Self-diffusion flow and heat coupling model applicable to the production simulation and prediction of deep shale gas wells

Clarifying the flow laws of shale gas under high temperature and high pressure is the prerequisite to accurately predicting the productivity of deep shale gas wells. In this paper, a self-diffusion flow model of flow field and temperature field coupling (referred to as self-diffusion flow and heat coupling model) was established based on the previously proposed self-diffusion flow model, while considering the influence of the temperature field change. Then, its calculation result was compared with that of the flow model based on Darcy's law and Knudsen diffusion (referred to as modified Darcy flow model). Based on the self-diffusion flow and heat coupling model, the self-diffusion flow behaviors of deep shale gas under the influence of temperature field change were analyzed, and the influence of bottomhole temperature on the degree of reserve recovery of deep shale gas was discussed. Finally, the self-diffusion flow and heat coupling model was applied to simulate the production of one shale-gas horizontal well in the Upper Ordovician Wufeng Formation–Lower Silurian Longmaxi Formation in the Changning Block of the Sichuan Basin. And the following research results were obtained. First, at the same parameters, the shale gas production calculated by the self-diffusion flow and heat coupling model is higher than the result calculated by the modified Darcy flow model. Second, when temperature field change is taken into consideration, the self–dviffusion coefficient profile presents a peak, the gas density profile presents a valley and the data points corresponding to the peak/valley move synchronously to the internal formation, which indicates that the self–diffusion coefficient influences the gas mass transfer rate, and the influence range of near well low temperature on gas self-diffusion increases continuously as the production continues. Third, when the bottomhole temperature is lower than the formation temperature, the self–diffusion coefficient of the gas near the well decreases and the gas is blocked near the well, which reduces the gas well production. Fourth, the production simulation result of the case well shows that the self-diffusion flow and heat coupling model can predict the production of deep shale gas more accurately if temperature field change is taken into consideration. In conclusion, the self-diffusion flow and heat coupling model established in this paper is of higher reliability and accuracy and can be used for productivity simulation and prediction of deep shale gas wells. The conclusion of this paper has certain guiding significance for deep shale gas production and gas well productivity prediction.