A Semi-Analytical Model for Productivity Testing of Multiple Wells

This paper presents a new, semi-analytical method for calculation of the productivity of vertical, horizontal or multilateral wells draining either gas or oil reservoirs. Well interference effects and the presence of natural or induced fractures are accounted for. The method is based on an earlier derived productivity prediction tool in which now moving pressure boundaries have been implemented to account for time dependence. The semisteady-state pressure equations are solved using combinations of exact solutions around the well in an infinite reservoir and additional solutions to the Laplace equation are introduced to approximate the boundary conditions. The pressures and rates for all the flowing wells are solved in a single step for each required value of the time. Both numerical and analytical approaches have been used to validate the new method. The validity of the moving-boundary approach for the transient well behaviour has been checked against analytical results, whereas a numerical method has been employed to analyse the multi-well response in homogeneous, isotropic reservoirs. Finally, the new method has been applied to real production test data. Both single-well and multi-well production tests performed in different types of reservoirs have been analysed with satisfactory results.