Combining autoencoder neural network and Bayesian inversion to estimate heterogeneous permeability distributions in enhanced geothermal reservoir: Model development and verification

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Determining permeability distributions in reservoirs is critical for the management of limited earth resources. While hydraulic fracturing is widely used to enhance the permeability of deep geothermal, gas and oil reservoirs, it remains challenging to infer heterogeneous distributions of permeability. Typically, a limited number of boreholes are available at which reservoir imaging and tracer testing can be conducted. The number of observations is often far fewer than the number of estimable permeability parameters, making model inversion ill-posed. To overcome this problem, the autoencoder neural network was combined with a Bayesian inversion algorithm based on Markov Chain Monte Carlo (MCMC) sampling, in order to estimate the spatial distributions of permeability in an enhanced geothermal reservoir, conditional to temperature and outflow rate observations from a single-well-injection-withdrawal test (SWIW). The autoencoder neural network was used to reduce parameter dimensionality by four orders of magnitude. MCMC sampling was used to estimate low-dimensional parameters via inversion of SWIW observations. A high-resolution permeability distribution was reconstructed from the low-dimensional parameterization through reapplication of the autoencoder neural network. Application to a synthetic enhanced geothermal system demonstrated that the methodology achieved rapid stabilization and low permeability estimation error (<10%). By combining deep-learning method with Bayesian inversion, permeability distributions in geo-energy reservoirs can be estimated from a limited set of borehole data.