Genuine two-phase flow dynamics with a free interface separating gas-liquid mixture from gas
Original version
Evje, S. (2013) Genuine two-phase flow dynamics with a free interface separating gas-liquid mixture from gas. SIAM journal on mathematical analysis, 45(5), pp. 2894–2923 10.1137/120904317Abstract
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 = qw(Pw − P) which appears in the gas continuity equation where qw is a
rate constant, and Pw 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 Pw.
Description
This is a copy of an article previously published in; SIAM journal on applied mathematics, which has been made available here with permission. The article was originally published at DOI. 10.1137/12087195X.