Data inversion in coupled subsurface flow and geomechanics models
Data inversion in coupled subsurface flow and geomechanics models
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耦合地下流和地质力学模型中的数据反演
DOI：
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发表时间：
2012
期刊：
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通讯作者：
D. McLaughlin
中科院分区：
文献类型：
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作者：
M. Iglesias;D. McLaughlin
我们提出了一种反模拟方法来估计地下岩石的物理和弹性性质。其目的是使用Girault等人的完全耦合的地质力学-流动模型(2011 Math.模型、方法、应用SCI。21 169-213)，用于联合反演井的地表变形和压力数据。我们使用泛函分析框架来构造一个正向算子(参数到输出的映射)，该算子源于Girault等人的地质力学流动模型。然后，我们遵循一个确定性的方法来提出从正向算子的输出的测量中寻找参数估计的反问题。我们证明了这个反问题在稳定性意义下是不适定的。然后用Hanke(1997 Numer)的牛顿共轭梯度(CG)算法实现反问题的正则化。功能。肛门。奥蒂姆。18 18-971)。为了使牛顿-CG格式得到一致的应用，我们建立了正向映射的可微性，并刻画了它的线性化的伴随性质。我们给出了Hanke理论保证牛顿-CG格式的收敛和正则化性质的假设。这些性质在数值实验中得到了验证。此外，我们的合成实验显示了所提出的反演方法通过数据反演来估计地下参数的能力。特别是，相对于用流动模型反演生产数据的标准历史匹配方法，对地表变形测量在绝对渗透率估计中的附加值进行了量化。拟议的方法有可能与生产数据结合起来用来反演卫星大地测量数据(例如InSAR和GPS)，以便对地下进行最佳监测和表征。
We present an inverse modeling approach to estimate petrophysical and elastic properties of the subsurface. The aim is to use the fully coupled geomechanics-flow model of Girault et al (2011 Math. Models Methods Appl. Sci. 21 169–213) to jointly invert surface deformation and pressure data from wells. We use a functional-analytic framework to construct a forward operator (parameter-to-output map) that arises from the geomechanics-flow model of Girault et al. Then, we follow a deterministic approach to pose the inverse problem of finding parameter estimates from measurements of the output of the forward operator. We prove that this inverse problem is ill-posed in the sense of stability. The inverse problem is then regularized with the implementation of the Newton-conjugate gradient (CG) algorithm of Hanke (1997 Numer. Funct. Anal. Optim. 18 18–971). For a consistent application of the Newton-CG scheme, we establish the differentiability of the forward map and characterize the adjoint of its linearization. We provide assumptions under which the theory of Hanke ensures convergence and regularizing properties of the Newton-CG scheme. These properties are verified in our numerical experiments. In addition, our synthetic experiments display the capabilities of the proposed inverse approach to estimate parameters of the subsurface by means of data inversion. In particular, the added value of measurements of surface deformation in the estimation of absolute permeability is quantified with respect to the standard history matching approach of inverting production data with flow models. The proposed methodology can be potentially used to invert satellite geodetic data (e.g. InSAR and GPS) in combination with production data for optimal monitoring and characterization of the subsurface.