A Strongly Coupled, Fully Implicit, Three Dimensional, Three Phase Reservoir Simulator
Authors: Bansal P.P. , McDonald A.E. , Moreland E.E. , 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/infection 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 that may be production/injection strategies that 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 the nonlinear 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 that 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. Appendix B gives a proposed terminology to categorize reservoir simulators, including a definition of strong coupling.
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 that 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 bottomhole 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 night 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 terminate the job.
All design goals were met. The result is a simulator that 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 enhanced further 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, and 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.
The strongly coupled method is computationally more expensive than a sequential formulation. But it has several offsetting advantages. Increased stability permits larger time steps than for sequential methods, especially far difficult problems. The coupling of the well constraints problems. The coupling of the well constraints yields a more reliable model than previously reported in the literature.