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The purpose of this paper is to present a detailed algorithm for simulating three-dimensional hydrocarbon reservoirs using the blackoil model.

The numerical algorithm uses a cell-centred structured grid finite volume method. The blackoil formulation is written in a way that an Implicit Pressure Explicit Saturation approach can be used. The flow field is obtained by solving a general gas pressure equation derived by manipulating the governing equations. All possible variations of the pressure equation coefficients are given for different reservoir conditions. Key computational details including treatment of non-linear terms, expansion of accumulation terms, transitions from under-saturated to saturated states and vice versa, high gas injection rates, evolution of gas in the oil production wells and adaptive time-stepping procedures are elaborated.

It was shown that using a proper linearization method, less computational difficulties occur especially when free gas is released with high rates. The computational performance of the proposed algorithm is assessed by solving the first SPE comparative study problem with both constant and variable bubble point conditions.

While discretization is performed and implemented for unstructured grids, the numerical results are presented only for structured grids, as expected, the accuracy of numerical results are best for structured grids. Also, the reservoir is assumed to be non-fractured.

The proposed algorithm can be efficiently used for simulating a wide range of practical problems wherever blackoil model is applicable.

A complete and detailed description of ingredients of an efficient finite volume-based algorithm for simulating blackoil flows in hydrocarbon reservoirs is presented.

The purpose of this paper is to present detailed algorithms for simulation of individual and group control of production wells in hydrocarbon reservoirs which are implemented in a finite volume-based reservoir simulator.

The algorithm for individual control is described for the multi-lateral multi-connection ones based on the multi-segment model considering cross-flow. Moreover, a general group control algorithm is proposed which can be coupled with any well model that can handle a constraint and returns the flow rates. The performance of oil production process based on the group control criteria is investigated and compared for various cases.

The proposed algorithm for group control of production wells is a non-optimization iterative scheme converging within a few number of iterations. The numerical results of many computer runs indicate that the nominal power of the production wells, in general, is the best group control criterion for the proposed algorithm. The production well group control with a proper criterion can generally improve the oil recovery process at negligible computational costs when compared with individual control of production wells.

Although the group control algorithm is implemented for both production and injection wells in the developed simulator, the numerical algorithm is here described only for production wells to provide more details.

The proposed algorithm can be coupled with any well model providing the fluid flow rates and can be efficiently used for group control of production wells. In addition, the calculated flow rates of the production wells based on the group control algorithm can be used as candidate solutions for the optimizer in the simulation-optimization models. It may reduce the total number of iterations and consequently the computational cost of the simulation-optimization models for the well control problem.

A complete and detailed description of ingredients of an efficient well group control algorithm for the hydrocarbon reservoir is presented. Five group control criteria are extracted from the physical, geometrical and operating conditions of the wells/reservoir. These are the target rate, weighted potential, ultimate rate and introduced nominal power of the production wells. The performance of the group control of production wells with different group control criteria is compared in three different oil production scenarios from a black-oil and highly heterogeneous reservoir.

The purpose of this paper is to present an efficient improved version of Implicit Pressure-Explicit Saturation (IMPES) method for the solution of incompressible two-phase flow model based on the discontinuous Galerkin (DG) numerical scheme.

The governing equations, based on the wetting-phase pressure-saturation formulation, are discretized using various primal DG schemes. The authors use H(div) velocity reconstruction in Raviart-Thomas space (RT_0 and RT_1), the weighted average formulation, and the scaled penalties to improve the spatial discretization. It uses a new improved IMPES approach, by using the second-order explicit Total Variation Diminishing Runge-Kutta (TVD-RK) as temporal discretization of the saturation equation. The main purpose of this time stepping technique is to speed up computation without losing accuracy, thus to increase the efficiency of the method.

Utilizing pressure internal interpolation technique in the improved IMPES scheme can reduce CPU time. Combining the TVD property with a strong multi-dimensional slope limiter namely, modified Chavent-Jaffre leads to a non-oscillatory scheme even in coarse grids and highly heterogeneous porous media.

The presented locally conservative scheme can be applied only in 2D incompressible two-phase flow modeling in non-deformable porous media. In addition, the capillary pressure discontinuity between two adjacent rock types assumed to be negligible.

The proposed numerical scheme can be efficiently used to model the incompressible two-phase flow in secondary recovery of petroleum reservoirs and tracing immiscible contamination in aquifers.

The paper describes a novel version of the DG two-phase flow which illustrates the effects of improvements in special discretization. Also the new improved IMPES approach used reduces the computation time. The non-oscillatory scheme is an efficient algorithm as it maintains accuracy and saves computation time.

This paper aims to introduce modeling, numerical simulation and convergence analysis of the problem of nanoparticles’ transport carried by a two-phase flow in a porous medium. The model consists of equations of pressure, saturation, nanoparticles’ concentration, deposited nanoparticles’ concentration on the pore-walls and entrapped nanoparticles concentration in pore-throats.

A nonlinear iterative IMPES-IMC (IMplicit Pressure Explicit Saturation–IMplicit Concentration) scheme is used to solve the problem under consideration. The governing equations are discretized using the cell-centered finite difference (CCFD) method. The pressure and saturation equations are coupled to calculate the pressure, and then the saturation is updated explicitly. Therefore, the equations of nanoparticles concentration, the deposited nanoparticles concentration on the pore walls and the entrapped nanoparticles concentration in pore throats are computed implicitly. Then, the porosity and the permeability variations are updated.

Three lemmas and one theorem for the convergence of the iterative method under the natural conditions and some continuity and boundedness assumptions were stated and proved. The theorem is proved by induction states that after a number of iterations, the sequences of the dependent variables such as saturation and concentrations approach solutions on the next time step. Moreover, two numerical examples are introduced with convergence test in terms of Courant–Friedrichs–Lewy (CFL) condition and a relaxation factor. Dependent variables such as pressure, saturation, concentration, deposited concentrations, porosity and permeability are plotted as contours in graphs, whereas the error estimations are presented in a table for different values of the number of time steps, number of iterations and mesh size.

The domain of the computations is relatively small; however, it is straightforward to extend this method to the oil reservoir (large) domain by keeping similar definitions of CFL number and other physical parameters.

The model of the problem under consideration has not been studied before. Also, both solution technique and convergence analysis have not been used before with this model.