We apply Massively Parallel Interface for MPFA-O scheme with state-of-the-art Operator-Based Linearization (OBL) approach for multiphase flow in porous media. The implementation of MPFA-O scheme enhances the modelling capabilities for non-K-orthogonal mesh. A fully implicit scheme is applied to guarantee the stability of solutions when a mass-based formulation is involved to keep the flexibility of the framework for general-purpose reservoir simulation. As the MPFA-O introduces more non-zeros elements in the Jacobian matrix than the traditional TPFA, massively parallel computations via Message Passing Interface (MPI) in this work help to guarantee competitive computational efficiency for high-fidelity geological models. Concerning the Jacobian assembly hassle, we apply the OBL approach which introduces operators combining the fluid and rock properties in the conservation equations and discretizes the operators in the physical parameter space. By computing values and derivatives of the operators via a multilinear interpolation, the assembly of Jacobian matrix and residual vector could be drastically simplified. Another benefit of the OBL is that by only evaluating operator values on the predefined nodes in the physical parameter space, the overhead related to complex phase behavior and property evaluation is significantly reduced. In the end, we present several benchmark cases to rigorously demonstrate the accuracy, convergence, and robustness of the framework and two challenging field-scale cases to further prove its computing performance and parallel scalability.

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The properties of fluids flowing in a petroleum reservoir are quantified by understanding the thermodynamic behavior of each flowing phase in the system. This work describes proper techniques to formulate and execute a thermodynamic model for accurately predicting the equilibrium behavior of oil-gas-brine systems within the practical range of pressure and temperature. The three-phase flash algorithm is validated against published data from the available literature. The multiphase flash procedure is implemented to generate linearized physical properties by using an Operator Based Linearization (OBL) modelling technique allowing for a combination of multiple complex physics in the nonlinear solution of governing equations. This is the first implementation of three-phase flash calculations for hydrocarbons and brines based on fugacity-activity models coupled with an advanced highly efficient linearization scheme. Our approach increases the efficiency and flexibility of the modelling process of physical phenomena such as fluid flow in porous subsurface reservoirs.@en

The continuous progress of reservoir monitoring technology provides encouraging capacities to reduceuncertainties in the subsurface characterization and to mitigate risks in field development applying thereservoir simulation approach. However, it is always challenging to take full advantage of the observationdata, since an accurate representation of strong heterogeneities requires a high-resolution grid. Most ofthe discretization methods cannot handle full tensor permeability, and high nonlinearity introduced bycomplex physical process drastically reduces simulation efficiency. In this work, we develop an advancedparallel framework for reservoir simulation with the implementation of state of the art discretizationand linearization methods. We apply the multipoint flux approximation (MPFA) method to handle thefull tensor permeability in unstructured grids. To keep the fidelity of the geological model and improvecomputational efficiency, we use massively parallel computations via Message Passing Interface (MPI).Complex subsurface physics is described by mass-based formulations making the framework flexible forgeneral-purpose reservoir simulation. However, the representation of phase behavior introduces additionalworkload when compared with the phase-based formulations in the traditional approach. Here, we apply theOperator-Based Linearization (OBL) approach which not only overcomes this drawback but also turns it toan advantage. In this method, the conservation equations are described in an operator form. By constructinga library of tabulated operators, the repeated work spent on complex phase behavior and property evaluationcan be significantly reduced. We benchmark the parallel framework with analytical solutions under single-phase flow and multiphase flow. The results demonstrate that the parallel framework provides accuratesimulation results for structured and unstructured grids. We validate that MPFA implemented in our parallelframework converges to real solutions when the permeability is a full tensor. Besides, several realisticcases have been rigorously tested confirming high computational capacity, efficiency, and accuracy of theadvanced massively parallel framework for general-purpose reservoir simulation. With the implementationof MPFA and OBL approaches, the parallel framework is fully equipped for the simulation of problemswith full tensor permeability, high-heterogeneities, and complex physical processes.

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We present a new fully-implicit, mixed-hybrid, finite-element (MHFE) discretization scheme for general-purpose compositional reservoir simulation. The locally conservative scheme solves the coupled momentum and mass balance equations simultaneously, and the fluid system is modeled using a cubic equation-of-state. We introduce a new conservative flux approach for the mass balance equations for this fully-implicit approach. We discuss the nonlinear solution procedure for the proposed approach, and we present extensive numerical tests to demonstrate the convergence and accuracy of the MHFE method using tetrahedral elements. We also compare the method to other advanced discretization schemes for unstructured meshes and tensor permeability. Finally, we illustrate the applicability and robustness of the method for highly heterogeneous reservoirs with unstructured grids.

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We present a fully implicit mixed hybrid finite-element (FE) formulation for general-purpose compositional reservoir simulation. The formulation is locally conservative, and the momentum and mass balance equations are solved simultaneously; including Lagrange multipliers on element interfaces. The method utilizes automatic differentiation for the Jacobian construction. This hybrid FE approach accommodates unstructured grids, and we present black-oil and compositional test cases with permeability tensors. We also discuss the accuracy and computational efficiency for the new formulation. For all tests, we compare the performance and accuracy of the proposed approach with the Multi-Point Flux Approximation (MPFA-O) method.@en