Numerical modelling of multiphase multicomponent flow coupled with mass and energy transport in porous media is crucially important for many applications including oil recovery, carbon storage and geothermal. To deliver robust simulation results, a fully or adaptive implicit method is usually employed, creating a highly nonlinear system of equations. It is then solved with the Newton-Raphson method, which requires a linearization procedure to assemble a Jacobian matrix. Operator Based Linearization (OBL) approach allows detaching property computations from the linearization stage by using piece-wise multilinear approximations of state-dependent operators related to complex physics. The values of operators used for interpolation are computed adaptively in the parameter-space domain, which is uniformly discretized with the desired accuracy. As the result, the simulation performance does not depend on the cost of property computations, making it possible to use expensive equation-of-state formulations (e.g., fugacity-activity thermodynamic models) or even black-box chemical packages (e.g., PHREEQC) for an accurate representation of governing physics without penalizing runtime. On the other hand, the implementation of the simulation framework is significantly simplified, which allows improving the simulation performance further by executing the complete simulation loop on GPU architecture. The integrated open-source framework Delft Advanced Research Terra Simulator (DARTS) is built around the OBL concept and provides a flexible, modular and computationally efficient modelling package. In this work, we evaluate the computational performance of DARTS for various subsurface applications of practical interests on both CPU and GPU platforms. We provide a detailed performance comparison of particular workflow pieces composing Jacobian assembly and linear system solution, including both stages of Constrained Pressure Residual solver.

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Several compositional reservoir simulators based on equations of state (EoS) have been designed. Yet, few of them can deal with thermal processes such as steam injection and no fully compositional thermal simulation of the steam injection process has been proposed with extra-heavy oils yet. Those simulations appear essential and will offer better tools to decide whether to carry out the exploitation of a heavy oil field or not. In those processes, the accurate modelling of the water/steam phase plays an important role and accurate multiphase equilibrium calculations are necessary. Thermodynamics generate highly nonlinear problems. Besides, in reservoir simulation a huge amount of phase equilibrium calculations is required, and a single failure may cause significant error propagations leading to false solutions. This study presents several improvements leading to a more robust and efficient phase equilibrium calculation (stability and flash) program. A general multiphase flash implementing all the developed algorithms is presented and tested against experimental and literature data. It can handle any number of phases; a numerical example consists in a four-phase simulation of CO₂ injection. Simulations of steam flooding are performed with highly heterogeneous reservoirs. Besides, a fully compositional simulation of the SAGD process for an extra heavy bitumen is performed, which appears to be the one of the first simulation of the kind in the literature.

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In this paper, we propose a strategy to bypass the phase identification of fluid mixtures that can form three, or more, phases. The strategy is used for reservoir simulation of multicomponent, three-phase, thermal compositional displacement processes. Since the solution path in compositional space is determined by a limited number of “key” tie-simplexes, the proposed “bypass” method uses information from the parameterized tie-simplexes and their extensions. The tie-simplex parameterization is performed in the discrete phase-fraction space. Once the phase-fraction space is discretized, a conventional three-phase flash is used adaptively to compute the phase states at the discretization nodes. If all discretization vertices of a given discrete cell, in phase-fraction space, have the same phase state, then this state is assigned to the entire cell and expensive flash calculations are bypassed. We demonstrate the robustness and efficiency of our phase identification bypassing strategy for several cases with three-phase flow, including a six-component ES-SAGD (enhanced solvent SAGD) model.

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Primary oil recovery methods in heavy oil basins generally extract 5-10% of the available resource, with the vast majority left in the ground and recoverable only through Enhanced Oil Recovery (EOR) methods. Traditional EOR methods, such as SAGD and solvent-assisted SAGD, generate steam in surface facilities and inject it underground to mobilize the oil for production. However, these methods can have considerable energy losses that significantly impact process performance. In contrast, the Solvent Thermal Resource Innovation Process (STRIP) technology, which uses down hole combustion of methane to produce CO2 and steam, reduces the operating and capital costs of surface facilities, saving more than 50% of the energy typically required for thermal production. In this work, simulations of conventional SAGD, SAGD with a non-condensing solvent (propane), and STRIP-SAGD for a typical bitumen reservoir in the Fort McMurray region in Alberta, Canada were performed using the combined software system ADGPRS/GFLASH. SAGD simulations used steam injection with a quality of 0.8 while STRIP simulations injected a vapor-liquid mixture with a quality of 0.8. Furthermore, both solvent-based EOR methods required longer operation periods than conventional SAGD to recover a similar amount of oil. However, when compared on the basis of cumulative oil produced for the same overall energy input, it is shown that STRIP-SAGD recovered more oil per kJ of energy input to the reservoir than either SAGD or SAGD with propane co-injection.@en

This paper presents a detailed numerical analysis of two methods for phase-behavior computations associated with thermal compositional reservoir simulation. Specifically, we analyze and compare the standard K-values approach with an Equation of State (EoS) model. We study steam and steam–solvent injection into a one-dimensional reservoir saturated with heavy oil in order to identify the impact of using different methods to describe the phase behavior. We then present results for complex displacement processes in multidimensional reservoir models. The investigation shows the differences in the predictions between K-values- and EoS-based simulations can vary from small to quite significant depending on the compositional interactions between the injected and resident fluids in the modeled displacement process.

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Fully compositional and thermal reservoir simulation capabilities are important in oil exploration and production. There are significant resources in existing wells and in heavy oil, oil sands, and deep-water reservoirs. This article has two main goals: (1) to clearly identify chemical engineering sub-problems within reservoir simulation that the PSE community can potentially make contributions to and (2) to describe a new computational framework for fully compositional and thermal reservoir simulation based on a combination of the Automatic Differentiation-General Purpose Research Simulator (AD-GPRS) and the multiphase equilibrium flash library (GFLASH). Numerical results for several chemical engineering sub-problems and reservoir simulations for two EOR applications are presented. Reservoir simulation results clearly show that the Solvent Thermal Resources Innovation Process (STRIP) outperforms conventional steam injection using two important metrics - sweep efficiency and oil recovery.

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In this paper, we present a novel strategy for phase-state identification that can be used to bypass the need for full Equation-of-State Computations in multicomponent, multiphase thermal-compositional displacement processes. Analysis based on the Method of Characteristics (MOC) indicates that the displacement path in compositional space is determined by a limited number of tie-simplexes. Our "bypass" method uses information from the parameterized extensions of these "key" tie-simplexes. The parameterization is performed in the discrete phase-fraction space. In this space, the phase fractions can be negative, or greater than unity; this allows for parameterization of the hyperplane that corresponds to a tiesimplex extension. Once the tie-simplexes extension is discretized, a conventional three-phase flash is used adaptively to compute the phase states at the discrete points in compositional space. If all discretization nodes for a given discrete cell that lie on the hyperplane have the same phase state, this state is assigned to the entire computational cell, and flash calculations are bypassed for the compositions of that cell. Here, we make use of the continuity of the tie-simplex parameterization, which was proven in earlier work. We demonstrate the efficiency and robustness of our "bypass'" strategy for the simulation of flow and transport in thermal, three-phase compositional models of heterogeneous reservoirs.

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We describe an Adaptive Compositional Space Parametrization (ACSP) method for compositional flow simulation. The method is based on casting the nonlinear governing equations, including those that describe the thermodynamic phase equilibrium, in terms of the tie-simplex (tie-lines for two-phase flow) space. The tie-simplex compositional space, which is a function of composition, pressure, and temperature, is then discretized using a limited number of tie-simplexes. The coefficients in the governing system of equations, including the composition, density, and mobility of the phases, are computed using multilinear interpolation in the discretized space. ACSP is different from the CSAT (Compositional Space Adaptive Tabulation) approach, which we have evolved over the last few years. In CSAT, the tie-line (tie-simplex) information, which is stored and updated adaptively, is used to accelerate the equation-of-state (EOS) computations in standard (e.g., natural variables) compositional reservoir simulators. This is why CSAT was used primarily to essentially replace the phase-stability test in the natural-variables formulation, but not the flash procedure. In ACSP, on the other hand, the full mathematical statement is cast in tie-simplex space and consistent discretization is applied directly. The ACSP framework is supplemented with a new tie-line based flash procedure that avoids the use of the Rachford-Rice equation. Thus, ACSP replaces all the standard EOS computations (phase-stability and flash). A grid refinement study of the ACSP method shows that the discrete formulation is convergent; more importantly, even for highly nonlinear near-miscible displacements, the number of tie-simplex needed is small.

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Primary oil recovery methods in Saskatchewan's heavy oil basin extract 5 to 10% of the available resource with the vast majority left in the ground and recoverable only through Enhanced Oil Recovery (EOR) methods. Traditional EOR generates steam in surface facilities and injects it underground to mobilize the oil for production with considerable energy losses inherent in the process. R.I.I. North America's Solvent Thermal Resource Innovation Process (STRIP) technology moves the steam generator underground, reducing the operating and capital costs of a surface thermal production facility by 30% and 50% respectively, and saving more than 30% of the energy typically required for thermal production. STRIP technology combusts methane to produce in situ CO 2 and steam. Because CO2 acts as a co-solvent, STRIP outperforms traditional steam-injection technology. This is demonstrated using a breakthrough modeling technique that couples fully compositional and thermal reservoir flow simulation capabilities. This new approach couples FlashPoint's equation-of-state solver for the multiphase, multi-component, isothermal, isobaric flash problem, GFLASH, with Stanford's Automatic Differentiation General Purpose Research Simulator for thermal reservoir flow simulations. This new computational framework exploits advanced techniques for skipping phase-identification computations and only uses exact phase equilibria from GFLASH when needed, reducing computational times by one to two orders of magnitude compared to the full rigorous solution.@en

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 How 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 mul-ticomponent 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 triangu-lated using Delaunay tessellation, and natural-neighbor interpola-tion 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 super-critical 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.

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Compositional formulations are necessary for numerical simulation of EOR (Enhanced Oil Recovery) processes, such as gas and steam injection. The coupling of the nonlinear conservation laws of multiphase flow and transport with the thermodynamic equilibrium relations poses significant challenges for compositional simulation. We describe a new framework, in which the thermodynamic phase behavior is cast in tie-simplex space as a function of composition, pressure and phase fraction. This parameter space is then used to specify the base nonlinear variables for fully-implicit compositional simulation. The compositional space is discretized using tie-lines. Thus, all the thermodynamic properties become piecewise linear functions in this space. The numerical implementation employs multilinear interpolation of the phase behavior using adaptively constructed tie-line tables. The computation of the phase behavior in the course of a compositional simulation then becomes an iteration-free procedure and does not require any EoS (flashes or phase-stability tests) computations. The efficiency and accuracy of the method are demonstrated for several multidimensional compositional problems for both miscible and immiscible displacements. For the tested problems, the proposed method reduces the computational cost of the thermodynamic calculations significantly compared with standard EOS-based approaches. Moreover, the method shows better nonlinear convergence behavior for nearmiscible gas injection displacements.@en

Compositional simulation is necessary for the modeling of complex EOR processes. For accurate simulation of compositional processes, we need to couple solution of nonlinear conservation laws for multicomponent multiphase flow and transport, with a system of equations describing the phase behavior of the mixture at q thermodynamic equilibrium. The complexity of the problem requires extensive computations and consumes significant CPU time. We present an efficient and robust framework for the computation of the thermodynamic phase behavior associated with multi-component multiphase flow in porous media. The method is based on adaptive interpolation of supporting tie-lines in compositional space. For the parameterization of full solution of a complex compositional problem we need only a limited number of supporting tie-lines in compositional space. We use a special approach for the adaptive construction of these tie-lines, depending on predefined precision. The parameterized tie-lines are triangulated using Delaunay tessellation, and natural-neighbor interpolation technique is used inside the supporting simplex. The computation of phase behavior for the composition simulation then becomes an iteration-free procedure and does not require any EoS computations. Based on this method, we developed a new nonlinear formulation for fully-implicit compositional simulation for both immiscible and miscible displacement. The treatment of nonlinearities, associated with complex thermodynamic behavior of the fluid, is based on the new set of unknowns - tie-line parameters, which allows for efficient representation of the subcritical region. For the supercritical region we use the standard compositional set of variables that based on the overall composition. A new criterion is proposed for the identification of changes between sub- and super-critical regions, and the robust variable substitution is applied during the simulation process. The efficiency and accuracy of the method is demonstrated for several multi-dimensional compositional problems of practical interest. For the tested problems, the proposed method significantly reduces the computational cost of the thermodynamic calculation compared with the standard EoS-based approach. Moreover, the method shows substantially better nonlinear convergence in the case of near-miscible gas injection simulation.@en

This paper presents an efficient methodology for the computation of the thermodynamic phase behavior associated with a multi-component multiphase flow in the porous media. The method is based on the interpolation of supporting points for both pressure and composition, adaptively computed in the tie-line space. For the parameterization of displacement curve, associated with the compositional process, only a limited number of supporting points in compositional space are needed, depending on predefined precision. Special techniques are used for the adaptive construction of supporting points, because of the complicated behavior of the solution route in the compositional space. The parameterized compositional space is triangulated using Delaunay tessellation and natural-neighbor interpolation technique is used inside the simplex. The following computation of phase behavior for the composition simulation is an iteration-free procedure and doesn t require any EoS calculations. Based on this method, we developed a new nonlinear formulation for general purpose compositional simulation for both immiscible and miscible displacement. Our numerical experience shows that the nonlinear behavior of the new formulation has some advantages in comparison with the standard approach. The one important advantage of the approach is the possibility for the direct analysis of the system of conservation law in the hyperbolic limit, since we can directly decouple characteristics, driven by thermodynamic behavior, with pressure and directly compute eigenvalues for each supporting simplex. The efficiency and accuracy of the method are demonstrated for several multi-dimensional compositional problems of a practical interest.

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