DFN modeling incorporating fracture stratigraphy constraints into the stereology inverse problem

We develop a methodology for building stochastic discrete fracture networks (DFNs) based on the solution of a generalized version of the stereology inverse problem incorporating constraints derived from fracture stratigraphy. The DFN is simulated inside a layer-cake model, whose interfaces conform to the available fracture stratigraphy information. For each layer, estimates of the power law exponent of fracture sizes and volumetric fracture intensity ($P_{32}$) are obtained for each fracture set from the solution of the inverse problem; the inputs are trace length distribution and areal fracture intensities ($P_{21}$) measured on multiple exposed surfaces. A Lagrangian formulation of the inverse problem allows the straightforward incorporation of geological constraints. However, the price to pay is having to solve the problem with global optimization methods; here we use a particle swarm optimization algorithm. Our approach is applied in a real cave setting, where multiple surfaces expose fracture traces. Using a simplified geometry of the cave setting, we obtain solutions honoring both synthetic and field measurements. Uncertainties in the $P_{32}$ estimates might be different for each layer, depending on the fracture intensity contrasts between the layers and on the angles between the exposed surfaces and the fracture planes. The interpreter can then evaluate the reliability of the parameter estimates obtained with the layer-cake model in comparison with those obtained with a homogeneous version of the investigated volume. In addition, we show that the $P_{32}$ estimates depend on the shape assumed for the fractures, being larger for rectangle-shaped fractures than for disk-shaped fractures.