System-Theoretical Model Reduction for Reservoir Simulation and optimization

This thesis is concerned with low-order modelling of heterogeneous reservoir systems for the purpose of efficient simulation and optimization of flooding processes with multiple injection and production (smart) wells. Typically, one is initially equipped with a physics-based ('white-box') model consisting of O(103-106) equations and parameters representing a (coupled) system of discretized PDEs defined on a geometric grid. The model-order reduction (MOR) methodology undertaken in this research is fundamentally different from the traditional, 'grid-coarsing' approximation methods, in that no coarse-grid approximation of the fine-grid problem is employed at all. Instead, the reduced-order models are here based on 'system-theoretic' and dynamically intrinsic properties of the fine-scale system. In single-phase flow problems that can be modelled as linear time-invariant state-space systems these properties are, e.g., the system's transfer function in the Laplace domain, the eigenstructure of the system matrix, or controllability and observability of the (particular state-space realization of the) system. For multi-phase flow problems resulting in nonlinear state-space models, intrinsic information needs to be sought in data obtained by simulating the fine-scale model. The contribution of this thesis can be divided into three themes: 1) Standard 'projection-based' MOR: assessment of the performance of modal truncation, singular perturbation, balanced truncation, transfer function moments maching (inc. Krylov-subspaces), and proper orthogonal decomposition (POD), 2) Acceleration of solving the fine-scale problem: use of MOR as a 'shadow simulation' to determine an improved fine-scale initial guess, and 3) Acceleration of waterflooding optimization: use of POD in the inner-loop of an adjoint-based optimization scheme.Civil Engineering and Geoscience

Use of POD in control of flow through porous media

During the design of development concepts for the exploitation of oil and gas reservoirs, frequent use is made of numerical simulation of the flow of multi-phase fluids through porous rock. Recently, increased attention has been paid to systematic optimization of well positions and operating parameters (rates, pressures) over the life of the reservoir. Here we consider optimization of the displacement of oil towards production wells through the injection of water in other wells. Model-based optimal control of this “water flooding” process generally involves multiple simulations, which makes it into a time-consuming process. A potential way to address this issue is through the use of proper orthogonal decomposition (POD), We addressed the scope to speed up optimization of water-flooding a heterogeneous reservoir with multiple injectors and producers. We used an adjoint-based optimal control methodology that requires multiple passes of forward simulation of the reservoir model and backward simulation of an adjoint system of equations. We developed a nested approach in which POD was first used to reduce the state space dimensions of both the forward model and the adjoint system. After obtaining an optimized injection and production strategy using the reduced-order system, we verified the results using the original, high-order model. If necessary, we repeated the optimization cycle using new reduced-order systems based on snapshots from the verification run We tested the methodology on a reservoir model with 882 states (441 pressures, 441 saturations) and an adjoint model of 882 states (Lagrange multipliers). We obtained reduced-order models with 35-43 states only. The reduction in computing time was 52%.Mechanical, Maritime and Materials Engineerin

Model-reduced gradient-based history matching

Gradient-based history matching algorithms can be used to adapt the uncertain parameters in a reservoir model using production data. They require, however, the implementation of an adjoint model to compute the gradients, which is usually an enormous programming effort. We propose a new approach to gradient-based history matching which is based on model reduction, where the original (nonlinear and high-order) forward model is replaced by a linear reduced-order forward model and, consequently, the adjoint of the tangent linear approximation of the original forward model is replaced by the adjoint of a linear reduced-order forward model. The reducedorder model is constructed with the aid of the proper orthogonal decomposition method. Due to the linear character of the reduced model, the corresponding adjoint model is easily obtained. The gradient of the objective function is approximated, and the minimization problem is solved in the reduced space; the procedure is iterated with the updated estimate of the parameters if necessary. The proposed approach is adjointfree and can be used with any reservoir simulator. The method was evaluated for a waterflood reservoir with channelized permeability field. A comparison with an adjoint-based history matching procedure shows that the model-reduced approach gives a comparable quality of history matches and predictions. The computational efficiency of the model-reduced approach is lower than of an adjoint-based approach, but higher than of an approach where the gradients are obtained with simple finite differences.Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc

Disruption of ER−mitochondria signalling in fronto-temporal dementia and related amyotrophic lateral sclerosis

Fronto-temporal dementia (FTD) and amyotrophic lateral sclerosis (ALS) are two related and incurable neurodegenerative diseases. Features of these diseases include pathological protein inclusions in affected neurons with TAR DNA-binding protein 43 (TDP-43), dipeptide repeat proteins derived from the C9ORF72 gene, and fused in sarcoma (FUS) representing major constituent proteins in these inclusions. Mutations in C9ORF72 and the genes encoding TDP- 43 and FUS cause familial forms of FTD/ALS which provides evidence to link the pathology and genetics of these diseases. A large number of seemingly disparate physiological functions are damaged in FTD/ALS. However, many of these damaged functions are regulated by signalling between the endoplasmic reticulum and mitochondria, and this has stimulated investigations into the role of endoplasmic reticulum-mitochondria signalling in FTD/ALS disease processes. Here, we review progress on this topic