Summary
Gas-well productivity is affected by two distinct mechanisms: liquid blocking and high-velocity flow in two-phase flow. The former has been studied extensively recently, but the understanding of the latter is limited. High-velocity gas flow in single phase has been studied thoroughly by a large number of authors. Despite the fact that high-velocity coefficient in the presence of an immobile and a mobile liquid phase is much higher than that in single phase, only a handful of studies have been made on the subject. In this work, we have measured the high-velocity coefficient, ß in steady-state two-phase gas/liquid flow. The results are presented as a function of liquid relative permeability and liquid saturation. In our measurements, the wetting state is varied by the treatment with a fluorochemical compound. Then, the effect of wettability on the high-velocity coefficient in two-phase flow is investigated. Results show that when the liquid is strongly wetting, the high-velocity coefficient increases approximately 270-fold in water/gas two-phase flow. However, our data show a systematic reduction of high-velocity coefficients for the altered wetting state in two-phase flow. We present measurements of the velocity coefficients in single-phase flow and two-phase flow, for both oil/gas and water/gas flow and strong liquid-wetting and altered-wetting states. On the basis of our measurements, we conclude that the treatment of the wellbore region can result in significant improvement in well deliverability from the large reduction of high-velocity coefficients.
Introduction
Gas deliverability in gas-condensate reservoirs can be significantly affected by liquid blocking, either from condensate accumulation or water blocking, and high-velocity flows in the near-wellbore. Hydrocarbon blocking in gas-condensate reservoirs results in a significant loss of well productivity; water blocking from hydraulic-fracturing operation often limits the advantage of fractures. In addition to liquid blocking, the increased pressure drop, caused by inertial effects at high gas velocity in both low-permeability and hydraulically fractured reservoirs, can also result in low productivity. The focus of this work is on the high-velocity gas flow in two-phase gas/liquid flow in gas reservoirs.
Darcy's law is inadequate to describe high-velocity gas flow in porous media. Through the high-velocity coefficient, ß, Darcy's law is modified, and the additional pressure drop from high-velocity flow can be expressed as the Forchheimer equation (1901). The general understanding is that the high-velocity coefficient in two-phase flow is higher than in single-phase gas flow in a dry rock. However, very few attempts have been made for conclusive experiments in determining the high-velocity coefficient in two-phase gas/liquid flow because of experimental difficulties in maintaining a constant liquid saturation for different pressure drops.
Gas flow at low velocity is governed by Darcy's law, which describes a linear relationship between pressure gradient and volumetric flux. At high gas velocity, the pressure gradient required to maintain a certain flow rate through porous media is higher than that predicted by Darcy's law. The effect of inertia has to be added. The result is the Forchheimer equation expressed by[Equation 1]
where µg is gas viscosity, kg is the effective gas permeability, ug is the gas volumetric flux, ß is a high-velocity coefficient, and ??g is gas density.
Eq. 1 is valid both for single-phase gas flow and for two-phase gas/liquid flow provided, that the capillary effect is negligible. In 1D, one may integrate Eq. 1 to obtain
[Equation 2]
Here, p1 and p2 are the inlet and outlet pressure; M and jg are molecular weight and mass flux of gas, respectively; R and Z are the gas constant and the gas deviation factor, respectively; T is temperature; and L is the length. Effective gas permeability and high-velocity coefficient are determined by plotting M?p2 / 2µgZRTLjg vs. jg / µg, provided that the saturation is constant. Fig. 1 shows a schematic of determining the effective gas permeability and the high-velocity coefficient. Note that the effective permeability in Eq. 2 becomes the absolute permeability when the rock is dry (Sg = 100%, krg = 1.0).
There has been much work in the literature on high gas velocity in single-phase flow in dry rocks. There has also been a fair amount of work in single-phase gas flow with immobile liquid saturation. Very little work, however, has been done in two-phase gas/liquid flow at high gas velocity. In the following, we will briefly review the literature in experimental studies and set the stage for our work in two-phase gas/liquid flow at high gas velocity.
Influence of Blade Type on the Flow Structure of a Vortex Pump for Solid-Liquid Two-Phase Flow