# Analyzing Fractures with Resistivity Data

**Investigator: **Jason Hu

## Background and Motivation

Hydraulic fracturing is the process of breaking low permeability reservoirs to create conductive channels in which oil and gas can flow through. Hydraulic fracturing will continue to play a key role in the future of oil and gas exploration and production, and characterizing hydraulic fractures is an important task to improve the understanding and utilization of the process.

As a potential approach to augment and improve on the existing methods, resistivity measurements can be used to characterize subsurface features because lithology, pore fluid chemistry, and water content affect the spatial distribution of low-frequency resistive and capacitive characteristics of rock. Hydraulic fractures are created by injecting water into the wellbore at high pressure. Fractures saturated with water effectively reduces the resistivity of rock matrix and create opportunities to extract fracture characteristics by monitoring the change in resistivity distribution.

## Methodology

**Resistivity Model**

The objective of this research is to investigate a fracture characterization approach by utilizing electric resistivity data. We will mainly focus on using electric field simulation and inverse analysis to test our hypothesis of subsurface electric field behavior due to fracture creation. In this research we will consider a new borehole method designed specifically for hydraulic fracture characterizations, by combining cross-borehole survey method with single-borehole survey method. This method would implement electrodes in or near boreholes and monitor the electric potential distribution near the horizontal fracture zone as shown in Figure 1.

The electric potential distribution in a steady-state flow through porous medium is the same as the electrical potential distribution in electrical conductive medium. Bouwer (1964), and Wind and Mazee (1979) showed that it is feasible to solve electric field using a flow simulator by drawing the analogy between Ohm’s Law and Darcy’s Law. By solving the Poisson equation in parallel with the flow equation using ADGPRS, a Stanford developed flow simulation tool, we can determine the fluid distribution and electric potential distribution at every single time interval.

We start investigating the behavior of electric potential during flow by considering a simple water injection problem; the water injection model can be visualized in Figure 2. In this model, we modified the length of the grids adjacent to the injection well, and increased the permeability of these grids so that we have a long, thin conductive channel just like a hydraulic fracture. Then we inject water and electric current at the same location indicated in the figure and simulate the behavior of water flow and electric current flow throughout this injection

process.

Moving forward we will use a more sophisticated hydraulic fracturing model as shown in figure 3. This model uses an unstructured grid, and has two clearly defined fractures within a horizontal well.

## Inverse Analysis

After acquiring time-lapse electric potential data, we can proceed to solve the inverse problem and estimate the properties of the hydraulic fracture. The general steps to solve the inverse problem can be described in figure 4:

We parameterized the forward model with hydraulic fracture length and proceed to solve for the true fracture length by applying the Direct Search Method. The algorithm successfully reach the global minimum of the objective function and find the right facture length (Figure 5).

## Forward Plan

- We will investigate the electric field sensitivity to electrode placement and therefore identify the best locations to set up electric survey device.
- Fracture length is just a starting point to test electric potential data’s ability to tell stories. We will examine the feasibility of solving for other fracture parameters using electric potential data.
- Optimization can be challenging when applied to nonideal data. We will test and tune our method on noisy data in order to find a robust optimization scheme.
- We will investigate the time-series electric potential behavior in the more sophisticated hydraulic fracture model, and apply the inverse problem optimization scheme to the data generated from this model.

References:

Magnúsdóttir, L.: *Fracture Characterization in Geothermal Reservoirs Using Time-Lapse Electric Potential Data. *PhD Thesis, Stanford University, 2013.** **

H.G. Botset.: *The electrolytic model and its application to the study of recovery problems*. Trans. AIME, 165:15, 1946.

G.P. Wind and A.N. Mazee.: *An electronic analog for unsaturated flow and accumulation of moisture in soils*. Journal of

Hydrology, 41.1:69-83, 1979.