Diagnosis and monitoring of hydraulic fracturing (HF) are important methods of optimizing the development of unconventional reservoirs. Meanwhile, determining the fracture geometry is the key to improve the understanding of the well productivity. In the process of HF, pressure decline curve analysis is usually conducted to determine the parameters under the assumption of a constant leak-off coefficient. Due to the effects of reservoir pressure and natural fractuers, HF typically exhibits nonlinear leak-off behavior (i.e., PDL, pressure-dependent leak-off). Sufficient studies have focused on how to judge different nonlinear leak-off types. However, the fracture parameters inversion model, suitable for the fracture leak-off process under nonlinear leak-off conditions, is absent.
In this paper, a new fracture parameters inversion model was deveploed to determine dynamic leak-off coefficient and fracture geometry of PDL. Firstly, considering fluid leak-off rate with pressure after shut-in, the dynamic leak-off coefficient was used to characterize fracture closure and dynamic leak-off process. Based on the dynamic leak-off coefficient, a new improved P3D model was derived to determine the dynamic fracture parameters with pressure and time of PDL. After that, using the new model, effects of the range of the power-law coefficient, minimum in-situ stress, and leak-off height on the pressure decline curve and fracture parameters are investigated in detail through three cases. Our model and results could provide some novel insigths to determine the fracture geometry by pressure decline curve under nonlinear leak-off conditions.
Hydraulic fracturing (HF) is one of the important stimulation methods for unconventional oil and gas development in recent years. In the process of hydraulic fracturing, before-closure analysis of fracture calibration test (BC) is conducted before the formal HF. The BC can be used to determine the fracture parameters (i.e., fractures closure pressure/time. Leak-off coefficient, fluid efficiency, fracture length, and fracture width), providing evidence for the interpretation of fracture geometry (fracture length and fracture width) and optimization of fracturing parameters (Liu Guoqing, 2015). The above process is called the fracture inversion analysis derived from BC. The earliest fracture inversion analysis was derived from a systematic pressure-decline analysis proposed by Nolte (Nolte, 1979). Based on the continuity equation of fluid in fracture presented by Nordgren (Nordgren R. P., 1972), the Nolte model was derived to effectively estimate fracturing fluid efficiency, closing pressure, and fracture geometry parameters. G Function, the dimensionless function of time, simplifies the calculation process of the leak-off coefficient in the model. Specifically, a basic fracture inversion process is composed of an analysis of the pressure-decline plot and calculation of the fracture propagation model. First, collect surface pressure from fracturing wells, and calculate the corresponding well bottom pressure (P). Meanwhile, determine the pressure-decline plot (P(t) vs. t) after shut-in. After that, calculate the dimensionless time by G Function, and convert the pressure-decline plot to the G function plot. Then determine match pressure (P*) used the G function plot. Finally, calculate the fracture parameters through the fracture propagation model (i.e. PKN and KGD). Also, the development of the fracture inversion model includes the development of pressure-decline plot analysis and the fracture propagation model.
