A production splitting method for gas wells based on double cycles and its application

The key parameter to calculate the production splitting coefficient is the gas drainage radius, which is usually unknown. Combining the productivity equation and material balance equation, a closed loop calculation model of production splitting coefficient is established, and the calculation method for internal and external double circles is proposed, where the internal and external circles are used to solve the gas drainage radius and the production splitting coefficient, respectively. Both the internal and external circles have unique solutions. The circle rules include forward recursion and reverse recursion, and the internal and external circles have the opposite circle rules. By setting the step size of cycle and the upper limit of error, the calculation process of double cycles is established. The external cycle includes the internal cycle, and it can only be realized when the internal cycle converges, moreover, it determines whether the internal cycle can converge. The production splitting coefficient shows different variation laws in different production layers at different producing stages and times. The numerical simulation results show that the mechanism of the double circles is correct and highly accurate. The gas production profiles show that the internal and external double circle also has a good accuracy in field application. The double cycle is a method of solving ternary equation group, which can calculate the production splitting coefficient, gas drainage radius and average formation pressure at the same time.