Mathematical Simulation of Polymer Flooding in Complex Reservoirs

Abstract

Abstract Simulation of polymer flooding in many complex reservoirs has requirements that preclude the use of either three-phase stream tube or two-phase finite-difference simulators. The development of a polymer flooding model used in a three-phase, polymer flooding model used in a three-phase, four-component, compressible, finite-difference reservoir simulator that allows the simulation of a variety of complex situations is discussed. The polymer model represents the polymer solution as a fourth component that is included in the aqueous phase and is fully miscible with it. Adsorption of polymer is represented, as is both (1) the resulting permeability reduction of the aqueous phase and (2) the resulting lag of the polymer injection front and generation of a stripped polymer injection front and generation of a stripped water bank. The effects of fingering between the water and polymer are taken into account using an empirical "mixing parameter" model. The resulting simulator is capable of modeling reservoirs with nonuniform dip, multiple zones, desaturated zones, gravity segregation, and irregular well spacing and reservoir shape. Two examples are presented. The first illustrates the polymer flooding of a multizone dipping reservoir with a desaturated zone due to gravity drainage. The second illustrates the flooding of a reservoir with a gas cap and an oil rim with polymer injection near the oil-water contact. In this example, the effects of nonuniform dip, irregular well spacing and field shape, and gravity segregation of the flow are all taken into account. The two examples presented illustrate the versatility of the simulator presented illustrate the versatility of the simulator and its applicability to a wide range of problems. Introduction The design of a polymer flood for a complex reservoir requires a model that represents the reservoir features that have a significant effect on the performance of the flood. These features may include the presence of a gas cap or a desaturated zone due to gravity drainage in a dipping formation, the presence of an aquifer, irregular well spacing and reservoir boundaries, multiple zones, reservoir heterogeneities, and a well performance that is limited by state proration, injectivity, and productivity. These reservoir features are being productivity. These reservoir features are being represented by most compressible, three-phase, three-dimensional simulators. However, to model polymer flood projects, it is necessary to include a polymer flood projects, it is necessary to include a conservation equation for the polymer, and to represent the adsorption of polymer, the reduction of be rock permeability to the aqueous phase after contact with the polymer, the dispersion of the polymer slug, and the non-Newtonian flow behavior polymer slug, and the non-Newtonian flow behavior of the polymer solution. PREVIOUS SIMULATOR DEVELOPMENT PREVIOUS SIMULATOR DEVELOPMENT Previous simulator development of polymer flooding has been reported in two different general categories: three-phase stream tube models and one- or two-phase, incompressible, finite-difference simulators. Jewett and Schurz developed a two-phase, multilayer Buckley-Leverett displacement simulator capable of modeling either linear or five-spot patterns. A mobile gas saturation also could be patterns. A mobile gas saturation also could be specified, but this was treated as void space and did not affect the flow characteristics of the system. Gravitational and capillarity effects were neglected. The residual resistance of the brine following a water slug was modeled as an increase in its viscosity; the viscous fingering of the brine through the polymer slug was treated by altering empirical relative permeability relationships to specify a more adverse mobility ratio. Slater and Farouq-Ali modeled five-spot patterns with a two-phase, two-dimensional, finite-difference simulator, neglecting gravity and capillarity. They obtained an empirical expression for the resistance factor of the porous medium as a function of a time-dependent mobility ratio. SPEJ P. 369