A Unified Treatment of the Effects of Wellbore Storage and Variable Sandface Flowrate on Gas Well Drawdown and Buildup Analysis

Abstract

This Paper is Subject to Correction American Institute of Mining, Metallurgical, and Petroleum Engineers Inc. Abstract A unified method for analyzing drawdown and buildup data for permeability, non-Darcy coefficient, and skin factor is presented. The method account for wellbore storage and variable sandface flow rate. Drawdown/buildup data for two rates from an experimental reservoir are analyzed with this method. The parameters obtained from that analysis were used in a mathematical reservoir simulator to generate a pressure-time history which matched the experimental history within 3 psi over the test period, thereby demonstrating the compliance of the experimental reservoir with accepted principles of compressible fluid flow in porous principles of compressible fluid flow in porous media. Introduction For several years we have been performing drawdown and buildup experiments using an apparatus which is a physical analog of a gas reservoir with a single, centrally located, production well. Although care has been taken to preserve dimensional similarity between our "model" reservoir and a actual reservoir wherever possible, the model necessarily has a larger well storage volume/surface flow rate ratio than its real counterpart because the equipment for measuring pressure and rate, and the valves used on the model apparatus cannot be built to dimensional scale. Also, attempts to control the model reservoir flow rate have been thwarted because of the storage volume associated with the apparatus. Thus, to analyze the model drawdown and buildup data we must take particular care to correct the data for wellbore particular care to correct the data for wellbore storage and variable sandface rate effects and have developed a procedure for doing this. This procedure has utility for reducing field test data procedure has utility for reducing field test data as well as our experimental model data. A number of papers have treated these effects-those of Ramey and Odeh and Jones cite most of the other relevant papers and present a good theoretical basis for the method presented here. Our paper unifies previous theory—presenting detailed procedures for properly analyzing drawdown and buildup data taken under variable flow rate conditions with appreciable wellbore storage present. The procedures are demonstrated by present. The procedures are demonstrated by applying them to data for two rates acquired from our experimental model. The values obtained for permeability and skin factor from this analysis permeability and skin factor from this analysis are used in a mathematical reservoir simulator to generate pressure-time histories for the experimental sandface rate-time history. Comparison of these computed pressure-time histories with those measured experimentally demonstrate the degree of compliance of the experimental reservoir with accepted principles of compressible fluid flow in porous media. porous media.