Summary

An efficient approach to compositional simulation is described. Application to micellar/polymer flooding resulted in a significant saving in computation time. A new method was developed to impose precisely the outflow boundary condition arising from continuity of flux across the reservoir/wellbore interface. In a manner analogous to classic well models, the above condition was used to define produced concentrations from the wellblock concentrations. Effects of numerical dispersion in multidimensional, multiphase, multicomponent flow and the effectiveness of a dispersion control scheme are also discussed.

Introduction

The basic equations that describe isothermal, multiphase, multicomponent flow in permeable media are the speciesconservation equations and an overall mass-continuity equation. With these as governing equations, several simulators have been developed during recent years to model compositional phenomena in petroleum reservoirs. Much of our effort on chemical flooding simulation has focused on consistent and accurate treatment of physical properties and phase relationships. With our properties and phase relationships. With our significantly expanded capability to model physical properties and extension to three dimensions (3D), computer run times have become very significant. Also, several difficulties associated with the numerical implementation of the equations and associated boundary conditions continue to persist. For example, there is no general method to persist. For example, there is no general method to impose the outflow boundary condition arising from continuity of flux across the reservoir/wellbore interface accurately. Particularly in the source/sink representation of wells, the produced composition, as a general rule, is taken to be identical with the composition of the fluid in the gridblock containing the well. This scheme is approximate at best and may be inadequate when the gridblocks are large and/or the well is not located at the center of the block. Numerical dispersion in the finite-difference solution of convection/diffusion-type equations significantly alters calculated quantities that are of interest in reservoir studies. Several schemes have been suggested to control numerical dispersion. However, their application to multidimensional, multicomponent, multiphase flow remains limited and largely unreported. Our objective in this paper is three-fold. First, we highlight certain properties typically associated with the equations in compositional simulation and how these properties translate into the difference equations and the resulting matrices. We show that suitable formulation allows us to use a highly efficient solution algorithm, leading to a significant saving in computation time and storage. Second, we describe a general scheme to impose the outflow boundary condition accurately. This method can be used to obtain the production composition even when the well is located arbitrarily within the gridblock. Finally, we extend a previously reported dispersion control scheme to multidimensional, multiphase, multicomponent flow. The effectiveness of the scheme has been demonstrated by specific applications to micellar/polymer flooding.

Mathematical Formulation

The general species conservation equation in permeable media can be written in the form:

------ + =r, .............................(1a)

where accumulation is

Ck=, ................(1b)

flux is

=, ................(1c)

and source is

, =, ...............(1d)

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