The Nature of Reservoir Fracture Heterogeneity: I - A New Conceptual and Computational Model

Abstract

The ability to quantitatively model geothermal well connectivity in fracture-heterogeneous reservoirs offers the opportunity to mold field data into physically accurate de facto models of reservoir-scale flow. Heretofore, however, incorporating fractures in reservoir flow models has tended to be mechanically ad hoc and computationally demanding. A large volume of well-log and well-core data points to a physically accurate and computationally tractable basis for simulating fluid flow in fractured reservoirs. Well-log fluctuation power S(k) tends almost universally to scale inversely with spatial frequency k, S(k) ~ 1/k, ~1/km < k < ~105/km. Such power-law scaling may be understood as long-range spatial correlation of in situ grain-scale fracturing of the cemented bonds that characterize most crustal rock. Sequences of porosity &#61546; and permeability &#61547; from hundreds of meters of clastic reservoir well core tend to obey the fluctuation relation &#61540;&#61546; &#61627; &#61540;log(&#61547;) at ~85% +/- 8% cross-correlation level. If porosity fluctuations &#61540;&#61546; in grain-scale fracture density &#61550; control permeability fluctuations &#61540;log(&#61547;) via permeability proportional to grain-scale fracture connectivity factor &#61550;!, the empirical spatial fluctuation relation is equivalent to the combinatorial identity &#61540;&#61550; &#61627; &#61540;log(&#61550;!). The well-log and well-core reservoir-empirical fluctuation relations for in situ fracture systems can be numerically represented in terms of 2D/3D fracture density fields with model realizations of porosity fluctuations scaled as S(k) ~ 1/k and associated permeability given by &#61540;&#61546; &#61627; &#61540;log(&#61547;)). Fracture-borne fluid flow is efficiently computed with finite-element solvers. Grids of dimension 32x64x64 to 64x128x128 can represent broadband in situ fracture heterogeneity to allow rapid quantitative simulation of interwell connectivity systematics.