A Three Dimensional, Three Phase Simulator With Strongly Oriented Field Features
Authors: Bansal P.P. , Harper J.L. , McDonald A.E. , Moreland E.E. , Odeh A.S. , Trimble R.H. 
Published: December 2007

Abstract
This paper describes ALPURS, a new three dimensional, three phase, strongly stable, black oil simulator. ALPURS is capable of modeling reservoirs with complex rock properties and well production/ injection controls. It can simulate reservoirs with large permeability contrasts, very active gravity segregation, and high flux rates. It rigorously adheres to well production/injection strategies which may be selected from a number of permissible options. The model couples the three phase flow equations with the constraints imposed on individual wells. It derives stability from a simultaneous solution for all unknowns. The paper presents the linearization of the non-linear finite difference equations and describes the solution of the resulting linear equations. Finally, it discusses various field oriented features of ALPURS and illustrates, by examples, two features important to several major reservoirs located in various parts of the world.

Introduction
ALPURS is a three dimensional, three phase, multiwell, black oil reservoir simulator which uses a strongly coupled, fully implicit method to solve simultaneously for all unknowns. Strong coupling requires that all cell and well equations for the entire grid system be solved simultaneously.
The principal use of ALPURS has been to model difficult problems such as high flux rates, gas resaturation, and gravity segregation. The original design called for a flexible, "user-proof" model which satisfies rigorously the individual well or well group constraints selected by the user. In addition to the usual features of constant voidage, constant rate, or fixed flowing bottom hole pressure, the model would be required to optionally produce wells or well groups at prescribed GOR, GLR, and WOR. The design also called for automatic selection of constraints in such a way that none could be violated. For example, the user should be permitted to operate a well at a fixed oil rate until a specified GOR is reached. At that time he might elect to shut in the well, or to operate at the specified GOR, or some alternate constraint. Similar options would be required for GLR and WOR. Any number of constraints could be requested simultaneously. The model would operate the well to satisfy all constraints. For physically contradictory ones the model would physically contradictory ones the model would terminate the job.
All design goals were met. The result is a simulator which handles difficult problems and production strategies without user intervention. production strategies without user intervention. There is no need for trial and error runs with varying well parameters to satisfy desired constraints.
ALPURS accounts for reservoir heterogeneity, rock compressibility, gravity, gas in solution in the oil and water phases variable bubble point pressure (gas resaturation), hysteresis in relative permeability data, tubing string pressure drop, and permeability data, tubing string pressure drop, and flash surface separation calculations. It is applicable to three dimensional, three phase studies. Fewer phases and/or dimensions can be modeled.
The utility of ALPURS is further enhanced by modern concepts of well flow equations. These include:
*The pseudo gas potential function * Skin factor to account for damage or improvement * Non-Darcy flow effect * Flow restriction due to restricted entry such as partial penetration * Effect of the shape of the well's drainage area and its location within the drainage area
ALPURS has been used to study three dimensional water and gas injection, above and below the saturation pressure, using CDC Cyber 172 and 175 computers. pressure, using CDC Cyber 172 and 175 computers.