A numerical simulation of pressure distribution and radius of drainage in infinite radial aquifers - constant rate case
"The diffusivity equation for the transient flow of slightly-compressible liquids has been solved for infinite radial aquifers, subject to constant terminal rates, by employing a Romberg integration of the Van Everdingen - Hurst explicitly solution over the transformed integral limits for .01<TD<̲500. For the dimensionless times of .01>̲TD>500, the classical solutions presented by Carslaw and Jaeger, Mortada, Theis, and others are incorporated in the digital analysis to yield dimensionless pressures for 40 selected dimensionless radius (RD) ratios between 1 and 64 for dimensionless time values of .0005 to 1000.0. A new expression for dimensionless pressure-distribution, PD'(RD, TD), as a fraction of well bore pressure drop is presented with cross plots of the results obtained. These plots permit the solution of field problems involving PD', RD, and TD without the aid of the computer and without interpolation. A radius of drainage relationship for an infinite radial aquifer is developed from the least squares polynomial curve fit of PD' = .01. additionally, an on-line mapping technique is presented which permits the aquifer pressure distribution to be displayed graphically on the I.B.M. 360/50 On-Line Printer"--Abstract, page ii.
Missouri University of Science and Technology
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