Dykstra Parsons Water Flood Theory Adapted to Chemical Flood Modelling

Abstract

The method of Dykstra-Parsons, originally developed to model water flood performance, has been adapted to screen reservoirs for their Chemical / Polymer Flood suitability.Firstly, this paper summarises Dykstra-Parsons' Theory alongside an automated method of tuning reservoir layer properties to [pre-chemical] water flood performance.(Methods of determining both layer permeability and oil-phase relative permeability end-points, from water-cut development, are presented.)Secondly, this paper describes the adaptation of Dykstra-Parsons' Water Flood theory to model both chemical flood and post-chemical flood production performance.Permeability adjustment, mobility control, and alkaline-surfactant flood models are discussed. Introduction Dykstra-Parsons' theory, governing the recovery of oil by water flood, has been well documented (ref 1, 2, 3).This theory is versatile but underutilised since the advent and proliferation of finite-difference reservoir simulation.More than fifty years on, however, Dykstra-Parsons remains an efficient yet rigorous method of modelling both water flood and chemical flood performance. Historically, techniques described by authors such as Stiles, Buckley-Leverett, and Welge (ref 2, 3) were integrated in order to model water flood performance via a fractional flow equation.Most importantly these techniques offered a link between: a geological model (albeit one dimensional); an oil in-place volume; and, water flood performance.Certain reservoir conditions must be met for these classical theories to be entirely honoured (ref 2, 3):Steady state flood conditions; voidage-replacement is maintained and the flood is operated above the bubble point pressure (true for many commercial water floods)Diffuse flow - meaning that fluid saturations at any point in the displacement path are uniformly distributed with respect to reservoir thickness. This condition requires either:capillary and gravity forces to be small relative to both high injection and production rates - true for many commercial water floods; or,low rates coupled with the vertical extent of any capillary pressure zone greatly exceeding reservoir thickness (a rarer condition for commercial water floods).The Stiles method of generating pseudo-relative permeability from reservoir layer properties assumes that the mobility ratio is unity.Dykstra-Parsons' theory assumes that reservoir layers flood-out in flow-velocity order. Dykstra-Parsons' theory offers an advantage compared to Stiles in that it is applicable for all mobility ratios (ref 3):Where M < 1 the velocity of frontal advance in each layer will be reduced as the flood progresses, which tends to stabilise the macroscopic flood frontWhere M > 1 the velocity of frontal advance in each layer increases as the flood progresses which promotes instability in the macroscopic flood front. This universal applicability is beneficial when considering that most chemical floods are initiated in order to correct an unfavourable mobility ratio. One misconception is that these classical theories do not apply should a water flood have:significant capillary pressure; or,a vertical permeability and geometry favourable to gravity slumping.This is not the case.In practical terms these theories only require the vertically-acting fluid-redistributive effects, such as capillary pressure and gravity, to be small relative to Darcy or viscous forces in order to remain applicable.It was noted by C. L. Hearn (ref 4) that: "Gravity and capillary forces are neglected and the vertical fluid saturation distribution is assumed to be controlled by viscous flow forces resulting from the vertical permeability variation.The success of stratified reservoir models in simulating waterflood performance indicates that this concept is often reasonable."

The Modification of the Dykstra-Parsons Method for Inclined Stratified Reservoirs

“…Much interest has been shown recently in the application of the Dykstra-Parsons method to chemical flooding, especially for polymer injection (Mahfoudhi and Enick 1990;Morrison 2005). The method has also been used with streamline simulation, which simplifies the computations significantly.…”