Petroleum Reservoir Simulation

Simulation of multiphase flow in heterogeneous two-porosity reservoirs such as naturally fractured systems is a difficult problem. In the last several years much progress has been made in this area. This paper focuses on the practical aspects of that technology. It describes a stable, flexible, fully implicit, finite-difference simulator in heterogeneous, two-porosity reservoirs. Flow rates and wellbore pressures are solved simultaneously along with fracture and matrix fluid saturations and pressures at all grid points. Hydrodynamic pressure gradient is maintained at formation perforations in the wellbore. The simulator is accurate enough to match analytical solutions to single-phase problems. The equations have been extended to include polymer flooding and tracer transport with nine-point connection for determining severe local channeling and directional tendencies. It is shown that the two-porosity model presented in this paper will produce essentially the same answers as the common single-porosity model of a highly heterogeneous system but with a substantial reduction of computing time. In addition, this paper describes in detail several two-porosity parameters not fully discussed in previous publications.

Improvements in Simulation of Naturally Fractured Reservoirs

Quantitative analysis of saltwater-freshwater relationships in groundwater systems—A historical perspective

This paper deals with a new implicit method for reservoir simulation. Rather than provide a fixed degree of implicitness in every gridblock at every time step or iteration, the adaptive implicit method operates with different levels of implicitness in adjacent gridblocks. These levels shift in space and time as needed to maintain stability. Shifting is accomplished automatically without user intervention. The technique can be applied to any simulation problem involving N unknowns. The advantage is substantial reduction in computing time and storage requirements compared to fully implicit formulations, while still yielding unconditionally stable solutions. The mathematical procedure involves labeling the implicit/explicit mix of unknowns and then composing the matrix problem. The latter is reducible as long as there is one or more unknowns to be computed explicitly; consequently, appropriate operations are performed to put it in reduced form. This leads to matrix equations of lower order than the original problem that are solved at less cost. Finally, applications to a three-phase coning problem and a three-dimensional (3D) Cartesian problem are presented.

Reservoir Simulation Using an Adaptive Implicit Method

This paper describes a robust and efficient method for solving the equations corresponding to an equation-of-state (EOS) compositional model. The method is developed for an adaptive-implicit simulator in which only a small number of blocks need to be solved implicity while the remaining blocks are solved explicitly. The salient features of the method are decoupling of the solution of flow equations from the flash calculations and switching from explicit to implicit formulations on the basis of a stability criterion. The performance of the adaptive-implicit approach is compared with that of a fully implicit approach and an explicit-transmissibility approach. Results show that the adaptive-implicit approach is two to three times facter than the other two methods

An Efficient Approach to Adaptive- Implicit Compositional Simulation With an Equation of State

The study describes a strongly coupled formation and discusses its utility in relation to other implicit models. The linearization of the nonlinear finite difference equations and solution of the resulting linear equations are discussed. Field applications are included to show the utility of user-supplied production constraints in determining well performance. 13 refs.

A Strongly Coupled, Fully Implicit, Three-Dimensional, Three-Phase Well Coning Model

A Strongly-Coupled, Implicit Well Coning Model

Efficient Use of Mass Storage During Elimination for Sparse Sets of Simulation Equations

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Papers

A Strongly Coupled, Fully Implicit, Three-Dimensional, Three-Phase Well Coning Model

A Strongly-Coupled, Implicit Well Coning Model

Efficient Use of Mass Storage During Elimination for Sparse Sets of Simulation Equations