In the performance evaluation of any reservoir, a knowledge of the pattern of fluid flow within the reservoir is essential. This is especially true in the case of reservoirs under waterflood, where an analysis of injected fluid migration within the porous medium is very important. Hence, reservoir simulation has become a valuable tool for reservoir engineers, allowing them to gain greater insight into fluid flow within the reservoir. If properly conducted, a simulation study can aid in Optimizing depletion by answering many specific questions related to a given reservoir.
This paper describes a single phase, two-dimensional, compressible front tracking model for microcomputers, which can be used to simulate waterfloods. It can be used for any type of heterogeneous reservoir with variable thickness, permeability, porosity and flow boundaries.
A complete discussion of the mathematical model, operating logic of the program, and sensitivity to input data is provided. Also, a listing of the program in FORTRAN is included. Anyone with access to a microcomputer can use the program to analyze the anticipated pattern of injected fluid migration within the reservoir as a function of time.
There are many sophisticated reservoir models on the market which could be used to simulate fluid flow within a given reservoir; however, the costs of running these models are high and in some instances cannot be justified.
Furthermore, the availability of good reservoir data is essential for use of these simulators.
Otherwise, the results obtained from a sophisticated model may not necessarily be superior to those obtained by a simpler and less expensive one. The model described in the paper is a simple two-dimensional, single phase, slightly compressible, block centered, finite difference, front-tracking model, which can be applied to one or two-dimensional problems involving steady state or transient flow.
The front tracking model is made up of two parts. The first part calculates a steady state pressure distribution within the reservoir. This is influenced by well geometry, rates, and the formation permeability-thickness distribution. The second part moves the water front through the reservoir around each injection well. The model assumes a unity mobility ratio between water and oil. Fluid movement is based on velocity calculations. Velocities are calculated from the knowledge of permeability, porosity, viscosity and pressure gradients. The velocity calculations are then used to establish the flood front.
To use the model, a study area is subdivided into a series of rectangular cells or grids (Fig. 1A). Smaller grid size results in better flood front resolution. The size of the grid is chosen to minimize the total cell count in the area. The wells are located in the center of appropriate cells based on their position in the field in order to give sufficient definition to the pressure solution. Formation properties and fluid saturations can be varied by grid, or can be constant for a given area. Some of the input data required includes thickness, permeability, porosity, viscosity, water saturation, fraction of oil displaced, and production and injection rates. The required input data are discussed in later sections.