Lithological Controls on the Permeability of Geologic Faults: Surrogate Modeling and Sensitivity Analysis

TL;DR

Fault-zone permeability is highly controlled by lithology, but traditional GSA is hindered by expensive flow-based upscaling. The authors introduce PREDICT, a probabilistic framework, and a UNet-based surrogate to replace MRST upscaling, enabling tractable global sensitivity analysis on $k_{xx}$ and $k_{zz}$. Sobol’ variance-based indices reveal that the maximum burial depth $z_{ ext{max}}$ is the dominant control and that strong nonlinear interactions shape extreme permeability outcomes. This surrogate-accelerated approach reduces computational cost by orders of magnitude and enhances uncertainty quantification for reservoir-scale applications such as CO$_2$ storage and hydrocarbon operations.

Abstract

Fault zones exhibit complex and heterogeneous permeability structures influenced by stratigraphic, compositional, and structural factors, making them critical yet uncertain components in subsurface flow modeling. In this study, we investigate how lithological controls influence fault permeability using the PREDICT framework: a probabilistic workflow that couples stochastic fault geometry generation, physically constrained material placement, and flow-based upscaling. The flow-based upscaling step, however, is a very computationally expensive component of the workflow and presents a major bottleneck that makes global sensitivity analysis (GSA) intractable, as it requires millions of model evaluations. To overcome this challenge, we develop a neural network surrogate to emulate the flow-based upscaling step. This surrogate model dramatically reduces the computational cost while maintaining high accuracy, thereby making GSA feasible. The surrogate-model-enabled GSA reveals new insights into the effects of lithological controls on fault permeability. In addition to identifying dominant parameters and negligible ones, the analysis uncovers significant nonlinear interactions between parameters that cannot be captured by traditional local sensitivity methods.

Figures (13)

• Figure 1: PREDICT's workflow (left to right). Stratigraphic section in the throw window of interest is described by input parameters, which PREDICT uses to compute ranges and probability distributions for intermediate variables. For each fault section, fault thickness $f_T$, residual friction angle ($\phi_r^\prime$), critical shale smear factor (SSFc), porosity ($n$), permeability ($k$), and permeability anisotropy ratio ($k^\prime$) are sampled and used to place fault materials and assign their properties. Subscript “c” refers to clay smear, and “s” refers to sand smear. Permeability is upscaled using 2-D fault volume.
• Figure 2: Four scenarios of the two-layer system: CSC, CSS, SCC, and SCS (left to right). The throw window spans 100 meters, with the footwall composed of two 50-meter-thick layers.
• Figure 3: Responses of permeability distributions to variations in individual parameters for the CSS scenario. Left: distribution changes of $\log_{10}(k_{xx})$ with varying $z_\text{max}$; Middle: distribution changes of $\log_{10}(k_{xx})$ with varying $f_\beta$; Right: distribution changes of $\log_{10}(k_{zz})$ with varying $V_\text{cl}^\text{HW}$.
• Figure 4: Tornado plots of the 10th (left), 50th (middle), and 90th (right) percentiles for $\log_{10}(k_{xx})$ (top row) and $\log_{10}(k_{zz})$ (bottom row) in the CSS scenario. Dark brown bars represent deviations caused by positive perturbations ($\Delta^+ Q^s_i$ in Eq. \ref{['eq: tornado_plus']}), while light orange bars represent deviations caused by negative perturbations ($\Delta^- Q^s_i$ in Eq. \ref{['eq: tornado_minus']}).
• Figure 5: Proposed workflow to enable global sensitivity analysis: replacing flow-based MRST upscaling by a CNN surrogate within PREDICT.