Analytical Representation of the van Everdingen-Hurst Aquifer Influence Functions for Reservoir Simulation
Abstract Linear regression analysis has been used to develop some simple analytical expressions for the van Everdingen-Hurst aquifer influx influence functions. Regression results are presented for a variety of aquifer radius/reservoir radius ratios. The regression equations are designed for use in reservoir engineering applications, especially reservoir simulation. Introduction A reservoir-aquifer system can be modeled by using a reservoir simulator in which small gridblocks define the reservoir and increasingly larger gridblocks define the aquifer. This approach has the disadvantage of increased computer storage and computing time requirements because additional gridblocks are needed to model the aquifer. A widely used and more cost-effective means of representing an aquifer is to compute aquifer influx with an analytical model. Among the more popular analytical aquifer models in use today is the Carter-Tracy modification of the van Everdingen-Hurst unsteadystate aquifer influx calculation. The Carter-Tracy aquifer influx rate calculation requires information about dimensionless pressure p and its first derivative P as functions of dimensionless time t . Usually, the relationship between t and p is available in the reservoir simulator in tabular form for the infinite acting constant terminal rate case only. The program determines p and p for a given t by using a numerical program determines p and p for a given t by using a numerical interpolation scheme. An alternative approach that requires less computer work while providing equivalent or greater accuracy than the table look-up method is presented here. Description of Method A linear regression analysis has been used to develop analytical representations of the Carter-Tracy influence functions. The regression equations, the regression coefficients, correlation range limits, and measures of the linear regression validity are presented in Table 1 for a number of commonly encountered r/r cases. Plots of these expressions are shown in Figs. 1a and 1b. JPT P. 405