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Prediction of Interfacial Tensions of Reservoir Crude Oil and Gas Condensate Systems
Abstract
In this work, the linear gradient theory (LGT) model, the simplified linear gradient theory (SLGT) model, the corresponding-states (CS) correlation, and the parachor method developed by the authors1–4 were extended to calculate interfacial tensions (IFT's) of crude oil and gas condensate systems. Correlations of the model parameters were presented for pseudocomponents. The characterization procedures of Pedersen et al.5 and the SRK equation of state (EOS)6 were used to calculate vapor-liquid equilibria (VLE). To the exclusion of the near-critical region, the IFT's calculated by all the models except the CS correlation were in good agreement with the measured IFT data for several crude oil and CO2/oil systems. The SLGT model and the parachor model perform better than the LGT model and the CS correlation. For N2 volatile oil systems, the performance of the LGT model is better than that of the SLGT model and the parachor model. For gas condensate systems, the predictions by use of the SLGT model are in good agreement with the measured IFT data. In the near-critical region, a correlation was proposed for estimations of IFT's for CO2/oil systems, and satisfactory correlated results were obtained.
... Several studies [38][39][40][41][42][43][44] have addressed the functionality of relative permeability to surface tension through laboratory experiments. Additionally, many researchers reported that surface tension tends to decrease with increasing temperature [39][40][41][42]44]. ...
... Several studies [38][39][40][41][42][43][44] have addressed the functionality of relative permeability to surface tension through laboratory experiments. Additionally, many researchers reported that surface tension tends to decrease with increasing temperature [39][40][41][42]44]. On the contrary, a few researchers have reported that with an increase in temperature, the surface tension also increases [38,43]. ...
... This downward variation in surface tension was also attributed to the CO 2 solubility in brine at higher temperatures of their study. Few other researchers [43,44] have also expressed the similar observations such as Longeron [15], Maini and Batycky [40], Polikar et al. [41], Asar and Handy [48], and Honarvar et al. [49] that surface tension was a strong function of both temperature and pressure. They postulated that an increase in pressure led to a reduction in surface tension between gas and liquid, as well as for the liquid-liquid systems. ...
Thermal recovery processes for heavy oil exploitation involve three-phase flow at elevated temperatures. The mathematical modeling of such processes necessitates the account of changes in the rock-fluid system's flow behavior as the temperature rises. To this end, numerous studies on effects of the temperature on relative permeabilities have been reported in the literature. Compared to studies on the temperature effects on oil/water-relative permeabilities, studies (and hence, data) on gas/oil-relative permeabilities are limited. However, the role of temperature on both gas/oil and oil/water-relative permeabilities has been a topic of much discussion, contradiction and debate. The jury is still out, without a consensus, with several contradictory hypotheses, even for the limited number of studies on gas/oil-relative permeabilities. This study presents a critical analysis of studies on gas/oil-relative permeabilities as reported in the literature, and puts forward an undeniable argument that the temperature does indeed impact gas/oil-relative permeabilities and the other fluid-fluid properties contributing to flow in the reservoir, particularly in a thermal recovery process. It further concludes that such thermal effects on relative permeabilities must be accounted for, properly and adequately, in reservoir simulation studies using numerical models. The paper presents a review of most cited studies since the 1940s and identifies the possible primary causes that contribute to contradictory results among them, such as differences in experimental methodologies, experimental difficulties in flow data acquisition, impact of flow instabilities during flooding, and the differences in the specific impact of temperature on different rock-fluid systems. We first examined the experimental techniques used in measurements of oil/gas-relative permeabilities and identified the challenges involved in obtaining reliable results. Then, the effect of temperature on other rock-fluid properties that may affect the relative permeability was examined. Finally, we assessed the effect of temperature on parameters that characterized the two-phase oil/gas-relative permeability data, including the irreducible water saturation, residual oil saturation and critical gas saturation. Through this critical review of the existing literature on the effect of temperature on gas/oil-relative permeabilities, we conclude that it is an important area that suffers profoundly from a lack of a comprehensive understanding of the degree and extent of how the temperature affects relative permeabilities in thermal recovery processes, and therefore, it is an area that needs further focused research to address various contradictory hypotheses and to describe the flow in the reservoir more reliably.
... A number of parachor model variants have been reported (Ali 1994;Escobedo and Mansoori 1998;Schechter and Guo 1998), in which different parachor constants for pure components are used and/or the quartic root is modified to better match experimental IFT data. Although the parachor model has broad applicability, its reliability and accuracy are inconsistent over a wide range of temperature, pressure, and composition: A number of studies (Huygens et al. 1996;Danesh 1998;Zuo and Stenby 1998;Liu et al. 2016;Pereira et al. 2016;Chen and Yang 2019) reported unsatisfactory performance for hydrocarbon-containing mixtures and water-containing mixtures with a small IFT. ...
... Statistical mechanics-based models and molecular simulations are other popular choices for IFT predictions. For statistical mechanics-based models, density gradient theory (Niño Amézquita et al. 2010;Breure and Peters 2012;Cumicheo et al. 2018), linear gradient theory (Zuo and Stenby 1998;Liang et al. 2016;Pereira et al. 2016), and density functional theory (Li and Firoozabadi 2009;Talreja et al. 2012;Klink et al. 2015) have been widely used to predict gas-alkane binary mixture IFT. Pereira et al. (2016) compared the predicted IFTs from density gradient theory, linear gradient theory, and parachor models with experimental data for various alkane and gas (CO 2 , C 1 , and N 2 ) mixtures at different temperatures. ...
Gas-alkane interfacial tension (IFT) is an important parameter in the enhanced oil recovery (EOR) process. Thus, it is imperative to obtain an accurate gas-alkane mixture IFT for both chemical and petroleum engineering applications. Various empirical correlations have been developed in the past several decades. Although these models are often easy to implement, their accuracy is inconsistent over a wide range of temperatures, pressures, and compositions. Although statistical mechanics-based models and molecular simulations can accurately predict gas-alkane IFT, they usually come with an extensive computational cost. The Shardt-Elliott (SE) model is a highly accurate IFT model that for subcritical fluids is analytic in terms of temperature T and composition x. In applications, it is desirable to obtain IFT in terms of temperature T and pressure P, which requires time-consuming flash calculations, and for mixtures that contain a gas component greater than its pure species critical point, additional critical composition calculations are required. In this work, the SE model is combined with a machine learning (ML) approach to obtain highly efficient and highly accurate gas-alkane binary mixture IFT equations directly in terms of temperature, pressure, and alkane molar weights. The SE model is used to build an IFT database (more than 36,000 points) for ML training to obtain IFT equations. The ML-based IFT equations are evaluated in comparison with the available experimental data (888 points) and with the SE model, as well as with the less accurate parachor model. Overall, the ML-based IFT equations show excellent agreement with experimental data for gas-alkane binary mixtures over a wide range of T and P, and they outperform the widely used parachor model. The developed highly efficient and highly accurate IFT functions can serve as a basis for modeling gas-alkane binary mixtures for a broad range of T, P, and x.
... Due to the comments mentioned above and to the successful use of the linear gradient theory in the works published in the literature for systems in vapor-liquid equilibrium (VLE) and vapor-liquid-liquid equilibrium (VLLE) [5,[10][11][12][13][14][15][16][17], the aim of this work is to study the adjustment of the interfacial tension of the hexane + ethanol, hexane + 1-propanol, hexane + 1-butanol, hexane + 2-butanol, hexane + 1-pentanol, hexane + 1-hexanol, hexane + 1-heptanol, and hexane + 1-octanol mixtures in the temperature range of 283.15 K to 313.15 K. ...
... The linear gradient theory was first presented by Zuo and Stenby [10,16,17] and proposes that density profile of each component in the mixture are distributed linearly between the bulk phases in equilibrium, i.e., the density of component i at position z, i (z) , in the interface can be represented by Eq. 7: ...
This work has been dedicated to modeling the interfacial tension of hexane + alcohol mixtures in the temperature range of 283.15 K to 313.15 K. The cubic plus association equation of state is applied to the liquid–vapor phase equilibrium calculations. The binary interaction parameters are obtained according to the experimental phase equilibrium data. The linear gradient theory is used as a predictive and adjustment approach to describe the interfacial tension of hexane + alcohol mixtures. The influence parameters of the pure components were correlated with the temperature and the symmetric parameters were correlated with the temperature and with the carbon number of the alcohol. The results of this work show that the equation of state used is capable of simultaneously representing the phase equilibrium and interfacial tension of the mixtures studied. Despite using the simplified version of the gradient theory, the results obtained in the interfacial tension are in agreement with those published in the literature.
... To simplify the gradient theory, Zuo and Stenby (Zuo and Stenby, 1996, 1998a, 1998b assumed that the density r (z) for component i in a mixture is linearly distributed between the equilibrium phases. According to the linear gradient theory, the surface tension is calculated with the Eq. ...
... Zuo and Stenby (Zuo and Stenby, 1996, 1998a, 1998b) estimated the influence parameter by the following expression: ...
... The linear gradient theory was first presented by Zuo and Stenby [9,22,23] and proposes that density profile of each component in the mixture are distributed ...
This work has been dedicated to modeling the interfacial tension of the heptane + alcohol mixtures in the temperature range of 288.15 K to 333.15 K. The cubic plus association equation of state is applied to the liquid–vapor phase equilibrium calculations. The binary interaction parameters are obtained according to the experimental isothermal and isobaric phase equilibrium data. For the binary interaction parameters, correlations have been obtained as a function of temperature for isothermal phase equilibrium, and a constant value for isobaric phase equilibrium. The linear gradient theory is used as a predictive and adjustment approach to describe the interfacial tension of the heptane + alcohol mixtures. The influence parameters of the pure components were constant and the symmetric parameters of the binary mixtures were correlated with the temperature. The results of this work show that the cubic plus association equation of state is capable of simultaneously representing the phase equilibrium and interfacial tension of the mixtures studied. The results obtained in the interfacial tension are in agreement with those published in the literature.
... The linear gradient theory was first presented by Zuo and Stenby [9,26,27] and proposes that density profile of each component in the mixture are distributed linearly between the bulk phases in equilibrium, i.e. the density of component i at position z, ρ i (z), in the interface can be represented by Eq. (7): ...
This work has been dedicated to modeling the interfacial tension of the heptane + alcohol mixtures in the temperature range of 288.15 K to 333.15 K. The cubic plus association equation of state is applied to the liquid - vapor phase equilibrium calculations. The binary interaction parameters are obtained according to the experimental isothermal and isobaric phase equilibrium data. For the binary interaction parameters, correlations have been obtained as a function of temperature for isothermal phase equilibrium, and a constant value for isobaric phase equilibrium. The linear gradient theory is used as a predictive and adjustment approach to describe the interfacial tension of the heptane + alcohol mixtures. The influence parameters of the pure components and the symmetric parameters of the binary mixtures were correlated with the temperature. The results of this work show that the cubic plus association equation of state is capable of simultaneously representing the phase equilibrium and interfacial tension of the mixtures studied. The results obtained in the interfacial tension are in agreement with those published in the literature.
... In order to reduce computational time, Zuo and Stenby [19,20] developed the linear gradient theory (LGT), which establishes the linearity of the density profiles at the interface, in addition, the LGT adjustment approach can be easily implemented in any computer program and ensures good results in surface tension modeling. According to the literature, the authors [19][20][21][22][23][24] used LGT and have obtained results according to the experimental surface tension of the mixtures using a symmetric parameter, i.e., GT or LGT adjustment parameter, constant, function of the mole fraction or function of temperature. ...
Surface tension and phase equilibria of N,N-dimethylcyclohexylamine (DMCA) mixtures with alcohol (propanol, iso-propanol, butanol, and iso-butanol) were modeled over the whole range of composition and different temperature ranging from (288.15 to 308.15) K. The predictive results of the Peng–Robinson equation of state with quadratic mixing rule indicated that the DMCA + alcohol mixtures are not azeotropic and that the bubble curve is linear, except for the DMCA + ethanol mixture. The surface tension of the binary mixtures was modeled with linear gradient theory, parachor method, Shereshefsky method, and Lamperski method. The linear gradient theory used as adjustment approach improved the results of surface tension prediction and correctly modeled this thermodynamic property for all mixtures, the flexibility of parachor method as an adjustment approach improved the predictive results for some mixtures, Shereshefsky method was able to successfully model the surface tension of the DMCA + ethanol, DMCA + propanol, and DMCA + butanol mixtures, and Lamperski method was able to successfully model the surface tension of the DMCA + propanol and DMCA + butanol mixtures, while the DMCA + ethanol and DMCA + isobutanol mixtures had an acceptable statistical deviation. Furthermore, Lamperski method was the best predicted model to model surface tension of the binary mixtures. Based on Shereshefsky model, the standard Gibbs energy of adsorption and the free energy change in the surface region were calculated. The free energy change was used to obtain the number of molecular layers in the surface region. Also, with Shereshefsky method it was obtained that alcohol is not absorbed at the surface which was also confirmed with Lamperski method. Finally, it is important to note that phase equilibria and surface tension of the DMCA + alcohol mixtures is modeled with theoretical approaches for the first time. On the other hand, for future experimental measurements of phase equilibria, our results could serve as an initial approximation of equilibrium, and the correlations obtained for the binary parameters of the linear gradient theory and parachor method can be used to predict surface tension at other temperatures outside the range 288.15 to 308.15 K.
... These correlations are mainly based on fluid bulk properties, although it is well known that interfacial tension is strongly dependent on the adsorption of interfacially active species at the interface ( van Hunsel and Joos, 1989;Maldonado-Valderrama et al., 2005;Staszak and Prochaska, 2006;Pauchard et al., 2014;. Most of the correlations, commonly used in the industry, can predict IFT of pure hydrocarbons and, to some extent, dead crude oil at ambient conditions (Macleod, 1923;Weinaug and Katz, 1943;Firoozabadi and Ramey, 1988;Zuo and Stenby, 1998;Sutton, 2006Sutton, , 2009Ling and He, 2012). Despite the multitude of available correlations, so far, none of them has been able to capture the true essence and true dynamics of the crude oil-water interfacial tension at reservoir conditions. ...
The interfacial tension (IFT) between crude oil and water governs the multiphase flow in porous media and is therefore of paramount importance for understanding reservoir behavior. IFT data is commonly, but inadequately, acquired at ambient conditions using samples of dead oil, because live crude oil samples are limited in availability and measurements under high pressure and temperature conditions are complex. In this study, ten live crude oil samples were used to establish the first correlation allowing to predict live crude oil interfacial tension based on dead oil IFT values and conventional PVT data. IFT experiments were executed for all samples at different pressure and temperature conditions. A common trend of IFT increase from the dead oil at ambient to the live oil at reservoir conditions was noted in the experiments. Based on the measured data, a correlation was established to predict live oil IFT at reservoir conditions from dead oil IFT at ambient condition, using dead oil viscosity and molecular weight, as well as gas to oil ratio and fluid densities as input parameters. The correlation showed a strong coefficient of determination (R² = 0.98) and was validated using three additional live crude oils from different fields. The IFT values at reservoir conditions were well predicted with average errors below 5%.
... Simpler models include the parachor model (Weinaug-Katz equation (Weinaug and Katz, 1943)) and those derived from a thermodynamic approach (e.g., the Shereshefsky model (Shereshefsky, 1967), the Connors-Wright (CW) model (Connors and Wright, 1989), the Fu et al. model (Jufu et al., 1986), and the Chunxi et al. model (Chunxi et al., 2000, which is also referred to in the literature as the Li et al. model)). More computationally intensive models of mixture surface tension employ principles of statistical mechanics, and this group of approaches includes density gradient theory (Breure and Peters, 2012;Cornelisse et al., 1993;Cumicheo et al., 2018;Enders and Kahl, 2008;Garrido and Polishuk, 2018;Liang et al., 2016;Lin et al., 2008;Miqueu et al., 2004;Pereira et al., 2016;Sahimi and Taylor, 1991;Zhu et al., 2014), linear gradient theory (Liang et al., 2016;Pereira et al., 2016;Zuo and Stenby, 1998), density functional theory (Klink et al., 2015;Li and Firoozabadi, 2009;Llovell et al., 2010;Sarman et al., 2000;Talreja et al., 2012), and Monte Carlo or molecular dynamics simulations (Cárdenas and Mejía, 2016;Miqueu et al., 2011;Neyt et al., 2013). ...
It is desirable to predict the surface tension of liquid mixtures for a wide range of compositions, temperatures, and pressures, but current state-of-the-art calculations (e.g., density gradient theory) are computationally expensive. We propose a computationally simple—but accurate—semi-empirical mathematical model of surface tension for a wide variety of multicomponent mixtures, including those with a supercritical compound when coupled with an equation of state (by introducing a reduced mole fraction scaled by a critical composition). Our predictions for binary systems with one supercritical component are an average of 0.22 mN/m away from literature experimental data (466 data points), and those for systems with two subcritical components (293–333 K) are within 0.09 mN/m (236 data points). We make predictions for methanol + ethanol + water using binary coefficients within an average of 0.71 mN/m (196 data points). Given its computational simplicity and wide applicability, the proposed model will be useful for many applications.
... with : vapor pressure, : liquid pressure, : interfacial tension (IFT) : contact angle between the surface of the wetting phase and the wall of the tube r: capillary radius The IFT is calculated by an analytical Parachor model proposed by Zuo and Stenby (1998): The cubic Peng and Robinson (1976) EOS function of compressibility factor Eq. (6) is used to model the confined fluid in liquid and vapor phase. and are expressed in Table 1. ...
... The interfacial tension (IFT) is considered as a function of composition and molar density. The authors use different analytical Parachor models formulations like 9 CHAPTER 1. INTRODUCTION the one proposed by Zuo and Stenby [159]: The flash algorithms used by the different authors are quite similar with few differences. ...
Tight oil and shale gas reservoirs have a significant part of their pore volume occupied by micro (below 2nm) and mesopores (between 2 and 50nm). This kind of environment creates strong interaction forces in the confined fluid with pore walls as well as between its own molecules and then changes dramatically the fluid phase behavior. An important work has therefore to be done on developing upscaling methodology of the pore size distribution for large scale reservoir simulations. Firstly, molecular simulations are performed on different confined fluids in order to get reference thermodynamic properties at liquid/vapor equilibrium for different pore sizes. Then, the comparison with commonly used modified equation of state (EOS) in the literature highlighted the model of flash with capillary pressure and critical temperature and pressure shift as the best one to match reference molecular simulation results. Afterwards fine grid matrix/fracture simulations have been built and performed for different pore size distributions. Then, coarse grid upscaling models have then been performed on the same synthetic case and compared to the reference fine grid results. A new triple porosity model considering fracture, small pores and large pores with MINC (Multiple Interacting Continua) approach, has shown very good match with the reference fine grid results. Finally a large scale stimulated reservoir volume with different pore size distribution inside the matrix has been built using the upscaling method developed here.
... Step 4: The interfacial tension (IFT) is calculated by the parachor model of Zuo and Stenby (1998). ...
Tight oil and shale gas reservoirs have a significant part of their pore volume occupied by micro (below 2nm) and mesopores (between 2 and 50nm). This kind of environment creates strong interactions forces in the confined fluid with pore walls as well as between its own molecules and then changes dramatically the fluid phase behavior and its thermodynamic properties. Pressure-Vapor-Temperature (PVT) modeling of such fluids becomes therefore a challenge in order to get accurate production forecast reservoir simulations. Furthermore along the flow from the matrix to the well through the fractures, the fluid will pass through a very heterogeneous pore size distribution which will alter it differently according to the pore size and the spatial distribution. An important work has therefore to be done on developing upscaling methodology of the pore size distribution for large scale reservoir simulations. Firstly molecular simulations will be performed on pure components and mixtures in order to get reference thermodynamic properties at liquid/vapor equilibrium for different pore sizes. The comparison with commonly used modified equation of state (EOS) in the literature highlighted the model of flash with capillary pressure and critical temperature and pressure shift as the best one to match reference molecular simulation results. Secondly fine grid matrix/fracture simulations have been built and performed for different pore size distributions. The study has shown that the pore size distribution has an important impact on reservoir production and that this impact is highly dependent of the volume fraction of nanopores inside the matrix. Capillary pressure heterogeneity and pore radius dependent EOS cause gas flow slowdown or gas trapping inside the matrix and postponed gas flow apparition in the fractures during depletion which reduce the GOR (Gas-Oil Ratio) at the well. Coarse grid upscaling models have then been performed on the same synthetic case and compared to the reference fine grid results. The commonly used upscaling methodology of dual porosity model with average pore radius for the pore size distribution is unable to match the fine grid results. A new triple porosity model considering fracture, small pores and large pores with their own capillary pressure and EOS, together with MINC (Multiple Interacting Continua) approach, has shown very good match with the reference fine grid results. Finally a large scale stimulated reservoir volume with different pore size distribution inside the matrix has been built using the upscaling method developed here. The proposed triple porosity methodology is able to model the PVT of the confined fluid and its flow across a very heterogeneous pore size distribution up to the well through fractures in a large scale reservoir simulation.
... Teklu et al. [25] reported the development of a computational approach to determine the MMP which mimics the VIT experiment. In their approach, they used parachor model [35] for modeling the VIT trend of equilibrium gas-oil with increasing pressure. They mentioned that other parachor models such as mechanistic parachor model [14] can also be used for obtaining VIT trend. ...
Different experimental and theoretical methods are used for predicting the minimum miscibility pressure (MMP) of complex CO2 + reservoir crude oil systems that are of particular interest to petroleum industry. In this paper, published physical and numerical vanishing interfacial tension (VIT) experimentations are critically examined for identifying best practices to reliably predict the CO
2
+ crude oil MMP. Some of the reported physical VIT experimentation studies appear to follow a portion of full scale VIT experimentation (i.e., a combination of the pendent drop method and the capillary rise technique). The physical VIT experimentation method in which the IFT measurements are made at varying pressures but with the same initial load of live oil and gas phases in the optical cell seems to be the most robust mechanistic procedure for experimentally studying the pressure dependence of IFT behaviors of complex CO
2
+ crude oil systems and thus determining the MMP using the VIT technique. The results presented here suggest that a basic parachor expression based on numerical VIT experimentation can reasonably follow the physical VIT experimentation in low IFT region, provided measured input data such as equilibrium phase densities and compositions are used in calculations.
... This simplification involved a linear distribution of the density of each component across the interface between the coexisting phases in contact (i.e, Linear Gradient Theory or LGT) and thus eliminating the need to solve the set of time-consuming density-profiles. This simplification has been successfully applied in the modelling of both weak and strong associating fluids and mixtures (Zuo & , 1996a, 1996b, 1998a, 1998bYan et al, 2001;Schmidt et al, 2007;Khosharay & Varaminian, 2013;Khosharay et al, 2013). According to the LGT approach, the density-profiles for each component in a mixture are linearly distributed across the interface and thus they can be readily calculated from: ...
In this paper, interfacial tension (IFT) of two ternary water-rich hydrocarbon systems were investigated at a representative reservoir temperature of 150 °C and equilibrium pressures up to 140 MPa. Two-phase and three-phase IFT measurements of water-methane-hexadecane and water-methane-toluene mixtures were carried out in our previously validated Pendant Drop facility and the equilibrium phase densities, required to determine pertinent IFT values, were determined by measuring the volume and mass of samples separately. The results showed a high pressure dependency of IFT values below the hydrocarbon dew point (i.e., three-phase region) whereas a slight increase on the interfacial tension was observed in the two-phase region.
Aiming at developing a general model for describing this property in multiphase systems, the generated and literature IFT data were used to develop and validate our model based on the Linear Gradient Theory (LGT). The LGT has been proven capable of describing vapor-liquid and liquid-liquid interfaces in systems containing polar and non-polar compounds when coupled with an appropriate thermodynamic model. In this work the LGT was coupled with the Cubic-Plus-Association equation of state (CPA EoS) for a correct description of the equilibrium properties of the phases involved. The modelling results confirmed the superiority of the LGT over classical models in that one single model can be used for describing the IFT of multiphase systems with greater accuracy.
... , The IFT between the liquid and gas phases can be estimated using the parachor model (Zuo and Stenby, 1998): Other parachor models (instead of Eq 2) for predicting interfacial tension, such as Ayirala and Rao (2006), can be also used. ...
Minimum miscibility pressure (MMP) is the minimum pressure at which the interfacial tension between reservoir oil and injected gas phase disappears. In the slim-tube experiment, MMP is the minimum pressure, which achieves maximum oil recovery in a sand-packed tube flow experiment. In Rising Bubble Apparatus (RBA), MMP is the pressure of gas phase disappearance at increasing pressures as a single gas bubble moves through the reservoir oil in a thin glass tube. In the Vanishing Interfacial Tension (VIT) technique, MMP is determined experimentally by measuring the decrease of the gas-oil IFT with increasing pressure, and extrapolating the trend to zero. In this paper, we determine the vanishing interfacial tension trend of equilibrium gas-oil with increasing pressure in subsurface pores, which includes capillary pressure. We extrapolate the decreasing IFT trend to zero IFT, at which the pressure is the MMP. This method resembles the experimental VIT approach for determining MMP, but obviously is faster, more convenient, and broader in scope. The result of our algorithm compares favorably with results from the multiple-mixing-cell algorithm for conventional and unconventional reservoirs. We also calculate the miscibility pressures for Bakken and Niobrara shale reservoirs for hydrocarbon and non-hydrocarbon gas injection. Our result show that the MMP of the reservoir oils occurs at lower MMPs compared to conventional reservoirs if the pore throat radius is less than 10 nm. The gases used in MMP calculation are CO 2, N2, CH4, CO, H2S, LPG, and NGL. Miscibility of N2, CH4 and CO is much lower in the same shale environment.
... where l L/V,i is the chemical potential of liquid/vapor phase of each component, r VL is the IFT between vapor and liquid phase, h is the contact angle (h ¼ 1808 assumed for this study), p is pressure, and x and y are liquid and vapor mole fraction (respectively), and r is radius. The IFT between the liquid and gas phases can be estimated with the the parachor model noted next (Zuo and Stenby 1998): ...
Numerous studies indicate that the pressure/volume/temperature (PVT) phase behavior of fluids in large pores (designated “unconfined” space) deviates from phase behavior in nanopores (designated “confined” space). The deviation in confined space has been attributed to the increase in capillary force, electrostatic interactions, van der Waals forces, and fluid structural changes.
In this paper, conventional vapor/liquid equilibrium (VLE) calculations are modified to account for the capillary pressure and the critical-pressure and -temperature shifts in nanopores. The modified VLE is used to study the phase behavior of reservoir fluids in unconventional reservoirs. The multiple-mixing-cell (MMC) algorithm and the modified VLE procedure were used to determine the minimal miscibility pressure (MMP) of a synthetic oil and Bakken oil with carbon dioxide (CO2) and mixtures of CO2 and methane gas.
We show that the bubblepoint pressure, gas/oil interfacial tension (IFT), and MMP are decreased with confinement (nanopores), whereas the upper dewpoint pressure increases and the lower dewpoint pressure decreases.
Miscible carbon dioxide (CO2) injection has proven to be an effective method of recovering oil from unconventional reservoirs. An accurate and efficient procedure to calculate the oil-CO2 minimum miscibility pressure (MMP) is a crucial subroutine in the successful design of a miscible CO2 injection. However, current numerical methods for the unconventional MMP prediction are very demanding in terms of time and computational costs which result in long runtime with a reservoir simulator. This work proposes to employ a one-dimensional convolutional neural network (1D CNN) to accelerate the unconventional MMP determination process. Over 1,200 unconventional MMP data points are generated using the multiple-mixing-cell (MMC) method coupled with capillarity and confinement effects for training purposes. The data set is first standardized and then processed with principal component analysis (PCA) to avoid overfitting. The performance of the proposed model is evaluated with testing data. By applying the trained model, the unconventional MMP results are almost instantly produced and a coefficient of determination of 0.9862 is achieved with the testing data. Notably, 98.58% of predicting data points lie within 5% absolute relative error. This work demonstrates that the prediction of unconventional MMP can be significantly accelerated, compared with the numerical simulations, by the proposed well-trained deep learning model with a slight impact on the accuracy.
This work has been dedicated to modeling the vapor–liquid equilibria and surface tension of carboxylic acids + water mixtures at different temperatures. The Peng–Robinson equation of state with modified Huron–Vidal + Wilson mixing rule correctly models the vapor pressure and vapor mole fraction of these mixtures. The modified Huron–Vidal mixing rule was better than quadratic mixing rule to model the phase equilibria properties for the mixtures studied in this work. The parachor method and linear gradient theory were used to model the surface tension of these mixtures. Finally, a new symmetric parameter dependent on the liquid molar fraction and temperature was necessary to correctly adjust the surface tension of the carboxylic acids + water mixtures using linear gradient theory. The surface tension results obtained in this work are better than those published so far.
Interfacial tension (IFT) plays a key role in enhanced oil recovery (EOR) processes that involve the injection of light hydrocarbon and non-hydrocarbon gases into oil reservoirs. Crude oil is a complex mixture of different hydrocarbons, its phase behavior is unknown in presence of miscible gas under reservoir conditions; therefore, most of the IFT measurement experiments are done using a certain fluid, such as n-alkanes. CO2 is a common gas used for EOR purposes. Since N2 and CH4 impurities in the injected CO2 stream substantially influence the IFTs and the MMP of the system, several experimental studies conducted on (N2 + n-alkane) and (CH4 + n-alkane) systems over a wide range of temperature and pressure to provide a comprehensive IFT database. Accurate prediction of this property under the thermodynamic conditions encountered in petroleum reservoirs is of paramount importance for achieving the highest amount of oil recovery. In this study, two different models are developed for prediction of IFT in binary mixtures containing (CO2 + n-alkane), (N2 + n-alkane), and (CH4 + n-alkane). These models include the thermodynamic-based model of Weinaug and Katz 1943 [1] combined with PR-EoS, and the mathematical-based model of Gene Expression Programming (GEP). A preprocessing based on Z-score method is applied on the assembled dataset to remove the outliers and duplicates from the data. The GEP and EoS models were able to predict accurate IFT results in all three systems with the EOS providing slightly inferior results in systems containing N2 gas. For some experimental observations the EoS model failed to provide any IFT results. In addition, to have a better understanding of the performance of the developed models, they were compared for IFT values less and greater than or equal to 1 mN/m for all the systems. The average squared coefficient of determination (R²) for the GEP model in CH4, CO2, and N2 – alkanes systems were 0.92, 0.94, and 0.91, and for EoS model were 0.94, 0.87, and 0.66, respectively. The findings of this study can help for a better understanding of interfacial tension under the thermodynamic conditions encountered in petroleum reservoirs is of paramount importance for achieving the highest amount of oil recovery.
In this study, new and pragmatic interfacial tension (IFT) correlations for n-alkane–water and n-alkane–CO2 systems are developed based on the mutual solubility of the corresponding binary systems and/or density in a pressure range of 0.1–140.0 MPa and temperature range of 283.2–473.2 K. In addition to being more accurate (i.e., the absolute average relative deviation (AARD) is 1.96% for alkane–water systems, while the AARDs for alkane–CO2 systems are 8.52% and 25.40% in the IFT range of >5.0 mN/m and 0.1–5.0 mN/m, respectively) than either the existing correlations or the parachor model (the AARDs for alkane–CO2 systems are 12.78% and 35.15% in the IFT range of >5.0 mN/m and 0.1–5.0 mN/m, respectively), such correlations can be applied to the corresponding ternary systems for an accurate IFT prediction without any mixing rule. Both a higher mutual solubility and a lower density difference between two phases involved can lead to a lower IFT, while pressure and temperature exert effects on IFT mainly through regulating the mutual solubility/density. Without taking effects of mutual solubility into account, the widely used parachor model in chemical and petroleum engineering fails to predict the IFT for CO2/methane–water pair and n-alkane–water pairs, though it yields a rough estimate for the CO2–water and methane–water pair below the CO2 and methane critical pressures of 7.38 and 4.59 MPa, respectively. However, the parachor model at least considers the effects of solubility in the alkane-rich phase to make it much accurate for n-alkane–CO2 systems. For n-alkane–CO2 pairs, the correlations developed in this work are found to be much less sensitive to the liquid density than the parachor model, being more convenient for practical use. In addition, all the IFTs for the CO2–water pair, methane–water pair, and alkane–CO2 pair can be regressed as a function of density difference of a gas–liquid system with a high accuracy at pressures lower than the critical pressures of either CO2 or methane.
Both the experimental and non-experimental approaches for characterizing and determining the CO2-reservoir oil miscibility in terms of the MMP have continued to evolve. The recent advancements that include improvements in existing experimental approaches and the development of new experimental approaches are presented and discussed. An analysis of the extension of existing and the newly developed experimental and non-experimental methods for characterizing and determining the MMP in unconventional (i.e., tight or shale) reservoirs is also presented.
This paper presents a theoretical and experimental study of direct fuel injection at conditions relevant to spark ignition (SI) and compression ignition (CI) engines. The focus of this work is identifying the conditions under which fuel droplet formation should occur or be suppressed. An experimental investigation of the injection of sub- and supercritical propane into gaseous nitrogen is first discussed. This includes study of one case in which the fuel remained supercritical with respect to temperature and pressure throughout the injection event, and which appears to be the first time that truly supercritical hydrocarbon fuel injection is examined experimentally. A non-dimensional parameter τ representing the ratio of the timescales of droplet formation and droplet evaporation is also proposed and used to explain the observed occurrence or suppression of fuel droplets at different conditions. Whilst instants of τ < 1 suggest that droplets should always be observed in any plausible SI or CI engine design, τ > 1 also occurs during the bulk delivery of heavier hydrocarbons in CI engines. In such cases, this should justify simplified modeling of the spray as a dense fluid that mixes with its surroundings, ignoring droplet transport during the less important parts of the injection event.
GeneralIntermolecular vs. interparticle forcesInterparticle forces in colloids and interfacesAcid–base concepts in adhesion studiesSurface and interfacial tensions from thermodynamic modelsHydrophilicityMicellization and surfactant solutionsAdsorptionConclusions
References
Surface tension calculations are important in many industrial applications and over a wide range of temperatures, pressures and compositions. Empirical parachor methods are not suitable over a wide condition range and the combined use of density gradient theory with equations of state has been proposed in literature. Often, many millions of calculations are required in the gradient theory methods, which is computationally very intensive. In this work, we have developed an algorithm to calculate surface tensions an order of magnitude faster than the existing methods, with no loss of accuracy. The new method can be used with any equation of state, and gives much improved performance. In this work, the new method for solving the gradient density theory equations is combined with cubic equations of state and the Cubic-Plus-Association model. Applications for both binary and multicomponent mixtures and for both hydrocarbon and associating systems are shown. For most systems, the predictions obtained are in good agreement with experimental data. However, cases have been identified where further investigation is needed.
Accurate determination of the minimum miscibility pressure (MMP) of a crude oil−CO2 system at the actual reservoir temperature is required in order to determine whether CO2 flooding is immiscible or miscible under the actual reservoir pressure. The objective of this study is to determine the MMPs of a crude oil−CO2 system from its measured and predicted equilibrium interfacial tension (IFT) versus equilibrium pressure data at a constant temperature. In the experiment, first, the CO2 solubilities in the crude oil are measured under four different equilibrium pressures. Second, the equilibrium IFTs of the crude oil−CO2 system are measured at 12 different equilibrium pressures and a constant temperature of T = 27 °C by applying the axisymmetric drop shape analysis (ADSA) technique for the pendant drop case. The detailed experimental results show that the CO2 solubility in the crude oil is increased almost linearly with the equilibrium pressure. It is also found that the measured crude oil−CO2 equilibrium IFT is reduced almost linearly with the equilibrium pressure as long as it is lower than a threshold pressure. The measured equilibrium IFT versus equilibrium pressure data are used to determine the MMP of the crude oil−CO2 system by applying the so-called vanishing interfacial tension (VIT) technique. In addition, the equilibrium IFT versus equilibrium pressure data of the crude oil−CO2 system are predicted by using the parachor model and linear gradient theory (LGT) model, respectively. The predicted equilibrium IFT data from each model are also used to determine the MMP of the same crude oil−CO2 system. Comparison of the MMPs determined from the two equilibrium IFT prediction models and that determined from the measured equilibrium IFTs shows that the LGT model is suitable for determining the MMP of the crude oil−CO2 system.
Compositional modeling of hydraulically stimulated naturally fractured liquid-rich shale (LRS) reservoirs is a complex process that is yet to be understood. The flow and multiphase mass transfer in the nano-, meso-, and macro-scale pores, as in Eagle Ford, Woodford and Bakken is of great interest. Understanding the production mechanisms from such reservoirs is crucial in the overall effort to increase the ultimate hydrocarbon production. Thus, we focused on deciphering the physical fundamentals of various recovery mechanisms via reservoir modeling. The starting point was examining the phase behavior issues in unconventional reservoirs. Specifically, we constructed phase diagrams using a new correlation to shift the critical properties of components in the nano and meso-scale pores. The correlation was applied to three recently published Eagle Ford fluid samples. The new phase behavior correlation was used in a dual-permeability compositional model to determine the nature of pore-to-pore flow and, eventually, the hydrocarbon production from wells. In the simulation models we allowed for the phase behavior differences between fracture and matrix and included a multi-level flow hierarchy from matrix (nano, meso, and macropores) to fractures and finally to the well. To make computation accurate we resorted to a series of detailed logarithmic local grid refinement (LS-LGR) in various strategic subdomains in the matrix and fracture.
As a result of this modeling study, we have concluded several reasons why hydrocarbon fluids can move in the shale reservoir nano, meso, and macro-scale pores and why we are able to produce from such low-permeability reservoirs. For instance, favorable phase envelope shift of hydrocarbon mixtures in the nano- and meso-scale pores is one of the contributing factors to economic production in gas-condensate and bubble-point systems. Also noted, when the phase envelope is crossed in gas-condensate systems, a large gas-to-oil volume split in the nano, meso, and macro-pores plays a crucial role in hydrocarbon recovery during depletion. For the bubble-point oil region, the low viscosity of the liquid phase and the delay in gas bubble evolution appears as the main reason for favorable oil production. Furthermore, 'rubblizing' the reservoir in the vicinity of hydraulic fractures creates another favorable environment for improved drainage, which is why multi-stage hydraulic fracturing is so critical in successful development of shale reservoirs.
Linear gradient theory Refrigerants a b s t r a c t In this work, the surface tensions of pure refrigerants and binary, ternary, and quaternary refrigerant mixtures were modeled. A simple and reliable model was used, combining the linear gradient theory (LGT) with the Heyen equation of state (Heyen EOS), to take advantage of the well described equilibrium densities of phases and surface tensions of refrigerant mixtures. The binary interaction parameters of the Heyen EOS were determined to improve the description of the equilibrium properties of bulk phases. A new correlation for the influence parameter is also proposed that is a function of the densities of the bulk phases. The geometric mixing rule for the mixture influence parameter is also selected without adjustable coefficients, making this model predictive. The surface tensions pre-dicted by the model agree well with experimental data for pure refrigerants and binary, ternary, and quaternary refrigerant mixtures (overall AADw3.27%). Crown Copyright ª 2013 Published by Elsevier Ltd and IIR. All rights reserved. Modé lisation de la tension superficielle des mé langes de frigorigè nes à l'aide de la thé orie du gradient liné aire Mots clés: : tension superficielle ; é quation d'é tat de Heyen ; thé orie du gradient liné aire ; frigorigè nes
Carbon dioxide capture and geological storage (CCGS) is an emerging technology that is increasingly being considered for reducing
greenhouse gas emissions to the atmosphere. Deep saline aquifers provide a very large capacity for CO2 storage and, unlike hydrocarbon reservoirs and coal beds, are immediately accessible and are found in all sedimentary basins.
Proper understanding of the displacement character of CO2-brine systems at in-situ conditions is essential in ascertaining CO2 injectivity, migration and trapping in the pore space as a residual gas or supercritical fluid, and in assessing the suitability
and safety of prospective CO2 storage sites. Because of lack of published data, the authors conducted a program of measuring the relative permeability
and other displacement characteristics of CO2-brine systems for sandstone, carbonate and shale formations in central Alberta in western Canada. The tested formations are
representative of the in-situ characteristics of deep saline aquifers in compacted on-shore North American sedimentary basins.
The results show that the capillary pressure, interfacial tension, relative permeability and other displacements characteristics
of CO2-brine systems depend on the in-situ conditions of pressure, temperature and water salinity, and on the pore size distribution
of the sedimentary rock. This paper presents a synthesis and interpretation of the results.
The linear gradient theory (LGT) combined with the Soave–Redlich–Kwong (SRK EoS) and the Peng–Robinson (PR EoS) equations of state has been used to correlate the interfacial tension data of the methane–water system. The pure component influence parameters and the binary interaction coefficient for the mixture influence parameter have been obtained for this system. The model was successfully applied to correlate the interfacial tension data set to within 2.3% for the linear gradient theory and the SRK EoS (LGT-SRK) and 2.5% for the linear gradient theory and PE EoS (LGT-PR). A posteriori comparison of data not used in the parameterisation were to within 3.2% for the LGT-SRK model and 2.7% for the LGT-PR model. An exhaustive literature review resulted in a large database for the investigation which covers a wide range of temperature and pressures. The results support the success of the linear gradient theory modelling approach for this system.
The parachor equation of Weinaug and Katz (1943) is still widely used for the prediction of surface tensions of mixtures, especially in the oil and gas industry, where data over a wide range of compositions, temperatures and pressures are needed. The method is simple, general, and never gives absurd (non-physical) results.The Weinaug-Katz method can be usefully modified by the use of a more generalised “mixing rule” for the parachor, incorporating adjustable binary parameters. This modified version leads not only to a better description of binary systems, but also to an improved prediction of ternary data.
A modified Redlich-Kwong equation of state is proposed. Vapor pressures of pure compounds can be closely reproduced by assuming the parameter a in the original equation to be temperature-dependent. With the introduction of the acentric factor as a third parameter, a generalized correlation for the modified parameter can be derived. It applies to all nonpolar compounds. With the application of the original generalized mixing rules, the proposed equation can be extended successfully to multicomponent-VLE calculations, for mixtures of nonpolar substances, with the exclusion of carbon dioxide. Less accurate results are obtained for hydrogen-containing mixtures.
We recently developed an extension of the three-parameter corresponding-state principle based on the properties of two nonspherical reference fluids for the viscosity and thermal conductivities of liquids and liquid mixtures. We extend the method here to surface tension. We have tested the method on six binary mixtures using the pure components as reference fluids. Good agreement between experimental and predicted values of surface tension was obtained using only the data for the pure components. The agreement is even better if a single binary interaction constant, independent of temperature and composition, is used in the mixture calculations. It is also shown how the unknown surface tension of any given fluid can be obtained from the known properties of two (similar) reference fluids.
The development of efficient, economical methods for second or tertiary recovery of petroleum reservoir fluids could substantially increase the usable reserves and supply of energy. Enhanced gas drive processes (e.g., carbon dioxide, enriched gas, or nitrogen injection) for the displacement of petroleum constitute an important class of enhanced oil recovery techniques. In immiscible displacements, the efficiency of the recovery process is influenced by the interfacial tension (IFT) between the fluid phases present in the reservoir. In this research work, the authors assumed that the densities of each component in a mixture are linearly distributed across the interface between the coexisting vapor and liquid phases, and they developed a linear gradient theory model for computing interfacial tensions of mixtures, especially mixtures containing supercritical methane, argon, nitrogen, and carbon dioxide gases at high pressure. With this model it is unnecessary to solve the time-consuming density profile equations of the gradient theory model. The model has been tested on a number of mixtures at low and high pressures. The results show excellent agreement between the predicted and experimental IFTs at high and moderate levels of IFTs, while the agreement is reasonably accurate in the near-critical region as the used equations of state reveal classical scaling behavior. To predict accurately low IFTs ({sigma} < 0.1 mN/m), an equation of state with proper scaling behavior at the critical point is at least required.
Experimental data are presented for equilibrium vapor and liquid densities and interfacial tensions (IFT's) for two multi-component mixtures. Data are presented at 120 and 150 F for a CO[sub 2]/synthetic-oil (containing the n-paraffins, methane to tetradecane) and at 130 F for a CO[sub 2]/recombined-reservoir-oil system. In both systems, measurements include the near-critical region, where IFT's become very low. These data should be useful in developing and testing models to predict phase behavior and IFT's for CO[sub 2] EOR operations.
This paper presents a multicomponent surface tension correlation based on scaling theory. In addition to particular exponents employed, the correlation contains two new features: (1) A corresponding-states equation is derived for a correlation coefficient, commonly referred to as a parachor. As a result, the hydrocarbon pseudocomponent parachors can be calculated through this equation, once their pseudocritical properties are estimated. (2) An approach is proposed to calculate the parachors of mixtures. In contrast to the conventional approach, which calculates the mixture parachor via molar mixing of component parachors, this approach first obtains the pseudocrtical properties of the mixture and then employs the corresponding-states equation to calculate the mixture parachor.
For various reservoir-fluid related pure components, the corresponding-states equation predicts parachor values to within 1% of those listed in the literature. The surface-tension correlation developed was tested against 45 sets of measured binary surface tension data and four sets of multi-component CO2-reservoir oil surface tension data. Other existing surface tension correlations, i.e. Weinaug-Katz's and Stegmeier-Hough's correlations, are also tested and compared. For the 45 sets of binary data, the average deviation of the new surface tension correlation is 3.71%, which is about 50% smaller than the deviations of the other two correlation cited. In addition, for the CO2-reservoir fluid data, the average deviation is about 7.3%, which is also a significant improvement over the existing correlations. It is worth noting that the surface tension correlation developed does not involve any adjusted parameter and it is also completely compatible with existing compositional numerical simulators.
The method of parachors is widely used in conventional thermodynamic codes and reservoir simulators to calculate oil/gas interfacial tensions of complex hydrocarbon mixtures. In the low-to-moderate interfacial tension regime, a value p≈11/3 has previously been shown to be the "best" parachor exponent. This exponent is a critical exponent and its value is consistent with the values of critical exponents characterizing the liquid/vapor critical behavior. Therefore parachors may be viewed as critical amplitudes.
By using critical scaling theory, parachors are related to other critical amplitudes and critical parameters that describe the bulk thermodynamic behavior of fluids. A simple expression relating the parachor of a pure compound to its critical temperature Tc, critical pressure Pc and acentric factor ω is proposed: P= (0.85-0.19ω)Tc12/11 /Pc9/11 where the parachor P is in units of (dyn/cm)3/11cm3/mol, Tc in K and Pc in MPa. This equation matches (within experimental error) the known parachor values of normal fluids (e.g. alkanes, aromatics, CO2, N2, H2S, etc…).
Sahimi, Davis, and Scriven recently presented predictions of interfacial tensions (IFT's) for CO2/hydrocarbon systems using the gradient theory of inhomogeneous fluid (GTIF) model. In the present paper, additional calculations from the GTIF model are presented at low IFT's, and comparisons are made with experimental measurements. The results show that the GTIF model predicts "classical" scaling behavior at low IFT's, in conflict with experimental observations. Thus, while the GTIF model has been documented by its authors to yield good predictions at high and moderate levels of IFT, it could be inappropriate for use at the low levels of IFT (σ<0.1 mN/m [0.1 dynes/cm]) that may be required to enhance the oil displacement efficiencies in enhanced gas drives.
This paper presents interfacial tension (IFT) measurements of a nitrogen/volatile oil system at conditions that are typical for North-Sea oil reservoirs. The volatile oil is a well-defined three-component oil, which can be displaced by nitrogen in a developed miscible manner.
Using the pendant drop method, we have measured the IFT of the nitrogen/volatile oil system at four characteristic compositions at a constant temperature of 100°C and in the pressure range of 30 MPa to 40 MPa. For the analysis of the pendant drops we have used advanced image processing techniques. Depending on composition and pressure, we have measured IFTs as low as 0.05 mN/m with an accuracy less than 2%.
Predictions of the IFT of our fluid systems with the parachor method and with Lee & Chien's method show large deviations from the experimental values. At near-critical conditions, the nitrogen/volatile oil system behaves in accordance with critical scaling theories.
Ali, J.K., 1994. Prediction of parachors of petroleum cuts and pseudocomponents. Fluid Phase Equilibria, 95; 383-398.The paper presents a review of methods to predict parachors of heptane-plus (C7+) fractions and pseudocomponents. A quantative comparison is made of seven existing correlations and one proposed in this study using the Weinaug-Katz interfacial tension model. With the exception of one (based on critical volumes) which gave very poor predictions, all the correlations predicted the results with mean absolute deviations around 20–40%. The study has been limited in scope and is inconclusive because of the paucity of experimental data. However, it serves to illustrate the problems to be addressed in the future.
The interfacial tension (I.F.T.) of petroleum reservoir fluids are commonly predicted by either the parachor method or the scaling law. Both methods have been evaluated against literature data of binary systems. The predictive capability of the methods have been improved by a simple modification of the original correlations. The superiority of modified methods have been demonstrated by comparing predicted results with experimental I.F.T. values for two gas condensate fluids at wide ranges of pressure and temperature.
Gas-condensate relative permeability curves are enhanced when the interfacial tension (IFT) is low. Parachor methods generally give poor predictions in the low IFT region. The paper presents new IFT, density, and composition data from a model six component gas-condensate, and IFT and density data from a rich reservoir gas-condensate. Low IFTs were collected using a laser light scattering technique. Single component, multicomponent, and reservoir fluid data were used to evaluate density based IFT correlations. Improved Stegemeier-Hough single component parachors, and parachors for crude oil cuts were derived.
February 1978
Original manuscript received in Society of Petroleum Engineers office Jan. 14, 1977. Paper accepted for publication Aug. 15, 1977. Revised manuscript received Sept. 21, 1977. Paper (SPE 6387) was presented at the SPE-AIME Permian Basin Oil and Gas Recovery Conference, held in Midland, Tex., March 10-11, 1977.
Abstract
This paper presents experimental phase behavior data on two CO2-reservoir oil systems at reservoir pressures and temperatures. pressures and temperatures. The data includepressure-composition diagrams with bubble points, dew points, and critical points;vapor-liquid equilibrium compositions and related K values;vapor and liquid densities compared with values calculated by the Redlich-Kwong equation of state;vapor and liquid viscosities compared with predictions by the Lobrenz-Bray-Clark correlation; andinterfacial tensions for six vapor-liquid mixtures compared with values calculated by the Weinaug-Katz parachor equation.
These and other published data contribute to development of the generalized correlations needed by reservoir and production engineers for evaluating, designing, and efficiently operating CO2-injection projects. projects
Introduction
This paper presents experimental phase behavior data for two CO2-reservoir oil systems. These data are used in predicting the performance of CO2 floods with a compositional simulator. The simulator calculates vapor and liquid compositions, densities, viscosities, and interfacial tensions to describe the phase behavior as the injected CO2 advances through phase behavior as the injected CO2 advances through the reservoir. The simulator predictions are used to evaluate proposed projects and to design and efficiently operate approved ones.
The data in this paper consist of pressure-composition diagrams with bubble points, pressure-composition diagrams with bubble points, dew points, and critical points; and compositions, densities, viscosities, and interfacial tensions of vapors and liquids in equilibrium in the two-phase region. These data were obtained by the experimental procedure shown in Fig. 1. procedure shown in Fig. 1. We have compared our measured data with values calculated by existing methods: Redlich-Kwong equation for densities, Lohrenz-Bray-Clark correlation for viscosities, and the Weinaug-Katz parachor equation for interfacial tension. We found parachor equation for interfacial tension. We found that these published methods give acceptable agreement in some areas, but in general, they are not satisfactory for engineering purposes. Therefore, we conclude that improved calculation methods are needed for CO2 systems. For the special case of compositional simulator applications, we devised a technique for obtaining satisfactory calculated density, viscosity, and interfacial tension values. This technique is discussed in the section on "Measurements vs Calculations."
We believe that our data, along with previously published information and information yet to come, published information and information yet to come, will advance the development of satisfactory correlations, thus reducing the need for extensive laboratory studies of individual systems.
PRESSURE-COMPOSITION DIAGRAMS PRESSURE-COMPOSITION DIAGRAMS OIL A
Ten mixtures of CO2 and Reservoir Oil A were prepared. These mixtures contained CO2 concentrations prepared. These mixtures contained CO2 concentrations of 0, 20, 40, 55, 60, 65. 70, 75, 80, and 90 mol percent. At 130 degrees F, pressure traverses were made with each mixture. These traverses started in the single-phase region at a pressure above the bubble (or dew) points and lowered the pressure in discrete steps, passing from the single-phase into the two-phase region. At each step, the vapor and liquid volumes were measured. The results are described in Fig. 2A. At 130 degrees F, the critical point of the CO2-Reservoir Oil A system (where intensive properties of the gas and liquid phases were equal) properties of the gas and liquid phases were equal) is 2,570 psia and 60-mol percent CO2.
OIL B
Eight mixtures of CO2 and Reservoir Oil B also were prepared and studied in the visual cell at 255 degrees F. CO2 concentrations for these mixtures were 0, 20, 40, 55, 65, 75, 80, and 85 mol percent. The pressure was varied from 800 to 6,100 psia, and the pressure was varied from 800 to 6,100 psia, and the relative vapor and liquid volumes measured. The results are given in Fig. 2B. The critical point of the CO2-Reservoir Oil B system at 255 degrees F is 4,890 psia and 74-mol percent CO2. psia and 74-mol percent CO2. SPEJ
P. 20
Prediction of interfacial tension (IFT) is essential for modeling many secondary and tertiary oil recovery processes. The parachor method (PM) has been widely used to predict IFT. There has been considerable confusion in the literature concerning the PM for estimating IFT. The confusion is based primarily on the lack of clarity concerning the scaling exponent and parachors derived from this exponent.
According to modern physics, the theoretical value ofthe scaling exponent is 3.88 for all pure substances, although several values may be found in the literature, usually altered to match existing data. This paper addresses clarification of the confusion about the scaling exponent, derivation of parachors for pure species occurring in petroleum fluids and oil cuts, and verification of the validity of these derived parachors in IFT prediction of reservoir fluids.
We have analyzed experimental data for various compounds occurring in reservoir fluids and found that 3.88 is a valid scaling exponent for pure species inside and outside, to some large extension, of the critical region. Taking 3.88 as a fixed scaling exponent, parachors of 139 crude oil components are back-calculated by means of surface tension and density data obtained from experiments by previous investigators. These parachors are compared with three selected parachor correlations for IFT prediction of six crude oil and CO2 mixtures and are found to be more accurate.
Improvements in predicting surface tensions for crude-oil/gas systems at reservoir conditions has been attributed to new parachors for distillation cuts of crude oil and the recognition that the last fraction or residue of distillation has a parachor not continuous with the distillation cuts.
For such reservoir gas/oil systems as condensates, which normally do not contain asphalt materials, the new parachors for the crude cuts would suffice for the surface-tension computation. For a reservoir fluid containing asphaltic substances, the calculation procedure should include a single measurement of the surface tension.
Simulation of the phase behavior of gas condensate mixtures is a severe test of the employed equation of state and of the C/sub 7+/ - characterization procedure. This paper presents experimental and calculated results for the phase behavior of different gas condensate mixtures, one of which is near critical reservoir conditions. The calculations are based on the Soave-Redlich-Kwong equation of state. For the plus-fraction a continuous logarithmic dependence is assumed for the mole fraction against carbon number. The critical properties of the C/sub 7+/-fractions are calculated directly from measured physical properties of the fractions (molecular weight and density). The procedure is fully predictive. Accurate results are obtained for the phase properties and for the phase compositions. The model may be used successfully also for heavy oil mixtures. It is shown that deviations between the measured and calculated results often can be related to inaccuracies of the data related to the composition in particular of the results for the molecular weight of the plus fraction.
Experimental data are presented for equilibrium vapor and liquid densities and interfacial tensions (IFT's) for two multi-component mixtures. Data are presented at 120 and 150°F for a CO2/synthetic-oil (containing the n-paraffins, methane to tetradecane) and at 130°F for a CO2/recombined-reservoir-oil system. In both systems, measurements include the near-critical region, where IFT's become very low. These data should be useful in developing and testing models to predict phase behavior and IFT's for CO2 EOR operations.
The simple principle of corresponding slates can be generalized lo include substances that depart from strict conformality by introducing state-dependent shape factors. This approach has been applied to the surface tension of simple inorganic compounds, hydrocarbons and their mixtures. Good agreement, generally within experimental error, has been obtained with available experimental results for both pure compounds and mixtures.
We have obtained experimental data on the interfacial tensions (IFT), equilibrium phase densities and phase compositions for a series of binary mixtures containing the solute gas CO2 or ethane in several hydrocarbon solvents, including n-butane, n-decane, n-tetradecane, cyclohexane, benzene, and trans-decalin. The measurements cover pressures from about 10 bar to the critical point in each system. These data have been used as a basis for comparing the abilities of several IFT correlations, including those of Weinaug-Katz, Lee-Chien and Hugill-Van Welsenes. The results indicate that each of these correlations can represent the data with average errors of less than 10% (when a scaling exponent of 3.6 is incorporated in the model).
Two methods for drastically reducing oil/gas flash calculation computing times using the SRK equation of state are described. (1) The characterization procedure given in parts 1 and 2 of this series has been extended with a procedure for grouping hydrocarbon fractions. The predictions of the phase behavior using a total of only six hydrocarbon fractions (C1-C30+) are as accurate as when 40 hydrocarbon fractions are used. (2) The abovementioned characterization procedure uses binary interaction coefficients (kij values) equal to zero for all hydrocarbon-hydrocarbon interactions. In naturally occurring oil and gas systems, the contents of non-hydrocarbons (mainly N2 and CO2) are often below 10 mol %. For such mixtures it is found that using kij = 0 for all interactions (also with the non-hydrocarbons) has virtually no effect on the calculated results. Explicit use of the assumption of zero kij values leads to substantial savings in the flash calculation computer time.
A generalized corresponding-states model based on two reference fluids and a parachor correlation were developed for the prediction of interfacial tensions for non-polar and weakly polar pure fluids and mixtures. Pure methane and n-octane were chosen as reference fluids of the corresponding-states model. The two models were tested on 86 pure substances, more than 30 binary and multicomponent mixtures, 11 naphtha reformate cuts, 6 petroleum cuts and 2 North Sea oil mixtures. The calculated results were found to be in good agreement with experimental data.
Un modèle d'états correspondants géneralisé s'appuyant sur deux fluides de référence et une corrélation de parachor a été mis au point pour la prédiction des tensions interfaciales pour des fluides et des mélanges purs non polaires et légèrement polaires. Du méthane et du n-octane purs ont été choisis comme fluides de référence du modéle d'états correspondants. Les deux modèles ont été testés sur 86 substances pures, plus de 30 mélanges binaires et multicomposants, 11 coupes de reformat de naphta, 6 coupes de pétrole et 2 mélanges de pètrole de la mer du Nord. On a trouvé un bon accord entre les résultats calculés et les données expérimentales.
A new method is proposed for the estimation of physical properties of pseudocomponents generated by any lumping procedure. The method is completely consistent with the equation of state to be used for description of the thermodynamic behaviour of the lumped system.This method tends to minimize the loss of information induced by component lumping. Applied to complex fluids, it has been proved to be very effective. For illustration purposes, some results are given for a light oil system.
In this research work, the gradient theory (GT) of inhomogeneous fluids was used to calculate interfacial tensions (IFTs). The correlations of the influence parameter are presented for pure hydrocarbons, which can improve the scaling behavior of pure fluids under near-critical conditions. The overall average absolute deviations (AADs) of the calculated IFTs from the GT model with the SRK, PR and PT equations of state (EOS's) for 86 non-polar and weakly polar pure substances are 2.34%, 2.10% and 2.29%, respectively. At low pressure, the lumping method proposed by Leibovici [Leibovici, C.F, 1993. A consistent procedure for the estimation of properties associated to lumped systems. Fluid Phase Equilibria, 87: 89–197] was used to lump a mixture into one pseudocomponent, and its IFTs were calculated by means of the method of pure fluids. On the basis of the SRK EOS, the overall AAD of mixtures was 3.26% at low pressure, and that of naphtha reformate cuts was 3.6%. In addition, the gradient theory was used to predict interfacial tensions for binary systems in the near-critical region. The results show excellent agreement between the predicted and experimental IFTs at high and moderate levels, while the agreement is reasonably accurate in the near-critical region as the models reveal classical scaling behavior. To predict low IFTs accurately (σ < 0.1 mN m−1), an equation of state with proper scaling behavior in the vicinity of the critical point is at least required.
18 —IFT/pressure isotherm for a real gas condensate at 413.15 K
- Fig
Fig. 18 —IFT/pressure isotherm for a real gas condensate at 413.15 K (experiment from Ref 29.).
Phase Equilibria and Transport of Multiphase Systems
- Knudsen
Knudsen, K.: "Phase Equilibria and Transport of Multiphase Systems,"
PhD thesis, Techical U. of Denmark, Lyngby, Denmark (1992).
Interfacial Tension and Viscosity of Petroleum Reservoir Fluids
- Dandekar
Dandekar, A.Y.: " Interfacial Tension and Viscosity of Petroleum Res-ervoir Fluids, " PhD dissertation, Heriot-Watt U., Edinburgh, U.K. (1994).
Prediction of Interfacial Tensions with a Simplified Gradient Theory Model
- Y.-X Zuo
- E H Stenby
Zuo, Y.-X. and Stenby, E.H.: "Prediction of Interfacial Tensions with
a Simplified Gradient Theory Model," Proc., Fourth Asian Thermophysical Properties Conference, Tokyo (September 1995).
Interfacial Tension of Nitrogen/Volatile Oil Systems
- R J M Huygens
- H Ronde
- J Hacques
Huygens, R.J.M., Ronde, H., and Hacques, J.: "Interfacial Tension of
Nitrogen/Volatile Oil Systems," paper SPE 26643 presented at the 1993
SPE Annual Technical Conference and Exhibition, Houston, 3-6 October.
DK-2800 Lyngby, Denmark, e-mail: yxz@olivia.kt. dtu.dk. His research interests include interfacial tensions, electrolyte systems, gas hydrates, and pressure/volume/temperature properties of reservoir fluids. He holds a PhD degree in chemical engineering from the U. of Petroleum
- A Y Dandekar
- U Heriot-Watt
- U K Edinburgh
Dandekar, A.Y.: "Interfacial Tension and Viscosity of Petroleum Reservoir Fluids," PhD dissertation, Heriot-Watt U., Edinburgh, U.K.
(1994).
Dept. of Chemical Engineering, Technical U. of Denmark,
Building 229, DK-2800 Lyngby, Denmark, e-mail: yxz@olivia.kt.
dtu.dk. His research interests include interfacial tensions, electrolyte systems, gas hydrates, and pressure/volume/temperature properties of reservoir fluids. He holds a PhD degree in
chemical engineering from the U. of Petroleum, Beijing. Erling H.
Stenby is a professor and Director of the Engineering Research
Center IVC-SEP, Dept. of Chemical Engineering, Technical U. of
Denmark, Building 229, DK-28800 Lyngby, Denmark, e-mail:
ehs@kt.dtu.dk. His research interests are applied thermodynamics and phase behavior of reservoir fluids. He served on the
Editorial Review Committee from 1995 to 1998.
Zuo
Stenby
Properties of Oils and Natural Gases
- Pedersen