Semi-analytical methods for the analysis and interpretation of well test data distorted by wellbore storage and skin effects

Abstract

Our objective is to develop approximations of the pressure-time behavior for use in analyzing the pressure response of a well in an infinite-acting reservoir influenced by wellbore storage and skin effects. Our resulting approximate models are semi-analytical, closed-form solutions. We propose five approximate models by assuming the behavior of dimensionless constant rate pressure at the sandface, P,D(tD), as follows: [ ] The advantage of our approach is that these solutions can be used to predict the pressure behavior of a well influenced by wellbore storage and skin effects in the real time domain. To our knowledge, this work is the first attempt to develop and apply real time domain solutions for all times of interest. To verify our new P,,CD(tD) models, we used the numerical inversion solution as the exact solution for wellbore pressure behavior that has been influenced by wellbore storage and skin effects. In particular, we have focused on the cylindrical source solution. As a comparison, we generated the "type curve" solutions for a well in an infinite-acting reservoir with wellbore storage and skin effects using the numerical inversion solution (as the "exact" solution) and our new relations as the "approximate" solutions. We also provided a graphical comparison of the residuals for each approximate solution (as compared to the numerical solution). All of the approximate solutions exhibited excellent agreement and consistency with the numerical inversion solution (except for Model 2). As a practical consideration, we found that it is generally better to compute the pressure derivative functions numerically, rather than by analytical differentiation, because in most cases the analytical derivatives are too tedious for hand calculations. For practical applications, we compare our new solutions to a number of field data cases. In order to perform history-matching of our new solutions, as well as the numerical inversion solution we developed and applied new modules for the historymatching program (PERANA). Again, for comparison, the results from the numerical inversion solution are used as the base results. In general, all of the models are as accurate as the Laplace transform numerical inversion solution, though Model I is clearly not appropriate in certain cases.