We are concerned with stochastic methods for predictive simulations of flows in the subsurface that can incorporate dynamical data (such as pressure data and production curves in field-scale operations) to reduce uncertainty in determining time-dependent subsurface properties such as absolute permeability, porosity and Young’s modulus in the context of poroelasticity. There exists a considerable amount of work in the development of these methods with focus on rigid porous media. Procedures such as Markov chain Monte Carlo methods and Kalman filters have been considered for rock characterization and Monte Carlo simulations applied for predicting fluid flow. This is not the case with deformable subsurface formations. Although clearly relevant for the exploration of oil and gas, considerably less developments have been reported in this case. Difficulty arises because subsurface properties (typically modeled by time-independent random fields) change with time and known uncertainty quantification and reduction methods may not be directly applicable. Our goal here is the development of a Bayesian modeling framework that allows for the characterization of time-dependent rock properties along with the prediction of multiphase flows in such formations. The proposed framework has performed well to characterize time-dependent porosity and permeability fields in single-phase flows in heterogeneous deformable media, considering the concept of rock compressibility. Despite its simplicity, this problem gathers several characteristics of more complex models currently employed in the coupling of fluid flow and mechanical response of the reservoir solid structure.

中文翻译：

---

耦合流体流动和岩土力学变形的地下特征描述的新方法：轻微压缩流动的情况

我们关注用于地下流动预测的随机方法，该方法可以结合动态数据（例如现场规模操作中的压力数据和生产曲线），以减少确定随时间变化的地下性质（如绝对渗透率，孔隙度和孔隙度）时的不确定性。孔隙弹性条件下的杨氏模量。在这些方法的开发中，有大量工作集中在刚性多孔介质上。已经考虑了诸如马尔可夫链蒙特卡罗方法和卡尔曼滤波器之类的程序来进行岩石表征，而蒙特卡罗模拟则用于预测流体流量。对于可变形的地下地层则不是这种情况。尽管与石油和天然气的勘探显然相关，但在这种情况下，所报道的发展却很少。之所以会出现困难，是因为地下属性（通常由与时间无关的随机字段建模）随时间变化，并且已知的不确定性量化和减少方法可能无法直接应用。我们的目标是开发一种贝叶斯建模框架，该框架可以表征随时间变化的岩石特性，并预测此类地层中的多相流。考虑到岩石可压缩性的概念，所提出的框架在描述非均质可变形介质中单相流中随时间变化的孔隙率和渗透率场方面表现良好。尽管简单，但此问题收集了当前在流体流动和油藏实体结构的机械响应耦合中使用的更复杂模型的几个特征。