Modelling of hydraulic fracturing often deals with elastic deformation of rocks and fractures. Some rocks, such as the rock-salt and shale, however, displayed viscoelastic behaviour in both field investigation and lab creep tests. This time-dependent deformation poses a challenge in modelling and characterising of fracture propagation in such formations, thus adding complexity in a multi-physics scenario. In this paper, we intend to numerically model fracture propagation in viscoelastic formation and investigate the effect of creep on crack propagation and crack geometry. To incorporate pore pressure effect, we couple fluid diffusion with shale matrix viscoelasticity in the hydraulic fracturing propagation model. Therefore, a procedure for numerical modelling hydraulically-driven fracture propagation in poro-viscoelastic formation is developed. The method uses a poro-viscoelasticity theory to describe the fluid diffusion and matrix creep in solid skeleton, in conjunction with cohesive law based damage criteria to simulate crack growth and fluid flow in the crack. The modelling took shale as the representative sample. The viscoelastic properties were obtained via creep tests of shale samples from Roseneath formation, Cooper Basin, Australia. Results show that the hydraulically induced fracture tends to be wider and longer in creep formation. What's more, the propagation pressure is also lower than that in poroelastic formation. Fluid diffusion from crack to the matrix is more efficient due to modulus decay. For mixed-mode fracturing, the creep of the formation facilitates the process of reorientation with higher fracture propagation speed between kink points.

水力压裂的建模通常涉及岩石和裂缝的弹性变形。但是，一些岩石，例如盐岩和页岩，在现场调查和实验室蠕变测试中均表现出粘弹性。这种随时间变化的变形在模拟和表征此类地层中的裂缝扩展方面提出了挑战，从而在多物理场场景中增加了复杂性。在本文中，我们打算对粘弹性地层中的裂缝扩展进行数值模拟，并研究蠕变对裂缝扩展和裂缝几何形状的影响。为了合并孔隙压力效应，我们在水力压裂扩展模型中将流体扩散与页岩基质粘弹性耦合。因此，开发了一种数值模拟孔隙粘弹性地层中水力驱动裂缝扩展的程序。该方法使用孔隙粘弹性理论来描述固体骨架中的流体扩散和基体蠕变，并结合基于内聚律的损伤准则来模拟裂缝的增长和裂缝中的流体流动。建模以页岩为代表样本。粘弹性是通过澳大利亚库珀盆地Roseneath地层页岩样品的蠕变试验获得的。结果表明，水力诱发的裂缝在蠕变形成中趋于变宽和变长。而且，其传播压力也低于多孔弹性地层中的传播压力。由于模量衰减，流体从裂缝扩散到基体的效率更高。对于混合模式压裂，地层的蠕变促进了重新定向的过程，并且扭折点之间的裂缝传播速度更高。