Modeling Technique For Throughput Rate Calculations Of Injection Operations
Authors: Reeves John L. 
Published: December 2007

Abstract
This paper describes the use of an electrical analog model to determine throughput rates. The technique is particularly valuable for adjusting (at unity mobility ratio) approximate equations to use for predicting throughput rates of systems with non-unity mobility ratios and/or irregular areal geometry and/or non-uniform permeability-thickness values.
The model is easily constructed and rapidly run. It consists of a sheet of carbon-impregnated paper cut to the areal shape of the reservoir, with nails driven through the paper representing the injection and producing wells. The electrical resistance of the model is converted to reservoir resistance by an equation developed using the analogy between electrical flow and fluid flow. The reservoir resistance so obtained is used to calibrate an empirical reservoir resistance equation. The variations of throughput rate during the injection operation are determined from this calibrated equation by introducing into the various segments of the equation the mobilities existing in those segments at given stages of advance of the injected material front.

Introduction
For predicting the performance of injection operations, it usually is necessary to know the variations in throughput rate which occur during the life. (Throughput rate can be defined as the steady state total rate of all fluids flowing which can be produced from a particular well pattern by imposing a given pressure drop. In magnitude it is equal to the pressure drop across the system divided by the total resistance of the system.)Mathematical equations of pattern resistance are available for predicting throughput rates of injection patterns composed of infinite arrays of regular geometry, such as five-spots and nine-spots.
However, such equations generally are not sufficient to define the throughput rates of real situations. Irregular patterns (such as peripheral injection schemes) for which equations are not available often are used. Even regular developments such as five-spots and nine-spots usually have irregular geometry because of the influence of field limits and missing inside locations. Also, the mathematical equations are for a mobility ratio of unity; that is, for situations where the mobility behind the injection front is the same as the mobility ahead of the front. Further, the mathematical equations require that average values of permeability and thickness be used to characterize all areas of the reservoir.
This paper describes a modeling technique that quickly calibrates (at unity mobility ratio) throughput rate equations for irregular patterns. The adjusted equations are in such form that mobility, permeability, and thickness differences can be introduced.
In this approach, approximating throughput rate equations first are developed. The electrical resistance of the pattern to be studied then is determined on the model. Next, the measured electrical resistance is converted to reservoir resistance using the analogy between electrical flow and fluid flow in the reservoir. The model results the are used to calibrate the approximating throughput rate equations, at unity mobility ratio. Finally, the throughput rate variations which occur during the progress of the flood are calculated from the calibrated equations.