Constant rate production of geothermal fluid from a two-phase vertical column I: Theory

Previous theoretical results on geothermal two-phase flows in porous media are extended and applied to the case of withdrawal of fluid at a constant rate from a vertical column. Dimensional considerations show that pressure and saturation behaviour is controlled by a single parameter which is the ratio of the withdrawal speed to buoyancy speed. For large flows (large) fluid withdrawal is a mining process, and a vapour dominated zone spreads out from the production level. Production enthalpies tend towards steam values. However if is small then gravity dominates, and buoyancy forces can lead to the formation of a steam bubble which escapes from the production boundary and rises towards the surface. Production enthalpy may then remain at the liquid value over long periods. In addition certain saturation ranges at the sink may be forbidden as a consequence of the constant rate boundary condition. Then saturation shocks will form at the production boundary and travel out from the sink. Internally generated shocks may also occur. Pressure and saturation response to a steady withdrawal of fluid is more complicated than in a two-phase gravity-free situation. Since gravity is an essential component of even horizontal two-phase flow this suggests that two-phase studies which ignore the role of gravity may be too simplistic.