A Novel Steady-State Productivity Equation for Horizontal Wells in Gas Reservoirs

This paper presents a new steady-state productivity equation for horizontal wells in gas reservoirs with upper and lower boundary enclosed. 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, with considering the above boundaries conditions. 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. Case-studies are given in the paper, and 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.