Inverting fluid conductivity logs for fracture inflow parameters

Fluid electrical conductivity logging experiments introduced by Tsang et al. [1990] represent a new technology for studying the hydraulic properties of discrete fractures in open boreholes. These experiments consist of replacing water in the well bore with deionized water and then pumping the well to induce formation water to return to the well bore. During and after the fluid exchange the entire well is logged to measure fluid electrical conductivity (FEC). At locations where formation water enters the well there are abrupt increases in the borehole FEC, thereby revealing the location of hydraulically conductive fractures. As pumping continues, high FEC water moves up the well bore at a rate proportional to the total inflow rate below the observation point. Inflow rates and FECs of formation water associated with each fracture can be inferred by modeling the FEC profiles with the one‐dimensional advective dispersion equation. In this paper I present an inverse model which estimates the inflow rates and formation FEC values that optimally fit observed FEC logs acquired during fluid exchange experiments described by Tsang et al. [1990]. With this inverse model, inflow rates are constrained by the rate at which the well is pumped during the experiment. The forward model is solved numerically using a control volume finite difference scheme with power law upstream weighting and source term linearization. The inverse problem is solved using the Gauss‐Newton iterative method. The rows of the Jacobian matrix, or the sensitivity coefficients, are calculated numerically with the same algorithm that solves the forward problem. Both constrained and unconstrained inverse models are used to interpret fluid logging experiments performed in research wells penetrating Piedmont rocks of North Carolina.