A novel steady-state productivity equation for horizontal wells in bottom water drive gas reservoirs

It is known that there is a discrepancy between field data and the results predicted from the previous equations derived by simplifying three-dimensional (3-D) flow into two-dimensions (2-D). This paper presents a new steady-state productivity equation for horizontal wells in bottom water drive gas reservoirs. Firstly, the fundamental solution to the 3-D steady-state Laplace equation is derived with the philosophy of source and the Green function for a horizontal well located at the center of the laterally infinite gas reservoir. Then, using the fundamental solution and the Simpson integral formula, the average pseudo-pressure equation and the steady-state productivity equation are achieved for the horizontal section. Two case-studies are given in the paper, the results calculated from the newly-derived formula are very close to the numerical simulation performed with the Canadian software CMG and the real production data, indicating that the new formula can be used to predict the steady-state productivity of such horizontal gas wells.