Abstract
The calibration of a reservoir model with observed transient data of fluid pressures and rates is a key task in obtaining a predictive model of the flow and transport behaviour of the earth's subsurface. The model calibration task, commonly referred to as "history matching", can be formalised as an ill-posed inverse problem where we aim to find the underlying spatial distribution of petrophysical properties that explain the observed dynamic data. We use a generative adversarial network pretrained on geostatistical object-based models to represent the distribution of rock properties for a synthetic model of a hydrocarbon reservoir. The dynamic behaviour of the reservoir fluids is modelled using a transient two-phase incompressible Darcy formulation. We invert for the underlying reservoir properties by first modeling property distributions using the pre-trained generative model then using the adjoint equations of the forward problem to perform gradient descent on the latent variables that control the output of the generative model. In addition to the dynamic observation data, we include well rock-type constraints by introducing an additional objective function. Our contribution shows that for a synthetic test case, we are able to obtain solutions to the inverse problem by optimising in the latent variable space of a deep generative model, given a set of transient observations of a non-linear forward problem.
Abstract (translated)
利用流体压力和速率的观测瞬态数据对储层模型进行校准是获得地下流体流动和输运行为预测模型的关键任务。模型校正任务，通常被称为“历史匹配”，可以形式化为一个不适定的逆问题，我们的目标是找到解释观测动态数据的岩石物理性质的潜在空间分布。我们利用地质统计对象模型预训练的生成对抗网络来表示油气藏综合模型的岩石性质分布。利用瞬态两相不可压缩达西公式对储层流体的动力学行为进行了模拟。我们首先利用预先训练的生成模型对储层的属性分布进行建模，然后利用正问题的伴随方程对控制生成模型输出的潜在变量进行梯度下降，从而反演下伏储层的属性。除了动态观测数据外，我们还引入了一个附加的目标函数，将井-岩类型约束包括在内。我们的贡献表明，对于一个综合测试案例，在给定一组非线性正问题的瞬态观测的情况下，我们能够通过在深生成模型的潜在变量空间中进行优化来获得反问题的解。
URL
https://arxiv.org/abs/1905.05749
