A COMPRESSIBLE TWO-PHASE MODEL WITH PRESSURE-DEPENDENT WELL-RESERVOIR INTERACTION

This paper deals with a two-phase compressible gas-liquid model relevant for modeling of gas-kick flow scenarios in oil wells. To make the model more realistic we include a natural pressure-dependent well-formation interaction term allowing for modeling of dynamic gas influx/efflux. More precisely, the interaction between well and surrounding formation is controlled by a term of the form A = q(w)(P-w - P) which appears in the gas continuity equation where q(w) is a rate constant, and P-w is a critical pressure, whereas P is pressure in the well. Consequently, an additional coupling mechanism is added to the mass and momentum equations. We obtain a global existence result for the new model. One consequence of the existence result is that as long as the well initially is filled with a mixture of gas and liquid, the system will regulate itself (in finite time) in such a way that there does not exist any point along the well where all the gas vanishes, e.g., by escaping into the formation. Similarly, the result guarantees that neither will any pure gas region appear in finite time, despite that gas is free to enter the well from the formation as long as the well pressure P is lower than the critical pressure P-w.