Quantifying the Sensitivity of Dielectric Dispersion Data to Fracture Properties in Fractured Rocks

Evaluation of fluid storage and flow capacity of a fractured rock system needs a comprehensive characterization of all the fracture properties. These properties include the fracture surface roughness, aperture size and distribution, fracture orientation, fracture network connectivity, and fracture-matrix connectivity. In-situ quantification of fracture properties is challenging as it relies on collected data from core samples, which are hard to acquire, or on indirect geophysical measurements, which often hold oversimplified assumptions for fracture properties. The objectives of this paper are to (a) quantify the sensitivity of dielectric measurements to fracture surface roughness, aperture size and distribution, fracture connectivity, and orientation through numerical modeling, (b) quantify the influence of fluid phase saturation, salinity, and temperature on the dielectric measurements in fractured formations, and (c) investigate the combined influence of fractures and matrix pore network on dielectric measurements. First, we developed synthetic models of fractured rocks with a wide range of fracture surface roughness using fractal theory. Then, we developed different cases where the fracture aperture size and distribution, fracture connectivity, and fracture orientation were allowed to vary. We used the synthetic fracture models as inputs to a numerical dielectric permittivity simulator under different fluid phase saturations, salinity, and temperature conditions. The numerical simulator solves Maxwell’s equations that describe the propagation of electromagnetic waves using a finite volume algorithm in the frequency domain. The outcomes of numerical simulations include real and imaginary parts of complex dielectric permittivity as a function of frequency in the range of 1 Hz to 3 GHz. We applied the aforementioned method to synthetically created fractured rocks covering a wide range of fracture properties (i.e., fracture roughness, aperture size and distribution, fracture orientation, and fracture network connectivity), rock matrix properties, and fluid properties/saturations. We observed an increase of one degree of magnitude (from 105 to 106) in the relative permittivity of the fractured rock models with increasing fracture roughness at low frequency (i.e., from 1 Hz to 10 KHz) in the presence of only one single fracture. This impact was more significant in the presence of more fractures. The outcomes of numerical modeling demonstrated that the fracture orientation with respect to the applied electrical field should be considered during the interpretation of dielectric measurements. Results of the sensitivity analysis demonstrated that dielectric permittivity measurements are sensitive to different fracture properties at different frequencies. This is promising for the simultaneous assessment of fracture properties through the interpretation of multifrequency dielectric measurements. The outcomes of the proposed methods enable reliable characterization of fractured formations through integrated analysis of multifrequency electrical measurements. The ability to assess fracture properties in real time from electromagnetic measurements will pave the way to building robust fluid-flow and reservoir simulation models. In addition, the proposed method enables reliably evaluating fluid flow and energy storage capacity of naturally fractured geothermal reservoirs.