دانلود رایگان مقاله مدل فشار محلی برای تحلیل دقیق شکستگی محوری فشار سیال در مواد متخلخل

Abstract

In this paper, we present an enhanced local pressure model for modelling fluid pressure driven fractures in porous saturated materials. Using the partition-of-unity property of finite element shape functions, we describe the displacement and pressure fields across the fracture as a strong discontinuity. We enhance the pressure in the fracture by including an additional degree of freedom. The pressure gradient due to fluid leakage near the fracture surface is reconstructed based on Terzaghi’s consolidation solution. With this numerical formulation we ensure that all fluid flow goes exclusively in the fracture and it is not necessary to use a dense mesh near the fracture to capture the pressure gradient. Fluid flow in the rock formation is described by Darcy’s law. The fracture process is governed by a cohesive traction–separation law. The performance of the numerical model for fluid driven fractures is shown in three numerical examples.

8. Conclusion

We have presented an enhanced local pressure model, within the framework of X-FEM, for fluid pressure driven fracture in porous saturated materials. By exploiting the partition-of-unity property of finite element shape functions the method captures the discontinuous fracture. The fracture process is modelled by means of a cohesive zone description. The local, additional, degree of freedom for the pressure ensures that fluid flow goes exclusively in the fracture. The steep pressure gradient that may occur locally near the fracture surface is reconstructed based on Terzaghi’s analytical solution. We have illustrated this effect with an example where fluid is being injected in an opened fracture. Using a X-FEM model with a continuous pressure approach the pressure gradient cannot be resolved at low time scales. The pressure in the fracture calculated with the ELP model is consistent with the analytical solution. We also have showed that at higher time scales the continuous X-FEM does describe the pressure gradient near the fracture surface. This indicates that the ELP model is better capable to model hydraulic fracturing at early stages while at later stages a switch to the continuous X-FEM should be considered.