At present, the research on the seepage flow models in low-permeable coalbeds is only limited to the single phase flow cases, which simultaneously considerate the existence of threshold pressure gradient in the seepage flow process, its produced moving boundary and the desorption function of adsorbed gas inside the moving boundary; however, the research on the gas and water two-phase seepage models with moving boundaries, which are more consistent with the actual situations, has not been reported yet. In comprehensive consideration of these influential factors including the desorption function of the adsorbed gas in coalbeds, gas-water two-phase seepage flow, the non-Darcy seepage flow characteristics in the low-permeable formations, the stress-sensitive effect of the formation, etc., modeling the gas-water two-phase seepage flow in low-permeable coalbeds is studied in this paper. According to the "phase separation" method involved in the well testing technology, both the comprehensive compressibility coefficient and the fluidity are modified for the two-phase seepage flow problem; and then based on the assumption of the linear spatial distribution of the gas saturation, a coupled model of gas-water two-phase seepage flow in low-permeable coalbeds is built. The mathematical model can not only depict the moving boundary that represents the change of the effectively disturbed coalbed area with time due to the existence of threshold pressure gradient in the seepage flow process in low-permeable coalbeds, but also can depict the desorption phenomena of the adsorbed gas in the effectively disturbed coalbed area, and the increase of the gas saturation in coalbeds caused by the desorption function of the adsorbed gas; furthermore, in order to improve the accuracy of the model, the quadratic pressure gradient term is retained in the governing equation of the model. A fully implicit finite difference method is adopted to numerically solve the model, and the correctness of the numerical method is also verified. Eventually, the log-log type curves regarding the transient wellbore pressure response and its derivative are obtained from the model, and then the sensitive-effects of some seepage flow parameters can be analyzed. The presented research results in the paper can provide theoretical foundations of seepage flow mechanics for the well testing technology for the gas-water two-phase seepage flow in the development of low-permeable coalbed gas reservoirs.

2017, 49(4): 828-835.
doi: 10.6052/0459-1879-17-034