The Nature of Reservoir Fracture Heterogeneity: II -- Rapid Interwell Connectivity Simulation for Reservoir-Scale Structure Modeling

Abstract

Reservoir well-log and well-core data show that geofluids tend to flow along microfracture-related percolation pathways. These pathways arise from scale-independent, long-range spatial correlation processes at scale lengths from mm (grain-scale) to km (reservoir-scale). Percolation pathway spatial fluctuation power S(k) scales inversely with spatial frequency k, S(k) ~ 1/k. As such the pathways are inherently spatially erratic and unpredictable at all scale lengths. Thus no valid statistical means relates well-scale sample data to reservoir-scale flow structures. It follows that standard flow models based on geometrically-regular geological and/or fracture formations derived from well-scale reservoir samples cannot accurately predict large-scale flow patterns. Flow predictions must, instead, be based on in situ reservoir flow data at the scale for which the flow is actually taking place.
For reservoir-scale modeling, interwell connectivity is a logical basis for defining flow structures that cannot be predicted from borehole-scale sampling. A new physical/
computational model of in situ fracture systems allows interwell connectivity field data to be built into adequate reservoir-scale flow models. Flow simulation in the physically-based fracture-heterogeneous model systems is efficiently computed by standard finite-element solvers. In the new flow-computational scheme for fracture-heterogeneous reservoirs, numerical grids of dimension
32 x 64 x 64 to 64 x 128 x 128 are used to compute inter-well connectivity. Interwell connectivity systematics can be expressed in relation to interwell flow in a uniform-permeability reservoir. Flow model data can distinguish between three spatial fracture density scaling regimes:
(i) 1/k0 (uncorrelated, white or Gaussian fluctuation noise),
(ii) 1/k1 (1/f-noise fluctuations), and
(iii) 1/k2 (Brownian noise equivalent to block-like flow spatial fluctuations).
Fracture density scaling regimes (i) and (iii) are often assumed for reservoir heterogeneity but are not validated by observation. Fracture density scaling regime (ii) is, instead, almost universally observed in well-log data. Whole-reservoir flow structures can thus be inferred from observing interwell connectivity deviations from the uniform permeability case. Interwell connectivity data quantified by the 1/k-scaling model physically links flow to individual well pressure, temperature, and solute concentration data. The physical basis for in situ flow modeling also provides a first-order geomechanics model for conducting massive fracturing of lower permeability rock volumes to boost geothermal well production, and allows related geophysical field data (seismic, micro-earthquake, magnetotelluric) to be quantitatively interpreted in terms of fracture-heterogeneous flow structures.