Integrating monitoring data to efficiently update reservoir pressure and CO2 plume distribution forecasts presents a significant challenge in geological carbon storage (GCS) applications. Inverse modeling techniques are commonly used to fuse observational data and refine reservoir model parameters, thereby improving state variable forecasts. However, these techniques often rely on linear or Gaussian assumptions, which can limit their effectiveness in accurately predicting state variables. Moreover, simulating large-scale three-dimensional (3D) GCS problems is computationally expensive, making iterative runs in inverse problems prohibitive. To address these challenges, we propose a conditional generative model utilizing the score-based diffusion method for real-time 3D pressure and saturation field distribution predictions. Our approach involves solving the score function with a mini-batch-based Monte Carlo estimator to generate labeled data. This data is subsequently employed to train a fully connected neural network, enabling it to learn the conditional sample generator within a supervised learning framework. This method enables the rapid generation of a large ensemble of predictions, facilitating comprehensive uncertainty quantification of state variables. We applied our method to forecast the dynamic 3D distributions of pressure and saturation fields over a 30-year injection period. The statistical assessment with low root mean square error (RMSE) values demonstrates that our method can accurately predict the spatiotemporal distributions of both pressure and saturation fields. Moreover, the developed conditional generative model shows high computational efficiency by generating 100 ensemble forecasts of 3D state variables in less than 10 min. The consistency between ensemble averages and ground truth values further illustrates the model’s capability to capture state variable dynamics during the CO2 plume injection process. Notably, the ground truth values fall within the ensemble forecasts, indicating that our uncertainty quantification effectively captures variability and potential noise in the observations. Thus, the developed conditional generative model proves to be a more efficient, accurate, and practical tool for GCS applications, facilitating timely risk analysis and informed decision-making.

中文翻译：

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一种用于大规模地质碳封存中状态变量高效集成预测的新型条件生成模型


整合监测数据以有效更新储层压力和 CO2 羽流分布预测，是地质碳封存 （GCS） 应用中的重大挑战。逆向建模技术通常用于融合观测数据和优化储层模型参数，从而改进状态变量预测。但是，这些技术通常依赖于线性或高斯假设，这可能会限制它们在准确预测状态变量方面的有效性。此外，模拟大规模三维 （3D） GCS 问题的计算成本很高，这使得逆问题中的迭代运行令人望而却步。为了应对这些挑战，我们提出了一种条件生成模型，利用基于分数的扩散方法进行实时 3D 压力和饱和场分布预测。我们的方法涉及使用基于小批量的 Monte Carlo 估计器求解 score 函数，以生成标记数据。这些数据随后用于训练完全连接的神经网络，使其能够在监督学习框架中学习条件样本生成器。这种方法能够快速生成大量预测，从而促进状态变量的全面不确定性量化。我们应用我们的方法预测了 30 年注入期间压力场和饱和场的动态 3D 分布。具有低均方根误差 （RMSE） 值的统计评估表明，我们的方法可以准确预测压力场和饱和场的时空分布。此外，开发的条件生成模型通过在不到 10 分钟的时间内生成 100 个 3D 状态变量的集成预测，显示出很高的计算效率。 集成平均值和地面实况值之间的一致性进一步说明了该模型在 CO2 羽流注入过程中捕获状态变量动态的能力。值得注意的是，地面实况值位于集成预测范围内，这表明我们的不确定性量化有效地捕获了观测中的可变性和潜在噪声。因此，开发的条件生成模型被证明是 GCS 应用的更高效、更准确和实用的工具，有助于及时进行风险分析和明智的决策。