Field statistics have shown that most fracturing fluid would be lost in shale formations after hydraulic fracturing treatment. This fracturing fluid retention in formations has led to some production and environmental issues. Some scholars suspected that the water with chemical additives might migrate to drinking water formations and contaminate them. Some also assumed that this imbibed water might lead to the swelling of shales, which may damage the permeability in the near wellbore area and, in turn, harm the production of the shale gas and oil wells in the long term. But some field studies showed that with a relatively long shut-in time period, the water leakage would benefit the production by enhancing the flow rate of shale gas at the early stage. To further explain the phenomena observed in fields and to end those debates, many scholars have paid attention to a special water imbibition mechanism working in shale formations: osmosis. The existence of osmosis makes the water imbibition process in shales not only related to the injection pressure, but also the concentration distribution in the porous medium, and accordingly Darcy’s law no longer holds in shale formations. So in this paper, in order to analyse the water flux influenced by osmosis in saturated shale formations, a mathematical model established by adding an additional term in the conventional Darcy’s law is employed. Ananalytical solution of the corresponding 1-D model is given under typical initial and boundary conditions, and the evolution of pressure and concentration distribution of the pore fluid in shales during the process are obtained. According to the solution, the existence of the osmotic effect will influence the hydraulic pressure propagation, which means that the osmotic effect couples with the Darcy flow. That is to say, it would cause additional water flux not only because of the concentration difference, but also because it can disturb the evolution of hydraulic pressure and thus influence the water imbibition. What is more, since these two types of water flux occur in opposite directions and compensate for each other to a great extent, the contribution of osmosis to the amount of water accumulation is very limited. Besides, the result shows that the early-stage water flux is generated by the initial hydraulic pressure difference, while the late water imbibition period is dominated by the osmotic effect. So, due to the generally low rate of the concentration diffusion compared to that of the pressure propagation, the existence of the osmotic effect will prolong the water imbibition process significantly.
Key words：
hydraulic fracturing in shale gas wells; osmotic effect; water uptake in shale; balance time
