Abstract
Slurry, as a proppant-laden fluid for hydraulic fracturing, is pumped into initial perforated cracks to generate a conductive pathway for hydrocarbon movement. Recently, numerous studies have been done to investigate mechanisms of proppant transport within vertical fractures. However, the distribution of proppant during stimulation becomes much more complicated if bedding planes (BPs), natural fractures (NFs) or other discontinuities pervasively distributed throughout the formation. Thus, how to capture the transport and placement mechanisms of proppant particles in the opened BPs becomes a significant issue. In this paper, we propose a closed-form continuous proppant transport model based on the conservation of total proppant volume and sedimentation of proppant particles. This model enables to integrate with the fluid flow section of a 3-D hydro-mechanical coupled fracture propagation model and then predict the distribution of proppant velocity and slurry volume fraction within a dynamic fracture network. Stokes’ law is applied to determine the sedimentation velocity. In the fracture propagation model, rock deformation is governed by the analytical solution of penny-shaped crack to determine fracture width. Fluid flow is characterized by finite differentiation scheme and then the fluid velocity is obtained. These two parameters above are inputs for the proppant transport model and both slurry viscosity and density are updated in this step. Afterwards, both fracture width and fluid velocity would be altered in the fracture model. Analysis of the proppant distribution within crossing-shaped fracture is conducted to study mechanisms of proppant transport along opened BPs. From our numerical analysis, we find that the distribution of proppant concentration is independent with the fluid viscosity, but highly dependent on the volume fraction of pumping slurry, under a given pumping pressure. Due to the difference of viscosity and proppant volume fraction at locations of upper and lower BPs, we observe that two symmetric BPs are unevenly opened, with different channel length along BP. Moreover, the width of opened upper BP is much smaller than that of opened lower BP as a result of discrepancy of proppant sedimentation. Last but not the least, a criterion of flow bed mobilization is established for dynamically tracking the sedimentation along the BP. Then the effect of different parameters (such as proppant size, proppant density, fluid viscosity, injection rate) on proppant distribution along opened BPs is also studied. Our model fully considers the proppant transport and settlement, proppant bed formation and interaction between fracture and proppant, which helps to predict the influence of proppant during fracturing treatment. Additionally, our model is also capable of dynamically tracking the settlement of proppant along opened BPs.
