Pressure Transient Analysis for Water Injection Wells with Waterflooding-Induced Nonsimultaneously Closed Multistorage Fractures: Semianalytical Model and Case Study

Waterflooding will induce the opening and extension of fractures, which will create some water flow channels. Due to fracture multiclosures, the obtained fracture half-length from conventional finite-conductivity models is less than the actual value, leading to water flow channels that have been formed but not detected by engineers. According to a large number of waterflooding-front matching schematics and interwell connection coefficient analyses, we find that waterflooding usually connects natural fractures to form bi-induced fractures, which will close nonsimultaneously during the falloff test. In this paper, we develop a waterflooding-induced nonsimultaneously closed multistorage fracture model (WNMF) to describe waterflooding-induced fracture characteristics accurately. The bi-induced fractures are separated into multiple segments to calculate their pressure response. The closed induced-fracture conductivities are constant, and the opened induced-fracture conductivities follow the exponential equation measured by the experiments. Induced-fracture interference and multistorage effects are considered. Finally, the Duhamel principle is used to characterize the storage effects of bi-induced fractures and the wellbore. Results show that the type curve of the WNMF model has bi-peaks on the pressure derivative curve, which was regarded as error data in the past. Closed induced-fracture half-length is identified quantitatively. We can obtain an induced-fracture angle by matching the interference flow (an innovative flow regime in this paper), which can guide engineers to prevent and monitor water breakthrough in time. Using the obtained parameters (induced-fracture angle and closed induced-fracture half-length) can guide well pattern encryption and reasonable well location determination. If the induced-fracture angle is 90°, an additional horizontal line will be shown on the pressure derivative curve. When the horizontal line is misidentified as a quasiradial flow regime, the obtained reservoir permeability will be amplified many times. The multistorage coefficient is obtained to correct the magnified storage coefficient. Equation calculation and model matching methods verify each other to improve closed induced-fracture half-length accuracy. In conclusion, the experiment and mathematical model methods work together to describe the pressure response behavior of water injection wells. The WNMF model is compared with the conventional finite-conductivity model to verify its accuracy. A field case demonstrates its practicality.