We combine a power-law microfracture size distribution function with an expression for fracture propagation rate derived from subcritical fracture propagation theory and linear elastic fracture mechanics, to derive a geomechanically based deterministic model for the growth of a network of layer-bound fractures. This model also simulates fracture termination due to intersection with perpendicular fractures or stress-shadow interaction. We use this model to examine key controls on the emergent geometry of the fracture network. First, we examine the effect of fracture propagation rates. We show that at subcritical fracture propagation rates, the fracture nucleation rate increases with time; this generates a very dense network of very small fractures, similar to the deformation bands generated by compaction in unconsolidated sediments. By contrast, at critical propagation rates, the fracture nucleation rate decreases with time; this generates fewer but much larger fractures, similar to the brittle open fractures generated by tectonic deformation in lithified sediments. We then examine the controls on the rate of growth of the fracture network. A fracture set will start to grow when the stress acting on it reaches a threshold value, and it will continue to grow until all the fractures have stopped propagating and no new fractures can nucleate. The relative timing and rate of growth of the different fracture sets will control the anisotropy of the resulting fracture network: if the sets start to grow at the same time and rate, the result is a fully isotropic fracture network; if the primary fracture set stops growing before the secondary set starts growing, the result is a fully anisotropic fracture network; and if there is some overlap but the secondary set grows more slowly than the primary set, the result is a partially anisotropic fracture network. Although the applied horizontal strain rates are the key control on the relative growth rates of the two fracture sets, we show that the vertical effective stress, the initial horizontal stress, the elastic properties of the rock and the inelastic deformation processes, such as creep, grain sliding and pressure solution, all exert a control on the fracture growth rates, and that more isotropic fracture networks will tend to develop if the vertical effective stress is low or if the fractures are critically stressed prior to the onset of deformation. Thematic collection: This article is part of the Naturally Fractured Reservoirs collection available at: https://www.lyellcollection.org/cc/naturally-fractured-reservoirs

中文翻译：

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裂缝成核和扩展速率对裂缝几何形状的影响：来自地质力学建模的见解

我们将幂律微裂缝尺寸分布函数与源自亚临界裂缝扩展理论和线弹性断裂力学的裂缝扩展速率表达式相结合，以推导出基于地质力学的层状裂缝网络增长的确定性模型。该模型还模拟由于与垂直裂缝相交或应力-阴影相互作用而导致的裂缝终止。我们使用该模型来检查对裂缝网络的紧急几何形状的关键控制。首先，我们检查裂缝扩展速率的影响。我们表明，在亚临界裂缝扩展速率下，裂缝成核速率随时间增加；这会产生一个非常密集的非常小的裂缝网络，类似于松散沉积物中压实产生的变形带。相比之下，在临界扩展速率下，断裂形核速率随时间降低；这会产生更少但更大的裂缝，类似于岩化沉积物中构造变形产生的脆性开放裂缝。然后我们检查对裂缝网络增长率的控制。当作用在其上的应力达到阈值时，裂缝组将开始增长，并将继续增长，直到所有裂缝都停止扩展并且没有新的裂缝可以成核。不同裂缝组的相对时间和增长速率将控制所得裂缝网络的各向异性：如果裂缝组同时和速率开始增长，则结果是完全各向同性的裂缝网络；如果主要裂缝组在次要裂缝开始生长之前停止生长，结果是完全各向异性的裂缝网络；如果有一些重叠，但次要组比主要组增长得更慢，结果是部分各向异性的裂缝网络。虽然施加的水平应变率是控制两个裂缝组相对增长率的关键，但我们表明垂直有效应力、初始水平应力、岩石的弹性特性和非弹性变形过程，如蠕变、晶粒滑动和压力溶解，都对裂缝生长速率施加了控制，如果垂直有效应力低或裂缝在变形开始前受到临界应力，则更趋向于发展各向同性的裂缝网络。专题收藏：本文是自然破裂水库收藏的一部分，可从以下网址获取：