Coupling model of gas-water two-phase productivity calculation for fractured horizontal wells in tight gas reservoirs

Tight gas reservoirs are exploited mostly by using horizontal wells in combination with multi-stage hydraulic fracturing. Up to now, there have been plenty of studies conducted to establish a series of productivity models that consider various factors. Despite this, insufficient consideration has been given to the ramifications resulting from secondary fractures, permeability anisotropy, wellbore pressure drop, and the actual distribution of fractures. To accurately evaluate productivity, the superposition principle of potential and the conformal transformation theory are adopted to define the two-phase generalized pseudo-pressure, with consideration given to the characteristics of non-Darcy seepage in tight gas reservoirs and the effects of secondary fractures and permeability anisotropy on productivity. On this basis, the homogeneous flow model of the horizontal wellbore is introduced to establish the coupling model of gas-water two-phase productivity calculation for fractured horizontal wells. The results obtained from the empirical calculation and analysis of various factors affecting productivity are as follows. Firstly, the relative error is 5.35% between the theoretical open flow capability obtained from the proposed model and the open flow capability determined through the deliverability test, which attests to the proposed model's accuracy. Secondly, in response to an increase in gas slippage factor, fracture conductivity, the number of fractures, and the degree of permeability anisotropy, there is an improvement in the productivity of the gas well. However, with a rise in the water-gas volume ratio, threshold pressure gradient, reservoir stress sensitivity index, and the angle formed between the horizontal wellbore and the main permeability, the productivity declines. Lastly, the pressure drop along the horizontal wellbore is relatively insignificant, which has no substantial impact on fracture production. However, when the effect of secondary fractures is ignored, the predicted productivity is relatively low. This study offers theoretical direction for the application of productivity prediction and fracturing optimization design.