Nonlinear Formulation Based on an Equation-of-State Free Method for Compositional Flow Simulation

SPE Journal ◽  
2012 ◽  
Vol 18 (02) ◽  
pp. 264-273 ◽  
Author(s):  
R.. Zaydullin ◽  
D.V.. V. Voskov ◽  
H.A.. A. Tchelepi

Summary Compositional simulation is necessary for modeling complex enhanced oil recovery (EOR) processes. For accurate simulation of compositional processes, we need to resolve the coupling of the nonlinear conservation laws, which describe multiphase flow and transport, with the equilibrium phase behavior constraints. The complexity of the problem requires extensive computations and consumes significant time. This paper presents a new framework for the general compositional problem associated with multicomponent multiphase flow in porous media. Here, adaptive construction and interpolation using the supporting tie lines are used to obtain the phase state and the phase compositions. For the parameterization of the full solution of a complex compositional problem, we need only a limited number of supporting tie lines in the compositional space. The parameterized tie lines are triangulated using Delaunay tessellation, and natural-neighbor interpolation is used inside the simplexes. Then, the computation of the phase behavior in the course of a simulation becomes an iteration-free, table look-up procedure. The treatment of nonlinearities associated with complex thermodynamic behavior of the fluid is based on the new set of unknowns—tie-line parameters that allow for efficient representation of the subcritical region. For the supercritical region, we use the standard compositional variable set based on the overall composition. The efficiency and accuracy of the method are demonstrated for several multidimensional compositional problems of practical interest. In terms of the computational cost of the thermodynamic calculations, the proposed method shows results comparable to those of state-of-the-art techniques. Moreover, the method shows better nonlinear convergence in the case of near-miscible gas-injection simulation.

SPE Journal ◽  
2013 ◽  
Vol 18 (06) ◽  
pp. 1140-1149 ◽  
Author(s):  
Alireza Iranshahr ◽  
Denis V. Voskov ◽  
Hamdi A. Tchelepi

Summary Enhanced Oil Recovery (EOR) processes usually involve complex phase behavior between the injected fluid (e.g., steam, hydrocarbon, CO2, sour gas) and the in-situ rock-fluid system. Several fundamental questions remain regarding Equation-of-State (EOS) computations for mixtures that can form three, or more, phases at equilibrium. In addition, numerical and computational issues related to the proper coupling of the thermodynamic phase behavior with multi-component transport must be resolved to accurately and efficiently model the behavior of large-scale EOR processes. Previous work has shown that the adaptive tabulation of tie-simplexes in the course of a compositional simulation is a reliable alternative to the conventional EOS-based compositional simulation. In this paper, we present the numerical results of reservoir flow simulation with adaptive tie-simplex parameterization of the compositional space. We study the behavior of thermal-compositional reservoir displacement processes across a wide range of fluid mixtures, pressures, and temperatures. We show that our approach rigorously accounts for tie-simplex degeneration across phase boundaries. We also focus on the complex behavior of the tie-triangles and tie-lines associated with three-phase, steam injection problems in heterogeneous formations. Our studies indicate that the tie-simplex based simulation is a potential approach for fast EOS modeling of complex EOR processes.


SPE Journal ◽  
2019 ◽  
Vol 24 (02) ◽  
pp. 579-595 ◽  
Author(s):  
Amir Salehi ◽  
Denis V. Voskov ◽  
Hamdi A. Tchelepi

Summary Enhanced-oil-recovery (EOR) processes involve complex flow, transport, and thermodynamic interactions; as a result, compositional simulation is necessary for accurate representation of the physics. Flow simulation of compositional systems with high-resolution reservoir models is computationally intensive because of the large number of unknowns and the strong nonlinear interactions. Thus, there is a great need for upscaling methods of compositional processes. The complex multiscale interactions between the phase behavior and the heterogeneities lie at the core of the difficulty in constructing consistent upscaling procedures. We use a mass-conservative formulation and introduce upscaled phase-molar-mobility functions for coarse-scale modeling of multiphase flow. These upscaled flow functions account for the subgrid effects caused by the absolute permeability and relative permeability variations, as well as the effects of compressibility. Upscaling of the phase behavior is performed as follows. We assume that instantaneous thermodynamic equilibrium is valid on the fine scale, and we derive coarse-scale equations in which the phase behavior may not necessarily be at equilibrium. The upscaled thermodynamic functions, which represent differences in the component fugacities, are used to account for the nonequilibrium effects on the coarse scale. We demonstrate that the upscaled phase-behavior functions transform the equilibrium phase space on the fine scale to a region of similar shape, but with tilted tie-lines on the coarse space. The numerical framework uses K-values that depend on the orientation of the tie-lines in the new nonequilibrium phase space and the sign of upscaled thermodynamic functions. The proposed methodology is applied to challenging gas-injection problems with large numbers of components and highly heterogeneous permeability fields. The K-value-based coarse-scale operator produces results that are in good agreement with the fine-scale solutions for the quantities of interest, including the component overall compositions and saturation distributions.


1980 ◽  
Vol 20 (05) ◽  
pp. 402-406 ◽  
Author(s):  
James E. Vinatieri

Abstract This paper describes a study of the emulsions which could occur during a pilot surfactant flood, such as that conducted by Phillips Petroleum Co. in the North Burbank Unit, Osage County, OK. The phase behavior of this surfactant system can be characterized by three types of microemulsions, with the transition from one type to another being a function of the salinity. The rate at which emulsions coalesce was seen to correlate directly with the type of microemulsion. Coalescence was slow for macroemulsions at low salinities, rapid at intermediate salinities (where the final state was a three-phase system), and varied from slow to rapid at salinities above the three-phase region. Knowledge of the correlation between phase behavior and emulsion stability can be useful in treating macroemulsions produced during a surfactant flood. Introduction With the increased emphasis currently being placed on the use of surfactants for tertiary oil recovery, a potential problem exists with emulsions which can be produced as a consequence of a surfactant flood. For example, if a channeling problem between an injection well and a production well should occur, it may be possible to produce relatively large amounts of surfactant at moderately high concentrations (0.2 to 2.0070). Under these conditions, emulsions of oil and brine could be stabilized by the presence of the surfactant and could pose a serious problem. Although these emulsions are thermodynamically unstable and ultimately should separate into bulk oil and water phases, the presence of surfactants can increase greatly the time required for such separations. Typical oilfield operations allow, at most, several hours for this separation of phases to occur, but some emulsions containing surfactants may require weeks or even months to separate. Thus, a definite need exists for being able to accelerate this coalescence process. Phillips Petroleum Co. is conducting a pilot surfactant flood in the North Burbank Unit (NBU) in Osage County.1,2 The work reported here was directed at developing a contingency plan for breaking emulsions which may be produced by this surfactant flood. The problem of studying emulsions produced by a surfactant flood has two aspects:the nature of the phases which result when thermodynamic equilibrium finally is attained andthe rate at which this equilibrium state is reached. This is not to imply that any emulsion can be described completely by characterization of these two properties but rather that these are the two properties most important to oilfield operations and, hence, form the basis for the work reported here. The next section discusses the equilibrium properties of surfactant systems and the one following discusses the coalescence of emulsions. The fourth section describes the use of chemical demulsifiers to accelerate coalescence. Equilibrium Phase Behavior The equilibrium phase behavior of systems of oil and water containing appreciable amounts of surfactant (i.e., 0.5%) is characterized by the presence of microemulsions.1,3-5 These microemulsion phases have a high degree of structure and may contain large amounts of both oil and water.


SPE Journal ◽  
2016 ◽  
Vol 21 (03) ◽  
pp. 0873-0887 ◽  
Author(s):  
Hangyu Li ◽  
Louis J. Durlofsky

Summary Compositional flow simulation, which is required for modeling enhanced-oil-recovery (EOR) operations, can be very expensive computationally, particularly when the geological model is highly resolved. It is therefore difficult to apply computational procedures that require large numbers of flow simulations, such as optimization, for EOR processes. In this paper, we develop an accurate and robust upscaling procedure for oil/gas compositional flow simulation. The method requires a global fine-scale compositional simulation, from which we compute the required upscaled parameters and functions associated with each coarse-scale interface or wellblock. These include coarse-scale transmissibilities, upscaled relative permeability functions, and so-called α-factors, which act to capture component flow rates in the oil and gas phases. Specialized near-well treatments for both injection and production wells are introduced. An iterative procedure for optimizing the α-factors is incorporated to further improve coarse-model accuracy. The upscaling methodology is applied to two example cases, a 2D model with eight components and a 3D model with four components, with flow in both cases driven by wells arranged in a five-spot pattern. Numerical results demonstrate that the global compositional upscaling procedure consistently provides very accurate coarse results for both phase and component production rates, at both the field and well level. The robustness of the compositionally upscaled models is assessed by simulating cases with time-varying well bottomhole pressures that are significantly different from those used when the coarse model was constructed. The coarse models are shown to provide accurate predictions in these tests, indicating that the upscaled model is robust with respect to well settings. This suggests that one can use upscaled models generated from our procedure to mitigate computational demands in important applications such as well-control optimization.


1979 ◽  
Vol 19 (05) ◽  
pp. 271-278 ◽  
Author(s):  
J.L. Salager ◽  
M. Bourrel ◽  
R.S. Schechter ◽  
W.H. Wade

Abstract Many formulations used in surfactant flooding involve blends of surfactants designed to glue the best oil-recovery efficiency. Because oil-recovery efficiency usually is presumed to relate closely to surfactant/brine/oil phase behavior, it is of interest to understand the effect of mixing surfactants or of mixing oils on this phase behavior.We show that a correlation defining optimal behavior as a function of salinity, alcohol type and concentration, temperature, WOR (water/oil ratio), and oil type can be extended to mixtures of sulfonated surfactants and to those of sulfonates with sulfates and of sulfonates with alkanoates, provided the proper mixing rules are observed. provided the proper mixing rules are observed. The mixing rules apply to some mixtures of anionic and nonionic surfactants, but not to all. These mixtures exhibit some properties that may be of practical interest, such as increased salinity and practical interest, such as increased salinity and temperature tolerance. Introduction Recent studies have shown that formulation of the surfactant/brine/oil system is a key factor governing the performance of microemulsions designed to recover residual oil. These studies demonstrate that all optimal formulations exhibit characteristic properties that are remarkably similar. In general, properties that are remarkably similar. In general, the optimal microemulsion can solubilize large quantities of oil and connate water; in the presence of excess quantities of oil and water, a third surfactant-rich middle phase is formed. The interfacial tensions (IFT's) between the excess phases and the surfactant-rich phase are both low - about 10 dyne/cm (10 mN/m). Given an oil/brine system from a particular reservoir, one can achieve this formulation by varying the surfactant or the cosurfactant. Different oils, brines, or temperatures require formulations correspondingly altered to maintain optimal conditions. Previous studies have shown that the three-phase region exists over a range of values when one parameter, such as cosurfactant concentration, parameter, such as cosurfactant concentration, salinity, temperature, etc., is varied systematically (often called a scan). Thus, some ambiguity may exist with regard to the selection of those parameters representing the optimal formulation. Clearly, the optimum is that which recovers the most oil. However, tests are laborious, difficult to reproduce precisely, and sensitive to other factors, such as precisely, and sensitive to other factors, such as mobility, surfactant retention, wettability, etc. Therefore, it is desirable to impose an alternative definition that can be used for screening, though the final design still is dictated by core floods.Healy and Reeds have shown that the optimal formulation for oil recovery closely corresponds to that for which the IFT's between the excess oil and water phases and the surfactant-rich phase are equal. An almost equivalent criterion also was shown to be that point in the three-phase region for which the volume of oil solubilized into the middle phase equals the volume of brine. Furthermore, Salager et al. have used still another criterion that seems to be essentially equivalent to those used by Healy and Reed - an optimal salinity is defined as the midpoint of the salinity range for which the system exhibits three phases.These criteria are useful because they permit the screening of microemulsion systems using simple laboratory tests. SPEJ P. 271


1968 ◽  
Vol 8 (04) ◽  
pp. 381-388 ◽  
Author(s):  
Leonal V. Pirela ◽  
S.M. Farouq Ali

Abstract Some interest has been expressed recently in the application of solvents in conjunction with a thermal drive, such as a steamflood. At least one field project of this type bas been reported. This paper makes the first attempt to provide some of paper makes the first attempt to provide some of the basic information necessary for choosing a solvent for such an application. Results of displacements conducted at elevated temperatures are also discussed. This paper shows that, in the case of alcohol-hydrocarbon-water or brine ternary systems, the system miscibility may increase, decrease, or both increase and decrease within the same system when the temperature increases. The distribution coefficient was consistently found to increase in favor of the oleic phase with an increase in temperature, which is advantageous from the standpoint of oil recovery. Results of solvent displacements in a sandstone core showed that even a relatively small temperature effect in the favorable direction (increase in miscibility and distribution coefficient) can lead to a 50 percent increase in oil recover, ton the other hand if the system miscibility decreases with the temperature, even though the distribution coefficient increases, the oil recovery at the higher temperature may not increase. Introduction Miscible displacement has been the subject of many investigations. Miscible-phase solvent flooding, employing solvents such as alcohols that are miscible with both oil and water, has received considerable attention. Investigations conducted by Gatlin and Slobod, Taber, Kamath and Reed, Holm and Csaszar, and Farouq Ali and Stahl have helped in understanding the mechanism of solvent flooding. While the use of alcohols and similar solvents as oil recovery agents is economically unattractive these solvents nevertheless provide a means of understanding the mechanistic aspects of important miscible-phase oil recovery processes such as the Maraflood process (discussed by Gogarty). As shown by Taber et al., the phase behavior of a solvent-oil-water system is of utmost importance in determining the efficiency of the oil displacement. This paper makes the first attempt to obtain the ternary phase behavior data for nine alcohol-hydrocarbon-water/brine systems at elevated temperatures. Results of core tests at elevated temperatures are also presented which corroborate the effect of temperature on oil recovery, as judged on the basis of phase-behavior data. The use of solvents at elevated temperatures has been suggested earlier by Farouq Ali. At least one field test of this type has been reported. With the widespread use of thermal recovery techniques, it is possible in some situations (especially in steamflooding) that the use of a suitable solvent in conjunction with the heat carrier may be economically feasible. This paper attempts to provide some of the basic information needed for judging such feasibility. LOCATION OF THE PLAIT POINT The phase behavior of a typical ternary system consisting of a solvent, hydrocarbon and brine (or water) can be represented by a triangular diagram such as the one shown in Fig. 1 (for temperature T,). Point P on the bimodal curve represents the plait point, being the limit of tie lines such as plait point, being the limit of tie lines such as YlY2,. The compositions of the coexisting oleic and aqueous phases are given by points Y2 and Y1, respectively, for any mixture composition along Y1Y2. The characteristics of ternary diagrams have been discussed by Findlay and others. Taber et al. have shown that the position of the plait point in a particular ternary system plays the plait point in a particular ternary system plays the decisive role in determining whether or not the oleic phase would be displaced in a continuous manner phase would be displaced in a continuous manner during an alcohol displacement. SPEJ P. 381


SPE Journal ◽  
2018 ◽  
Vol 23 (06) ◽  
pp. 2376-2393 ◽  
Author(s):  
Olav Møyner ◽  
Hamdi A. Tchelepi

Summary Compositional simulation is necessary for a wide variety of reservoir-simulation applications, and it is especially valuable for accurate modeling of near-miscible gas injection for enhanced oil recovery. Because the nonlinear behavior of gas injection is sensitive to the resolution of the simulation grid used, it is important to use a fine grid to accurately resolve the compositional and saturation gradients. Compositional simulation of highly detailed reservoir models entails the use of small timesteps and large, poorly conditioned linear systems. The high computational cost of solving such systems renders field-scale simulations practically unfeasible. The coupling of the flow and transport to the phase-equilibrium calculations adds to the challenge. This is especially the case for near-miscible gas injection, in which the phase state and the phase compositions are very strong functions of space and time. We present a multiscale solver for compositional displacements with three-phase fluid flow. The thermodynamic phase behavior is described by general nonlinear cubic equations of state (EOS). The fully implicit (FI) natural-variables formulation is used as the basis to derive a sequential implicit (SI) solution strategy, whereby the pressure field is decoupled from the multicomponent transport. The SI scheme is mass conservative without the need to iterate between the pressure and transport equations during the timestep. This conservation property allows the errors caused by fixing the total-velocity field between the pressure- and transport-updating steps to be represented as a volume error. The method computes approximate pressure solutions—within a prescribed residual tolerance—that yield conservative fluxes on the computational grid of interest (fine, coarse, or intermediate). We use basis functions computed using restricted smoothing to allow for generally unstructured grids. The new method is verified against existing research and commercial compositional simulators using a simple conceptual test case and also using more-complex cases represented on both unstructured and corner-point grids with strong heterogeneity, faults, and pinched-out and eroded cells. The SI method and the implementation described here represent the first demonstrated multiscale method applicable to general compositional problems with complexity relevant for industrial-reservoir simulation.


1979 ◽  
Vol 19 (06) ◽  
pp. 411-422 ◽  
Author(s):  
Ron G. Larson

Abstract This paper analyzes by mathematical modeling the role of phase behavior in surfactant flooding. In the absence of dispersion, miscible, immiscible, and semimiscible displacements are distinguished by the position of the injected composition relative to the position of the injected composition relative to the binodal envelope and extended tie lines. Even with dispersion, these concepts prove useful in analyzing slug miscibility breakdown in surfactant floods. Introduction Two design philosophies of tertiary oil recovery by surfactant flooding exist. In one, the chemical slug is designed to be miscible in some proportions with reservoir oil and brine, the goal being miscible displacement of resident oil. The second philosophy is to attain, rather than miscibility, philosophy is to attain, rather than miscibility, ultralow interfacial tension (IFT) between the slug fluid and resident oil. Correlations obtained by immiscible displacements of oil from natural and artificial porous media show that the saturation of residual oil (i.e. trapped, unrecoverable oil) decreases as IFT decreases. In reality, the distinction between philosophies is a matter of degree. Miscible displacements have regions of immiscibility. (e.g., the oil/brine bank). Furthermore, advocates of miscible displacements concede that breakdown into immiscible displacement occurs in the later stages of their processes; others argue that the breakdown occurs processes; others argue that the breakdown occurs early and that miscible displacements are, by and large, immiscible. On the other hand, since most slug formulations advocated by both schools are single phases capable of absorbing some amount of oil and phases capable of absorbing some amount of oil and brine without splitting into multiple phases, even chemical flood displacements designed to be immiscible are miscible for some time, however short. A related area of contention concerns the alleged advantages or disadvantages of formulating oil-rich, as opposed to brine-rich, slugs. Another area of contention concerns whether small, high-concentration chemical slugs are preferred to larger, lower-concentration slugs. The purpose of this paper is to shed light on these questions by paper is to shed light on these questions by incorporating equilibrium phase concepts as represented on a ternary diagram into the simulation of surfactant flood displacements. This study indicates that immiscible and miscible displacements are, in fact, closely related. Specifically, miscible recovery of oil is enhanced if the multiphase region of the ternary diagram contains a substantial subregion of ultralow tension. Furthermore, the success of miscible displacements is affected strongly not only by the position of the slug composition relative to the multiphase envelope on a ternary diagram but also by the position of slug composition relative to the tie lines, with better oil recovery attained when the injected composition point lies away from the region through which point lies away from the region through which extended tie lines pass. Thus, this study stresses the importance of the partition coefficient, a parameter shown to be important in an earlier study. For the purpose of this study, two simulation techniques for three-component, one- and two-phase flow in porous media were developed, each with its own restrictions. The first, a method-of-characteristics scheme (extended from a method developed earlier) allows phase volumes to change by solubilization of components phase volumes to change by solubilization of components but considers only continuous injection of micellar fluid, not the more realistic slug injection. The second method is a finite-difference approach that handles slug injection and solubilization and builds in dispersion, which cannot be considered when the method of characteristics is used. Because of the large number of parameters that arise in this study, base-case values (Table 1) of all parameters have been selected. For all results given in parameters have been selected. For all results given in this paper, the value of each parameter is the base-case value, unless otherwise specified. SPEJ P. 411


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