Effect of the pseudotime function on gas reservoir drainage area determination

Abstract

The gas flow equation is normally linearized to allow the liquid solution of the diffusivity equation to satisfy gas behavior when analyzing transient test data of gas reservoirs. When wellbore storage conditions are insignificant, drawdown tests are best analyzed using the pseudopressure function. On the other hand, buildup pressure tests require linearization of both pseudotime and pseudopressure. It is not the case for the TDS technique which is indifferently applied to either drawdown or buildup tests. However, whichever the case, pseudotime has certain effect at very long testing times in formations of moderate to high permeability.  In this paper, we implemented the Tiab’s Direct Synthesis (TDS) technique, to include pseudotime effects, and observe its influence on the interpretation results of gas well test data at early and late time periods. New analytical equations to estimate reservoir permeability, wellbore storage coefficient, pseudoskin factor and reservoir drainage area are presented. Then, a comparison of results against rigorous time was carried out for simulated and field cases. We found acceptable results for permeability, pseudoskin factor and wellbore storage coefficient. However, for the case of reservoir drainage area, the deviation error was of 4,1% for a simulated case and 17,9% for a field case. However, the smaller of these deviations may be small if related to pressure transient analysis results. However, this deviation in a gas reservoir with reserves of one tera standard cubic feet is equivalent to a huge difference of 38 gigas of standard cubic feet of gas which may have an economic impact to any oil company.