Numerical Simulation of Coning Using Implicit Production Terms

Publisher Website
Google Scholar
Abstract
This paper describes the use of a multiphase, multidimensional mathematical model to predict two- and three-phase coning behavior. Severe computational instability in the form of saturation oscillations in grid blocks near the wellbore is commonly encountered in the mathematical simulation of coning. This instability is due to the explicit (dated at the beginning of a time step and held constant for that time step) handling of saturation - dependent transmissibilities and production terms in the finite-difference solution of production terms in the finite-difference solution of the flow equations. An analysis of stability with respect to explicit handling of saturation-dependent transmissibilities is presented in this paper. This analysis shows why explicit transmissibilities can result in a severe time-step restriction for coning simulation. The use of implicit production terms in the difference equations to reduce instabilities is discussed and examples are given. These examples show that the implicit handling of production terms alone can result in a fivefold increase and permissible time step for a coning simulation with virtually no increase in computing time per time step. A laboratory water-coning experiment was simulated and excellent agreement was obtained between computed and observed results. A three-phase coning example for a gravity-segregation reservoir is also presented. Introduction Simulation of coning behavior is normally done by numerically solving the flow equations expressed in cylindrical (r, z, theta) coordinates with symmetry in the theta direction. The finite-difference technique of numerical solution of differential equations requires that the portion of the reservoir being simulated be divided into grid blocks as shown in Fig. 1. Since coning is a well phenomenon and not a gross reservoir phenomenon, the grid blocks must necessarily be relatively small in the vicinity of the wellbore because both pressures and saturations vary rapidly in this region. Severe computational instability is commonly encountered in the simulation of coning due to the relatively small grid-block sizes and high flow velocities in the vicinity of the wellbore. During a time step that would be considered normal for most reservoir simulation problems, a block near the wellbore is required to pass a volume of fluid many times its pore volume. SPEJ P. 257

This publication has 0 references indexed in Scilit: