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.

确定储层中的渗透率分布对于有限地球资源的管理至关重要。虽然水力压裂广泛用于提高深层地热、天然气和油藏的渗透率，但推断渗透率的非均质分布仍然具有挑战性。通常，可以进行储层成像和示踪剂测试的钻孔数量有限。观测次数通常远少于可估计渗透率参数的数量，使得模型反演不适定。为了克服这个问题，自动编码器神经网络与基于马尔可夫链蒙特卡罗 (MCMC) 采样的贝叶斯反演算法相结合，以估计增强型地热储层渗透率的空间分布，以单井注采试验 (SWIW) 的温度和流出速率观察为条件。自编码器神经网络用于将参数维度降低四个数量级。MCMC 采样用于通过 SWIW 观测值的反演来估计低维参数。通过重新应用自动编码器神经网络，从低维参数化重建高分辨率渗透率分布。应用于合成增强地热系统表明该方法实现了快速稳定和低渗透率估计误差 (<10%)。通过将深度学习方法与贝叶斯反演相结合，可以从一组有限的钻孔数据中估计地能储层的渗透率分布。