Article

A Correlation for Interference Testing With Wellbore-Storage and Skin Effects

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Abstract

A new correlation and set of pressure-response and pressure-derivative type curves are presented for interference test analysis. The influence of wellbore storage and skin effects at active and observation wells on interference pressure response is examined. In the case of wellbore storage and skin in one well, the correlating parameter [CDe2s]CD/rD2 is used to combine wellbore storage and skin variables in a way that makes it possible to display, on a single type curve, all interference test data that would ordinarily require a number of type curves for various combinations of CD/rD2 and CDe2s. The product of the correlating parameter is used when wellbore storage and skin effects are active at both wells. The difference in the shapes of the single-well storage type curves compared to the two-well storage case at early times can be used as a diagnostic feature in interference testing.

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... A method to analyze interference data including wellbore storage and skin was presented by [17]. As a result, [15] presented a technique whereby wellbore storage and skin existing in one well are correlated. After that, [4] proposed the development pressure derivative type curve for use in build-up and drawdown tests in double-porosity reservoirs. ...
... ( 1.05 / 0.86 ) = 1 (15) Replacing the dimensionless variables and solving for storativity ratio, ω, gives: (16) Pressure and derivative pressure intersection: The governing equation is: /( * 2 ) = 0.55 (17) Replacing the dimensionless variables and solving for storativity ratio, ω, gives: ...
Article
Full-text available
The naturally fractured reservoir characterization is crucial because it can help to predict the flow pattern of fluids, and the storativity ratio of the fractures and to understand whether two or more wells have communication, among others. This paper presents a practical methodology for interpreting interference tests in naturally fractured reservoirs using characteristic points found on the pressure derivative curve. These kinds of tests describe a system that consists of a producing well and an observation well separated by a distance (r). Using characteristic points and features found on the pressure and pressure derivative log-log plot, Analytical expressions were developed from the characteristic points of the pressure and pressure derivative log-log plot to determine the interporosity flow parameter (λ) and the storativity ratio of the fractures (ω). Finally, examples are used to successfully verify the expressions developed so that the naturally-fractured parameters were reproduced with good accuracy.
... This parameter can be determined using CRM or other direct and indirect methods. Direct methods such as 4D seismic (Huang and Ling 2006;Huseby et al. 2008;Yin et al. 2015Yin et al. , 2016, pulse testing (Dinges and Ogbe 1988;Fokker et al. 2012), interference (Al-Khamis et al. 2005;Ogbe and Brigham 1989;Stewart and Gupta 1984) well tests and tracer tests (Du and Guan 2005;Dugstad et al. 1999;Huseby et al. 2008;Lichtenberger 1991;Refunjol and Lake 1999) are operationally implemented in the field. Although indirect methods are data-driven models and are based on input-output signals which are developed mathematically or statistically, they include artificial neural networks (ANN) (Demiryurek et al. 2008;Panda and Chopra 1998;Artun 2017), wavelet analysis (Jansen and Kelkar 1997), Spearman rank correlation (Heffer et al. 1997;Fedenczuk and Hoffmann 1998;Refunjol and Lake 1999), extended Kalman filter (Liu et al. 2009), pressure-based method (Dinh and Tiab 2008), multiwell productivity method (Valko et al. 2000;Kaviani and Valkó 2010), network model (Gherabati et al. 2017a, b), and streamline simulation (SS) (Batycky et al. 1997(Batycky et al. , 2005Thiele et al. 2010;Thiele and Batycky 2006;Baker 2001). ...
Article
Full-text available
Reservoir performance prediction is one of the main steps during a field development plan. Due to the complexity and time-consuming aspects of numerical simulators, it is helpful to develop analytical tools for a rapid primary analysis. The capacitance–resistance model (CRM) is a simple technique for reservoir management and optimization. This method is an advanced time-dependent material balance equation which is combined with a productivity equation. CRM uses production/injection data and bottom-hole pressure as inputs to build a reliable model, which is then combined with the oil-cut model and converted to a predictive tool. CRM has been studied thoroughly for water flooding projects. In this study, a modified model for gas flooding systems based on gas density and average reservoir pressure is developed. A detailed procedure is described in a synthetic reservoir model using a genetic algorithm. Then, a streamline simulation is implemented for validation of the results. The results show that the proposed model is able to calculate interwell connectivity parameters and oil production rates. Moreover, a sensitivity analysis is carried out to investigate effects of drawdown pressure and gas PVT properties on the new model. Finally, acceptable ranges of input data and limitations of the model are comprehensively discussed.
... Early in 1936, Theis [8] proposed the type-curve of the interference test for homogeneous reservoirs but did not account for the impact of the wellbore storage effect and the skin effect, which were later studied by Obge Brigham et al. [9]. In 1972, Gringarten and Witherspoon [10] presented the curves of the interference test for vertically fractured wells. ...
Article
Full-text available
: Pressure communication between adjacent wells is frequently encountered in multi-stage hydraulic fractured shale gas reservoirs. An interference test is one of the most popular methods for testing the connectivity of a reservoir. Currently, there is no practical analysis model of an interference test for wells connected by large fractures. A one-dimensional equation of flow in porous media is established, and an analytical solution under the constant production rate is obtained using a similarity transformation. Based on this solution, the extremum equation of the interference test for wells connected by a large fracture is derived. The type-curve of pressure and the pressure derivative of an interference test of wells connected by a large fracture are plotted, and verified against interference test data. The extremum equation of wells connected by a large fracture differs from that for homogeneous reservoirs by a factor 2. Considering the difference of the flowing distance, it can be concluded that the pressure conductivity coefficient computed by the extremum equation of homogeneous reservoirs is accurate in the order of magnitude. On the double logarithmic type-curve, as time increases, the curves of pressure and the pressure derivative tend to be parallel straight lines with a slope of 0.5. When the crossflow of the reservoir matrix to the large fracture cannot be ignored, the slope of the parallel straight lines is 0.25. They are different from the type-curves of homogeneous and double porosity reservoirs. Therefore, the pressure derivative curve is proposed to diagnose the connection form of wells.
... Moreover, although we can estimate the permeability, pore/throat radius or pore volume of thief zones with pipeline model (Liu et al., 2003;, it is so ideal that basic flow characteristics of thief zones have been neglected. (4) Well testing, injection well pressure drawdown test (Feng et al., 2011) and interference test (Dinges and Ogbe, 1988;Ogbe and Brigham, 1989;Feng et al., 2010) are included. But only qualitative description of thief zone can be obtained by the present interpretation method for pressure drawdown test, and neither the properties nor the location can be determined. ...
Article
The characterization of thief zone, which evolves from long-term waterflooding, has become imperative in the enhanced oil recovery process. As one typical kind of thief zone, pressure transient performance of high-permeability streak is analyzed in this work. A mathematical model is established for a well intersected by a high-permeability streak, and the solution in Laplace space is derived by Ozkan's source function. To ensure improved accuracy and better efficiency, the solution is inverted into real space numerically through de Hoog Algorithm. Investigation of the pressure transient behavior indicates that the process can be divided into three periods: (1) the early-time flow period, which is comprised of streak storage-type flow and bilinear flow; however, it occurs too early to be of practical interest; (2) the linear flow from the formation to the streak, which is characterized by a half-slope straight line; (3) pseudo-radial flow, exhibited by a horizontal line on the derivative curve. The sensitivities of corresponding parameters have also been discussed. Furthermore, Gravitational Search Algorithm (GSA) is successfully applied as a non-linear regression technology to match measured pressure with this model and to characterize high-permeability streak. Compared to previous technologies, this approach is more cost-effective and less time-consuming. Moreover, the quantitative characterization of high-permeability streak can play a very important role in the design of conformance control project. Thus this approach has been extensively employed in many China Oilfields. And field cases are also presented to substantiate its validity.
... Then several extremely contributing researches ; Abbaszadeh-Dehghani and Brigham 1984; Brigham and Abbaszadeh-Dehghani 1987; Ghori and Heller 1992; Datta-Gupta et al. 1995; Saad and Kalkomey 1996; Ali et al. 2000) offer the opportunity to quantify the reservoir connectivity, i.e. the permeability, thickness, pore radius and so on, which are obtained from the analysis of tracer concentration curve. Furthermore, another direct method, which is also used to detect the interwell connectivity is well testing, especially the interference test (Ogbe and Brigham 1989;Feng et al. 2010) and pulse test (Dinges and Ogbe 1988). However, both the interwell tracer test and interference test or pulse test are time-consuming and high-cost, which impede those tests from being widely conducted during routine production. ...
Conference Paper
Pressure Index (PI) is a significant parameter, which is commonly used for profile control project design and injection well performance analysis in China, due to its simple and economical application. However, PI can only reflect the current fluid flow capacity and present heterogeneity of the formation. It’s well known that the formation structure will change distinctly after long-term waterflooding for the pressure variation and its in-situ heterogeneity, during which thief zones or high-conductive channels may come into being. Therefore, PI can not take into account the dynamic change of the formation structure, and thief zones can not be identified by PI. As a result, efficiency of profile control decision might be not as good as expected. The objective here is to develop a new parameter which can identify thief zones easily and to verify its validity from both the synthetic model and the pilot test. Dimensionless Pressure Index (DPI) is established on the basis of PI, which not only takes the transformation of fluid flow capacity into consideration, but also keeps its initial advantages—simple and low-cost. Synthetic models are used to validate the methodology. And the pilot test shows that identification of thief zones by DPI is in good accordance with other approaches. Moreover, DPI can also be applied to determine the severity of the thief zone for a certain oilfield. Another advantage of DPI is that the combination of PI and DPI will make the profile control project design more effective and improve waterflooding surveillance. This approach has been applied successfully in several China oilfields.
... Transient-pressure tests involving pressure pulses, generated by carefully designed rate perturbations, provide quantitative information about interwell connectivity. Amongst the plethora of publications in this regard, the studies of Kamal (1979), Dinges and Ogbe (1988), and Ogbe and Brigham (1989) are worthy of note. Execution of pulse tests may be time-consuming because of large interwell distances, coupled with low-rock permeability and high-system compressibility in a given setting. ...
Article
This paper demonstrates the value of collecting and interpreting real-time data. With an intensive data gathering strategy, starting at wells’ inception to the mature production phase, we show how transient pressure and rate data can be used to manage a complex carbonate gas reservoir. In particular, reservoir connectivity is discerned with pulse testing and with the leading-edge p/q graph, and continuous updates of in-place volume are made with both static and dynamic material-balance methods and corroborating the same with rate-transient analysis. Interwell connectivity information was deduced during underbalanced drilling by way of interference test between two pairs of wells. Thereafter, transient-pressure tests on individual wells characterized the layered, dual-porosity system, with production logs corroborating the notion of layering. Production maturity over three years has paved the way for estimating connected in-place gas volume associated with each well using the transient-PI, and also with a new method introduced here. This new approach entails plotting both static and dynamic material-balance data on the same graph, yielding the same solution. Errors associated with real-time rate measurements presented interpretation challenges for rate-transient analysis; however, application of a physics-based filtering algorithm resolved this issue. Flow-after-flow tests that were embedded in monthly variable-rate production allocations, in turn, allowed us to obtain average-reservoir pressure explicitly to do the static material-balance analysis.
... However, only transientpressure tests involving pressure pulses, generated by carefully designed rate perturbations, provide quantitative information about interwell connectivity. Among the plethora of publications in this regard, the studies of Kamal (1979), Dinges and Ogbe (1988), and Ogbe and Brigham (1989) are worthy of note. Execution of pulse tests may be time-consuming because of large interwell distances, coupled with lowrock permeability and high-system compressibility in a given setting. ...
Article
Interwell connectivity is a key issue in any field development planning, especially when secondary and tertiary recovery methods are contemplated. Stakes are particularly high in deepwater and other costly environments where the well count largely dictates project economics. Traditional approaches to discerning reservoir compartments include fluid PVT properties, geochemical fingerprints, tracer testing, and transient-pressure testing. While fluids may provide clues about reservoir connectivity or lack thereof, they cannot tell us about the degree of connectivity between wells. In contrast, pulse testing may provide the necessary information, but the interwell permeability so estimated is skewed toward the observation well, and therefore may not be entirely satisfactory. This study presents an alternative method for establishing interwell connectivity involving production and injection wells. We show that capacitance-resistive modeling (CRM) is a viable alternative to solving transient-flow problems. Equivalence of streamline simulations and CRM is established for fractional flow directed at each producer. We also showed that one can discern connectivity between the injector and producers in an inverted-five-spot pattern and in channelized reservoirs, with limited injection in prebreakthrough scenarios. In closed systems, even low-signal quality may suffice for characterization, provided reasonable injection perturbation exists. Excessive voidage appears to be a nonissue as far as signal propagation is concerned.
... Transient-pressure tests involving pressure pulses, generated by carefully designed rate perturbations, provide quantitative information about interwell connectivity. Amongst the plethora of publications in this regard, the studies of Kamal (1979), Dinges and Ogbe (1988), and Ogbe and Brigham (1989) are worthy of note. Execution of pulse tests may be time-consuming because of large interwell distances, coupled with low-rock permeability and high-system compressibility in a given setting. ...
Article
This paper demonstrates the value of collecting and interpreting real-time data. With an intensive data gathering strategy, starting at wells' inception to the mature production phase, we show how transient pressure and rate data can be used to manage a complex carbonate gas reservoir. In particular, reservoir connectivity is discerned with pulse testing and with the leading-edge p/q graph, and continuous updates of in-place volume are made with both static and dynamic material-balance methods and corroborating the same with rate-transient analysis.Interwell connectivity information was deduced during underbalanced drilling by way of interference test between two pairs of wells. Thereafter, transient-pressure tests on individual wells characterized the layered, dual-porosity system, with production logs corroborating the notion of layering. Production maturity over three years has paved the way for estimating connected in-place gas volume associated with each well using the transient-PI, and also with a new method introduced here. This new approach entails plotting both static and dynamic material-balance data on the same graph, yielding the same solution.Errors associated with real-time rate measurements presented interpretation challenges for rate-transient analysis; however, application of a physics-based filtering algorithm resolved this issue. Flow-after-flow tests that were embedded in monthly variable-rate production allocations, in turn, allowed us to obtain average-reservoir pressure explicitly to do the static material-balance analysis.
... However, only transientpressure tests involving pressure pulses, generated by carefully designed rate perturbations, provide quantitative information about interwell connectivity. Among the plethora of publications in this regard, the studies of Kamal (1979), Dinges and Ogbe (1988), and Ogbe and Brigham (1989) are worthy of note. Execution of pulse tests may be time-consuming because of large interwell distances, coupled with lowrock permeability and high-system compressibility in a given setting. ...
Article
Interwell connectivity is a key issue in understanding any field performance, especially when secondary and tertiary recovery methods are initiated. This paper shows that capacitance–resistance modeling (CRM) is a viable alternative to solving the prebreakthrough flow problems in a variety of situations. In each case, CRM is able to mimic the results of streamline simulations for establishing fractional flow directed at each producer. We show that one can discern connectivity between the injector and producers in an inverted-five-spot pattern and in channelized reservoirs, and even with limited injection in prebreakthrough scenarios in heterogeneous media. In closed systems, low-signal amplitude may suffice for characterization, provided reasonable injection perturbation exists. The field case reinforced the notion of nonintuitive reservoir connectivity in an actual situation.
... This assumption seems reasonable in the context of the DPHP method insofar as the probes of DPHP sensors typically have a thermal conductivity much greater than that of the soil. The solution presented here is similar to solutions in the groundwater literature that take into account the finite radius and finite storage capacity of paired pumping and observation wells (Tongpenyai and Raghavan, 1981;Ogbe and Brigham, 1984;Novakowski, 1989), but it avoids the need for numerical evaluation of integrals in the Laplace domain. ...
Article
Full-text available
The dual-probe heat-pulse (DPHP) method is useful for measuring soil thermal properties. Measurements are made with a sensor that has two parallel cylindrical probes: one for introducing a pulse of heat into the soil (heater probe) and one for measuring change in temperature (temperature probe). We present a semianalytical solution that accounts for the finite radius and finite heat capacity of the heater and temperature probes. A closed-form expression for the Laplace transform of the solution is obtained by considering the probes to be cylindrical perfect conductors. The Laplace-domain solution is inverted numerically. For the case where both probes have the same radius and heat capacity, we show that their finite properties have equal influence on the heat-pulse signal received by the temperature probe. The finite radius of the probes causes the heat-pulse signal to arrive earlier in time. This time shift increases in magnitude as the probe radius increases. The effect of the finite heat capacity of the probes depends on the ratio of the heat capacity of the probes (C-0) and the heat capacity of the soil (C). Compared with the case where C-0/C = 1, the magnitude of the heat-pulse signal decreases (i.e., smaller change in temperature) and the maximum temperature rise occurs later when C-0/C > 1. When C-0/C < 1, the magnitude of the signal increases and the maximum temperature rise occurs earlier. The semianalytical solution is appropriate for use in DPHP applications where the ratio of probe radius (a(0)) and probe spacing (L) satisfies the condition that a(0)/L <= 0.11.
... Wellbore skin effects can be examined mathematically in two ways: (1) by assuming the skin to be infinitesimally thin, and (2) by assuming it to be of finite thickness [8]. The effect of both wellbore storage and the skin region on the results of pumping tests has long been investigated in the petroleum industry [10,24,28] and in groundwater studies [5,13,[19][20][21][22]25,27]. These solutions account for wellbore storage and an infinitesimally thin skin in both pumping and observation wells. ...
Article
Full-text available
An analytical model is presented for the analysis of constant flux tests conducted in a phreatic aquifer having a partially penetrating well with a finite thickness skin. The solution is derived in the Laplace transform domain for the drawdown in the pumping well, skin and formation regions. The time-domain solution in terms of the aquifer drawdown is then obtained from the numerical inversion of the Laplace transform and presented as dimensionless drawdown–time curves. The derived solution is used to investigate the effects of the hydraulic conductivity contrast between the skin and formation, in addition to wellbore storage, skin thickness, delayed yield, partial penetration and distance to the observation well. The results of the developed solution were compared with those from an existing solution for the case of an infinitesimally thin skin. The latter solution can never approximate that for the developed finite skin. Dimensionless drawdown–time curves were compared with the other published results for a confined aquifer. Positive skin effects are reflected in the early time and disappear in the intermediate and late time aquifer responses. But in the case of negative skin this is reversed and the negative skin also tends to disguise the wellbore storage effect. A thick negative skin lowers the overall drawdown in the aquifer and leads to more persistent delayed drainage. Partial penetration increases the drawdown in the case of a positive skin; however its effect is masked by the negative skin. The influence of a negative skin is pronounced over a broad range of radial distances. At distant observation points the influence of a positive skin is too small to be reflected in early and intermediate time pumping test data and consequently the type curve takes its asymptotic form.
Conference Paper
The current research on interference well test technology is based on water flooding reservoir, but the analysis method of interference well test in polymer flooding reservoir has not been reported, which leads to unclear understanding of the physical property changes between wells in polymer flooding reservoir. Considering the characteristics of polymer flow, a two-phase interference well test model of polymer flooding multi-layer reservoir is established. The pressure, water saturation and polymer concentration are all implicitly solved to improve the stability of the numerical solution, and the typical curve is drawn. The results show that: the water phase viscosity is greater during the polymer flooding process, the pressure fluctuation of the active well is later, which affects the observation well, and the pressure fluctuation received by the observation well is greater. The results show that the interference well test curve of polymer flooding is farther to the right than that of water flooding in the early stage and higher than that of water flooding in the middle and late stage. The application example shows that coincidence rate with commercial software well test interpretation is over 90% when the model is degenerated to conventional water flooding, which proves the accuracy of polymer flooding interference well test model, and provides technical support for the improvement of well test method of polymer flooding reservoir.
Article
Interwell connectivity identification between injector-producer well pairs and hydrocarbon production estimation are essential parameters in reservoir management, which can determine unrecovered oil volume and reservoir continuity. Although there are several published methods for determination of interwell connectivity in water-oil systems, there is no such comprehensive study on gas flooded reservoirs. Due to the high mobility of gas, interwell connectivity is a critical criterion in channelized, faulted and heterogeneous reservoirs for reservoir characterization, production optimization, infill drilling and performance predication. There are physical and statistical techniques to determine interwell connectivity mathematically and identify reservoir flow dynamics without using any operational activities. All methods are working with limited production data and unlike the numerical simulators, they are simple and do not require detailed data. In this paper, modified capacitance-resistance model (or M-CRM as a physical approach) and combination of least square support vector machine and multiple linear regression (as a statistical approach) are applied to two immiscible gas injection cases with different assumptions, and the results are compared. The results show that both methods are reliable in terms of validity, speed and flexibility. The physical approach (M-CRM) is more accurate for interwell connectivity prediction while the statistical method is more precise for producer total rate estimation.
Conference Paper
The offshore polymer flooding reservoirs are mostly in the middle and late stages of oilfield development, and there are multi-well systems. At present, most of the well testing methods for polymer flooding reservoirs are based on single well system, which leads to the fact that the actual data fitting effect is not ideal. By considering the influence of adjacent production well or polymer injection well and the physical and chemical effects of polymer solution such as shear, diffusion and convection, the well test interpretation method of polymer injection well considering adjacent well interference is established, type curves were plotted and its influencing factors were discussed by the numerical inversion method. The result showed that the type curves have five regimes, the pressure derivative curves show obvious upward warping under interference from production well, while the pressure derivative curves first decrease and then continue to rise under interference from polymer injection wells. Polymer injection well test curves show obvious non-Newtonian fluid characteristics when considering adjacent well interference, and can not be analyzed by conventional adjacent well interference test method. The example application proves the correctness and reliability of this method, which provides a theoretical basis for dynamic adjustment of polymer flooding reservoir.
Chapter
This chapter introduces the purpose, development history, test design methods, data acquisition and interpretation methods, and typical field examples of applications of interference tests between wells or layers and pulse tests. The interference test can be used to solve many problems concerning the connectivity between wells or layers, and obtain the parameters of the connectivity between wells and the size of the connected area in the reservoir, making this a very effective method in dynamic study. However, there are some special difficulties and special requirements in data acquisition and operation in the field that cause the success rate of the data acquisition of these tests to be low. The author makes some suggestions on effective design and operation procedures for successful interference test on the basis of his own experience accumulated in the field over many years. Some typical field practice examples are given in this chapter: for example, the study results of interference tests between wells in the JB gas field make clear the connectivity of the thin zones with low permeability in an area 2 km long in Ordovician formation, but the heterogeneity there is quite serious. The study of interference tests between wells in the SLG gas field probed into the characteristics of lithological boundaries of the fluvial facies deposited sandstone in the Permian System formation. The study of interference tests in the SL gas field provided valuable results, such as confirming the sealing of some faults and the anisotropy of the permeability, among others.
Article
High water-cut has been observed for many multiply fractured horizontal wells (MFHWs) in China soon after water flooding begins. Available well-testing models of single well ignored the effect of adjacent wells on the MFHW, and they are unable to evaluate whether MFHW (producer) and surrounding vertical wells (injectors) are in good pressure communication. To fill this gap, this work presents a multi-well interference testing (MWIT) model to consider the interference of injectors and further match the interference pressure data of the MFHW. The MWIT model is established to investigate the effect of multiple injection wells on transient-pressure behavior of the MFHW. Due to the interferences from injectors, the pressure and pressure-derivative curves of MWIT move down beginning with the biradial flow regime for single MFHW model, and pseudo-radial flow (horizontal line with the value of 0.5 on pressure-derivative curve) disappears. Sensitivity analysis was conducted to discuss the effects of crucial parameters on the pressure response, including total injection rates, unequal injection rates of injectors, well spacing, injector distribution, number and production of hydraulic fractures. When total injection rates are lower than the production rate, the pressure derivative will eventually stabilize at 0.5*(1-Σ(q IncjD )) during the interference-flow regime on the log-log type curves. Since only the positive number can be shown in the log-log graph, semi-log curves are introduced to fully characterize the flow regimes of MWIT. A novel finding is that pressure derivative also ultimately behaves as a horizontal line with the value of 0.5*(1-Σ(q IncjD )) when total injection rates are equal or higher than production rates on the semi-log curves. The total injection rates and well spacing between the MFHW and injectors have a significant effect on middle and late pressure behaviors, whereas the number and production of fractures mainly affects the pressure responses during early to middle period. Type curves indicate that the effect of surrounding injectors is significant and cannot be ignored, and the novel characteristics provide potential application of the MWIT model to estimate formation parameters. Case studies highlight the application of the proposed method in effectively matching the interference pressure data.
Conference Paper
High water-cut has been observed for many multi-fractured horizontal wells (MFHWs) in China soon after waterflooding begins. Available well-testing models of single well ignored the effect of adjacent wells on the MFHW, and they are unable to evaluate whether MFHW (producer) and surrounding vertical wells (injectors) are in good pressure communication. To fill this gap, this work presents a multi-well interference testing (MWIT) model to consider the interference of injectors and further match the interference pressure data. The MWIT model is established to investigate the effect of multiple injection wells on transient-pressure behavior of the MFHW. Due to the interferences from injectors, the pressure and pressure-derivative curves of MWIT move down beginning with the biradial flow regime for single MFHW model, and pseudo-radial flow (horizontal line with the value of 0.5 on pressure-derivative curve) disappears. Sensitivity analysis was conducted to discuss the effects of crucial parameters on the pressure response, including total injection rates, unequal injection rates of injectors, well spacing, injector distribution, number and production of hydraulic fractures. When total injection rates are lower than the production rate, the pressure derivative will eventually stabilize at 0.5*(1-Σ(qIncjD)) during the interference-flow regime on the log-log type curves. Since only the positive number can be shown in the log-log graph, semi-log curves are also developed to fully characterize the flow regimes of MWIT. A novel finding is that pressure derivative also ultimately behave as a horizontal line with the value of 0.5*(1-Σ(qIncjD)) when total injection rates are equal or higher than production rates on the semi-log curves. The total injection rates and well spacing between the MFHW and injectors have a significant effect on middle and late pressure behaviors, whereas the number and production of fractures mainly affects the pressure responses during early to middle period. Type curves indicate that the effect of surrounding injectors are significant and cannot be ignored, and the novel characteristics provide potential application of the MWIT model to estimate formation parameters. Case studies highlight the application of the proposed method in effectively matching the interference pressure data. Interference-testing analysis of the MWIT provides a better reservoir evaluation compared to single-well testing model.
Article
Interwell connectivity is an important parameter in reservoir management and optimization during water/gas injection. As an analytical approach, the Capacitance‐Resistance Model (CRM) is a rapid tool that only needs some common and available data for field performance prediction. The non‐linear signal processing technique is used with the CRM to determine reservoir continuity between production and injection wells. Current CRMs are applicable in water flooding systems. In this study, a Modified Capacitance‐Resistance Model (M‐CRM) for interwell connectivity calculation in immiscible gas flooding projects is developed based on the mass balance equation. Slightly compressible flow is one of the main assumptions in CRM development while gas is compressible and gas properties variation with pressure should be scrutinized in the equations. Therefore, new equations need gas PVT properties to consider the effect of gas compressibility. Moreover, the productivity equation for oil and gas production should be revised. The constructed model that considers mass balance and the productivity equation is applied in two synthetic models and one real sector reservoir model. The Genetic Algorithm, as an optimization tool for solving new model is used and streamline simulation is selected as a validation tool for interwell connectivity parameters calculation. Based on streamline results, it was observed that a M‐CRM is able to predict the reservoir behaviour better than a common CRM for pre/post breakthrough conditions in gas injection scenarios. Also, an analysis is performed for different parameters that affect the new model in immiscible gas flooding. Results show that modification on the mass balance equation has a greater influence than the productivity equation. This article is protected by copyright. All rights reserved
Book
Data accumulation, analysis, and interpretation technology are critical in hydrocarbon exploration and extraction to maximize petroleum recovery and development. Dynamic Well Testing in Petroleum Exploration and Development presents modern petroleum exploration and well testing interpretation methods, emphasizing their application and development under special geological and development conditions in oil and gas fields. More than 100 case studies and 250 illustrations-many in full color-aid in the retention of key concepts. Extensive analysis of pressure data acquired from well testing through advanced interpretation software can be tailored to specific reservoir environments. This timely, state-of-the-art reference will be of particular interest to petroleum geoscientists and engineers working for oil and gas companies worldwide. Includes graphs that can be used as templates to accurately plot hydrocarbon reservoir data accumulation, analysis, and interpretation Field-practical case studies break information down into real-world examples which can be put into practice-not found in other books on well testing Illustrations-many in full color-help you retain key concepts. © 2013 Petroleum Industry Press. Published by Elsevier Inc. All rights reserved.
Conference Paper
The determination of the preferential flow direction in a reservoir becomes a very important subject for the development of an oilfield, especially for the selection of the optimum exploitation strategy taking into account that porous media is a very complex environment in which representing the flow behavior of fluids becomes a tough task, mainly in carbonates where the distribution of fractures, lithology changes and diagenesis play a major role in this topic. Naturally Fractured Reservoirs (NFR) represent a great technical challenge for the petroleum industry because they behave as a heterogeneous medium with a strong influence of diagenesis, a term that encompasses fractures, dissolution, compaction, dolomitization, cementation and recrystallization to conform a reservoir with totally different distribution of properties. The dynamic data must be evaluated in order to match with the static model achieving a good reservoir characterization. In this paper we present a way to determine the preferential flow direction by the monitoring of the field through permanent real-time downhole gauges that allowed the identification of the interference between wells in a deep naturally fractured reservoir that originally did not show any degree of communication. Suddenly, after some producing time, the field demonstrated a great level of interference among wells and as a consequence, the determination of the preferential flow direction was possible through Pressure Transient Analysis (PTA) and Rate Transient Analysis (RTA). Emphasizing the Palacio-Blasingame1 type curves (PBTC), in which we compare the results obtained using this analysis with its standard form and the one achieved with Material Balance Time (MBT). Additionally, Fetkovich2 decline type curves were also used in the rate analysis. Finally, a comparison of the geological model with the dynamic data was also applied to further enhance the quality of the data. The results showed conclusive preferential flow direction with the wells tested.
Article
Pulse testing is used to determine the transmissivity and storativity of a reservoir. A pulse test is conducted by creating a series of flow-rate changes at an active (pulsing) well and observing the pressure response at a nearby observation (responding) well. Previous studies have shown that wellbore storage and skin effects should be accounted for when analyzing a pulse test. This study presents the data required for the analysis and design of pulse tests considering wellbore storage and skin effects at the pulsing or responding well, for tests run with unequal producing and shut-in periods. Before this study, data were limited to tests run with equal producing and shut-in periods. The use of unequal producing and shut-in periods is necessary to optimize test design and analysis. To reduce the amount of data required in this method, a new correlation is used and a set of regression coefficients is provided. A field example is included to illustrate how to use this method.
Article
This paper presents a new general solution for an interference slug test in a two-region composite system with both active well and observation well having wellbore storage and skin. The solution technique, which employs the Laplace transformation and addition theorem of Bessel function, is new and different from past works. As a reduced form of the general solution, slug test interference analysis in a homogeneous domain is readily obtained by letting the properties in both regions be identical. The paper presents the characteristic pressure responses for interference slug tests, as well as some slug test design criteria. Dimensionless correlation parameters and parametric analyses are discussed, An interpretation technique for a slug test in a homogeneous system is presented. Two type curves are presented along with two correlation groups. The first correlation group, (CD/LD2)(LnCD+2S), is applicable for the case when the effects of the wellbore storage and skin in the observation well are negligible. The second correlation group, (CD/LD2)[LnCD+0.8( S1+S2)], is applicable when wellbore storage values in both wells are identical, and skin values are arbitrary. Interference slug testing in various composite reservoirs is discussed, including oil-gas well interference, and interference in the presence of a linear boundary.
Article
A composite analytical model is developed for analyzing the results of pumping tests where the influence of well bore storage and a skin region of finite thickness are present at the pumping well. The solution of the boundary value problem for dimensionless drawdown in the pumping well, skin region, and formation is derived using the Laplace transform method. The solution is verified by comparison to solutions of pumping test problems with well bore storage only, with a composite formation only, and with well bore storage and infinitesimally thin skin. Type curves obtained by numerically inverting the solution for drawdown in the formation are used to illustrate the influence of well bore storage, the effect of skin region characteristics, and the effect of radial distance. These show that the influence of a finite thickness skin of reduced permeability is clearly identifiable over a fairly broad range of radial distance from the pumping well when well bore storage effects are minimized. Conversely, the effects of finite skin of enhanced permeability are more easily identified where the influence of well bore storage is greater. In both cases the type curves are uniquely defined provided that the skin region is of nonzero thickness. Type curves obtained for the solution for drawdown in the skin region are used to illustrate the effect of outer or far-field boundary conditions. These type curves show that early time data not influenced by well bore storage effects are required to detect the presence of outer boundaries of reduced permeability. Drawdown data at late time, although less influenced by well bore storage effects, are subject to nonuniqueness with regard to the characteristics of the skin and formation regions. Outer boundaries of enhanced permeability are identified only at early time and are almost entirely masked by well bore storage at later time.
Article
Bei einem Interferenztest werden zwei oder mehrere Bohrungen gleichzeitig untersucht. Dabei wird mindestens in einer Bohrung gefördert oder injiziert, während in den anderen Bohrungen die Druckreaktion infolge von Förderung/Injektion gemessen wird. Ziel solcher Tests ist es Informationen über die Eigenschaften der Schicht zwischen den Bohrungen zu erhalten (inter – zwischen, ferre – bringen, tragen).
Article
This study presents an analytical method to determine double-porosity reservoir properties with interference pressure data in an infinite reservoir producing at constant pressure. Wellbore-storage and skin effects at production and observation wells are neglected. The effects of rD, λ, and ω on interference pressure responses are examined. For dimensionless interwell distances ≥ 100, the pressure responses are practically collapsed. As a result, a general type curve, which can be used for any value of rD, is presented that yields unique values of λ and ω for a given pressure response and rD. In addition to the log-log type curve, a semilog type curve that is more useful for pD values >0.1 is presented. Semilog derivatives of the interference pressure responses are considered. The pressure derivatives enhance small variations that occur in the pressure response during the flow period affected by the double-porosity nature of the reservoir. It is observed that for a simple correlation with λ and rD, the derivative curves for rD values > 100 can be collapsed. Hence, a semilog derivative type curve is developed. This type curve has two maxima. Early- and late-time behaviors are influenced by λ. The time separation between the first and second maxima is a function of ω.
Article
A two-well system in an infinite-acting, commingled, two-layer reservoir is considered. One well, the active well, is produced at a constant total rate, and the second well, the observation well, is shut in at all times. An analytical solution in Laplace space is presented, and the parametric groups that uniquely determine the pressure and rate solutions are identified. Results regarding crossflow through the observation well are presented. Conditions under which the line-source solution can be used to analyze observation-well pressure data are delineated. Results generally show that the analysis of such pressure data is tenuous unless individual layer flow rates are measured at the active well and the layers are isolated at the observation well, or unless layer flow rates are measured at both wells.
Article
This paper presents new analytical solutions for two-well systems with storage and skin in both wells. The solutions are generated by the application of the addition theorem and the Laplace transformation. Previously presented research in this area is limited to one-dimensional radial flow. In contrast, the new solutions presented in this paper are true two-dimensional, and do not make use of the superposition principle for solving the basic cases. Hence, limitations stemming from the incorrect application of the superposition principle in the presence of finite sources are overcome. The paper describes the mathematical formulation for sixteen different configurations and some calculations showing the pressure transient response of both the active well and the interference well. The results of this study show that under certain conditions, storage in the observation well may have a significant effect on the analysis procedure. The presented solutions show that an impermeable linear boundary has a significant effect on the pressure response of a slug test. In addition, the traditional constant rate test with storage and skin can also be used for linear boundary detection. However, current techniques are limited in that the boundary effects must occur after the storage effects have ended. The new solutions presented here show the combined effects of an impermeable boundary and wellbore storage and skin.
Article
The existing body of theoretical studies on interference testing usually applies for constant-rate conditions at the active well. For constant-pressure situations, which are fairly commonly encountered during injection tests in low-permeability rocks (e.g., crystalline rocks, which are often tested for waste repository projects), alternative approaches must be sought for analysing interference tests. This paper presents a new method for analysis of interference tests with the active well at constant pressure. This new analytical technique makes use of both type curve matching and straight line fitting methods for analysis of such tests. We show in this paper that with a proper grouping of the relevant variables, a constant-pressure interference test can be analysed using constant-rate Cartesian (or semilog) derivative type curves for interference testing. Thus, this method utilizes existing constant-rate solutions for interpretation of constant pressure interference tests. The solution is exact and extends a previously presented approximate solution. Moreover, for rD > 20 and tDr2D > 0.5, we can also use a semilog plot to conduct a straight line analysis of the data from a constant pressure interference test for estimation of interwell transmissivity and storativity. Introduction In an interference test between two wells, the active well undergoes a variety of production or injection tests, with the observation well used only to monitor the pressure transients released into the formation by the active well. Analysis of interference tests are commonly performed using the assumption of a constant rate or of a series of constant rate steps. Such analyses of the observation well data can be performed using wellbore storage and skin at both active and observation wells(l). In the groundwater industry, constant pressure tests are fairly common in tight formations where a constant rate test is dominated by wellbore storage effects for a significantly long time. The constant pressure situation is also well-suited to injection testing, as constant rate methods need a prior knowledge of the formation permeability to select a suitable rate(2). Constant pressure situations are also a useful means of controlling off-site migration of contaminated groundwater(3). Uraiet and Raghavan(4,5), Ehlig-Economides and Ramey(6) and Ozkan et al.(7), among others, have presented a number of tools to aid in analysis of constant pressure tests in a variety of flow situations and reservoir conditions. Analytical methods to interpret constant pressure interference tests in a double porosity situation have been detailed by Grasman and Grader(8). In a very recent study, Hiller and Levy(3) demonstrated the use of an approximate method to analyse the late time data at an observation well, when the active well is being produced at a constant pressure. Their method yields the formation diffusivity directly from the analysis. Mishra and Guyonnet(9) presented a simple but elegant technique to compute formation transmissivity and storativity from analysis of observation well data during constant pressure tests. Their method involves a generalization of the Theis exponential integral solution for constant pressure situations.
Article
Classical interference testing techniques are based on the superposition of the line source solution. The use of this method is limited by the precision and time resolution that is normally obtained when measuring the production rate in active wells. In the new technique proposed, the pressure signal is measured at the active well and it is used to accurately calculate its diffusion in the reservoir. The higher precision in pressure calculation at the observing well gives more resolution to the analyst and provides more confidence when evaluating local reservoir heterogeneities. The new method and related equations are presented and applied to a field example where a five-spot injection pattern is evaluated for a future CO2 injection pilot project. The diffusivity distribution estimated from the interference tests agrees with the description of the advance of the injected water obtained from radioactive tracer techniques. Introduction Interference testing is a pressure transient measurement technique used to study the interaction between wells in a reservoir and to measure reservoir parameters. The basic theory states that the pressure transient generated by a well producing at constant rate in a homogeneous, isotropic, infinite reservoir of constant thickness saturated with a small compressibility fluid is described by the line source solution... P. 155^
Article
A simple method for computing transmissivity and storativity from the analysis of observation-well response during constant-head aquifer tests is presented. The proposed methodology is based on approximate solutions developed using the Boltzmann transformation technique, and is demonstrated to be valid for many practical situations. It is shown that familiar constant-rate solutions (e.g., the Theis equation) can be generalized for the constant-head case if the head change at the observation well is normalized by the flow rate at the test well and then used as the time-dependent variable. A generalized form of the Jacob-Lehman approximation which is valid at every point in the aquifer is presented. Analysis of several hypothetical constant-head test data using the suggested approach indicate that estimates of transmissivity are much more reliable than those of storativity. However, both hydraulic parameters appear to be reasonably estimated if the interwell distance is at least two orders of magnitude larger than the wellbore radius.
Article
A semi-analytical model is developed to determine transmissivity and storativity from the interpretation of transient flow in an observation well due to pumping in a source well where the two wells are connected by a single fracture. Flow rate can be determined using a heat-pulse flowmeter located above the intersection of the fracture in the observation well. The results of a field experiment were interpreted using the new model and compared with drawdown data from the same test. Good agreement between the transmissivity estimates was observed whereas estimates of storativity were found to be better determined from the analysis of flow rate.
Article
To explore the viability of Steam Enhanced Remediation (SER) in fractured rock a small-scale steam injection and water/vapour extraction pilot study was conducted at the former Loring Air Force Base in northern Maine, USA. A detailed well testing program was undertaken to assist in the design of the injection and extraction well array, and to assess the possibility of off-site heat and contaminant migration. A structurally complex limestone having low matrix porosity and a sparse distribution of fractures underlies the study site. To characterize the groundwater and steam flow pathways, single-well slug tests and more than 100 pulse interference tests were conducted. The results of the well testing indicate that the study site is dominated by steeply dipping bedding plane fractures that are interconnected only between some wells in the injection/extraction array. The SER system was designed to take advantage of interconnected fractures located at depth in the eastern end of the site. An array of 29 wells located in an area of 60 by 40 m was used for steam injection and water/vapour extraction. The migration of heat was monitored in several wells using thermistor arrays having a 1.5 m vertical spacing. Temperature measurements obtained during and after the 3 month steam injection period showed that heat migration generally occurred along those fracture features identified by the pulse interference testing. Based on these results, it is concluded that the pulse interference tests were valuable in assisting with the design of the injection/extraction well geometry and in predicting the migration pathways of the hot water associated with the steam injection. The pulse interference test method should also prove useful in support of any other remedial method dependant on the fracture network for delivery of remedial fluid or extraction of contaminants.
Article
Recently developed type curves are presented, which greatly simplify the evaluation of buildup-type well test information. The basis on which these curves were developed and actual examples of their use are discussed. Curves used in the discussion are those that apply to the most commonly found situation, that is, a well with wellbore storage and skin in a homogeneous reservoir.
Article
A mathematical model for pulse testing is presented that examines the influence of wellbore storage and skin effects on pulse-test data. Two new correlations are provided for correcting the storage-dominated response amplitude and time lag to within 3% of the values expected without wellbore storage. The formation transmissivity and storativity can be determined from the corrected response amplitude and time lag. Proposed correlations are applicable to pulse testing with wellbore storage at the active or observation well. Examples illustrate use of the new correction technique.
Article
Bremer et al. described a mathematical model for analysis of a verticalinterference test across a low-permeability zone. The test configuration calledfor recording wellbore pressure vs. time opposite one permeable layer whilefluid is produced from the second permeable layer. permeable layer while fluidis produced from the second permeable layer. The two permeable layers areseparated by a tight zone of low vertical permeability. This paper offers amore general interpretation technique permeability. This paper offers a moregeneral interpretation technique that allows for distinct properties in the twopermeable layers and includes wellbore-storage and skin effects. The purpose ofthe vertical interference test across a low-permeability zone is to determinethe vertical permeability of tight zone separating the two permeable strata. The results of such a test may influence well completion decisions for primary, secondary, and enhanced oil recovery. Of particular interest is the estimationof the fluid rate into or out of the packed-off layer. Field test data have been analyzed with the new techniques. By includingwellbore-storage and skin effects, the model presented in this study provides amuch better fit with the data presented by Bremer et al. Because this methodallows for determination of formation properties in both permeable zones, simultaneous recording of the pressures in both the producing and packed-offlayers is recommended. Results indicate that the producing and packed-offlayers is recommended. Results indicate that the wellbore- pressure differencebetween the flowing and packed-off zones becomes constant after sufficient timeand depends only on the permeabilities in the three zones. If wellbore-storageeffects can be permeabilities in the three zones. If wellbore-storage effectscan be minimized, the behavior of pressure vs. log time may exhibit twodistinct slopes: the first providing for calculation of the permeability in theflowing layer, and the second allowing calculation of the permeability in thepacked-off layer. Type curves are presented for analysis of both the pressureand pressure- derivative transients. pressure and pressure- derivativetransients. The interpretation method is suitable for broader application thanprevious methods would allow. An important result is an estimate of me previousmethods would allow. An important result is an estimate of me rate of crossflowbetween layers separated by a low-permeability zone. Introduction The vertical flow behavior in a producing formation is an important factorin the prediction of well and reservoir performance. The vertical interferencetest is a method for determining horizontal and vertical flow properties nearthe well by analysis of pressure transients properties near the well byanalysis of pressure transients opposite an isolated set of perforations whilethe well is flowed or pulsed at another depth. Vertical interference tests havebeen used for several purposes, including determination of verticalpermeability in a single zone, determination of crossflow between two layersseparated by a low-permeability layer, and detection of leaks behind casing. Methods for determination of vertical permeability in a single zone wereprovided by Bums, Prats, Falade and Brigham, and Hirasaki. Practicalconsiderations and comparisons of the various methods were offered byEarlougher. In particular, Earlougher considered the effects of wellborestorage at both the active and observation levels, communication behind thecasing, and vertical flow across a permeability barrier in the formation. Therecent study by Bremer et al. provided a simple analysis technique fordetermination of the vertical permeability of a low-permeability layerseparating two permeability of a low-permeability layer separating two layers. Their model assumed identical formation properties in the two producing layersand neglected the effects of wellbore storage and skin associated with theproducing layer. The purpose of our work was to provide a more general modelthat accounts for distinct properties in the productive layers and for wellboreand near-wellbore productive layers and for wellbore and near-wellboreeffects. A second objective of this study was to quantify the rate of crossflowbetween the two layers. Studies of crossflow behavior in multilayered systemsare included in Refs. 8 through 15. The studies by Deans and Gao and Gaoprovided considerable insight on the location and magnitude of transientcrossflow effects between communicating layers for certain well and outerboundary conditions. This study shows that the crossflow behavior in aninfinite-acting system when one layer is prevented from flowing is distinctlydifferent from that with two flowing layers. Model Description As Bremer et al. discussed, the reservoir consists of two permeable layersseparated by a third layer of permeable layers separated by a third layer ofcomparatively low permeability. Unlike the previous study, however, this modelallows for different properties in the two permeable layers. In addition, wellbore-storage and skin permeable layers. In addition, wellbore-storage andskin effects are incorporated. The test configuration and reservoir geometryare diagrammed in Fig. As shown in the figure, one layer flows to the well, while flow to the well from the second layer is prevented by a packer assembly. Because the permeabilities of the two layers may be different, it is necessaryto record pressures in both the flowing and packed-off layers. SPEFE p. 425
Article
Agarwal, Ram G., Pan American Petroleum Corp. Tulsa, Okla., Pan American Petroleum Corp. Tulsa, Okla., Al-Hussainy, Rafi, Junior Members AIME, Mobil Research and Development Corp., Dallas, Tex., Ramey Jr., H.J., Member AIME, Stanford U. Stanford, Calif. Abstract Due to the cost of extended pressure-drawdownor buildup well tests and the possibility of acquisitionof additional information from well tests, the moderntrend has been toward development of well-testanalysis methods pertinent for short-time data."Short-time" data may be defined as pressureinformation obtained prior to the usual straight-lineportion of a well test. For some time there has been portion of a well test. For some time there has been a general belief that the factors affecting short-timedata are too complex for meaningful interpretations. Among these factors are wellbore storage, variousskin effects such as perforations, partial penetration, fractures of various types, the effect of a finiteformation thickness, and non-Darcy flow. A numberof recent publications have dealt with short-timewell-test analysis. The purpose of this paper isto present a fundamental study of the importance ofwellbore storage with a skin effect to short-timetransient flow. Results indicate that properinterpretations of short-time well-test data can bemade under favorable circumstances. Upon starting a test, well pressures appearcontrolled by wellbore storage entirely, and datacannot be interpreted to yield formation flowcapacity or skin effect. Data can be interpreted toyield the wellbore storage constant, however. Afteran initial period, a transition from wellbore storagecontrol to the usual straight line takes place. Dataobtained during this period can be interpreted toobtain formation flow capacity and skin effect incertain cases. One important result is that thesteady-state skin effect concept is invalid at veryshort times. Another important result is that thetime required to reach the usual straight line isnormally not affected significantly by a finite skineffect. Introduction Many practical factors favor short-duration welltesting. These include loss of revenue during shut-in, costs involved in measuring drawdown or buildupdata for extended periods, and limited availabilityof bottomhole-pressure bombs where it is necessaryto survey large numbers of wells. on the other hand, reservoir engineers are well aware of the desirabilityof running long-duration tests. The result is usuallya compromise, and not necessarily a satisfactoryone. This situation is a common dilemma for thefield engineers who must specify the details of specialwell tests and annual surveys, and interpret theresults. For this reason, much effort has been givento the analysis of short-time tests. The term"short-time" is used herein to indicate eitherdrawdown or buildup tests run for a period of timeinsufficient to reach the usual straight-line portions. Drawdown data taken before the traditional straight-lineportion are ever used in analysis of oil or gas portion are ever used in analysis of oil or gas well performance. Well files often contain well-testdata that were abandoned when it was realized thatthe straight line had not been reached. This situationis particularly odd when it is realized that earlydata are used commonly in other technologies whichemploy similar, or analogous, transient test. It is the objective of this study to investigatetechniques which may be used to interpret informationobtained form well tests at times prior to the normalstraight-line period. THEORY The problem to be considered is the classic oneof flow of a slightly compressible (small pressuregradients) fluid in an ideal radial flow system. Thatis, flow is perfectly radial to a well of radius rwin an isotropic medium, and gravitational forces areneglected. We will consider that the medium isinfinite in extent, since interest is focused on timesshort enough for outer boundary effects not to befelt at the well. SPEJ p. 279
Article
The modern trend in well testing (buildup or drawdown) bas been toward acquisition and analysis of short-time data. Pressure data early in a test are usually distorted by several factors that mask the conventional straight line. Some of the factors are wellbore storage and various skin effects such as those due to perforations, partial penetration, non-Darcy flow, or well stimulation effects. Recently, Agarwal et al. presented a fundamental study of the importance of wellbore storage with a skin effect to short-time transient flow. This paper further extends the concept of analyzing short-time well test data to include solutions of certain drillstem test problems and of cases wherein the storage constant, CD, undergoes an abrupt change from one constant value to another. An example of the latter case is change in storage type from compression to liquid level variations when tubinghead pressure drops to atmospheric Arks production. The purpose of the present paper is to: production. The purpose of the present paper is to:present tabular and graphical results for the sandface flow rate, qsf, and the annulus unloading rate, qa, as a fraction of the constant surface rate, q, andillustrate several practical well test situations that require such a solution. Results include a range of values of the storage constant, CD, and the skin effect, s, useful for well test problems. problems. Annulus unloading or storage bas been shown to be an important physical effect that often controls early well test behavior. As a result of this study, it appears that interpretations of short-time well test data can be made with a greater reliability, and solutions to other storage-dominated problems can be obtained easily. Techniques presented in this paper should enable the users to analyze certain short-time well test data that could otherwise be regarded as useless. Introduction In a recent paper, Agarwal et al. presented a study of the importance of wellbore storage with a skin effect to short-time transient flow. They also presented an analytical expression for the fraction presented an analytical expression for the fraction of the constant surface rate, q, produced from the annulus Although the rigorous solution (inversion integral) and long- and short-time approximate forms were discussed, neither tabular nor graphical results ofdpwD the annulus unloading rate, CD, were given.dtD It now appears that such solutions are useful in certain drillstem test problems and in cases wherein the storage constant, CD, changes during a well test. An example is change in storage type from compression to liquid level change when tubinghead pressure drops to atmospheric during production. pressure drops to atmospheric during production. The purpose of this study is to (1) present tabular and graphical results for the sandface flow rate and the annulus unloading rate and (2) illustrate several practical well test situations that require the practical well test situations that require the solutions. THE CLASSIC WELLBORE STORAGE PROBLEM The problem to be considered is one of flow of a slightly compressible fluid in an ideal radial flow system. SPEJ P. 453
Article
A solution for analyzing interference test data influenced by wellbore storage and skin effects at the active and observation wells is presented. The results presented here can be used to analyze and/or design presented here can be used to analyze and/or design interference test data influenced by storage and skin effects at the active and/or observation wells. Introduction Interference tests have become popular due to the need for information about reservoir heterogeneity. The advent of sensitive and high-precision pressure gauges has hoped to make this kind of test procedure a practical tool. Estimates of the mobility-thickness product kh/ and the storativity-thickness product product kh/ and the storativity-thickness product Cth usually are obtained from interference test data. In addition, as already mentioned, the degree of heterogeneity in the reservoir can be obtained from an interference test.Most investigators in this area of pressure analysis have directed their efforts toward examining the effect of reservoir heterogeneities on the observation well response. A few investigators have examined the effect of wellbore conditions at the flowing well -i.e., the effects of wellbore storage and skin and vertical fractures. Surprisingly, the effect of wellbore conditions at the observation well has not received attention. Virtually all studies have assumed that the observation well is shut in at the sandface and that plane radial flow conditions govern the measured pressures. However, if wells are shut in at the surface (which is usually the case), the wellbore storage and skin effects at the observation well should affect the pressure response.In this work, we examine the effects of wellbore storage and skin at the observation well on the pressure response. A new analytical solution to the pressure response. A new analytical solution to the problem is presented. The solution includes the problem is presented. The solution includes the effects of wellbore storage and skin at both wells.To our knowledge, only Fenske and Prats and Scott have considered the effect of wellbore storage at the observation well. Prats and Scott briefly examined the effect of wellbore storage at the observation well on pulse test data, and Fenske considered the influence of wellbore storage and both wells on interference test data.The results given here, however, are more comprehensive and complete. Unlike the earlier studies we have considered the influence of the skin region around both wells, as well as wellbore storage, and have been able to correlate the results in terms of dimensionless groups commonly used in well test analysis. This is a unique feature of our study. The dimensionless groups reduce the number of computational runs and type curves that are needed to analyze the data. In this regard our work provides a significant improvement over Fenske's results because we have been able to combine the parameters of interest and obtain correlations of general utility. Furthermore, as mentioned earlier, this solution also can be used when the wellbore storage and skin effects exist at only one of the wells (active or observation). Assumptions and Mathematical Model The mathematical model considered here assumes the flow of a slightly compressible (small pressure gradients) fluid in a homogeneous, uniform, and isotropic porous medium. Gravitational forces are assumed to be negligible. The reservoir is assumed to be infinitely large - i.e., the outer boundaries have no effect on the pressure response. The initial condition assumes that the pressure Pi is constant at all points in the reservoir. JPT P. 151
Article
A new type-curve matching technique significantly easier than those previously published allows the estimation of permeability, skin factor, and wellbore storage coefficient from short-time transient test data. The method is explained here and is illustrated with several examples. Introduction Occasionally, insufficient transient test data are available for analysis using semilogarithmic plotting methods. This usually happens when data collection stops before wellbore storage (afterflow) has become negligible. Under those circumstances, the semilogarithmic straight line does not develop, and common semilogarithmic analysis methods cannot be used. When such methods cannot be used, the engineer either obtains no information from the test or must use the available, short-time data to estimate reservoir characteristics. This paper presents a technique for the approximate analysis of such short-time transient test data. The method applies to buildup, falloff, drawdown, and injectivity tests when wellbore storage effects are important. It should not be used if data can be analyzed by more conventional, semilogarithmic plotting methods.It has long been recognized that wellbore storage (afterflow) can impede pressure transient test analysis. Several ways have been suggested for determining when well known semilogarithmic techniques can be used for transient test analysis. Gladfelter et al. and Russell present calculational methods for analyzing the portion of transient test data influenced by wellbore storage. Curve matching, and regression techniques have also been proposed for accomplishing such analyses.All these methods have disadvantages. The techniques presented by Gladfelter et al. Russell, and Earlougher and Kersch, utilize either trial-and-error analysis or require that the afterflow schedule be calculated, or both. These approaches are tedious and not always successful.In spite of its disadvantages, curve matching seems to be the most promising of the methods, particularly for the engineer who does not have a computer available. Cooper et al. present type curves and an analysis technique for specific flow and injection tests with the well shut in before testing. At the start of the test, the pressure instantaneously changes to some new value. Then both pressure and flow rate vary during the test. The Cooper-Bredehoeft-Papadopulos type curves are useful for analyzing data taken during the flow period of a drillstem test. Agarwal et al. point out that neglect of the skin effect makes the Cooper-Bredehoeft-Papadopulos type curves of dubious value. In any case, those curves do not apply to the more common transient testing situations: buildup, falloff, injectivity, and drawdown. Ramey and Agarwal et al. suggest type-curve matching for these kinds of transient tests. They present applicable type curves that form several families of curves with skin factor and wellbore storage coefficient as parameters. Ramey's curve-matching method requires that the data plot be slid both horizontally and vertically to obtain a match. This feature and the fact that the curves have very similar shapes make the matching technique difficult to use unless there are data at least onto the start of the semilog straight line.McKinley uses a similar approach, but with a different kind of type-curve plot. JPT P. 793
Article
This paper presents new solutions for analyzing interference test data affected by wellbore storage and skin effects at the flowing well. Three parameters of interest - wellbore storage phenomenon, skin effects, and distance between two wells - are considered simultaneously. The new type curves should improve significantly the ability to analyze such data. Introduction With the advent of sensitive pressure gauges and because of the need to obtain precise information on reservoir heterogeneity for implementation of tertiary recovery programs, interference tests have become popular. It is well-established that the results of a multiwell test are influenced more by reservoir heterogeneity than those of a single-well test. The line source solution presented first by Theis1 serves as a starting point for the analysis of interference test data. This solution assumes that the storage capacity of the flowing well and the skin region around the sand-face have a negligible effect on the observation-well response. This assumption is valid if the distance between the flowing well and the observation well is large. However, if the distance is small, then the effect of storage and skin on the observation-well response can be significant. The pressure response at any point in the reservoir will be damped and delayed as a result of the storage effect at the active well (with or without the skin effect), because the main effect of the storage capacity of the flowing well is to cause a lag in the time required for the surface rate to equal the sand-face rate. For given reservoir properties, the magnitude of the delay depends on the wellbore volume, the nature of the storage phenomenon, and the skin effect. To our knowledge, the effect of wellbore storage on interference data was examined first in the groundwater hydrology literature.2,3 In petroleum engineering literature, Prats and Scott4 were the first to consider the effect of wellbore storage on the response of a pulse test. They concluded that the porosity-compressibility product, fct, of the formation would be overestimated and the hydraulic diffusivity, k/fctµ, would be underestimated if the wellbore storage effect was significant and not considered in the data analysis. Also, they noted that care should be taken in measuring pressure data if the wellbore storage effect was significant, because the magnitude of the actual pressure response would be lower than expected. They did not quantify the effect of a skin region around the well but did discuss qualitatively the influence of the skin factor. However, Prats and Scott assumed that the storage effect existed at the observation well and not the flowing well. In a subsequent paper, we show that their results can be used to analyze pulse test data influenced by the storage effect at the active well.
Article
This paper shows that wellbore storage and wellbore damage reduce the pressure response at an observation well, especially at early times, and pressure response at an observation well, especially at early times, and can cause great error in estimating transmissivity and storativity if not account for properly. New type curves are presented that include the effects of wellbore storage and damage. Introduction Interference testing is used to estimate the mobilitythickness product and the reservoir thickness -porositytotal compressibility product. These two terms are referred respectively to as transmissivity and storativity. In the past, wellbore storage and wellbore damage at the active well have been assumed to cause no detrimental effect on interference test analysis. Only one type curve has been used to analyze interference tests, namely the exponential-integral-solution type curve. Interference testing has been used to estimate transmissivity and storativity in the petroleum and ground-water industries for many years. The mathematical basis for interference testing was first presented by Theis. The most practical and easiest way to analyze interference tests is by type-curve matching. The method of type-curve matching is adequately described by Ramey and Earlougher and Kersch. The type curve is a plot of log PD vs log tD/rD. Thus, for the classical exponential-integral solution, only one theoretical type curve is required to analyze all interference tests. A recent paper presented type curves for a vertically fractured presented type curves for a vertically fractured reservoir with drawdown measured at the observation well. In single-well pressure transient tests, wellbore storage and wellbore damage have been recognized as adversely affecting the tests, and errors can be made in analyzing these tests if the period dominated by wellbore storage is not properly identified. In multiwell tests, wellbore storage and wellbore damage at the active well have always been ignored and assumed to have essentially no effect on the observation-well pressure response. Recently, Prats and Scotts presented the pressure response. Recently, Prats and Scotts presented the effects of wellbore storage at the responding well on pulse-test pressure response. pulse-test pressure response.This paper shows that wellbore storage and wellbore damage at the active well can, in certain cases, cause large error in determining transmissivity and storativity from an interference test or pulse test. The Model The mathematical model used to generate the following results is presented in the Appendix. This model solves the diffusivity equation by finite-difference techniques. Reservoir properties, flow rates. wellbore storage, and wellbore damage are variable in this model. However, the results presented in this paper assume an isotropic. homogeneous reservoir containing a slightly compressible fluid, the reservoir is infinite-acting for the time period under consideration, the surface flow rate at the period under consideration, the surface flow rate at the active well is constant; and the wellbore storage coefficient and wellbore damage are constant during the testing period. The Need To Account for Wellbore Storage Fig. 1 shows the increase in flowing bottom-hole pressure above initial pressure vs time in an injection well pressure above initial pressure vs time in an injection well for cases with dimensionless wellbore storage coefficient, CD, equal to zero and 10', where (1) JPT P. 851
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Article
This study investigates the effect of wellbore storage and damage (skin effect) at a produced well on the pressure response (interference) in the reservoir, away from the produced well. The same problem had been investigated earlier by Jargon, and by Garcia-Rivera and Raghavan, using finite difference or approximate methods. In this work the problem was solved analytically by using the Laplace transformation method. When dimensionless time, tD, was greater than approximately 100, the results from this study were the same as those presented in ref. 4. But when tD was less than 100, the results did not agree. The correlation used in ref. 4, based on an effective wellbore radius, was also found to be poor for tD less than 100. A new correlation was found for tD less than unity. In order to compute results, a numerical Laplace transform inversion method was used. The characteristics of the method were studied for two purposes:to determine the properties of the inversion method for negative values of the skin effect, andto determine whether the inversion method might provide an analytic tool to study the dimensionless provide an analytic tool to study the dimensionless groups which control a solution. Both studies were successful. The Laplace transform inversion method was used to prepare original tables of dimensionless pressures for the subject problem for both positive and negative skin effects. No other such tables appear to exist. Introduction Interference testing is a multiple-well test which requires at least one active well and at least one observation well. The active well is either a producer or an injector, and the observation wells are shut-in wells in which pressure effects caused by the active well are measured. This kind of testing has the advantage of investigating more reservoir volume than a single-well test. Usually both the mobility-thickness product, and the porosity-compressibility-thickness product, phi phi ct h, may be estimated from multiple-well product, phi phi ct h, may be estimated from multiple-well tests. The data from the test may be analyzed by type-curve matching. Interference testing has become popular as more sensitive pressure gages have become available, thus making interference testing feasible in systems of high compressibility. As the accuracy and sensitivity of pressure data has improved, it has been recognized that the line-source solution neglects the finite radius of the active well, wellbore damage (skin effect), and wellbore storage. This can introduce significant errors. The effect of storage is to cause a changing sandface flow rate. Ideally, the skin effect does not have a transient effect (steady state or zero-storage skin). However, a skin effect can make wellbore storage-influenced sandface flow rate changes last longer. For the case of constant surface production rate, the combined effect of skin effect and wellbore storage causes the sandface flow rate to increase gradually from zero toward the constant surface flow rate, over a period of time. The time required for the sandface flow rate to essentially equal the surface flow rate is a function of the skin effect and wellbore storage. The higher the skin effect and wellbore storage, the longer the time will be. In the case of the line source solution, the sandface flow rate is equal to the surface flow rate, instantaneously. Thus one should expect a smaller pressure drop at a particular time and radius in the pressure drop at a particular time and radius in the case of a well with a skin effect and wellbore storage than for the line source well solution. The aim of this study was to solve the problem of constant surface production rate from a well with a skin effect and wellbore storage analytically, and to check the results with previously published data obtained by using others' methods. Another objective was to correlate the interference data if possible.
Article
A simple extension of the Theis equation removes the requirement that discharging wells have infinitesimal diameter. Further, in this extension, observation wells also have finite diameters and storage. Type curves for dimensionless drawdown versus dimensionless time can be calculated for the discharging well and all observation wells for conditions of constant discharge or constant drawdown. For an observation well with no storage approaching infinite distance from the discharging well, the type curves became the Theis type curve. For observations at the discharging well with no storage, the type curves become the Hantush type curve. For observations at the discharging well with storage and no observation wells, the type curves become the type curves of Papadopulos and Cooper. The effect of observation-well storage increases with increasing observation-well diameter and number of observation wells. The effect also becomes greater as the discharging well is approached and as the storage coefficient is decreased.
Article
A pulse test is conducted by creating a series of short-time pressure transients in an active (pulsing) well and recording the observed pressure response at an observation (responding) well. Using the pressure response and flow rate data, the transmissivity and storativity of the tested formation can be determined. Like any other pressure transient data, the pulse-test response is significantly influenced by wellbore storage and skin effects. The purpose of this research is to examine the influence of wellbore storage and skin effects on interference testing in general and on pulse-testing in particular, and to present the type curves and procedures for designing and analyzing pulse-test data when wellbore storage and skin effects are active at either the responding well or the pulsing well. A mathematical model for interference testing was developed by solving the diffusivity equation for radial flow of a single-phase, slightly compressible fluid in an infinitely large, homogeneous reservoir. When wellbore storage and skin effects are present in a pulse test, the observed response amplitude is attenuated and the time lag is inflated. Consequently, neglecting wellbore storage and skin effects in a pulse test causes the calculated storativity to be over-estimated and the transmissivity to be under-estimated. The error can be as high as 30%. New correlations and procedures are developed for correcting the pulse response amplitude and time lag for wellbore storage effects. Using these correlations, it is possible to correct the wellbore storage-dominated response amplitude and time lag to within 3% of their expected values without wellbore storage, and in turn to calculate the corresponding transmissivity and storativity. Worked examples are presented to illustrate how to use the new correction techniques. 45 references.
Conference Paper
In this paper, a well test interpretation method based on the analysis of the time rate of change of pressure, together with the actual pressure response, is discussed. A differentiation algorithm is proposed and several field examples are provided to illustrate how the method simplifies the analysis process. Interpretation of well tests is therefore easier and more accurate. Introduction The interpretation of pressure data recorded, during a well test has been used for many years to evaluate oil and gas reservoir characteristics. Static reservoir pressure, measured in shut-in wells, is used to predict reserves in place through material balance calculations. Transient pressure analysis provides a description of the reservoir flowing behavior. Many methods have been proposed for interpretation of transient tests (ref. 1), but the best known and most widely utilized by petroleum engineers is that published by Horner (ref.2) in 1951. More recently, type curves were introduced which indicate the pressure response of flowing wells under a variety of reservoir descriptions (ref. 3 to 6). Comparison of transient pressure measurements with type curves provide,; the only reliable means for identifying that portion of provide,; the only reliable means for identifying that portion of the pressure data which can be analyzed by conventional straight line analysis methods. In recent years, the quality of well test interpretations has considerably improved due to the availability of accurate pressure data (from electronic pressure gauges) and to the development of new software for computer-aided analysis. An increasing number of theoretical interpretation models are now in current use which allow one to reach a detailed definition of the flow behavior in the producing formation. Surprisingly, the commonly used analysis techniques have not followed the general progress evident in hardware and in interpretation models, thus making the interpretation procedure complicated and time consuming. Type curves are seen by various analysts as overly simplistic, or overly complex, difficult to distinguish, and/or cumbersome to use. Yet mere identification of straight lines on pressure versus time graph is a "ruler approach", convenient for hand analysis, but ignoring powerful computing facilities that are currently available. Furthermore, powerful computing facilities that are currently available. Furthermore, the conventional straight line analysis methods fail to make use of all the data available and can result in significant errors. In this work, an interpretation method is proposed, based on the analysis of the derivative of the pressure with respect to the appropriate time function: natural logarithm of time or Horner/ superposition times. This method considers the response as a whole, from very early time data to the last recorded point and uses the type curve matching technique. It provides a thorough description of the flow behavior in the reservoir but, with the logarithmic derivative, it also emphasizes the infinite acting radial flow regime, of prime interest in well test interpretation. The new approach is a natural extension of the Horner method to analyse the global response with an improved definition. Use of the derivative of pressure versus time is mathematically satisfying because the derivative is directly represented in one term of the diffusivity equation, which is the governing equation for all the models of transient pressure behavior currently in use in well test analysis. Consequently, the derivative response is more sensitive to small phenomena of interest which are integrated and, hence, diminished, by the pressure versus time solutions presently used in well test pressure versus time solutions presently used in well test interpretation. One practical limitation of the use of the pressure derivative in analysis is the ability to collect pressure derivative in analysis is the ability to collect differentiable pressure transient data. Accurate and frequent pressure measurements are required. However, as will be shown in pressure measurements are required. However, as will be shown in this paper, current pressure measurement and computer processing technologies allow use of pressure derivative in analysis.
The Fenske Conservation Method for Pressure Transient Solutions With Storage
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