Methods for Numerical Simulation of Water and Gas Coning

This paper describes and evaluates three numerical methods for the simulation of well coning behavior. The first method employs the implicit pressure-explicit saturation (IMPES) analysis with pressure-explicit saturation (IMPES) analysis with the production terms treated implicitly. The second technique is similar to the first model except that the interblock transmissibilities are also treated implicitly in the saturation equation. The third model is fully implicitly with respect to all variables in a manner qualified in the introduction and utilizes simultaneous solution of the difference equations describing the multiphase flow. The use of implicit transmissibilities in the IMPES model results in a several-fold increase in the allowable time-increment size over that attainable with the implicit production IMPES scheme, while the computing time per step is increased by less than 10 percent. The fully implicit model accepts larger time-increment sizes than possible with the first two methods but requires 3.3 times the computing time per time step needed by the second model. The fully implicit model is substantially more efficient for problems involving high capillary forces (treated explicitly in the IMPES methods) and small computing grid blocks at the wellbore. In problems involving moderate capillary forces and larger grid spacings, the fully implicit method and the implicit transmissibility IMPES technique are comparable in computing efficiency. The results of three coning studies are presented: a water-oil problem, a three-phase coning presented: a water-oil problem, a three-phase coning example, and a comparison of simulation results with a laboratory coning experiment. Also presented is an analysis of truncation error and a comparison of computational work requirements. Introduction This study was performed to evaluate three finite-difference schemes for simulating well coning behavior. The basis for this evaluation was the IMPES (implicit pressure-explicit saturation) model with explicit transmissibilities and implicit production terms. This model is referred to hereafter production terms. This model is referred to hereafter as Model 1. The next model evaluated in this work is an IMPES model similar to Model 1, except that the saturation-dependent interblock transmissibilities are treated implicitly rather than explicitly in the saturation equation. The third model is fully implicitly with respect to all variables and terms transmissibilities, pressure, saturation an capillary pressure - and utilizes simultaneous solution of the difference equations describing the multiphase flow. These two models are referred to hereafter simply as Model 2 and Model 3. For the purpose of clarity all models are described in purpose of clarity all models are described in reference to the problem of incompressible, two-phase flow. The techniques are equally applicable, however, to compressible, three-phase flow models. The examples chosen for illustration employ both incompressible and compressible simulation models. SPEJ p. 425