Interpretation of flow-after-flow tests for gas wells

Abstract

Flow-after-flow testing of gas wells was first reported in 1929[]. This method of testing was subsequently adopted by various regulatory bodies in the United States and became a statutory requirement in most states. This method of testing was used for determining deliverability and by extrapolation, the AOF (absolute open flow potential). The AOF has traditionally been used for proration and for determining allowables. In 1965, Jones and Odeh2 described a method to determine permeability and skin for flow-after-flow testing and verified the method by computer simulation. The interpretation method uses superposition and a trial and error process to arrive at a straight line Cartesian plot of variables involving the data and an unknown parameter. The permeability can be determined from the slope of this line and the skin calculated with knowledge of the permeability. The boundary condition assumed a constant sandface rate and only low values of Reynolds numbers were investigated. This work develops a simulator that models actual field conditions, i.e. a fixed choke at the surface for each flow period and a storage volume in the tubing. A method is developed to directly compute the unknown parameter which yields the best straight line and the slope of that line. Superposition applies strictly only to a linear system. The governing equation for this problem is non-linear and the degree of non-linearity is a function of the Reynolds number. Therefore, one might suspect that superposition may give poor results for Reynolds numbers above some value. A range of Reynolds numbers from .1 to 8 is investigated to determine their effect on the interpreted results for permeability and skin. Flow-after-flow tests are normally conducted with either an increasing rate schedule (normal sequence) or a decreasing rate schedule (reverse sequence). If superposition applies, then the results for the normal sequence should be the same as for the reverse sequence. This proposition is tested. The effects of wellbore storage are investigated and finally, manual history matching of test data generated by the simulator is investigated.