Semi-analytical Modelling of Water Injector Test with Fractured Channel in Tight Oil Reservoir

It is well known that long-term water injection may induce fractured channel(s), and that the fracture geometry would change with the decrease of bottom-hole pressure (BHP) during shut-in. This results in difficulties in modelling BHP behavior. This paper presents a pressure-transient procedure to analyze the BHP performance of water injectors by taking the dynamic behavior of the water injection fractured channel into consideration. Perturbation theory is adopted to solve the non-linear equations caused by decreasing fracture conductivity, while the finite-difference method is used to include the shrinking conductive fracture length during the shut-in period. Then, Duhamel’s principle is deployed to characterize the bi-storage effect; that is, fracture-storage caused by fracture closure and wellbore storage because of wellbore after-flow. Since the mobility outside of channel walls are much poorer than that in the channel, the walls are modeled as two parallel sealed boundaries. Therefore, the method of images is lastly applied to obtain the BHP response. The bi-storage phenomenon is characterized by two unit slopes in the pressure-derivative curve, and the variable fracture-storage is identified as a new flow regime in water injectors that is caused by fracture shrinkage. The interpreted storage coefficient will be much larger than the true value if the fracture-storage flow is mistakenly regarded as wellbore-storage flow. Because of the fractured channel walls and decreasing fracture conductivity, the pressure-derivative curve would increase in late time. Finally, two cases from the Changqing Oilfield are discussed to demonstrate the capabilities of the proposed approach.