples of a given reservoir obtained from a reference depth in the reservoir (bottom hole sample) or at the surface from a separator (recombined oil and gas surface sample) is usually subjected to some standard Pressure-Volume-Temperature (PVT) laboratory tests. These standard experiments provide suitable PVT fluid properties (data) needed to study and understand the behaviour of the fluids in the reservoir, within the wells, in the piping system, and at surface conditions [1][2][3]. PVT fluid properties are also needed to estimate: well stream composition as a function of time, completion design, possible miscibility effects due to gas injection, surface facility specification, contaminants (Hydrogen Sulfide, Carbondioxide and Nitrogen) concentration in produced fluids [1][2][3]. Such PVT fluid properties include the oil and gas formation volume factor, fluid compressibility factor, solution gas-oil ratio, fluid density and specific gravity, fluid viscosity and API gravity, saturation pressures, mole percent and molecular weight of components [1][2][3]. ...

... These standard experiments provide suitable PVT fluid properties (data) needed to study and understand the behaviour of the fluids in the reservoir, within the wells, in the piping system, and at surface conditions [1][2][3]. PVT fluid properties are also needed to estimate: well stream composition as a function of time, completion design, possible miscibility effects due to gas injection, surface facility specification, contaminants (Hydrogen Sulfide, Carbondioxide and Nitrogen) concentration in produced fluids [1][2][3]. Such PVT fluid properties include the oil and gas formation volume factor, fluid compressibility factor, solution gas-oil ratio, fluid density and specific gravity, fluid viscosity and API gravity, saturation pressures, mole percent and molecular weight of components [1][2][3]. ...

... At this location on the main pipeline, the fluid must arrive at certain conditions. The flow through the reservoir(s), flow through the production strings of the wells, flow through the field gathering system and processing equipment, compression of the gas, and, finally, flow through an auxiliary pipeline to the point of sale and /or transfer are all required components of the overall production system [1,2]. ...

... Reservoir deliverability graphs for various tubing head pressures may be used to determine the field development timetable. Here, we would simulate two patterns of field development plans [1][2][3][4][5][6]. ...

... Water removes oil from the pore spaces, however the effectiveness of this removal relies on a variety of circumstances (e.g., oil viscosity and rock characteristics). Voidage replenishment has also been utilized in oil fields like Wilmington (California, US) and Ekofisk (North Sea) to reduce further surface subsidence [2,37]. Petroleum industry and scientific societies have released several important and in-depth books on waterflooding technology during the past four decades, for example those that are written by Craig [39], Willhite [40], and Rose, et al. [41]. ...

A secondary recovery techniques are those used after natural energy depletion of an oil or a gas reservoir to boost its production such as gas lift and water injection. Both methods have been proved their success and effectiveness for enhancing field production. However, each reservoir or field has its own criteria and they may be ineffective depending field criteria and future plans. Furthermore, a field development strategy is considered as a key activity for enhancing the field recovery. Therefore, the aim of this article is to do well thermal simulation and analysis during making gas lift and water injection for Magurele field development at different conditions such temperature, tubing size, and production parameters. Several strategies are suggested from putting a new drilled well (M#206) on production till abandonment. A sensitivity study is done to know the effect geothermal zones and tubing size on well performance and flow regimes. It was found that utilizing a reservoir temperature of 70°C and tubing 3 1/2, all production activities displayed normal fluid and wellbore temperature profiles, using larger tubing or producing from the high temperature (HT) zone has only a minimal impact on the pressure profile, only slightly increasing surface pressures and The suggested production activities are unaffected by the higher temperature. With regard to the flow regime created by strategies, starting usage circumstances for tubing 3 1/2", with the exception of injection, which is turbulent in all scenarios, the flow regime is slug flow between 70°C and HT zones. Additionally, it seems like the bubbly flow is at shallower depths. Due to the use of 4 1/2-inch, the flow regime is altered to transitional and bubbly flows at deeper depths. This study helps to maximize the reservoir output and keep the new drilled wells usable and useful as long as possible.

... = (2)(3)(4)(5)(6)(7)(8) Where, = reference cell volume = sample cell volume = grain volume of sample P 1 = initial pressure in reference cell P 2 = final pressure in system Further, the cell volumes V c and V R are difficult to measure with the desired accuracy. This instrument is, however, easily calibrated with precisely known solid volumes such as steel balls. ...

... If all measurements are then started at the same P 1 , it is a simple matter to obtain V s from a previously determined calibration plot of V s vs P 2 . Grain volume may also be calculated from (2)(3)(4)(5)(6)(7)(8)(9) = sand grain density. Equation (2)(3)(4)(5)(6)(7)(8)(9) is often used with the typical value for of 2.65 gm/cc. ...

... Grain volume may also be calculated from (2)(3)(4)(5)(6)(7)(8)(9) = sand grain density. Equation (2)(3)(4)(5)(6)(7)(8)(9) is often used with the typical value for of 2.65 gm/cc. ...

The class notes introduces the scope, objectives, and main properties of reservoir rocks, especially porosity, permeability, saturation, and properties acquisition and analysis. discusses the measurements of rock properties such as porosity, absolute and relative permeability, formation resistivity, fluid saturation, petrophysical parameters, and the properties of porous media containing multiphase. describes the common routine and special core analysis techniques. It supports the educational process as it serves as a textbook reference during the teaching of the properties of reservoir rocks for petroleum engineering programs.

... It is an irreversible process in which the injected polymer adheres-retains in the rock due, among other reasons, to its chemical and electrical affinity with it. This process causes a decrease in the permeability of the rock to the flow of the aqueous phase and is correlated with the concentration of adsorbed polymer [13]. ...

... Resistance factor. It is the correlation between the mobility of water and the mobility of the polymer solution [13]. ...

... Residual resistance factor. It is the water mobility ratio, which can also be expressed in terms of water permeabilit y initially and after the injection of the chemical agent such as polymers [13]. ...

... In particular, it is a small positive constant for (isothermal) slightly compressible fluids such as crude oil and water. This condition is commonly used in petroleum and reservoir engineering [1,12], ...

... Let ω andν be the same constants as in Theorem 4.5. Denote β 1 =κα 0 , ω 1 = ω/κ, ω 2 = µ 2 ω, ω 3 = µ 3 ω, ω 4 = ω 3 +ν β 1 and ...

... Regarding the H 2 S molar volume correction factor, a value of −0.10356, as proposed by Stamatakis and Magoulas [21], is recommended. The critical properties involved in the EoS are retained in their lab values, whereas the acentric factor is estimated by the Soave approach [22]. ...

... For the CO 2 -HCs pairs above methane, correlations from standard engineering textbooks can be used [22]. Since H 2 S presence is crucial in the studied mixtures, a dedicated solution is preferred for the H 2 S-HCs pairs. ...

This study provides insights into the experience gained from investigating the thermodynamic behavior of well and reservoir fluids during acid gas injection (AGI) in a hydrocarbon field to enhance oil recovery (EOR) and to reduce greenhouse gas emissions. Unlike conventional water and natural gas injection, AGI involves complicated phase changes and physical property variations of the acid gas and reservoir fluids at various pressure-temperature (P-T) conditions and compositions, and both constitute crucial parts of the EOR chain. A workflow is developed to deal with the reservoir fluid and acid gas thermodynamics, which is a key requirement for a successful design and operation. The workflow focuses firstly on the development of the thermodynamic models (EoS) to simulate the behavior of the reservoir fluids and of the injected acid gas and their integration in the field and in well dynamic models. Subsequently, the workflow proposes the thermodynamic simulation of the fluids’ interaction to determine the Minimum Miscibility Pressure (MMP), yielding the dynamic evolution of the fluids’ miscibility that may appear within the reservoir. Flow assurance in the acid gas transportation lines and in the wellbore is also considered by estimating the hydrate formation conditions.

... Additionally, in order to calculate the absolute permeability of the micro-throats type 2, we ignore the pressure drop happening in the void section of the micro-throat ( Fig. 3.6b-4 and Fig. 3.6d-4). Considering that the absolute permeability of a series of elements is mainly controlled by the smallest permeability value [203], this assumption is reasonable. connection with a meso-pore (details of figure elements are described in Table 3. ...

... To calculate the analytical permeability of the whole geometry, we assume a system of parallel conductors with the same length. Thus, the equivalent analytical permeability of the whole geometry (K e ) is [203]: ...

... Crude oil viscosity is a paramount parameter determining the success of oil recovery using waterflooding. Oil viscosity can affect the mobility ratio which directly control the sweep efficiency [15]. Generally, the viscosity ratio between the displaced fluid to the displacing fluid affect the waterflood displacement or sweep efficiency. ...

... The types of systems can be determined by estimating the water saturation within the reservoir. As mentioned by Ahmed [15], for initial water saturation more than 50%, it is a water-wet system whereas for initial water saturation less than 50%, it is an oil-wet system. ...

Waterflooding is a secondary oil recovery process that commonly utilized. However, there are several factors affecting the efficiency of water-flooding. Current research focused on the effects of injection rate and oil viscosity on the waterflooding efficiency. Fluid Structure Interaction (FSI) is utilized to predict the effect of the injection rate and oil viscosity towards waterflooding. Volume of fluid (VOF) and Realizable k- ɛ models are utilized in this research. Ergun’s equation also utilized in this research for estimation of permeability and inertial loss within the porous medium. The research found viscous fingering occurred when the mobility ratio is more than unity and instability number, Ni > 1000. The phenomenon of viscous fingering is directly affected by injection rate and viscosity ratio. The phenomenon directly affects directly sweep efficiency during waterflooding process thus affecting oil recovery process. The research found as injection rate and viscosity ratio increase; viscous fingering predominantly seen within the porous medium.

... The reservoir property models, including shale volume (Vsh), porosity (φ), rock type (RT), and permeability (k), are propagated by facies-constrained stochastic algorithms to realize geologic characters recognized by the geological genesis analysis. A water saturation (Sw) model is calculated by saturation height function (SHF) [27] and a net-to-gross ratio (NTG) model is calculated by given cutoffs in porosity and Vsh from petrophysical interpretation results. The hydraulic fractures in the tight gas reservoir are also complied into the model. ...

... Sw model is calculated by SHF of the four rock types. The Leverett-J function [27], shown as Equation (1), is adopted in the Sw calculation. ...

The hydrocarbon-bearing formation of Miano gas field belongs to the Early Cretaceous and it is bounded by two shale intervals, which are considered as maximum flooding surfaces (MFS). The hydrocarbon-bearing interval includes two reservoir units: a tight gas reservoir and its overlying conventional reservoir. Core samples, borehole logs, and well production performance revealed that the two reservoirs present reversed trends in reservoir quality through the gas field without obvious barriers. The average shale volume of the tight gas reservoir changes from 24.3% to 12.2% and the average permeability changes from 32.65 mD to 0.02 mD from the south to north. However, the average effective porosity of the overlaying conventional reservoir increases from 20% to 26% and the average permeability increases from 10 mD to 300 mD. The reversed trends in the two reservoirs lead to challenges in production forecast and development well proposals in the tight gas reservoir. Therefore, reservoir characterization and a predictive reservoir model are essential for further exploitation of Miano gas field. The geological genesis analysis integrating cores, borehole logs, and three-dimensional (3D) seismic data reveals that the producing interval of the tight gas reservoir is tidal-influenced shore facies deposition with intergranular pore space reduced by mineral cementation during burial diagenesis, while the overlaying conventional reservoir is fluvial-influenced deltaic deposition with abundant, well-connected intergranular macropores, which leads to a better reservoir quality. A reservoir model containing both the tight gas reservoir and the conventional reservoir is constructed considering the reservoir nature understanding, and the accuracy of the model is confirmed by reservoir surveillance activities with the simulation model. The study will be critical to the further reservoir development and hydrocarbon production in Miano gas field.

... Usually, for textiles, arithmetic or harmonic averages are proposed [81]. Such averages are relevant respectively for parallel configuration (textile stacking) or series configuration (textiles placed end to end) [82]. There is some order in the FVF repartition, and in a unidirectional flow simulation a combination of both averaging may be most pertinent. ...

... However, to simplify average calculation, the geometric average ̅̅̅̅ (equation 1.24) has been used instead. It has been recommended for averaging in media with random permeability distribution in reservoir engineering [82,83]. In equation 1.24, ℎ and are respectively the thickness and the permeability of the individual volume. ...

In order to manufacture thermoplastic composites using liquid composite moulding processes (LCM), the use of reactive systems for in-situ synthesis of polyamide 6 (PA6) with ε caprolactam has proved itself a promising possibility due to its low initial viscosity. However, at certain temperatures, crystallization of PA6 has been shown to occur simultaneously with its polymerization. Therefore, in these conditions, crystallization of PA6 depends on its polymerization kinetics. These phenomena affect the viscosity, the temperature, and the repartition between the non-polymerized, the amorphous and the crystallized phases of the reactive system during the process. Furthermore, the dual scale of porosity present in a fibrous preform complicates description of the flow. Therefore, the coupling of these different scales with PA6 synthesis kinetics is source of variabilities in homogeneity and quality of LCM processes manufactured composites.To understand and predict these phenomena and their effects on the quality of manufactured composites, a modelling method taking into account both the resin reactivity and the presence of the preform has been developed. A simulation method of flow in a fibrous preform using Brinkman's equation within the finite volume method (FVM) framework is proposed. At the same time, a new coupling model for polymerization and crystallization is elaborated in order to enable their simulation in 3D geometries. The advantages of this model are demonstrated comparatively to existing models. A viscosity model taking these phenomena into account is also proposed with the help of rheological tests. An experimental injection setup is developped to compare results of the process simulation of reactive thermoplastics injection in a fibrous preform to observations obtained from experimental injections.

... Equation (1) can alternatively be expressed as (Ahmed, 2001): ...

... The above expression which shows the plot of P wf against Q o is a straight line with a slope of (-1/J) as shown schematically in Figure 1. This graphical representation of the relationship that exists between the oil flow rate and bottom-hole flowing pressure is called the inflow performance relationship and referred to as IPR (Ahmed, 2001). ...

... The viscosity of such oil is called dead oil viscosity. The undersaturated oil viscosity is the viscosity of the crude oil at a pressure above the bubble point and reservoir temperature [17]. If crude oil is undersaturated at the initial reservoir pressure, the viscosity will drop somewhat as reservoir pressure falls. ...

... When combined with other single-based algorithm in voting, significantly rose with R 2 values (0.73399, 0.87540, 0.88078, 0.88015 and 0.92915) for each of the combinations in voting approach. Figures 6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26 ...

Background
Prediction of accurate crude oil viscosity when pressure volume temperature (PVT) experimental results are not readily available has been a major challenge to the petroleum industry. This is due to the substantial impact an inaccurate prediction will have on production planning, reservoir management, enhanced oil recovery processes and choice of design facilities such as tubing, pipeline and pump sizes. In a bid to attain improved accuracy in predictions, recent research has focused on applying various machine learning algorithms and intelligent mechanisms. In this work, an extensive comparative analysis between single-based machine learning techniques such as artificial neural network, support vector machine, decision tree and linear regression, and ensemble learning techniques such as bagging, boosting and voting was performed. The prediction performance of the models was assessed by using five evaluation measures, namely mean absolute error, relative squared error, mean squared error, root mean squared error and root mean squared log error.
Results
The ensemble methods offered generally higher prediction accuracies than single-based machine learning techniques. In addition, weak single-based learners of the dataset used in this study (for example, SVM) were transformed into strong ensemble learners with better prediction performance when used as based learners in the ensemble method, while other strong single-based learners were discovered to have had significantly improved prediction performance.
Conclusion
The ensemble methods have great prospects of enhancing the overall predictive accuracy of single-based learners in the domain of reservoir fluid PVT properties (such as undersaturated oil viscosity) prediction.

... The contact angle for such system at lab conditions is 0 and the IFT is 72 dyne/cm, while at the reservoir conditions the values are 30 and 30 dyne/cm for the contact angle and IFT respectively. The important application of the capillary pressure concept is how the reservoir fluids are in fact distributed across the thickness of the reservoir prior to its exploitation, Ahmed [17]. A final conversion to reservoir height is required to represent the saturation profile at any certain depth above the reservoir free water level. ...

... where ðJÞ is the Leverett-J Function, Ahmed [17], calculated as per the following equation: ...

The saturation calculation in complex reservoirs remains a major challenge to the oil and gas industry. In simple formations, a tendency towards simple saturation models such as Archie or Simandoux for clean and shaly reservoirs respectively is always preferable. These models were found to be working effectively in homogeneous formations within which the porosity and permeability are linked in the light of a simple facies scheme. Where the rocks show some degrees of heterogeneity, the well-logs are usually affected by different factors. This adversely results in a compromised or averaged log profiles that may affect the saturation calculations. Four wells drilled across a shaly sand of high heterogeneity have been studied in the Perth Basin, Western Australia. The aim is to resolve the hydrocarbon saturation and explain the high productivity results, despite the high water saturation, obtained through a conducted formation well test across the interested reservoir zones. A new integration technique between a suite of conventional and advanced logging tools together with the capillary pressure measurements has been carried out to generate a high-resolution reservoir saturation profile, that is lithofacies dependent. Three different independent methods were used in the studied wells to calculate the saturation and to reduce the uncertainty of the final estimated profiles. The methods are the resistivity-based saturation, the NMR-based irreducible saturation, and a new application through saturation height modeling. Furthermore , through the workflow, an effective calibration for the magnetic resonance T2 cutoff has been applied that is supported by the excellent reservoir production behavior from such complex reservoir. The methodology will help resolve the saturation calculation as one of the most challenging reservoir parameters, particularly where the resistivity logs are affected in complicated shaly sand environments. The effectiveness of the workflow shines the possibility to predict high resolution facies and saturation profiles in the lack of resistivity logs. A further possibility can complete the analysis on real time basis, which can certainly provide facies and saturation profiles extended to the uncored wells. Application of this methodology in the uncored wells has shown very encouraging results in various well trajectories, either vertical, deviated or horizontal long boreholes.

... For any secondary or tertiary recovery method, the overall recovery efficiency (RF) is a product of two efficiency factors as given by the following generalized expression (Ahmed, 2006): ...

... The microscopic displacement efficiency (E D ) is the fraction of the moveable oil that has been displaced from the swept zone at any given time or pore volume of injected fluids (Ahmed, 2006). This efficiency is affected by the presence of surface tension and interfacial tension, capillary forces, and rock wettability. ...

Excessive water production represents a major industry challenge because of its serious economic and environmental impacts. Polymer gels have been effectively applied to mitigate water production and extend the productive lives of mature oilfields. However, selecting a proper gel technology for a given reservoir is a challenging task for reservoir engineers because of the associated geological and technical complexities and the absence of efficient screening tools.
A comprehensive review for the worldwide gel field projects was conducted to develop an integrated systematic methodology that determines the applicability of three injection well gel technologies including bulk gels, colloidal dispersion gels, and weak gels. Comparative analysis, statistical methods, and a machine learning technique were utilized to develop a conformance agent selection advisor that consists of a standardized selection system, conventional screening criteria, and advanced screening models.
The results indicated that gel technology selection is a two-step process that starts by matching problem characteristics with gel technical specifications and mechanisms. Then, the initial candidate technology is confirmed by screening criteria to ensure gel compatibility with reservoir conditions. The most influential conformance problem characteristics in the matching process are channeling strength, volume of problem zone, problem development status, and the existence of crossflow. In addition to crossflow, the presence of high oil saturations or unswept regions in the offending zones requires the application of flood-size treating technologies that combine both displacement and diversion mechanisms. The selection and design of gel technologies for a given conformance problem greatly depend on the timing of the gel treatment in the flood life.

... It is essential to capture other aspects of the spatial context, i.e., the spatial feature heterogeneity and the scale, volume support size of the data, in model predictions. Heterogeneity is the variation in subsurface features as a function of spatial location and is a vital factor to predict subsurface resource recovery [9]. Also, subsurface datasets and models span a large range of scales from well and drill hole cores, core plugs, well logs, remote sensing and production or recovery data sources. ...

Heterogeneity is a vital spatial feature for subsurface resource recovery predictions, such as mining grade tonnage functions, hydrocarbon recovery factor, and water aquifer draw-down predictions. Feature engineering presents the opportunity to integrate heterogeneity information, but traditional heterogeneity engineered features like Dykstra-Parsons and Lorenz coefficients ignore the spatial context; therefore, are not sufficient to quantify the heterogeneity over multiple scales of spatial intervals to inform predictive machine learning models. We propose a novel use of dispersion variance as a spatial-engineered feature that accounts for heterogeneity within the spatial context, including spatial continuity and sample data and model volume support size to improve predictive machine-learning-based models, e.g., for pre-drill prediction and uncertainty quantification. Dispersion variance is a generalized form of variance that accounts for volume support size and can be calculated from the semivariogram-based spatial continuity model. We demonstrate dispersion variance as a useful predictor feature for the case of hydrocarbon recovery prediction, with the ability to quantify the spatial variation over the support size of the production well drainage radius, given the spatial continuity from the variogram and trajectory of the well. We include a synthetic example based on geostatistical models and flow simulation to show the sensitivity of dispersion variance to production. Then we demonstrate the dispersion variance as an informative predictor feature for production forecasting with a field case study in the Duvernay formation.

... Since water influx occurs when the reservoir pressure drops due to a long period of fluid production, the water influx rate in the general material balance equation must be equal to the volumetric withdrawal rate. This is caused by the aquifer water influx expansion and influx into the reservoir, so the water influx average, or dWe/dt, = [average of active oil volumetric voidage] + [average of free gas volumetric voidage] + [average of water volumetric voidage] [13]. ...

This paper was conducted to delimit the water influx in the Hamzeh oil reservoir, located in northeastern Jordan approximately 150 km east of Amman. Petroleum reservoirs are frequently encompassed by water aquifers that back up the reservoir pressure through water inflow. When the pressure declines in a petroleum reservoir, the water aquifer responds by providing an influx of water. Gradually, the damage is reduced and then eliminated, and more oil is produced from the reservoir. The material balance equation (MBE) is used as the fundamental method for this study, predicting reservoir performance for a period of 11 years. The results for this study prove that the reservoir has a water drive mechanism and that the original oil in place (OOIP) was 24,958,290 m3. The projected oil recovery factor ranges from 10.9 to 25 percent for the Hummar and Shueib formations, respectively, depending on the areal efficiency assumed in the calculations. The water influx for the 11-year period was predicted by an MBE, an unsteady-state model, and the results of the performance reservoir.

... Understanding the spatial variations of reservoir properties and their consequences is a critical step in reservoir modeling. Heterogeneities are mainly determined by the depositional environment in which the reservoir was formed, as well as subsequent structural and diagenetic events (Ahmed, 2006). As a result of the heterogeneity, a petroleum accumulation can be separated into individual fluid or pressure segments due to flow prevention across sealed reservoir boundaries . ...

The reservoir characterization of the Brazilian Santos Basin's pre-salt carbonates is a major challenge due to the faciological and depositional complexity, providing high lateral and vertical heterogeneities, and consequently, the formation of static/dynamic intraformational seals. Regarding this context, there is a massive pre-salt accumulation known as the Iara Cluster. During the early development stage, this cluster was split into three distinct accumulations named Berbigão, Sururu, and Atapu. This study aims to characterize the geological and hydrodynamic factors that affect the Iara Cluster reservoir compartmentalization. To achieve this objective, we applied an integrated analysis based on 3D seismic interpretation, well logs, pressure formation and fluid geochemistry analysis. The spatial distribution of the reservoir range's five main seismic patterns indicates potential stratigraphic-structural barrier zones. The well log analysis correlated with formation pressure data enabled the identification of several irregular oil-water contacts and free water levels. Small relative variations are associated with the perched-water phenomenon, while large variations are related to compartmentalization. The formation pressure analysis shows the hydraulic compartmentalization of the reservoirs in the Berbigão Field. Sururu and Atapu fields' oil zones are possibly connected by a dynamic sealing zone or a common aquifer, which provides a pressure balance on a geological time scale, since their oil gradients are similar. Our analyzes identified stratigraphic components in reservoir trapping associated with reservoir quality lateral obliteration. Dissimilarities in the oil sample composition and properties indicate different petroleum charge histories along with the distinct CO2 contamination timing. The Berbigão oil-associated gas formed in earlier stages of maturation than the Sururu and Atapu samples. The results integration through a risk matrix revealed areas with a greater chance of compartmentalization and perched-water phenomenon. Our study highlights the importance of multidisciplinary analysis to comprehend complex carbonate reservoirs connectivity, and offers input to de-risk new ventures' pre-salt reservoir quality.

... La caracterización del acuífero 101 (Figura 9) permitió estimar el volumen poroso en 169.570,84 ac-pies, definiendo una relación de dimensión con el yacimiento 95 Y-102 de 46,13 (volumen poroso del acuífero / volumen poroso del yacimiento) (Ahmed, 2010). Esta relación de dimensión acuífero / yacimiento es muy importante debido a que indica la capacidad del acuífero para suministrar energía al yacimiento (Dake, 1978), que para el caso en estudio se puede calificar de un acuífero moderadamente activo. ...

Resumen La inyección endógena de agua es menos conocida por revitalizar campos maduros. De cualquier manera, en el Campo Boca, específicamente en el Yacimiento 95 Y-102, esto fue exactamente lo que sucedió. Revisiones periódicas de este campo maduro resultó en la sugerencia de abandonar el único pozo productor en este yacimiento, el X-3, debido a que el pozo vecino X-6, localizado arriba en la estructura había probado 99% de corte de agua. Aun cuando hubo otros pozos productores en el yacimiento, solo se había logrado el 12% del recobro, lo cual representa un poco más de la mitad del recobro primario estimado (20%). Por este motivo, comenzó en el año 2005 un estudio integrado para reevaluar los parámetros y propiedades del yacimiento 95 Y-102. Durante el análisis de pozos, se encontró que la producción de agua del pozo X-6 era el resultado de la comunicación por detrás del revestidor del pozo con el acuífero 101, subyacente y no debido al avance del contacto agua-petróleo como fue sugerido inicialmente. Fue recomendada la completación del pozo X-3, ya que estaba ocurriendo un proceso de inyección conocido como inyección endógena. Adicionalmente, el soporte de la producción por el acuífero durante los 7 años previos indicó que la inyección endógena produciría los incrementos deseados. La inyección endógena de agua accidental, de hecho rejuveneció el pozo productor, incrementando la producción a más de 300 BND con un corte de agua aceptable de 61%. A continuación, en términos generales se describen los pasos seguidos para el análisis y comprensión del proceso y de cómo se obtuvo ventaja de esta inyección, que elevó la producción de casi cero a más de 100.000 barriles producidos en un solo año. Se considera que lo ocurrido accidentalmente en el yacimiento 95 Y-102 y bajo condiciones sub-óptimas (comunicación detrás del revestidor por mal cemento) fue altamente beneficiosa para la producción de este yacimiento y se presume que un proceso planificado y diseñado (comunicando el acuífero no asociado con el yacimiento a través de la tubería de producción o revestidor del pozo inyector) según las características de un yacimiento y/o campo dado debe ofrecer resultados aún más exitosos que los mostrados en este estudio. Esto sentó las bases para el uso de la inyección endógena de agua, como estrategia de desarrollo de producción para otros proyectos en el área. Introducción Desde comienzos de la década de 1970, la inyección endógena de agua o inyección de agua por gravedad, ha sido estudiada como un método alterno a la inyección convencional de agua. Se puede describir como un proceso de inyección donde se permite que el agua desde un acuífero con alta presión fluya hacia un yacimiento productor de petróleo de baja presión. Este método es económicamente atractivo debido a la ausencia de instalaciones de inyección en superficie, lo cual ahorra gastos iniciales de capital y gastos de rutina en operaciones (Ofei y Amorin, 2011). El proceso es conocido por generar mantenimiento de presión de yacimiento o recuperación secundaria, pero menos conocido por revitalizar campos maduros inactivos. De cualquier modo, en el Campo Boca, específicamente en el yacimiento 95 Y-102 fue exactamente lo ocurrido y motivo para realizar este estudio.

... The Niger Delta region consists of 606 oil field enriched with various kind of crude oil, 353 are onshore and 251 are offshore (Ahmed, 1992). The study of viscosity of crude oil in Niger delta can be determined by the use of viscometer at different temperature IJSER ISSN 2229-5518 IJSER © 2015 http://www.ijser.org ...

This research work compared the effect of temperature on the viscosity of Niger Delta oils. The investigation was carried out on five crude oil samples obtained from different reservoirs in the Niger Delta region. Experimental method was used to determine the effect of temperature on the viscosity of these crude oil samples under gravity flow in a capillary tube viscometer inserted in a thermostatically controlled water bath at temperatures below and above room temperature from 100C to 900C. The results show the variation of their kinematics and dynamics viscosities with temperature. It shows that NOAC crude oil had the highest API value of 36.392, while Umuechem 7L had the least API value of 20.095. The results show that the viscosity of Niger Delta crude oils reduces with an increase in temperature in all capillary or pipeline system. Pipes with larger diameter should be designed for locations in the Niger Delta to ease flow in pipeline transportation.

... Generally, black oil, crude oil, and gas are the most common petroleum fluid systems based on the phase diagram and prevailing reservoir conditions (physical properties, composition, gas-oil ratio, appearance, pressure, and temperature) [130]. Of these categories, researchers have recently focused on gas reservoirs which are divided into dry, wet, and condensate gas-bearing formations, as a preferable choice for underground gas storage, especially CO 2 due to the compressive nature [131][132][133]. ...

Hydrogen future depends on large-scale storage, which can be provided by geological formations (such as caverns, aquifers, and depleted oil and gas reservoirs) to handle demand and supply changes, a typical hysteresis of most renewable energy sources. Amongst them, depleted natural gas reservoirs are the most cost-effective and secure solutions due to their wide geographic distribution, proven surface facilities, and less ambiguous site evaluation. They also require less cushion gas as the native residual gases serve as a buffer for pressure maintenance during storage. However, there is a lack of thorough understanding of this technology.
This work aims to provide a comprehensive insight and technical outlook into hydrogen storage in depleted gas reservoirs. It briefly discusses the operating and potential facilities, case studies, and the thermophysical and petrophysical properties of storage and withdrawal capacity, gas immobilization, and efficient gas containment. Furthermore, a comparative approach to hydrogen, methane, and carbon dioxide with respect to well integrity during gas storage has been highlighted. A summary of the key findings, challenges, and prospects has also been reported.
Based on the review, hydrodynamics, geochemical, and microbial factors are the subsurface’s principal promoters of hydrogen losses. The injection strategy, reservoir features, quality, and operational parameters significantly impact gas storage in depleted reservoirs. Future works (experimental and simulation) were recommended to focus on the hydrodynamics and geomechanics aspects related to migration, mixing, and dispersion for improved recovery. Overall, this review provides a streamlined insight into hydrogen storage in depleted gas reservoirs.

... ormation of any hydrocarbon reservoir requires aquifers, porous rocks, which basically let the oil or gas flow through them and get accumulated in a porous and permeable layer bounded by an impermeable soil [1-3]. These aquifers may be substantially larger than the oil or gas reservoir they adjoin as to appear infinite in size, and/or they may be as small in size as to be negligible in their effect on reservoir performance [4][5][6]. To determine the effect that an aquifer has on oil and gas production, it is important to estimate the amount of water that has entered into the reservoir from the aquifer [7-10]. ...

This paper is conducted in order to determine the water influx in the Volve oil field situated in the Southern Viking Graben in the North Sea in block 15/9, approximately 200 kilometres west of
Stavanger at the southern end of the Norwegian sector.
Material balance (MB) equation is used as principal method in order to achieve the objectives of this work, predicting reservoir future performance over a stated period of five years is considered as the second part of the work. A variety of data particularly pressure, volume and temperature data, production and reservoir data are entered in the MBAL software and computed in Excel software using material balance equation. The result showed that the reservoir had a water influx of 67,678 Sm3 before injection requiring the use of secondary recovery method, water injection at the early stage of production. Subsequently, cumulative oil production predicted a total amount of 10.77 MMSm over a period of five years. This therefore implies that thanks to the model obtained which is the pot model production prediction can be made for any date in the future.

... Understanding the spatial variations of reservoir properties and their consequences is a critical step in reservoir modeling. Heterogeneities are mainly determined by the depositional environment in which the reservoir was formed, as well as subsequent structural and diagenetic events (Ahmed, 2006). As a result of the heterogeneity, a petroleum accumulation can be separated into individual fluid or pressure segments due to flow prevention across sealed reservoir boundaries . ...

... One can mention, for example, its application in oil/gas recovery operations; subsurface energy production systems (geothermal, petroleum, hydrogen); and geological storage of carbon dioxide or natural gas. 2,3 In recent years, interest in this phenomenon has dramatically increased when it was realized that it can be used as the driving mechanism for the transport of working liquids in pump-less, paper-based, capillary-driven, microfluidic redox-flow batteries. 4 Further interest in spontaneous imbibition arises from the fact that it is the driving force behind sample transport in paper-based microfluidic kits used in biomedicine, agriculture, food, and environmental sciences for quality control or diagnostic purposes. ...

In the present work, spontaneous imbibition of shear-dependent fluids is numerically investigated in a two-layered, rectangular/fan-shaped, paper-based diagnostic kit using the modified Richards equation. It is shown that the average velocity at the test line of the kit is strongly influenced by the absorbent pad's microstructure with its contact angle playing a predominant role. Assuming that the test fluid is shear-thinning, a generalized version of the Richards equation, valid for power-law fluids, was used to investigate the effect of shear-thinning on the quasi-steady regime. The shear-thinning behavior of the test fluid is predicted to shorten the duration of the constant-velocity regime on the nitrocellulose membrane used as the test cell. By manipulating the contact angle and/or choosing appropriate microstructure for the absorbent pad, it is still possible to establish a constant velocity regime at the test line for nearly five minutes even for such fluids. A comparison between our numerical results and published numerical results obtained using simplistic theories has revealed the key role played by the transition, partially-saturated zone near the advancing front during the liquid imbibition. The general conclusion is that use should preferably be made of robust models such as Richards equation for the design of lateral-flow, paper-based assays.

... Modelling flow in porous media is important not only in groundwater flow but in many other areas such as suspension dewatering (Aziz et al. 2000;Buscall and White 1987) and fluid recovery, e.g. oil recovery (Ahmed 2006;Grassia et al. 2014). The study of this phenomenon requires detailed and careful formulation of the governing equations which depend not only on the fluid, but also on the properties of the porous media in question. ...

Richards equation describes water transport in soils, but requires as input, soil material property functions specifically relative hydraulic conductivity and relative diffusivity typically obtained from the soil–water retention curve (SWRC) function (involving capillary suction head). These properties are often expressed via particular functional forms, with different soil types from sandstones to loams represented within those functional forms by a free fitting parameter. Travelling wave solutions (profile of height ξ^ against moisture content Θ) of Richards equation using van Genuchten’s form of the soil material property functions diverge to arbitrarily large height close to full saturation. The value of relative diffusivity itself diverges at full saturation owing to a weak singularity in the SWRC. If, however, soil material property data are sparse near full saturation, evidence for the nature of that divergence may be limited. Here we rescale the relative diffusivity to approach unity at full saturation, removing a singularity from the original van Genuchten SWRC function by constructing a convex hull around it. A piecewise SWRC function results with capillary suction head approaching zero smoothly at full saturation. We use this SWRC with the Brooks–Corey relative hydraulic conductivity to develop a new relative diffusivity function and proceed to solve Richards equation. We obtain logarithmic relationships between height ξ^ and moisture content Θ close to saturation. Predicted ξ^ values are smaller than profile heights obtained when solving using the original van Genuchten’s soil material property functions. Those heights instead exhibit power law behaviour.

... where a is the angle of flow with respect to positive x axis, k p′ is the effective permeability of displacing phase, g is the gravitational constant, is the interfacial tension between the phases, θ is the contact angle, is the flow potential of displacing phase, is the pressure of displacing phase, D is the depth, and ρ p and are the densities of displaced and displacing phases, respectively. Moreover, ΔD in Equation 13 is the positive vertical distance between the datum level and a point below it (Ahmed, 2000). ...

Polymer flooding is a well-established chemical enhanced oil recovery (CEOR) technique that effectively improves oil recovery after waterflooding. Due to a large number of studies conducted in this area and extensive field data availability, this technique has gained solid practical and theoretical knowledge. Conventionally, the polymer injection is believed to increase volumetric sweep efficiency by producing movable oil that is remained unswept after waterflooding. Nevertheless, studies demonstrated that specific viscoelastic polymers might also mobilize residual oil and improve microscopic displacement efficiency, in addition to macroscopic sweep efficiency.
Although polymer flooding is an extensively applied CEOR technique in sandstones, its applicability in carbonates is still limited. This is related to the prevailing complicated conditions in carbonates including mixed-to-oil wettability nature, high heterogeneity with low permeability, and harsh conditions of high temperatures (above 85°C), high salinity (above 100,000 ppm), and high hardness (above 1,000 ppm). Recently, new polymers have been developed to overcome the challenges of harsh conditions in carbonates. These novel polymers incorporate specific monomers that protect the polymer from thermal and chemical degradations. However, the viscoelasticity of these synthetic polymers and their effect on oil mobilization are not yet comprehended and requires further investigation and research.
In this paper, we review the recent studies conducted on viscoelastic polymer flooding in sandstones and carbonates. The article describes viscoelastic polymer recovery mechanisms, polymer viscoelastic properties and the factors controlling them, and the effect of viscoelastic polymers on residual oil mobilization. This study also provides insights into the challenges faced during viscoelastic polymer flooding operations as well as field applications in sandstone and carbonate reservoirs.

... Porosity was utilized in hydrogeology, geology, building science, and soil science. It is defined by the ratio [6]: ...

This article focuses on two aims the first one is to define and modeling rock types of Zubair formation in Basrah and the second one is to modeling the petrophysical properties of Zubair formation. Accurate methods have been used to achieve these aims. The rock formations of the Zubair oil field was analyzed and important results were obtained from that analysis, then 4 rock samples from the reservoirs in the Zubair formation have taken at different depths at different temperature, pressure, and rock type. We used Mercury Injection and Gamma-ray Logging to determine and calculate the porosity of these rock samples, also we used deep autoencoders in borehole image logs to determine and calculate permeability. At "Mercury Injection" Method, the results of this study have suggested that the estimated accessible porosity has been considerably decreased in the case of implementing new corrections on the MICP (i.e. Mercury Injection Capillary Pressure) test data. From the “Gamma Ray “method we found that the level of the gamma-ray has been assumed to be associated with the size of the grain. We found that the best depth to calculate the properties of sandstone is (650 – 1100 m) underground. We found that the best depth to calculate the properties of shale is (1300 – 1650 m) underground.

... On top of the above concerns, the compositional variability of the injected gas stream, as influenced by the production planning of the field, must be further considered. This is due to the commingling of fluids originating from different parts of the reservoir which contain diverse fluids with respect to their acid components concentration [25]. ...

An “energy evolution” is necessary to manifest an environmentally sustainable world while meeting global energy requirements, with natural gas being the most suitable transition fuel. Covering the ever-increasing demand requires exploiting lower value sour gas accumulations, which involves an acid gas treatment issue due to the greenhouse gas nature and toxicity of its constituents. Successful design of the process requires avoiding the formation of acid gas vapor which, in turn, requires time-consuming and complex phase behavior calculations to be repeated over the whole operating range. In this work, we propose classification models from the Machine Learning field, able to rapidly identify the problematic vapor/liquid encounters, as a tool to accelerate phase behavior calculations. To set up this model, a big number of acid gas instances are generated by perturbing pressure, temperature, and acid gas composition and offline solving the stability problem. The generated data are introduced to various classification models, selected based on their ability to provide rapid answers when trained. Results show that by integrating the resulting trained model into the gas reinjection process simulator, the simulation process is substantially accelerated, indicating that the proposed methodology can be readily utilized in all kinds of acid gas flow simulations.

... If the length of the fracture is long but the width and height are small, the well's productivity will be affected. Furthermore, the greater these parameters, the slower the decrease in reservoir pressure is achieved; the slower decrease in reservoir pressure is advantageous because it increases the time of production [5], [6] and [7]. The use of proppants is also critical when performing hydraulic fracturing. ...

Hydraulic fracturing is a well-stimulation technique that uses a large amount of water mixed with proppants at high pressure to enhance and boost oil and gas production. Proppants, in conjunction with water, facilitate the cracking process, acting as a catalyst for the oil and gas to pass through the formation and into the producing well. The primary goal of this research is to look into the parameters that influence hydraulic fracturing quality. Moreover, such parameters that improve the productivity of oil in unconventional reservoirs are evaluated. The field properties of the Eagle Ford Shale were used to create a geological model on the Navigator software for this purpose. This software is used to simulate three different horizontal and vertical wells to observe the production of oil and gas. Then, hydraulic fracturing is performed on the same wells with different scenarios using three parameters, namely the length of fracture, the width of fracture, and the height of fracture. These parameters are selected because the usage of proppants can be dependent on them. The findings are quite convincing and demonstrate the importance of hydraulic fracturing in an unconventional reservoir. Besides, it is observed that the greater the width, length, or height of the fracture, the greater the productivity of oil and gas in an unconventional reservoir due to the increment of the seepage area of the hydrocarbons. Thus, hydraulic fracturing can make any potential unconventional reservoir economically viable.

... The most common well testing technique utilized in practice belongs to pressurebuildup. The pressure build-up test is accomplished by shutting-in a producing well to measure the pressure build-up versus time [16]. Different graphical techniques are developed for well test data interpretation and these techniques depend basically on pressure drop equations. ...

In the present study, well logs and well test data of both conventional build-up tests and Mini-DST from different oil and gas fields are utilized to evaluate the effects of uncertainty in petrophysics and test techniques on well test results. This includes producing wells from the Nile Delta and Western Desert-Egypt together with published results from West Qurna oil field-Iraq. Results indicated that permeability is strongly dependent on petrophysics interpretation, particularly pay thickness, while the radius of investigation is significantly dependent on fluid properties, especially compressibility. The skin factor calculations showed great sensitivity towards the pressure measurements with medium influences on porosity and oil viscosity. The calculations of Mini DST and Build-up test are compared within the uncertainty context for effective permeability, radius of investigation, and skin factor, and the findings are discussed in detail. In all cases, error analysis indicated that well test results and interpretation of conventional build up data are largely stable and may reduce overall uncertainty to 30% of the corresponding Mini-DST results/interpretation. The results of this study not only characterize each input parameter involved in the interpretation of well test data but also confirms the superiority of conventional build-up on Mini-DST techniques.

... Waterflooding is a relatively inexpensive technique to recover oil since water is generally available in large quantities [9]. However, the percentage of oil recovered by using primary and secondary techniques is only around 35%-55% of the Original Oil In Place (OOIP) [9][10][11][12]. The oil viscosity influences the recovery factor. ...

This paper presents a 2D model of the Ghawar field and investigates the flow behavior in the field during secondary and tertiary recoveries using a simplified well scheme. For the latter, the focus is on chemical Enhanced Oil Recovery (EOR), using polymer solutions. The difference in efficiency between secondary and tertiary recovery and the influence of factors such as degradation are analyzed and presented. Furthermore, the influence of oil viscosity on the recovery factor is investigated as well as the efficiency of the well placement of the model studied. In order to do this, a combined shear-thinning/-thickening model, the Unified Viscosity Model (UVM), is used. COMSOL Multiphysics is used in order to study the model, combining the fluid flow and mass transfer in one study, showing the interdependence of both physics transport phenomena. The results show how the influence of the polymer properties and the rock formation affect the recovery behavior. The particle tracing study allows us to determine the percentage of the chemical agent recovered in the producing wells. This paper shows how EOR agents works coupled with advanced numerical models in real-scale fields.

Well testing is a productive way of monitoring reservoir performance and oil or gas well conditions. The transient behavior may be influenced to a significant extent by reservoir features such as faults, barriers and stratigraphic interface. Drillstem tests are normally conducted on exploration wells, and are generally the solution to investigating if a well has found a hydrocarbon reservoir that is commercial. Well F-6 is a newly completed well in trofani field, situated in the Niger delta region of Nigeria with unidentified formation properties and potential performance. This investigation reviews a simulation solution technique employing the KAPPA software 'Ecrin v4.20.03' to validate gauge data from Well F-6. The measured data of both an upper and lower recording gauge was compared and further analysis was conducted for the purpose of reservoir description. Actual real-time pressure data from recording down-hole gauge and flow-rate data were used in the pressure transient analysis to obtain reservoir parameters and assess well potentiality. An extremely high permeability of 7350md and a skin value of 15.3 was achieved at the end of the simulation process. This result indicates Well F-6 is of commercial quality and also denotes a damaged formation. Information obtained from this work can be employed to optimize development plans for this exploration well.

Water coning is one of the most important phenomena that affect the oil production from oil reservoirs having bottom water aquifers. Empirical model has been developed based on numerical simulator results verified for wide range variation of density difference, viscosity ratio, perforated well interval, vertical to horizontal permeability ratio and well to reservoir radius ratio; the effect of all these parameters on breakthrough time of raising water have been recorded for five different oil flow rate. Since, the model reflects the real situations of reservoir-aquifer zone systems; in which the aquifer has a specific strength to support the reservoir pressure drop depending on its characteristics and water properties. Moreover, the numerical model has been constructed using very fine grids near the wellbore especially in vertical direction, so that very accurate results can be obtained. and (625)runs were performed to generate the breakthrough time model using the numerical simulator verifying all parameters affecting on breakthrough time. The results show that water coning is complex phenomena that depends on all reservoir and fluid properties; the dynamic critical flow rates affected simultaneously by both of the displacing fluid zones. The results show that the breakthrough time of the presented formula provides extreme accuracy with many numerical simulator cases of same reservoir and fluid properties; thus, the suggested formula can be considered as an alternative, quick and easy use tool than numerical simulation models, which consumes time and efforts.

Ссылка для цитирования: Ильясов И.Р. Методика оценки эффективности применения технологии полимерного заводнения на примере Восточно-Мессояхского месторождения // Известия Томского политехнического университета. Инжиниринг георесурсов. – 2022. – Т. 333. – № 3. – С. 217-226. Актуальность. Полимерное заводнение является технологией, позволяющей повысить эффективность разработки действующих месторождений нефти и газа. При этом реализация проекта полимерного заводнения требует дополнительных инвестиций. Для обоснования дополнительных инвестиций и оценки экономической эффективности всего проекта необходима методика оценки эффективности применения технологии полимерного заводнения, охватывающая все элементы сложной системы. Цель: исследование основных составляющих элементов проекта полимерного заводнения; разработка методики оценки эффективности применения технологии полимерного заводнения на примере Восточно-Мессояхского месторождения. Объекты: эксплуатационные слабоконсолидированные коллектора вязкой нефти, а также традиционные коллектора. Методы: критический анализ, контент-анализ, анализ, обобщение и систематизация имеющегося опыта пилотных проектов полимерного заводнения, системный подход. Результаты. Разработана методика оценки эффективности применения технологии полимерного заводнения, включающая детальную оценку доходной части с применением аналитических и численных инструментов, оценку затратной части и оценку экономической эффективности всего проекта. Особое внимание уделено оценке дополнительной добычи нефти с применением существующих методов на различных этапах проекта. Также показано влияние полимера на операционные затраты. Концептуально исследованы и описаны основные статьи затрат при реализации полимерного заводнения. Методика является универсальной и применима на различных этапах реализации полимерного заводнения от этапа планирования пилотного проекта до этапа тиражирования, и позволяет системно и комплексно оценивать эффективность проектов полимерного заводнения.

Sumur AMP-01 ini telah dilakukan proses Stimulasi, selanjutnya dilakukanpengujian sumur yaitu Pressure Trasient Analysis. Tujuan dilakukannya welltesting pada sumur AMP-01 adalah untuk membuktikan keberhasilan stimulasiyang dilakukan pada sumur ini dengan menentukan parameter-parameterreservoir seperti tekanan reservoir, permebilitas (k), factor skin, dan penurunantekanan akibat skin (∆Pskin). Analisis yang dilakukan adalah Pressure Build Up(PBU). Metode yang digunakan adalah Horner Plot dengan pendekatan PseudoPressure Ψ(P). Selain itu dilakukan juga Uji Deliverabilitas dengan metodeModified Isocronal Test (MIT). Analisis Pressure Build Up dan Uji Deliverabilitasini dilakukan dengan menggunakan software dan perhitungan manual denganSpreadsheet menunjukan hasil yang hampir sama. Hasil analisis ini menunjukanbahwa model reservoir pada sumur AMP-01 adalah Two Porosity Sphere dengan Boundary Rectangle. Selanjutnya dilakukan uji deliverabilitas pada sumur AMP-01 dengan menggunakan metode Modified Isochronal Test. Plot yang dilakukan yaitu dengan memplot laju alir gas vs penurunan tekanan, nilai AOFP (Absolute Open Flow Potential) pada sumur ini berdasarkan analisis uji deliverabilitas yaitu sebesar 4147.85 MSCF/D dengan nilai back pressure coefficient (C) sebesar 6.179 dan nilai slope (m) 0.5.

PT Pertamina Hulu Energi West Madura Offshore (PHE WMO) berupayameningkatkan produksi minyak, salah satu cara yaitu melakukan optimalisasi pipa penyalur dari PHE-30 menuju fasilitas proses PPP dengan mengurangi slug flow pada pipa penyalur tersebut. Saat ini produksi minyak, gas dan air dari lapangan PHE-30 sebesar 2.070 Bopd, 5,1 MMscfd dan 10.800 Bwpd. Produksi minyak dari lapangan PHE-30 dapat dioptimalkan dengan menjaga gas liquid ratio (GLR) pada pipa penyalur tersebut. Optimalisasi ditujukan untuk menjaga fasilitas proses tetap aman dan terhidar dari kondisi shutdown atau terhenti sementara akibat terjadinya slug flow yang terjadi disepanjang pipa penyalur.Slug flow terjadi karena ketidakseimbangan perbandingan antara distribusi laju alir gas dan laju alir liquid pada pipa penyalur atau dapat disebut dengan gas liquid ratio (GLR).Perbedaan GLR ini disebabkan oleh tingginya air terproduksi dari dalam sumur PHE-30. Analisa dilakukan dengan menggunakan software Pipesim untuk melakukan simulasi flow regime pada pipa penyalur dari PHE-30 menuju PPP. Parameter yang digunakan yaitu laju alir minyak, gas dan air serta kecepatan superficial gas dan liquid. Hasil menunjukkan bahwa dengan pengurangan air terproduksi dari lapangan PHE-30 dengan GLR 2.463 scf/bbl, dapat merubah kondisi flow regime dari yang sebelumnya slug flow menjadi stratified flow.

Oil viscosity plays a prominent role in all areas of petroleum engineering, such as simulating reservoirs, predicting production rate, evaluating oil well performance, and even planning for thermal enhanced oil recovery (EOR) that involves fluid flow calculations. Experimental methods of determining oil viscosity, such as the rotational viscometer, are more accurate than other methods. The compositional method can also properly estimate oil viscosity. However, the composition of oil should be determined experimentally, which is costly and time-consuming. Therefore, the occasional inaccessibility of experimental data may make it inevitable to look for convenient methods for fast and accurate prediction of oil viscosity. Hence, in this study, the error in viscosity prediction has been minimized by taking into account the amount of dissolved gas in oil (solution gas–oil ratio: Rs) as a representative of oil composition along with other conventional black oil features including temperature, pressure, and API gravity by employing recently developed machine learning methods based on the gradient boosting decision tree (GBDT): extreme gradient boosting (XGBoost), CatBoost, and GradientBoosting. Moreover, the advantage of the proposed method lies in its independence to input viscosity data in each pressure region/stage. The results were then compared with well-known correlations and machine-learning methods employing the black oil approach applying least square support vector machine (LSSVM) and compositional approach implementing decision trees (DTs). XGBoost is offered as the best method with its greater precision and lower error. It provides an overall average absolute relative deviation (AARD) of 1.968% which has reduced the error of the compositional method by half and the black oil method (saturated region) by five times. This shows the proper viscosity prediction and corroborates the applied method's performance.

Characterizing an oil reservoir requires one to understand the Pressure- Volume-Temperature (PVT) properties of reservoir fluids, especially bubble point pressure, solution gas oil ratio and oil formation volume factor because of its more often utilization in reservoir engineering studies. The current correlations are restricted by the use of sample from a particular field. As the physical properties and the composition of the crude oil varies the results becomes erroneous after a specific range. This correlation will give results only over a specific range of properties like specific gravity, viscosity, composition etc. The challenge is to develop a new approach which overcomes the current shortcomings. In this paper a new machine learning based model has been developed using Interactive Multivariate Linear Regression (I-MLR) method by integrating a large number of datasets to predict above mentioned properties. It overcomes the restriction of the previous correlations as it does not use data from any particular field. As such it is applicable over wide range of physical properties and composition. This model does not require any laboratory studies which makes it more economical. The validation of the model is done after detailed comparative study done with various commercially used empirical correlations.

A capillary high-pressure optical cell (HPOC) combined with a confocal Raman system was used in this study of high-pressure methane/brine contact angles on a quartz surface. The contact angle was determined from the shape of the methane/brine/quartz interface; it increased with fluid pressure from 41° to 49° over a pressure range of 5.7–69.4 MPa. A linear relationship between the contact angle and the Raman shift was also observed. The experimentally measured contact angle was more accurately applied in calculations of capillary resistance than the empirically estimated 0°, and it provides an important parameter in the study of gas migration and production processes. For a natural gas reservoir, pore-throat capillary resistance was 33% lower than the traditionally accepted value, and low capillary resistance is conducive to deeply buried tight gas reservoirs becoming more gas saturated. As burial depth increases, capillary resistance initially decreases and passes through a maximum before decreasing again, rather than increasing linearly with depth. Our results provide critical parameters for gas reservoir production, modeling, and resource assessment. This non-destructive method may be useful for predicting contact angles through measurement of the Raman shift of the HPOC and fluid inclusions in the reservoir.

Estimating the downhole leaks is very important in order to evaluate the well performance and assess the wellbore integrity. Different approaches can be used to estimate the downhole leaks such as temperature surveys, noise logs, and corrosion logs. However, most of the available techniques require downhole measurements which will increase the operational cost and time. This study presents an integrated approach for predicting downhole leaks based on surface measurements, which will reduce the cost and effort significantly. The proposed method was implemented on actual field data, where reasonable accuracy was observed. In this work, the casing leaks were quantified by diagnosing the pressure and flow rate profiles at the surface, without using any downhole flow spinner. Three main steps were used to estimate the downhole leaks; building the inflow performance relationship (IPR) model, predicting the reservoir productivity/injectivity index, and calculating the pressure profiles along the wellbore using the nodal analysis technique. The suggested approach can be used to predict the downhole leaks for production wells as well as injection wells. In this study, the proposed technique was tested for a water injection well, where the fluid leakage was detected and the leak depth was determined. The studied well suffers from severe corrosion problems, that resulted in downhole leakage. For the well under investigation, the leakage rate is 8500 barrels per day (bpd) and the expected leakage depth is around 1374 ft., based on the wellbore survey. Applying the proposed approach showed that the leak rate is 8831 bpd and the leakage depth is 1380 ft. Therefore, the estimations errors are 3.89% in the flow rate and 0.43% in the leakage depth. Overall, an integrated approach is proposed to detect the downhole leaks, the proposed method has been analytically derived and tested using actual field data. The presented method uses surface measurements without a need to stop the production or injection operations. The new method showed very acceptable prediction performance, where estimation errors of 3.89 and 0.43% were obtained for the leakage rate and depth, respectively.

Foam cement memiliki densitas yang ringan untuk mengurangi tekanan hidrostatik pada formasi dengan tekanan yang lebih rendah dari pada tekanan pada kolom semen untuk penanggulangan masalah loss circulation dan cara ini sangat efektif untuk operasi penyemenan pada pemboran minyak & gas. Desain komposisi foam cement slurry yang tepat dapat mengisolasi zona rekahan, mengurangi invasi fluida dan gas serta volume lost circulation yang terjadi. Komposisi semen dengan penambahan foam agent yang tepat merupakan parameter penting untuk menentukan kualitas core foam cement nantinya. Pada penelitian ini, Kelengkapan alat di laboratorium seperti unit porositas tes merk Coreval 700 dan compressive strength test unit merk Vinci digunakan untuk mengevaluasi porositas dan compressive strengthcorefoam cement. Pada penelitian ini foam agent Sika-aer dipakai sebagai bahan pembuat gelembung dalam cement slurry. Semen kelas G dan pasir mesh 80 dipakai sebagai material utama dalam pembuatan rasio variasi foam cement. Kualitas porositas dan compressive strengthcore foam cement inilah yang menjadi paramater dasar untuk dievaluasi dalam penelitian ini. Pengujian dilakukan pada suhu 75˚C/167˚F. Sehingga, dapat disimpulkan core foam cement dengan foam agent Sika-aer dapat mengurangi volume lost circulation pada sumur minyak dan gas khusunya pada lapangan geothermal. Hasilnya, tebukti bahwa pada suhu 75˚C dengan rasio cement slurry 1 : 0.25 : 0.5 konsentrasi Sika-aer 0.15% BWOCcore foam cement menghasilkan porositas 33.064% dan compressive strength pada umur 3 hari sebesar 1701. 459 psia

Analisa decline ditujukan untuk mengetahui nilai EUR (Estimated Ultimated Recovery) atau perolehan maksimal dari produksi suatu lapangan dann nilai Rf (Recovery Factor) atau presentase perbandingan nilai EUR dengan nilai OOIP (Original Oil In Place).

Lapangan AA sumur RR merupakan salah satu sumur explorasi yang terletak di cekungan Jawa Barat Utara. Pemboran sumur RR pertama kali dilakukan pada tanggal 22 Maret 2011. Pemboran sumur RR menembus Lapisan CSB Sand Stone yang terdapat pada formasi parigi dan lapisan ini pertama kali diperforasi pada tanggal 19 Agustus 2011. Setelah diperforasi selanjutnya dilakukan pengujian sumur dengan pressure build up test. Selain dilakukan pressure build up test, pada sumur RR dilakukan pengujian deliverabilitas dengan metode modified isochronal test sehingga didapatkan nilai absolute open flow potential, yaitu sebesar 8.214MMscf/d dengan mengunakan simulator saphir.Selanjutnya sumur RR ini dapat dilakukan perhitungan volume gas awal ditempat dengan menggunakan metode volumetric, yaitu sebesar 458,355 MMscf. Dengan mendapatkan nilai volume gas awal ditempat selanjutnya dapat membuat peramalan produksi pada sumur RR dengan menggunakan simulator Mbal. Peramalan produksi dilakukan untuk mendapatkan perencanaan pengembangan lapangan yang paling optimum dengan mempertimbangkan besar recovery factor nya ,yaitu dilakukan dengan memproduksikan gas melalui satu sumur dan mengaplikasikan compressor pada sumur tersebut.

The amount of oil reserves in Indonesia is currently still large, but has not been able to meet the needs of enegi. To overcome this imbalance, one of the efforts that the government has made in improving oil lifting is through Enhanced Oil Recovery (EOR). The purpose of this research, is to determine the right EOR method for a reservoir by conducting a screening criteria on one of the fields in Indonesia. EOR is a method of increasing the volume of oil that previously could not be produced. This condition usually occurs in heavy crude oil, poor permeability and irregular faultlines. EOR is applied to fields that have been produced long enough (mature field) with the aim of taking the remaining oil that cannot be produced by primary and secondary (water flooding) methods. Some of the EOR techniques that are widely known to date are steam flooding, chemical flooding, and gas injection (gas flooding). The study is a reservoir X that has a six-aspect match from seven aspects suggested by Taber et al. namely polymer injection as an EOR method. The six aspects are the magnitude of oil gravity, oil viscosity, porosity, permeability, depth and temperature. From this research it can be concluded that, in Field X is very suitable for the EOR Method with the Chemical Flooding Method, by injecting polymer compounds.

Shale gas reservoirs have huge amounts of reserves. Economically evaluating these reserves is challenging due to complex driving mechanisms, complex drilling and completion configurations, and the complexity of controlling the producing conditions. Decline Curve Analysis (DCA) is historically considered the easiest method for production prediction of unconventional reservoirs as it only requires production history. Besides uncertainties in selecting a suitable DCA model to match the production behavior of the shale gas wells, the production data are usually noisy because of the changing choke size used to control the bottom hole flowing pressure and the multiple shutins to remove the associated water. Removing this noise from the data is important for effective DCA prediction. In this study, 12 machine learning outlier detection algorithms were investigated to determine the one most suitable for improving the quality of production data. Five of them were found not suitable, as they remove complete portions of the production data rather than scattered data points. The other seven algorithms were deeply investigated, assuming that 20% of the production data are outliers. During the work, eight DCA models were studied and applied. Different recommendations were stated regarding their sensitivity to noise. The results showed that the clustered based outlier factor, k-nearest neighbor, and the angular based outlier factor algorithms are the most effective algorithms for improving the data quality for DCA, while the stochastic outlier selection and subspace outlier detection algorithms were found to be the least effective. Additionally, DCA models, such as the Arps, Duong, and Wang models, were found to be less sensitive to removing noise, even with different algorithms. Meanwhile, power law exponential, logistic growth model, and stretched exponent production decline models showed more sensitivity to removing the noise, with varying performance under different outlier-removal algorithms. This work introduces the best combination of DCA models and outlier-detection algorithms, which could be used to reduce the uncertainties related to production forecasting and reserve estimation of shale gas reservoirs.

El presente documento muestra la realidad, desafíos y perspectivas de recuperación secundaria del reservorio “U Inferior” (UI) en el campo Sacha, localizado al flanco occidental del “Play Central” (Corredor Sacha-Shushufindi) del oriente ecuatoriano. El histórico de producción inició en el año 1972 con perforación de pozos, y años después, con proyectos de recuperación secundaria, se logró el incremento de la producción petrolera. La arenisca UI es uno de los principales reservorios productores del campo, se destaca por su alto volumen de reservas 3P y la presente oportunidad de recuperarlo a mediano plazo sin ser este el único reservorio productor con recuperación secundaria. La realidad del campo muestra que las intervenciones a las zonas productoras y la aplicación de técnicas de optimización de producción como fracturamiento hidráulico, producción commingled, estimulación matricial, cambio de zonas, perforación, entre otras, se han visto limitadas por las bajas presiones en los reservorios de la formación Napo; los cuales se encuentran depletados y con presencia de gas libre. Por ello, se generan retos adicionales en diferentes escenarios evaluados de incrementos de producción, para el manejo de los fluidos y sistemas de levantamiento artificial tradicionales. El desafío es buscar el desarrollo del campo bajo estas condiciones, mediante simulación, aplicando el método de Buckley-Leveret e implementando proyectos adicionales para recuperar la presión de la arenisca UI definiendo arreglos de inyección y repotenciación de facilidades existentes (actualmente limitadas), logrando así exponer los casos ideales ajustados a la realidad y mostrar el aumento de volumen de producción acumulada del campo bajo ciertas perspectivas a favor de los intereses del país.

The XY Field is an oil field in the Sunda Basin which was developed since 1981 and has been produced in the Baturaja carbonate layer and Talang Akar sandstone layer. Decreasing the amount of oil production in the reservoir can have a detrimental impact on the company so it is necessary to analyze the remaining reserves of the reservoir. The calculation used to evaluate the remaining reserves use the Volumetric, Material Balance and Decline Curve methods. From the three methods, the results that are close to the reserve of the XY field reservoir are 14 MMSTB. OOIP is obtained from the volumetric method and material balance which is divided into P10, P50 and P90. The reserve OOIP for P10 is 110.8 MMSTB and P90 is 60.34 MMSTB, with the last cumulative production in December 2019 being 9.3 MMSTB, where the economic limit of the field is 46 bbl. / day and the contract will be expired in 2038. From the results of the subsurface analysis, the four infill wells are candidates for infill wells because they have hydrocarbon potential. Then in terms of economics this development scenario is feasible to be developed with NPV reaching 9,140 MUSD, the ROR reaching 41% for PSC and 60% for Gross Split, and increases field recovery factor (RF) up to 56%.

Hydrocarbon exploration basically requires effective drilling and efficient overpowering of frictional and viscosity forces. Normally, frictional power losses occur in deep well systems and it is essential to analyse each component of any well system to determine where exactly pressure is lost, and this can be done using Nodal Analysis. In this study, nodal analysis has been carried out with the use of PROSPER, a software for well performance, design and optimisation. Artificial lifts can then be used to solve the problem of frictional power losses. To increase the production of Barbra 1 well in the Niger Delta and hence extend its functional life, we have applied nodal analysis. Modelling results for three artificial lift methods; continuous gas lift, intermittent gas lift and electrical submersible pump were found to be 1734.93 bbl/day, 451.50 bbl/day and 2869 bbl/day respectively. The output from the well performance without artificial lift was 1370.99 bbl/day by applying Darcy's model. Meanwhile, the output from the well without artificial lift is 89.90 bbl/day when aided with productivity index (PI) entry, the normal model for intermittent gas lift. Hence, from the comparative analysis of the results obtained from this study, it was deduced that when artificial lifts are employed, the well output increases significantly from 1370.99bbl/day to 2869 bbl/day (electrical submersible pump). This study concludes that wells such as Barbra 1 are good candidates for artificial lift, and this is evidenced by increasing productivity.

Saat ini, CO<sub>2</sub> flooding adalah salah satu teknik pemindahan yang paling menarik di lapangan-lapangan minyak. Injeksi CO<sub>2</sub> akan memungkinkan minyak berinteraksi dengan CO<sub>2</sub> dan memberikan peningkatan positif, sehingga minyak akan lebih mudah mengalir. Tujuan dari penelitian ini adalah untuk mendapatkan skenario penginjeksian terbaik yang memberikan perolehan minyak tertinggi antara injeksi air, injeksi CO2, serta injeksi air dan CO2 secara kontinyu pada kondisi batuan reservoir dengan kebasahan minyak dan reservoir dengan kebasahan air. Penelitian dilakukan pada Lapangan SNP menggunakan simulasi model material balance dengan lama penginjeksian sekitar 30 tahun. Lapangan SNP memiliki tiga regional (antiklin). Pengamatan dilakukan pada Region 2 dan Region 3. Untuk setiap region dibuat sepuluh skenario dengan variasi laju injeksi air dari 0 hingga 2000 STB/D dan variasi injeksi CO<sub>2</sub> dari 0 hingga 0.5 MMSCF/D. Hasil simulasi menunjukkan perolehan minyak pada Region 2 berkisar antara 40.90% hingga 52.65%. Sedangkan perolehan minyak pada Region 3 berkisar antara 48.88% hingga 60.08%. Dari hasil perbandingan keduapuluh skenario pada kedua region, diperoleh bahwa injeksiCO2 memberikan kinerja terbaik pada reservoir oil wet. Sedangkan pada reservoir water wet kinerja injeksi air lebih baik daripada injeksi CO2. Skenario terbaik pada reservoir water wet adalah dengan penginjeksian air dan CO2 secara kontinyu.

A great number of petroleum-engineering calculations require knowledge of deviation factors for natural gases. But experimental data from P-V-T measurements are seldom available. In such cases, use of the Standing-Katz Z-factor chart, or its tabulated form, is generally accepted. This article evaluates eight methods that have been devised to make the original Standing-Katz chart of supercompressibility, or Z-factor, readily usable in complex calculations. A chart and a table are presented to help choose the proper method for a given range of reduced temperature and pressure. Considerations on the computer programming of every method are given with an eye on possible use of minicomputers.

A theoretical study was carried out to developthe general equations relating-time lags and responseamplitudes to the length of the pulse cycles andthe pulse ratios of these cycles for pulse testswith unequal pulse and shut-in times. Thesevariables were related to the reservoir parameters using appropriate dimensionless groups. Theequations were developed by using the unsteady-stateflow model of the line source for an infinite, homogeneous reservoir that contains a single-phase, slightly compressible fluid. A computer programwas written to calculate the values of The three corresponding time lags and the response amplitudesat given dimensionless cycle periods and pulseratios using these general equations.
For different values of the pulse ratio rangingfrom a 0.1 to 0.9, the time lags and responseamplitudes were calculated for dimensionless cycleperiods ranging from 0.44 to 7.04. This range ofcycle period and pulse ratio covers all practicalranges over which pulse testing can be usedeffectively. Curves relating the dimensionless timelag to the dimensionless cycle period and thedimensionless response amplitude were constructed JOT each case. It was also found that both thedimensionless cycle period and the dimensionlessresponse amplitude can be represented as simple exponential junctions of the dimensionless timelag. The coefficients of these relations are functionsonly of the pulse ratio.
Introduction
Two wells are used to run a pulse test.These two wells are termed the pulsing well and theresponding well. A series of flow disturbances isgenerated at the pulsing well and the pressureresponse is recorded at the responding well.Usually, alternate periods of flow and shut in (or injection and shut in) are used to generate the flowdisturbances at the pulsing well. The pressureresponse is recorded using a highly sensitive differential pressure gauge.
Pulse testing has received considerable attentionbecause of be advantages A has over theconventional interference tests. The pressureresponse from a pulse test can be easily detectedfrom unknown trends in reservoir pressure. Pulsetest values are more sensitive to between-wellformation properties; thus, a detailed reservoirdescription can be obtained from pulse testing.
In all the work that has been reported on pulsetesting, it was assumed that the flow disturbancesat the pulsing well were generated by alternate periods of flow and shut in or injection and shut in.The pulsing period and shut-in period were alwaysequal. There bas been no study of pulse testing with unequal pulse and shut-in periods. Such a studymight have indicated whether other pulse ratioswill produce higher response amplitudes than theequal-period tests. The main purpose of this studyis to determine the response of pulse testing tounequal pulse and shut-in periods and to find theoptimum pulse ratio that gives the maximum responseamplitude.
PULSE-TEST TERMINOLOGY
Fig. 1 shows the pulse-test terminology as usedin this paper.
SPEJ
P. 399

This paper presents an interpretation method for injectivity and falloff testing in a single-layer oil reservoir that is under waterflooding and develops analytical solutions for pressure and saturation distributions. The effects of relative permeability, wellbore storage, and skin are considered in these solutions. New field-dependent type curves for falloff tests, which exhibit features that do not appear in the currently available single-phase-flow type curves, are also presented. Matching of field data on these curves yields fluid mobilities in various banks, skin, formation permeability, and flood-front location. Field data interpretation with the new method shows that falloff tests can be used to monitor the progress of waterfloods.

Two methods are presented for predicting critical oil rate for bottomwater coning in anisotropic, homogeneous formations with the well completed from the top of the formation. The first method is based on an analytical solution where Muskat's assumption of uniform flux at the wellbore has been replaced by that of an infinitely conductive wellbore. The potential distribution in the oil zone, however, is assumed unperturbed by the water cone. The method is derived from a general solution of the time-dependent diffusivity equation for compressible, single-phase flow in the steady-state limit. We show that very little difference exists between our solution and Muskat's. The deviation from simulation results is caused by the cone influence on potential distribution.
The second method is based on a large number of simulation runs with a general numerical reservoir model, with more than 50 critical rates determined. The results are combined in an equation for the isotropic case and in a single diagram for the anisotropic case. The correlation is valid for dimensionless radii between 0.5 and 50 and shows a rapid change in critical rate for values below five. Within the accuracy of numerical modeling results, Wheatley's theory is shown to predict the correct critical rates closely for all well penetrations in the dimensionless radius range from 2 to 50.

Published in Petroleum Transactions, AIME, Vol. 204, 1955, pages 7–15. Paper presented at Petroleum Branch Fall Meeting in San Antonio, Oct. 17–20, 1954.
Abstract
A series of both water and gas pattern floods was made in the laboratory to study the oil recovery performances of such operations. These tests were conducted on consolidated sandstone models, using oil, water, and gas. The model floods were scaled to reproduce field performance under gas and water five-spot injection, X-ray shadowgraphs permitted observation of the gross fluid movement within the models.
A method was developed for applying the mobility ratio concept to water flooding and dispersed gas drives in a five-spot well pattern. The areal sweep efficiency at breakthrough for dispersed gas drives is much higher than previously expected, lying in the range of 50 to 100 per cent.
A method is presented for predicting the water-oil ratio performance of five-spot pattern water floods in uniform sands. This method is verified experimentally for the condition of no free gas initially present and for values of gas saturation normally encountered in fields following depletion operations. Production performance for pattern gas injection is also predictable by this method.

A method to predict the percent recovery of volumetric, high-pressured gas reservoirs from the initial pressure to the abandonment pressure with only initial reservoir data is presented. This method can also be used with early-life production data to predict the initial gas in place. The method is based on an incremental solution to the general material-balance equation. All parameters in the material balance are pressure-dependent and are recalculated for every 100-psi [690-kPa] drop in reservoir pressure. Procedures were developed to calculate these parameters with correlations and data available in the literature. The reservoir depletion model presented here was applied to a field example, as were three published techniques for determining reserves in abnormally pressured reservoirs. When predictions of initial gas in place were compared, the reservoir depletion model yielded a more accurate value than the other techniques.

Published in Petroleum Transactions, AIME, Volume 210, 1957, pages 341–344.
Introduction
Increasing emphasis is being placed on the necessity for obtaining reasonably accurate estimates of the physical properties of reservoir fluids well in advance of more accurate laboratory data. One such factor is the isothermal coefficient of expansion of an undersaturated hydrocarbon liquid which may be contained in a particular reservoir. This coefficient, or liquid "compressibility", has often been assumed to be relatively insensitive and nearly constant. Although this assumption may be nearly correct in the case of high specific gravity liquids, it cannot apply in the case of medium to low specific gravity liquids. Any treatment of the nature of liquid compressibilities must give consideration to the variable nature of the isothermal expansion coefficient and the fact that it can be both pressure sensitive and temperature sensitive.

Published in Petroleum Transactions, AIME, Volume 219, 1960, pages 288–292.
Abstract
One of the major difficulties in predicting the performance of oil reservoirs from their early pressure history lies in the uncertainty of estimating the volume of the liquid hydrocarbons contained in them. As a first step in filling this need, an equation was developed to determine the molal liquid volume of pure hydrocarbons over a wide range of temperature and pressure. The second step consisted of adapting the equation to apply to mixtures, with the heavy hydrocarbons expressed as C7+.
The equations are similar in form to van der Waals' equation, but the constants a and b are considered as functions of temperature. In addition to the gas constant R, there are four constants characteristic of each hydrocarbon.
When compared with experimental values found in the literature, the average absolute deviation in the calculated molal volumes is found to be a maximum of 0.33 per cent for any of the pure liquid hydrocarbons studied. This maximum deviation was that found when comparing the calculated and observed values over a temperature range of 86° to 482°F and a pressure range from the bubble-point to 10,000 psia.
The equations expressing the correlation for mixtures were developed from 647 experimental measurements of volume on 47 bottom-hole samples covering a temperature range of 72° to 250°F and a pressure range from bubble-point to 5,000 psig. The average absolute deviation was found to be 1.6 per cent with the maximum for any measurement of 4.9 per cent.
Introduction
Accurate information of the pressure-volume-temperature behavior of hydrocarbon liquids is of considerable importance in the field of both applied and theoretical science and, especially, in the solution of petroleum reservoir engineering problems. These PVT relationships can be expressed graphically, in tabular form or as equations of state.

Published in Petroleum Transactions, AIME, Volume 219, 1960, pages 313–319.
Abstract
A new method for obtaining equilibrium vaporization ratios (K-values) for reservoir fluids has been developed and tested. By application of the method, complex experimental measurements of liquid and vapor phase compositions are eliminated. This simplified technique reduces the cost of experimental equilibrium ratio data for reservoir studies of condensates and volatile crude-oil systems.
The method is designed for systems of constant composition and, therefore, is best suited for depletion studies where compositional changes at high pressures are minor. The basic data required, in addition to the composition of the initial reservoir fluid, are the relative vapor-liquid volumes and densities at reservoir temperature and various reservoir pressures.
Tests demonstrated that the method predicts equilibrium ratios accurately for condensates. A single test on a crude oil was not conclusive; further testing will be necessary before the accuracy of the method can be determined for crude-oil systems.
In addition to determining equilibrium ratios, the calculation method provides information on the physical properties of the "plus" component in the vapor and liquid phases. The "plus" component is that mixture of components heavier than the least volatile fraction analyzed. This information is useful in studies of both natural depletion and cycling operations for condensate reservoirs where the heptanes-plus component in the gas phase is produced from the reservoir.
Introduction
As more volatile oil and condensate reservoirs are found, the use of phase behavior techniques to predict their performance is increasing in importance. These techniques have long been used for condensate fields and have more recently been applied to crude-oil fields containing oils of medium-to-high volatility. In these phase behavior methods, equilibrium ratios (K-values) are used to predict compositional changes in the reservoir fluids-thereby accounting for the recoverable oil that exists in the gas phase. The reliability of the predictions depends to a large extent on the equilibrium ratios used. These values must be obtained for each component for the entire pressure range being investigated.

This paper presents significantly improved yet simple method to predict future oilwell deliverability and inflow performance relationship (IPR) curves. For the 21 reservoirs studied, current empirical techniques overpredicted future performance by 117%, while the new approach reduced the average error to only 9%. This new method, when coupled with nodal analysis, could affect equipment sizing, investment planning, and property sales economics significantly because it provides more realistic predictions.

Published in Petroleum Transactions, AIME, Volume 201, 1954, pages 182–191.
Abstract
A method has been developed for calculating the average pressure in a bounded reservoir. The reservoir is first divided into the individual drainage volumes of each well, by using the criterion that at steady state each individual drainage volume is proportional to a well's production rate. The average pressure in each drainage volume is then calculated by a method developed in the report. By volumetrically averaging these individual drainage volume pressures, the average pressure in the entire reservoir is obtained.
To calculate the average pressure in each drainage volume, a correction is applied to the ordinary extrapolated pressure, i.e., the pressure obtained by extrapolating to infinite time the linear portion of the graph of closed-in pressure versus log [?t/(t + ?t)], where ?t is the closed-in time and t the production time. The correction, which is a function of the production time, is presented in graphical form for different shapes of the drainage area (horizontal cross section of the drainage volume).
Introduction
It is important to be able to find the volumetric average pressure in a reservoir so that the size of the reservoir may be determined from material balance calculations. It is also desirable to be able to find the approximate distribution of pressure within a reservoir for detection of fluid movement. The purpose of this paper is to present a method for calculating both the average reservoir pressure and the approximate distribution of pressure within a bounded reservoir that is, a reservoir with no water drive.
In reservoirs where the pressure builds up rapidly after wells are shut in, the determination of average pressure generally poses little problem, for one often need only average the final buildup pressures. It is when pressure buildup is slow that difficulties arise. For practical and economical reasons, the time allowable for closing in wells is limited. If at the maximum allowable closed-in time the pressure has not reached a constant value (and this is more often the case than is generally realized), calculation of average pressure presents difficulties.

A method has been developed whereby one may calculate the productivityfactors of producing formations from a knowledge of the reservoir conditions.Account is taken not only of the heterogeneous character of the gas-oil flowsystem but also of the detailed variations with pressure of the shrinkage andviscosity of the oil, the solubility of the gas in the oil, and even thevariability of the gas viscosity and the deviation of the gas from idealbehavior. Curves are shown giving the results of numerical calculations on theproduction rate as a function of the pressure differential for a highpressureand a low-pressure system, three values of gas-oil ratio being treated in eachcase. Curves are also given showing the variation with distance from the wellof the pressure, oil saturation, and permeability. The effect of connate wateris briefly discussed in relation to the apparently large discrepancies betweenthe calculated and observed productivity-factor values.
Introduction
The significance of the productivity factor as a measure of the capacity ofan oil-bearing formation to produce is well recognized; for it is the compositeand integrated resultant of the physical properties of both the porous mediumand the fluid stream passing through it with respect to the ease with which theparticular petroleum fluids present in the formation can flow through it andinto producing wells.
The most direct method of determining the productivity factor of a wellconsists, as is well known, in the simultaneous measurement ofreservoir-pressure differentials and rates of production and the expression ofthe data in terms of rate of flow per unit pressure drop. Actual measurementscarried out in this manner on producing wells have given factors that generallylie in the range of 0 to 100 bb1. per day per pound pressure drop. This widerange arises not only from variations in permeability but also from the varyingsand thickness of producing formations.
T.P. 1352

Fluid samples must be taken early in the life of a reservoir to obtain samples truly representative of the reservoir fluid. They should be taken only after a carefully planned well conditioning and testing program. When the PVT data obtained from these samples are used, care should be taken to adjust FVF's and gas/oil ratios (GOR's) for surface separator conditions.

Improved prediction of the P-V-T relationships for gas mixtures containing Câ/sup +/ or Câ/sup +/ components is obtained with better characterization of the heavy ends. Predicted vaporization characteristics are much closer to those of the real fluid than those predictions previously possible. Resulting predictions preserve the integrity of the molar/mass/volume relationships that are necessary for custody transfer and purchasing agreements. Nearly all naturally occurring gas and crude oil fluids contain some quantity of materials that are not well defined and not mixtures of discretely identified components. These pseudo (Câ/sup +/ or Câ/sup +/) components must be properly characterized if the P-V-T behavior of the gas mixture is to be accurately predicted. Perhaps the most widely used procedure is to describe the pseudo component as being made up of one or more normal paraffins. Use of this technique has been encouraged by the fact that most chromatographic analyses for natural gases report the heavier fractions as a series of equivalent normal paraffins.

Theoretical and experimental investigations of a constant pressure gravitydrainage system are reported. Experimental data are presented to show thatrecovery to gas breakthrough by gravity drainage is inversely proportional torate. The gravity drainage reference rate, which is numerically equal to theso-called "maximum theoretical rate of gravity drainage" is shown tohave no particular significance from a recovery standpoint. Before this ratecan be used as a basis of comparison for recoveries, it is necessary that therelative permeability and capillary pressure characteristics and displacingfluid viscosities be identical for the systems compared.
A method is presented by which accurate prediction of the performance of agravity drainage system can be made. Close agreement between experimental andcalculated drainage performance shows that steady state relative permeabilityand static capillary pressure data can be used to describe fluid displacementbehavior. The very wide range of liquid recoveries before gas breakthroughwhich result from production rate variation alone demonstrates the importanceof this factor in planning depletion of a gravity drainage reservoir.Calculated results are presented which show that little additional recovery canbe expected from a high pressure gravity drainage system between the times ofgas breakthrough and attainment of such high gas/liquid ratios as to makefurther pressure maintenance impractical.
Introduction
It has been recognized for some time that gravity forces play an importantpart in the recovery of oil from some types of reservoirs. Field experience hasshown that under certain conditions, gravity drainage can result in very highoil recoveries. Qualitative reasoning has led most engineers to the generalconclusions that:
(1) Where gravity drainage is important, the reservoir pressure should bemaintained by gas injection at the crest of the structure to prevent shrinkageof the oil in place and to keep a low viscosity so the oil can drain at thefastest possible rate.
(2) Recovery by gravity drainage is rate sensitive.
A survey of the literature indicates that while considerable work has beendone on the effects of gravity in oil production problems, no satisfactorymethod of calculating the performance of gravity drainage reservoirs has beenreported. In the absence of any proven method of calculating reservoirperformance, the level at which pressure should be maintained and the rate ofproduction for most efficient operation has been open to debate.
T.P. 3199

Planning of the efficient operation of a gas-condensate reservoir requires a knowledge not only of the gross phase behavior of the system but also of the equilibrium distribution of the various components between the gas and condensate phases. This equilibrium distribution can be calculated with appropriate equilibrium constants. In this paper are presented equilibrium constants determined experimentally for the oil and gas phases initially present in the same reservoir and for the gas and condensate phases of the gas cap material at a series of pressures below the original reservoir pressure. Also presented is a method for the correlation of the experimentally determined equilibrium constants. The utility of the correlation is demonstrated further by an example of its use in adjusting the equilibrium data to permit their application to another gas-condensate system of similar composition.
Introduction
Planning of the efficient operation of a gas-condensate reservoir requires a thorough knowledge not only of the gross phase behavior of the particular hydrocarbon system but also of the equilibrium distribution of the various components between the gas and condensate phases. At the initial conditions of reservoir temperature and pressure, the original hydrocarbon materials in a gas-condensate reservoir or in the gas-cap of an associated reservoir exist in a single, homogeneous vapor phase. However, some condensation of hydrocarbons to a liquid phase usually occurs in the reservoir as pressure declines incident to production. Because of this condensation, the produced gas changes composition continuously. The composition of the produced gas, as well as that of the condensed liquid, can be calculated from the composition of the original reservoir material through the application of appropriate equilibrium constants or "K"-values provided these values are known.
Equilibrium constants have been used for many years in problems of surface separation of gas and oil and natural gasoline recovery. However, no satisfactory equilibrium data at reservoir conditions have been available for the higher boiling hydrocarbons which acquire abnormal volatility at high pressure and are therefore present in the gas phase in condensate reservoirs. Early work in this field indicated that the behavior of the higher boiling hydrocarbons largely determines the behavior of gas-condensate systems at high pressure.

A new correlation for the compressibility of sweet and sour natural gases ispresented. This correlation is derived from an equation of state whichadequately represents the Standing-Katz Z-Factor chart. The algebraicexpression for compressibility presented here is suitable for computercalculations. A FORTRAN subroutine to perform this computation is alsopresented, along with a graphical form of the correlation.
INTRODUCTION
IN THE PRESSURE ANALYSIS of transient or pseudo-steady-state flow Dataacquired during gas well testing, a knowledge of the variation of fluidcompressibility with pressure and temperature is essential. For liquid flow, the compressibility is small and is usually assumed to be constant. For gasflow, the compressibility is neither valid nor necessary of a real gas can becomputed readily.
Trube (1957) has presented graphs from which the compressibility of natural gases may be obtained. This correlation is, however, difficult to usein a computer program. Recent developments have made possible a more consistentand convenient approach.
The purpose of this paper, therefore, is to present An analytical technique forcalculating the compressibility of natural gases. The procedure may be readilycomputerized and was used to generate curves of pseudo-reduced compressibility, which are useful for manual calculations.
Theory
(Equation in full paper)
Graphical Presentation
The computer subroutines mentioned above were used to generate cr as a function of Pr and Tr. Figure 1 is aplot of c r versus pr for various values of Tr. In this figure, the curves are too close together for easy andunambiguous reading. In order to increase the separation of the isotherms, especially for the low-pr range, c r T r wasgenerated and plotted versus Pr for various values of Tr as shown in Figures 2 and 3. The separation between the isothermsin these figures is sufficient to make them easy to read and hence suitable forreasonably accurate manual calculations of compressibility.
Sour Gases
The correlation developed for c r in terms of (aZapr) and the graphical representation of cr Trare applicable to sour as well as sweet natural gases. A simple method has beendeveloped by Wichert and Aziz (1972) to account for the presence of H.S and CO2 in the use of the Standing-Katz Z-Factor chart. Inthis method, the pseudo-critical properties of a sour gas are adjusted togive:
(Equation in full paper)
The calculation procedures are then exactly the same as discussed previously, except that T12 and p1c must beused instead of T2 and po respectively.
Discussion
Figure 4 compares some of the isotherms for reduced compressibilitydeveloped by Trube (1957) with corresponding isotherms from Figure 1 Thedifference between the two methods is no doubt due to the different techniquesutilized to obtain Z and (aZ/a2r)Tr.
Trube used the Standing-Katz Z-Factor chart re- produced by Brown et al.(1948, p.38) to obtain values of Z and (aZ/apr)substituted thesevalues into Equation (4), and calculated c, as a function of pr and Tr.

This paper presents a new method that applies to wells that are shut in after having reached pseudosteady-state flow conditions. Based on the complete Miller-Dyes-Hutchinson (MDH) equation, a corrected pressure is defined that allows extension of the semilog straight line by about two log cycles for symmetric systems and one-half log cycle for others. The drainage area is directly computed. If the final recorded shut-in pressures depart from the straight line, it is also possible to compute the shape factor and the average pressure independently of the initial pressure.

This paper examines normalized forms of Stone's two methods for predicting three-phase relative permeabilities. Recommendations are made on selection of the residual oil parameter, S om, in Method I. The methods are tested against selected published three-phase experimental data, using the plotting program called CPS-1 to infer improved data fitting. It is concluded that the normalized Method I with the recommended form for S om, is superior to Method II.
Introduction
Stone has produced two methods for estimating three-phase relative permeability from two-phase data. Both models assume a dominant wetting phase (usually water), a dominant nonwetting phase (gas), and an intermediate wetting phase (usually oil). The relative permeabilities for the water and gas are assumed to permeabilities for the water and gas are assumed to depend entirely on their individual saturations because they occupy the smallest and largest pores, respectively. The oil occupies the intermediate-size pores so that the oil relative permeability is an unknown function of water and gas saturation. For his first method, Stone proposed a formula for oil relative, permeability that was a product of oil relative permeability in the absence of gas, oil relative permeability in the absence of gas, oil relative permeability in the absence of mobile water, and some permeability in the absence of mobile water, and some variable scaling factors. He compared this formula with the experimental results of Corey et al., Dalton et al., and Saraf and Fatt. The formula is likely to be most in error at low oil relative permeability where more data are needed that show the behavior of residual oil saturation as a function of mixed gas and water saturations. In particular, the best value for the parameter S om that occurs in the model is not well resolved. In his second method, Stone developed a new formula and compared it against the data of Corey et al., Dalton et al., Saraf And Fatt, and some residual oil data from Holmgren and Morse. Stone suggested that his second method gave reasonable agreement with experiments without the need to include the parameter S om. If in the absence of residual oil data, S om = 0 is used in the first method, the second method is then better than the first method, although it tends to under predict relative permeability. Dietrich and Bondor later showed that Stone's second method did not adequately approximate the two-phase data unless the oil relative permeability at connate water saturation, k rocw, was close to unity. Dietrich and Bondor suggested a normalization that achieved consistency with the two-phase data when k rocw, was not unity. This normalization can be unsatisfactory because k roc an exceed unity in some saturation ranges if k rocw is small. More recently this objection has been overcome by the normalization of Method II introduced by Aziz and Settari. Aziz and Settari also pointed out a similar normalization problem with Stone's first method and suggested an alternative to overcome the deficiency. However, no attempt was made to investigate the accuracy of these normalized formulas with respect to experimental data. In the next section of the paper we review the principal forms of Stone's formulas, and introduce some new ideas on the use and choice of the parameter S om. Later we examine the first of Stone's assumptions that water and gas relative permeabilities are functions only of their respective saturations for a water-wet system. This involves a critical review of all the published experimental measurements. Earlier reviews did not take into account some of the available data. Last, we examine the predictions of normalized Stone's methods for oil relative permeability against the more reliable experimental results. It is concluded that the normalized Stone's Method I with the improved definition of S om is more accurate than the normalized Method II.
Mathematical Definition of Three-Phase Relative Permeabilities
We briefly review the principal forms of the Stone's formulas that use the two-phase relative permeabilities defined by water/oil displacement in the absence of gas,
k rw = k rw (S w)
and
k row = k row (S w)
and gas/oil displacement in the presence of connate water,
k rg = k rg (S g)
and
k rog = k rog (S g).
SPEJ
p. 224

This paper describes a method for obtaining compositions of gas and oil phases in equilibrium with each other at a given reservoir temperature and pressure as lean or enriched gas is injected into a reservoir oil not in equilibrium with the gas. The method is based on calculation of equilibrium constants, K, from the equation log Kp= A + B F, where p is pressure and F is component characterization factor. A and B are constants that vary with a composition parameter. The paper explains how A and B could be determined with a minimum amount of data. The method consists of calculating equilibrium constants as a function of liquid composition and using the K's to calculate changes in composition of injection gas as it successively contacts original reservoir oil at the gas-oil front and the change in composition of reservoir oil as it is successively contacted by the injection gas in the vicinity of an injection well. An iterative process is required. Two examples of the method are given which show how oil and gas compositions and properties are calculated with the aid of a computer.
Introduction
The calculation of recovery from lean-gas or enriched-gas injection into a saturated or under-saturated reservoir oil requires a knowledge of how phase properties change in a reservoir between injection well and producing well. To determine the phase compositions or properties experimentally would be difficult and time consuming, especially if one wanted to look at the effect of various injection gas compositions. For some fields an engineer would want to make preliminary calculations on the economics of gas injection before he makes the decision to spend a considerable sum of money for laboratory work to obtain the necessary fluid properties. A method for calculating compositions and properties based on a minimum of laboratory data is described. The minimum amount of data required is injection gas and reservoir oil composition and injection gas solubility as a function of pressure for an undersaturated oil, or the compositions of mixtures of reservoir fluid with two or more enriched gases, which mixtures have a bubble-point pressure that is the same as the expected average displacement pressure. On the other hand, if the economics appear to be attractive, more laboratory data can be obtained in the form of equilibrium constants for three or more mixtures of the reservoir fluid and injection gases. The method is based on the calculation of K's from the equation, log Kp= A + B F, where K is equilibrium constant, p is pressure and F is component characterization factor. This method of plotting K data by means of the above equation is described by Hoffman, Crump and Hocott. A and B are constants that vary with a composition parameter. It is shown how experimental data are used to determine how A and B vary with composition.
BASIS OF METHOD
EQUILIBRIUM CONSTANTS
Equilibrium constant (K) data are required for this method. The K of each component is obtained from an equation that gives the product of K and pressure as a function of component characterization factor. The characterization factor F= b(1/Tb- 1/T), where b is a constant characteristic of a given component, Tb is the boiling point in oR at atmospheric pressure of the given component, and T is the temperature of the system in oR. This method of plotting K data is described by Hoffman, Crump and Hocott. The straight-line equation of the log Kp - F plot is
log kip= log Kop + BFi
where Kop is at F= o, i designates the component, and B is the slope of the line.
SPEJ
P. 239ˆ

Pressure buildup and flow tests conducted in wells that do not completely penetrate the producing formation or that produce from only a small portion of the total productive interval can generate noncylindrical flow regimes and require special interpretation procedures. Frequently a spherical flow regime is representative, and a new equation based on the continuous point-source solution to the diffusivity equation in spherical coordinates is presented for analyzing tests of this nature. The practical utility of the equation is demonstrated by practical utility of the equation is demonstrated by analyzing tests involving restricted producing intervals that cannot be treated with existing analytic methods.Practical guidelines for applying the proposed equation are developed by analyzing pressure data generated by a numerical simulator and more complex analytic solutions for variety of special completion situations. Equations for determining static reservoir pressure, formation permeability, and skin factors pressure, formation permeability, and skin factors are derived and their validity verified under theoretical test conditions. The equations presented should have a variety of applications, but are particularly suited for analyzing pressure data from particularly suited for analyzing pressure data from drillstem tests with short flow periods.
Introduction
The fundamental equation for analyzing pressure buildup tests of oil wells was presented by Horner in 1951. This equation is based on the "line source" solution to the boundary value problem describing the pressure distribution resulting from the cylindrical flow of a slightly compressible fluid in an infinite reservoir. To achieve cylindrical flow the wellbore of a well must completely penetrate the producing formation. Although this restriction is often satisfied, in many tests it is not; for example, oil wells producing through perforated casing may have only a small portion of the total production interval perforated, or in the case of production interval perforated, or in the case of drillstem tests only a small interval (often 10 to 15 ft) of a thick (hundreds of feet) homogeneous formation may be selected for testing. Tests involving restricted producing intervals of this type have a characteristic buildup curve as described by Nisle and by Brons. These authors demonstrated that Horner's conventional equation could also be used for restricted producing interval problems, provided the correct portion of the buildup problems, provided the correct portion of the buildup curve is used. They showed that during a short period after starting production (or equivalently period after starting production (or equivalently after shut-in) the well behaves as if the total sand thickness were equal to the interval open to flow. That is, Horner's equations apply if the total sand thickness, h, is replaced by the producing interval thickness, h. They also showed that after a transition period the late part of the buildup curve could be used in the conventional manner to calculate formation permeability and static reservoir pressure. Kazemi and Seth extended the work of pressure. Kazemi and Seth extended the work of Nisle by including the effect of anisotropy; they also presented an equation, based on an analytic solution developed by Hantush, for estimating the shut-in time required for the development of the second straight-line portion in a conventional plot --i.e., p vs In (t + Deltat/Deltat. The first straight-line part o the buildup curve usually lasts only a few part o the buildup curve usually lasts only a few minutes and may often be obscured by afterflow, whereas the latter straight-line portion may take several hours to develop and may not even occur for practical shut-in times if the formation is thick and the producing time is relatively short. This paper demonstrates that the transition period paper demonstrates that the transition period between the two cylindrical flow periods can be analyzed with the spherical* flow equations presented here. In addition, practical guidelines presented here. In addition, practical guidelines cue developed for their application.Moran and Finklea first suggested that a pressure buildup equation based on spherical now pressure buildup equation based on spherical now was necessary to correctly analyze pressure data obtained from wireline formation testers. In many respects this study is similar; in fact, the basic pressure buildup equation (although it was derived pressure buildup equation (although it was derived from a different starting equation) presented here was used by Moran and Finklea in analyzing wireline formation test data.
SPEJ
P. 545

The pressure buildup behavior of multiple-layer systems that communicate only at wellbores may be different from that of single-layer systems. However, different properties of layered reservoirs cause such different pressure transient responses that there is no generally valid criterion pressure transient responses that there is no generally valid criterion for recognizing multiple-layer systems from transient tests.
Introduction
Pressure transient testing has been used in reservoir Pressure transient testing has been used in reservoir diagnosis for many years, yet, until quite recently, little attention was given to the transient behavior of layered systems with no crossflow (also called commingled systems). These are reservoir systems with two or more layers but with communication between the layers only through wellbores. The transient behavior of such systems can be much different from the behavior of single-layer system - or it can be very similar. Although there is information available about single-well, two-layer, closed circular systems in the literature, the information does not provide a valid general description of the transient pressure behavior of layered systems. The pressure behavior of systems of different geometry and layer properties varies from behavior similar to that for two-layer circular systems to behavior indistinguishable from that of single-layer systems. To illustrate this variation, we shall present simulated pressure buildup behavior for several layered-reservoir situations. The mathematically simulated results are for only a small fraction of the systems actually studied; they are presented as illustrative of the range of responses presented as illustrative of the range of responses seen.Information similar to some of the material presented here is available in Refs. 1, 4, and 7. Lefkovits presented here is available in Refs. 1, 4, and 7. Lefkovits et al. present an analytical solution for the two-layer problem, indicate several distinct differences between problem, indicate several distinct differences between one- and two-layer pressure buildup behavior, show that the time to pseudosteady state is much longer for two-layer systems than for single-layer systems, and suggest techniques for estimating permeability and average reservoir pressure. Cobb et al. present similar data and investigate various analysis techniques for pressure buildup tests in two-layer reservoirs with equal layer thickness and phi mu ct. Raghavan et al. later expanded this work to include layers of unequal thickness and provided a technique for estimating the layer permeability ratio from buildup test results. Refs. 1, permeability ratio from buildup test results. Refs. 1, 4, and 7 all consider a single well in the center of a closed, circular, two-layer system with constant and equal layer porosity; their main purpose is to illustrate behavior and propose interpretation techniques for those limited situations.Although we suggest some analysis techniques, it is not the goal of this paper to propose widely usable interpretative techniques for pressure buildup tests in noncommunicating layered reservoirs. Rather, we wish to show a wide variety of simulated buildup test results to illustrate that there is no general description for pressure buildup behavior in layered reservoirs. For completeness, we present some information for a closed square system that is similar to that given in Refs. 1, 4, and 7. However, results in this paper include a much wider range of conditions than reported previously. The number of layers, the porosities, the permeabilities, and the thicknesses are varied.
JPT
P. 1178

Viscosity values of crude oils and crude oils containing dissolved natural gas are required in various petroleum engineering calculations. In evaluation of fluid flow in a reservoir, the viscosity of the liquid is required at various values of reservoir pressure and at reservoir temperature. This information can be obtained from a standard laboratory PVT analysis that is run at reservoir temperature. There are cases, however, when the viscosity is needed at other temperatures. The most common situation requiring viscosities at various pressures and temperatures occurs in the calculation of two-phase, gas-liquid flowing pressure traverses. These pressure traverses are required in tubing-string design, gas-lift design, and pipeline design. Calculation of these pressure traverses involves dividing the flow string into a number of length increments and calculating the pressure gradient at average conditions of pressure and temperature in the increment. Calculation of pressure and temperature in the increment. Calculation of pressure gradients requires knowledge of oil viscosity. In pressure gradients requires knowledge of oil viscosity. In many cases, the only information available on the fluid properties are the separator gas gravity and stock-tank oil properties are the separator gas gravity and stock-tank oil gravity; therefore, correlations requiring a knowledge of crude oil composition are not applicable. The most popular methods presently used for predicting oil viscosity are those of Beal for dead oil and Chew and Connally for live or saturated oil. Beal correlated dead oil viscosity as a function of API gravity and temperature. Chew and Connally presented a correlation for the effect of dissolved gas on the oil viscosity. The dead oil viscosity and the amount of dissolved gas at the temperature and pressure of interest must be known. pressure of interest must be known. When these correlations were applied to data collected for a study of dissolved gas and formation volume factor, considerable errors and scatter were observed. These data, therefore, were used to develop new empirical correlations for dead or gas-free crude oil as a function of API gravity and temperature, and for live oil viscosity as a function of dissolved gas and dead oil viscosity. A description of the data used, which were obtained from Core Laboratories, Inc., is given in Table 1. The correlation for dead oil viscosity was developed by plotting log 10 (T) vs log 10 log 10 (mu OD + 1) on cartesian plotting log 10 (T) vs log 10 log 10 (mu OD + 1) on cartesian coordinates. The plots revealed a series of straight lines of constant slope. It was found that each line represented oils of a particular API gravity. The equation developed is
= ,........................(1)
where
X =
y =
Z =
The correction of the dead oil viscosity for dissolved gas was developed by taking advantage of the fact that a linear relationship exists between log 10 mu OD and log 10 mu for a particular value of dissolved gas, Rs. Live oil viscosity may be calculated from
= ...........................(2)
TABLE 1 - DESCRIPTION OF DATA USED
Variable Range Solution GOR, scf/STB 20 to 2,070 Oil gravity, API 16 to 58 Pressure, psig 0 to 5,250 Pressure, psig 0 to 5,250 Temperature, F 70 to 295 Number of oil systems - 600 Number of dead oil observations - 460 Number of live oil observations 2,073
P. 1140

Introduction
It is common practice in some reservoir engineering and well-testing problems to plot a certain function A vs. another function B such that a straight line results. One well-known example is the graphical interpretation of the material-balance equation as a straight line. However, most of the time there is an unknown factor in either A or B. A trial-and-error procedure for estimating this factor until a straight line results is the method usually mentioned in the literature. This paper presents a simple technique for computing, the unknown factor directly.
Technique
Using common algebraic notations, a straight line has the equation y = mx + b.
A plot of y vs. x will give a straight line with slope m and intercept b. Also, if three (or more) pairs of data, (x1, y1),(x2, y2), and (x3, y3), are known,
y2 - y1 y3 - y1 --------- - --------- = m x2 - x1 x3 - x1
or y2 - y1 y3 - y1 --------- - --------- = 0. x2 - x1 x3 - x1
If y is comprised of a certain unknown constant, say c, this equation can be expressed as
f(c) = ----------------- - ---------------- = 0.......(1) x2 - x1 x3 - x1
Similar expression holds for x being a function of c.
Eq. 1 is the formulation of the common root-solving problem, where c is the root to be determined such that problem, where c is the root to be determined such that f(c)=0. Depending on the nature of the equation, the solution of f(c)=0 can be obtained with a closed type formula or, if this is not possible. with an efficient iterative root-solving algorithm such as the Newton's method.
Selection of Data Points
The current technique requires the use of three data points for formulating Eq. 1. If more than three points points for formulating Eq. 1. If more than three points are available, the selection of any three points from the given data would be adequate if all the data points are known to be correct. This is valid because any three correct data points would yield the same root c in Eq. 1. However, if it is not known which data points are correct, which three points to choose is a problem. One logical approach is to choose the two endpoints, (x1, y1) and (xn, yn) and the median or central point from the given set of n data points (x1, y1),(x2, y2),....., (xn, yn) to span the whole data set.
The following examples illustrate the current technique.
Example 1-Determination of Pressure Buildup Correction Factor C
The after flow analysis of Russell for pressure buildup analysis requires the plot of p/(1–1/C t) vs. log t to be a straight line. The correction factor C is usually an unknown. Russell suggested that C be determined by trial and error until the plot is a straight line. The current technique instead solves for C directly. Dake's after flow analysis data are used in this example and there are 15 data points available. Select the two endpoints and the central point (Table 1).
JPT
P. 1140

The pore-volume compressibilities and porosities presented here were derived from 256 samples of sandstone and limestone representing 40 reservoirs. These and previously published data are in poor agreement with compressibility-porosity correlations in the literature. The salient conclusion is that to evaluate rock compressibility for a given reservoir it is necessary to measure compressibility in the laboratory.
Introduction
The use of pore-volume compressibility-porosity correlations in engineering calculations is well known. The correlations developed by Hall for both sandstones and limestones have been widely distributed. Van der Knaap published a similar correlation using limestone samples from a single well and also correlated the data with net pressure. Such correlations are attractive because of the simple relationship established. However, those correlations were intended only for well consolidated samples; correlations for friable or unconsolidated samples have not been published. This study compares our laboratory data with the published correlations of consolidated samples as published correlations of consolidated samples as well as with values for friable and unconsolidated sandstones. Compressibility values are presented for 256 rock samples from 40 reservoirs - 197 samples from 29 sandstone reservoirs and 59 samples from 11 limestone reservoirs. Porosities ranged from less than 1 percent to 35 percent. Compressibility values from the literature for 79 samples are added, including Hall's and Van der Knaap's.
The Experiments Sampling
To obtain a representative sample of a formation for testing, one must avoid grain rearrangement. This problem is unlikely to occur with consolidated problem is unlikely to occur with consolidated samples or friable samples containing some cementation, although the effect of removing the overburden is still unknown. Unconsolidated samples, on the other hand, present a much more complex problem, in that grain rearrangement is very likely during either coring or subsequent handling. The advent of the rubber-sleeve core barrel much improved the chances of obtaining, representative samples. We have some evidence that, if carefully handled. rubber-sleeve cores will provide reasonably undisturbed samples. However, even if the sand is captured undisturbed in the rubber sleeve, internal gas can expand the core during the trip to the surface. The history of all the samples used in this study is not complete, but most of the unconsolidated samples were obtained from rubber-sleeve cores.
Preparing the Samples Preparing the Samples The consolidated and friable samples used in this study were generally plugs 1 in. in diameter and 3 in. long, and their condition ranged from well preserved to dry and weathered. The core plugs were extracted in solvent to remove water and hydrocarbons, put into a flexible jacket, and saturated with a refined oil. The unconsolidated samples of about the same dimensions were generally cored from rubber-sleeve cores that had been frozen in liquid nitrogen and for which liquid nitrogen had been used as a drilling fluid. The frozen samples were placed in a Teflon sleeve and allowed to thaw. End plates and screens were then placed on the ends of the samples.
JPT
P. 129

If a reservoir is characterized by a special type of heterogeneity such as stratification with no crossflow, the usual methods of determining reservoir limits are either not applicable or not practical. Proposed here is a way of estimating the drainage radius from pressure buildup data - a method especially useful whenever the drawdown data are not reliable.
Introduction
The reservoir limit test is a method of determining either the proximity of the boundaries of a reservoir to a flowing well or the size of drainage volume associated with the well. This method makes use of the usual equations for pressure drawdown and was first introduced by Park J. Jones. Other types of flow and pressure buildup tests that yield similar results, or pressure buildup tests that yield similar results, or additional improvements, can also be considered as reservoir limit tests; this is a natural extension of the basic ideas stated by Jones and others. If the reservoir is either homogeneous or heterogeneous with crossflow between various components, it has been shown that almost identical sets of pressure drawdown equations can be used for reservoir pressure drawdown equations can be used for reservoir limit calculations. Examples should be found in stratified reservoirs with crossflow and in some naturally fractured reservoirs. If, on the contrary, there prevail special types of heterogeneity such as stratification with no crossflow, then the usual methods are either not applicable or impractical. This latter type of reservoir is the subject of this work. The basic principles of the reservoir limit calculations can be summarized as follows. 1. During the early transient period of a drawdown or a buildup test, the wellbore pressure is linear with the logarithm of time, and the onset of non-linearity is related to the proximity of the reservoir boundaries. The distance to the nearest boundary can be approximated by Eq. 1 for drawdown and by Eq. 2 for buildup:
(1)
(2)
For an ideal circular reservoir with a centrally located well, Odeh and Nabor reported to be about 0.4, and to be about 0.25 . Their work was based on an RC analyzer. Our approach, based on a numerical finite difference solution, yielded a value of 0.214 for , which will be used as a norm in this paper. The value of will be taken as 0.25 . In paper. The value of will be taken as 0.25 . In fact, no precise value can be assigned to and . Their value depends mostly on the nature of the reservoir and the accuracy of the pressure measurement. 2. During the semisteady period the wellbore pressure of a drawdown test is linear with time, and the pressure of a drawdown test is linear with time, and the onset of this linearity is given by Eq. 3:
(3)
where for an ideal circular reservoir is about 0.1. Nonsymmetrical drainage boundaries give rise to larger values of . For instance, its value is 0.7 for a well in the center of a 4 X 1 rectangular reservoir. For a crossflow system is still about the same as that of its equivalent homogeneous reservoir of the same geometry. For no-crossflow stratified systems is much larger than the aforementioned figures.
JPT
P. 503

This paper explains a simple and effective method for graphically solving all three types of production decline. The three types of declines are: (1) exponential (2) hyperbolic, and (3) harmonic. The mathematical development of these curves was by Arps.
Decline curves are one of the most extensively used forms of data analysis employed in the evaluation of oil properties. Often future production is extrapolated as a straight line on semilog paper (exponential or constant-percentage decline) because this type of decline is the easiest to handle mathematically and graphical. This is done irrespective of the fact that several investigators have reported that this type of decline is rare and that actual oil production usually follows a hyperbolic decline. production usually follows a hyperbolic decline. However, the hyperbolic decline is difficult to analyze mathematically or graphically. The most recent method utilizes transparencies, as proposed by Slider.
The method outlined below greatly simplifies the solution and extrapolation of decline curves. The first four columns of Table 1 list the rate:time and cumulative-production:rate relationships as developed by Arps. The equations are all solutions of the differential equation D = Kq = - (dq/dt)/q. In each instance two unknowns must be calculated from the two relationships. They are the decline exponent n and the initial decline rate Di. The third unknown, qi, can be obtained from the production history of the well. First. the rate:time relationship is manipulated to solve for the value of Dit in terms of the ratio (qi/qt). These relationships are shown in Column 5 of Table 1. Next, the rate:time relationship is solved for Di, and this value of Di is substituted into the cumulative-production:rate relationship. This relationship is then solved for the value of Qt/(qit) in terms of (qi/qt), These relationships are shown in Column 6 of Table 1. Two graphs can then be constructed by selecting a value for n and then substituting values of (qi/qt into the relationships. A curve on each graph for the selected value of n will be produced. This can be done for any desired number of n values from 0 n 1. (See Figs. 1 and 2.) These curves can then be used to analyze and extrapolate decline curves from actual production history.
P. 38

The transient pressure behavior of a well which produces a single compressible fluid through a single-plane vertical fracture has been investigated mathematically. The fracture is assumed to possess infinite flow capacity, to be of limited radial extent, and to penetrate the producing formation completely in the vertical direction. Previous studies of vertically fractured wells have been concerned primarily with production rate performance or semisteady-state pressure behavior. This study was undertaken to ascertain the influence of vertical fractures on transient pressure tests such as pressure build-ups and flow tests. In a vertically fractured system, flow in the region nearest the fracture is practically linear, whereas farther away from the fracture essentially radial flow prevails. Thus, transient pressure analyses based on radial flow theory are sometime inaccurate. As fracture penetration increases radially, kh values calculated from pressure build-up and flow test curves become increasingly larger than true values. Failure to consider the effect of fracture penetration also introduces inaccuracies into the calculation of fracture length from the apparent skin factor and into the determination of average reservoir pressure. If the total length of the fracture is 20 per cent, or greater, of the drainage radius of the well, corrections must be made to pressure build-up and flow test results. Methods for correcting such results are discussed in this paper. For wells with prefracturing pressure build-up or flow test data, it is possible to estimate fracture length by comparison with postfracturing build-up or flow test results. In new wells or wells without prefracturing build-up or flow test data, fracture length must be estimated to correct the values obtained from analysis of pressure tests after fracturing. Fracturing efficiency calculations should be made whenever possible to provide an estimate of fracture length. Tables of the dimension less pressure drop as a function of time and fracture penetration are included in this paper. Using these values should permit analysis of other types of transient pressure behavior in vertically fractured wells.
Introduction
Hydraulic fracturing has been used quite successfully for over a decade as a completion and stimulation technique in oil and gas wells completed in low-permeability reservoirs. During this period a considerable amount of theory has evolved on the performance of hydraulically fractured reservoirs and on more efficient means of artificial fracturing. Although theory has been developed, no rigorous investigation has been made of pressure build-up and flow test behavior in such wells. Prats et al. first discussed the performance of vertically fractured reservoirs for the case of a compressible fluid. Their work was primarily concerned with production performance at constant flowing pressure. These authors also considered large-time (semisteady-state) constant production rate behavior for vertically fractured wells: however, transient pressure behavior at constant rate was not investigated. McGuire and Sikora and Dyes, Kemp, and Caudle employed an electrical analog to investigate the influence of artificial vertical fractures on well productivity and pressure build-up. They found that fractures which extend beyond 15 per cent of the drainage radius away from the well alter the position and slope of the straight-line portion of the build-up curve. They concluded that these effects must be considered both in the determination of the effective permeability of the formation and in any calculations of final build-up pressure. Although these authors did not undertake an exhaustive study of the influence of vertical fractures on pressure build-up performance, their limited results were quite interesting from the standpoint of the effects they demonstrated. In a more recent paper, Scott reported the results of an investigation of the effect of vertical fractures on pressure behavior, which was conducted with a heat flow model. Scott's results appear to be consistent with those reported in Refs. 1 and 2. However, the effects of different fracture lengths on performance were not investigated. Pressure build-ups and transient flow tests are among the most diagnostic tools available to the reservoir engineer or production engineer. Since a very high percentage of present-day well completions incorporate the hydraulic fracturing technique, a definite need exists for information on the effect of fractures on transient pressure performance. For these reasons we have undertaken a rigorous study of pressure build-up and flow test behavior in vertically fractured reservoirs. The objectives of this study wereto obtain synthetic pressure build-up and flow test curves to assess the effects of a vertical fracture, andto determine the modifications which need to be made to conventional pressure build-up and flow test analysis theory for the case of a vertically fractured well.
JPT
P. 1159ˆ

Theoretical and potentiometric model studies have been made of the effect of non-uniform lateral permeabilities on pattern sweep efficiency and production capacity in waterflood and gas-cycling programs.
It is shown that a difference in directional permeability by a factor of three may result in a sweep efficiency of only 43 per cent for a five-spot pattern or a sweep of either 79 or 38 per cent for a direct line-drive square pattern, depending on the direction of the line-drive flood. Changes in the pattern conductivity varied from about 0.8 to 1.34 over this same permeability variation, depending on the pattern used.
It is suggested that measurements be made to determine the possible magnitude and extent of the directional permeability phenomenon early in the field development and certainly prior to the initiation of any fluid-injection program.
Introduction
Irregularities in reservoir sand properties long have been a major difficulty to anyone attempting to explicitly describe the field characteristics of oil production. In particular, it is well known that vertical and lateral permeabilities often differ appreciably; however, the existence of large regions with lateral permeability variation is not widely recognized. A number of years ago, extensive studies were conducted by the Secondary Recovery Research Laboratory of the Pennsylvania Grade Crude Oil Association, primarily on the Bradford field. Johnson and Hughes reported a permeability trend in the northeast-southwest direction. They indicated that flow in the preferred direction may be 25 to 30 per cent greater in that direction than in the northwest-southeast direction. They also reported that similar effects may be found in other nearby fields. The origin of the permeability variation has been discussed by Griffith. Hutchinson described the results of laboratory tests on limestone cores, pointing out that preferential directional permeabilities were significant in one-half of 10 formations studied and that the average permeability ratio was 16:1.

The viscosity of hydrocarbon mixtures, whether in the gas or liquid phase, is a function of pressure, temperature, and phase composition. This paper presents methods for the prediction of the viscosity of the gas or less dense fluid phase over the practical range of pressure, temperature, and phase compositions encountered in surface and subsurface petroleum production operations. The correlation necessary to predict the effect of pressure on viscosities is presented in Part I. Serious discrepancies in high pressure gas viscosity data in the literature are discussed.
The application of the correlation to predict absolute viscosities is discussed in Part II. Auxiliary correlations are presented to enable calculations of viscosities from a knowledge of the pressure, temperature, and gravity of the gas phase.
Introduction
A knowledge of the viscosity of hydrocarbon fluids is needed to study the dynamical or flow behavior of these mixtures through pipes, porous media, or more generally wherever transport of momentum occurs in fluid motion. Since flow is predominantly in the laminar region in petroleum reservoirs, the influence of fluid viscosity on this flow is especially important.
As early as 1894, Onnes and Onnes and de Haas noted that the viscosities of homologs under corresponding states could be correlated. The theorem of corresponding states has been further developed and applied to the viscosity of pure, nonpolar gases under pressure by Comings, Mayland, and Egly.
Serious discrepancies in the viscosity of pure hydrocarbon gases at high pressures have been called to our attention by Comings, Mayland, and Egly. They made a careful analysis of the following methods commonly used to measure gas viscosities:
1. Oscillating disc viscometer.
2. Rolling ball viscometer.
3. Capillary tube viscometer

This paper presents two new correlations for calculating vertical coverage and areal sweep efficiency. Use of these correlations can facilitate the waterflood performance calculations.
Coverage
The determination of coverage (vertical sweep efficiency) is an important step in forecasting the performance of any waterflood project. This parameter is a function of the mobility of the injected fluid to the mobility of reservoir oil, M; the WOR, F and the Dykstra-Parsons permeability variation, V. The coverage curves first permeability variation, V. The coverage curves first introduced by Dykstra and Parsons have been widely used in the oil industry. Generally, these curves are available at each WOR as a function of V and M (Fig. 1). Thus for any coverage calculations, a set of curves at WOR's of 0.1, 0.2, 0.5, 1, 2, 5, 10, 25, 50, and 100 is needed.
For numerical simulation studies, it is most efficient to use equations of these curves or to find a correlation parameter that can reduce these curves into one curve. parameter that can reduce these curves into one curve. Recently, the latter task was accomplished by desouza and Brigham, 2 who grouped the coverage curves for 0 less than M less than 10 and 0.3 less than V less than 0.8 into one curve by regression analysis. These authors used a combination of F, V, and M in a parameter henceforth referred to as the Y correlation parameter. The equation for Y is
(1)
where
Fig. 2 shows the data of Dykstra and Parsons plotted against the Y parameter. The curve suggested by desouza and Brigham is also plotted in this figure. As shown, the Y parameter effectively groups these data together.
To simplify the calculations further, this graph was curve-fitted. The following equation was found to match this curve very closely:
(2)
where a =3.334088568, a =0.7737348199, and a = - 1.225859406. The comparison between the
Dykstra-Parsons coverage curves and C calculated with Eq. 2 is shown in Table 1 and Fig.
In this table, C was calculated for different F, M, and V with both Eq. 2 and the coverage curves. As shown, there is a close agreement between the C values calculated with Eq. 2 and deSouza and Brigham's curve. Notice that the same restrictions that are imposed on desouza and Brigham's curve are also true for Eq. 2 (i.e., this equation is valid only for 10 greater than M greater than 0 and 0.8 greater than V greater than 0.3).
Areal Sweep Efficiency
Areal sweep efficiency, E, is the fraction of the pattern area contacted by water. E is a function of the pattern geometry, mobility ratio, M, and the amount of water injected, W . Dyes et al. measured E for five-spot, direct line drive, and staggered line drive in a homogeneous, two-dimensional (2D) model with the X-ray shadowgraph technique. Their data are currently used as the standard procedure for calculating E in the waterflood monograph . The Dyes et al. data were curve-fitted by use of a nonlinear regression program. The equation used was
(3)
The coefficients of Eq. 3 for patterns such as five-spot, staggered line drive, and direct line drive are provided in Table 2. These coefficients are valid both before and after breakthrough for mobility ratios in the range of 0 less than M less than 10. This restriction is caused by the limitation of their experimental data to these mobility ratios. The comparison between the actual and the correlated sweep efficiencies is very good, as shown in Fig. 3.
Notice that the Dyes et a 1. 3 data for the five-spot pattern approaches 1 at a mobility ratio of 0.17, contrary to the fact that E should reach 1.0 only at zero M. Also, these data are generally higher than those reported by later investigators in better-scaled experiments, especially at higher mobility ratios.
P. 604

This paper presents a new water influx model that differs from traditional approaches in that it includes the effect of vertical flow at the reservoir/aquifer interface. The results are presented in the form of dimensionless groups, which makes the model readily applicable to a wide range of systems. The paper concludes with a sample calculation showing how the predictions of this new model can be significantly different from those of conventional radial flow models.
Introduction
Petroleum reservoirs are often in contact with an aquifer that Petroleum reservoirs are often in contact with an aquifer that provides pressure support through water influx. Thus, the prediction provides pressure support through water influx. Thus, the prediction of reservoir behavior usually requires an accurate model of the aquifer. Reservoir/aquifer systems are commonly classified on the basis of flow geometry as either edgewater or bottomwater drive. For edgewater drive, the most rigorous aquifer influx model developed to date is that of van Everdingen and Hurst, 1 which is essentially a solution to the radial diffusivity equation. Although the assumptions made in deriving this model are not strictly valid for bottomwater drive systems, water influx in this case can sometimes be closely approximated by radial flow. Therefore, because the results are often quite adequate and for lack of a better model, it has been common practice to apply the van Everdingen and Hurst method to both bottomwater and edgewater systems. Coats has developed a model that takes into account vertical flow effects and has shown these effects to be fairly significant. The model as presented, however, has two principal limitations:the solution given applies to the "terminal-rate" case, which allows the user to calculate pressure from a known influx rate rather than the reverse, andthe solution is applicable only to infinite aquifers.
This paper is essentially an extension of the work of Coats. The bottomwater model presented here is a solution to the "terminal-pressure" case and applies to both finite and infinite aquifers. The results are presented in the form of dimensionless groups that are tabulated in a manner similar to that of van Everdingen and Hurst. The paper concludes with a sample calculation that illustrates the use of this new model and shows that predictions of the bottom-water model can be significantly different from those of the radial flow model. The calculation of water influx is important in a number of reservoir engineering applications, such as material-balance studies and the design of pressure maintenance schemes. The fact that a large percentage of reservoirs have adjoining aquifers means that percentage of reservoirs have adjoining aquifers means that development of an accurate aquifer model is critical to proper understanding of reservoir behavior. It is not surprising, therefore, that considerable research effort has been devoted to this subject. During the past 50 years, a large number of models describing water encroachment have emerged, and the majority of these have been subject to a great deal of modification. In these models, the reservoir is typically visualized as a right cylinder surrounded by a series of concentric cylinders representing the aquifer. Most of the models, such as me steady-state model of Schilthuis or the finite-aquifer, pseudosteady-state model of Fetkovich, are applicable to only a limited range of flow conditions or reservoir/ aquifer geometries. The model that possesses the most general applicability is the unsteady-state model of van Everdingen and Hurst. In fact, this model is a solution to the radial diffusivity equation and as such is valid for all flow regimes, provided, of course that the flow geometry is actually radial.
The radial flow geometry assumed by van Everdingen and Hurst is best understood by means of an illustration. Fig. 1 shows, in cross section, a reservoir subject to edgewater drive and the idealized radial flow model that represents this reservoir/aquifer system. The flow vectors in this case are horizontal, and water encroachment occurs across a cylindrical plane encircling the reservoir. This situation can be compared to the bottomwater drive system shown in Fig. 2. In this case, the flow vectors have a significant vertical component, and water encroachment occurs across a horizontal circular plane representing the oil/water contact. Thus, a rigorous bottomwater influx model must take into account vertical flow, and as will be shown below, the effect of vertical flow becomes increasingly more pronounced as the ratio of aquifer thickness, h, to reservoir radius, rR, becomes larger. The discussion below provides a detailed treatment of the bottomwater flow model depicted in Fig. 2. The diffusivity equation governing flow for this system is reduced to dimensionless form by introducing dimensionless variables. The resultant equation is then solved with a numerical simulator, and as in the work of van Everdingen and Hurst, the results are presented in the form of tables of dimensionless influx, WD, vs. dimensionless time, tD. Included in the discussion is an example calculation for a hypothetical bottom-water drive reservoir. This example illustrates the use of the new model and, by calculating influx with both the radial and bottom-water models, clearly shows that ignoring vertical flow can result in very significant error.
Discussion
Basic Equations. The partial-differential equation governing flow of a slightly compressible fluid in a system such as that shown in Fig. I is the well-known radial diffusivity equation:
..........................................(1)
For the bottomwater flow model depicted in Fig. 2, an additional term is added to this equation:
..........................................(2)
where Fk is the ratio of vertical to horizontal permeability. There are an infinite number of solutions to Eq. 2, representing all possible reservoir/aquifer configurations.
SPERE
p. 179

To use the Peng-Robinson equation of state (PREOS) to predict the phase and volumetric behavior of hydrocarbon mixtures, one needs to know the critical pressure, pc, critical temperature, Tc, and acentric factor, ω, for each component present in the mixture. For pure compounds, the required properties are well-defined, but nearly all naturally occurring gas and crude oil fluids contain some heavy fractions that are not well-defined and are not mixtures of discretely identified components. These heavy fractions often are lumped and called the "plus fraction" (e.g., C7+ fraction). Adequately characterizing these undefined plus fractions in terms of their critical properties and acentric factors has long been a problem. Changing the characterization of the plus fraction can have a significant effect on the volumetric and phase behavior of a mixture predicted by the PREOS. This limitation of the PREOS results from an improper procedure of determining coefficients a, b, and α for the plus fraction and for hydrocarbon components with critical temperatures less than the system temperature (i.e., methane and nitrogen). This paper presents a practical approach to calculating the parameters of the PREOS for the undefined fractions to improve the predictive capability of the equation. Use of the modified equation is illustrated by matching laboratory data on several crude oil and gas-condensate systems.

In this article we generalize the concept of the pseudosteady-state productivity index for the case of multiple wells producing from or injecting into a closed rectangular reservoir of constant thickness. The work complements the analytical study by Rodríguez and Cinco-Ley1 for systems produced at constant flowing pressures. Wells are represented by fully penetrating vertical line sources located arbitrarily in a homogeneous and isotropic reservoir. The multiwell productivity index (MPI) is a square matrix of dimension n, where n is the number of wells. The MPI provides a simple, reasonably accurate and fast analytical tool to evaluate well performance without dividing the cluster into single-well drainage areas. The MPI approach is used to obtain approximate analytical solutions for constant (but possibly different) wellbore flowing pressures, and to visualize the resulting pressure field. In addition, the skin factor trace technique is introduced as a tool to monitor a cluster of wells. The MPI technique is illustrated using a synthetic example taken from Ref. 2, as well as two field cases.

An empirical equation relating the critical volume, Vc, the acentric factor, ω, the critical pressure, Pc, the critical temperature, Tc, and the gas constant, R, has been obtained. This equation accurately predicts the values of Vc for numerous normal fluids.