Grand Forks - Modelling a Three-Dimensional Reservoir With Two-Dimensional Reservoir Simulators
Authors: Stright D.H. 
Published: March 2010

Abstract
The purpose of this paper is to discuss techniques that can be used to simulatea three-dimensional reservoir using two-dimensional reservoir simulators. Thetechniques were applied in a two-dimensional areal simulation of waterfloodingin the Grand Forks Lower Mannville D Pool to account for gravity segregationand water coning phenomena.
A coning correlation was developed for the range of rates expected in the arealmodel using a two-dimensional radial coning model. The coning correlation andpseudo relative permeability curves for modelling vertical segregation wereincorporated into the areal model to match reservoir history and predictwaterflood performance. The predicted water-oil ratios using the coning'correlation appear to be reasonable when compared with the water-oil ratioscalculated using the laboratory relative permeability curves – the usualassumption in areal modelling. It is concluded from this study that it ispossible to generate pseudo relative permeability curves to approximate waterconing in areal simulation of a three-dimensional reservoir. In developingthese curves velocity sensitivity should be evaluated.

Introduction
NUMERICAL SIMULATION MODELS are currently available to most reservoir engineersfor simulation of oil and gas reservoir performance. In studying a reservoir.where numerical simulation is justified, the engineer must first select theappropriate model. The model selected could vary from a one-dimensionalsingle-phase model to a three-dimensional, fully compositional model.
Generally, study costs are directly proportional to the number of dimensionsand phases or components modelled; therefore, in the case of athree-dimensional problem it is desirable to use a two-dimensional simulatorproviding, of course, that three-dimensional performance can be adequatelyapproximated.
In simulating three-dimensional performance with two-dimensional areal models, flaw and fluid distribution in the vertical direction and individual wellperformance must be approximated. Several authors(1–3) havesuggested using pseudo relative permeability and pseudo capillary pressurecurves in two-dimensional areal models to approximate flow and fluiddistribution in the vertical direction. However, except for van Poollen etal.(4) who discussed correspondence been model and measuredpressures, none of these investigations were concerned with approximatingindividual well performance in areal models.
Modelling individual well performance is perhaps the most difficult problemencountered in two-dimensional areal simulation of a three-dimensional problem.Initial bottom water, slumping or under-running of injected water can result inwater caning, which is difficult to simulate on two-dimensional areal orthree-dimensional models because block geometry does not adequately definesaturation or pressure distribution near the wellbore. Coning behaviour is bestsimulated with two-dimensional radial coning models, which, unfortunately, cannot predict areal conformance.
Mrosovsky and Ridings(7) suggested coupling a three-dimensionalmodel and a radial coning model to simulate coning in a field-wide study. Thisapproach would probably be prohibitively expensive for simulation studies withlarge numbers of wells. One could use analytical approximations such as theradial flow equation or correlations proposed by Sobosinsky(8) or Telkov(9) to approximate coning behaviour. However, to model coningthese approximations must be calibrated to actual field performance forreliable results.