Farid Mohammadi

Abstract

Existing model validation studies in geoscience often disregard or partly account for uncertainties in observations, model choices, and input parameters. In this work, we develop a statistical framework that incorporates a probabilistic modeling technique using a fully Bayesian approach to perform a quantitative uncertainty-aware validation. A Bayesian perspective on a validation task yields an optimal bias-variance trade-off against the reference data. It provides an integrative metric for model validation that incorporates parameter and conceptual uncertainty. Additionally, a surrogate modeling technique, namely Bayesian Sparse Polynomial Chaos Expansion, is employed to accelerate the computationally demanding Bayesian calibration and validation. We apply this validation framework to perform a comparative evaluation of models for coupling a free flow with a porous-medium flow. The correct choice of interface conditions and proper model parameters for such coupled flow systems is crucial for physically consistent modeling and accurate numerical simulations of applications. We develop a benchmark scenario that uses the Stokes equations to describe the free flow and considers different models for the porous-medium compartment and the coupling at the fluid–porous interface. These models include a porous-medium model using Darcy’s law at the representative elementary volume scale with classical or generalized interface conditions and a pore-network model with its related coupling approach. We study the coupled flow problems’ behaviors considering a benchmark case, where a pore-scale resolved model provides the reference solution. With the suggested framework, we perform sensitivity analysis, quantify the parametric uncertainties, demonstrate each model’s predictive capabilities, and make a probabilistic model comparison.

Abstract

Geochemical processes in subsurface reservoirs affected by microbial activity change the material properties of porous media. This is a complex biogeochemical process in subsurface reservoirs that currently contains strong conceptual uncertainty. This means, several modeling approaches describing the biogeochemical process are plausible and modelers face the uncertainty of choosing the most appropriate one. The considered models differ in the underlying hypotheses about the process structure. Once observation data become available, a rigorous Bayesian model selection accompanied by a Bayesian model justifiability analysis could be employed to choose the most appropriate model, i.e. the one that describes the underlying physical processes best in the light of the available data. However, biogeochemical modeling is computationally very demanding because it conceptualizes different phases, biomass dynamics, geochemistry, precipitation and dissolution in porous media. Therefore, the Bayesian framework cannot be based directly on the full computational models as this would require too many expensive model evaluations. To circumvent this problem, we suggest to perform both Bayesian model selection and justifiability analysis after constructing surrogates for the competing biogeochemical models. Here, we will use the arbitrary polynomial chaos expansion. Considering that surrogate representations are only approximations of the analyzed original models, we account for the approximation error in the Bayesian analysis by introducing novel correction factors for the resulting model weights. Thereby, we extend the Bayesian model justifiability analysis and assess model similarities for computationally expensive models. We demonstrate the method on a representative scenario for microbially induced calcite precipitation in a porous medium. Our extension of the justifiability analysis provides a suitable approach for the comparison of computationally demanding models and gives an insight on the necessary amount of data for a reliable model performance.

Abstract

We present version 3 of the open-source simulator for flow and transport processes in porous media DuMux. DuMux is based on the modular C++ framework Dune (Distributed and Unified Numerics Environment) and is developed as a research code with a focus on modularity and reusability. We describe recent efforts in improving the transparency and efficiency of the development process and community-building, as well as efforts towards quality assurance and reproducible research. In addition to a major redesign of many simulation components in order to facilitate setting up complex simulations in DuMux, version 3 introduces a more consistent abstraction of finite volume schemes. Finally, the new framework for multi-domain simulations is described, and three numerical examples demonstrate its flexibility.

Abstract

Calcium oxide/Calcium hydroxide can be utilized as a reaction system for thermochemical heat storage. It features a high storage capacity, is cheap, and does not involve major environmental concerns. Operationally, different fixed-bed reactor concepts can be distinguished; direct reactor are characterized by gas flow through the reactive bulk material, while in indirect reactors, the heat-carrying gas flow is separated from the bulk material. This study puts a focus on the indirectly operated fixed-bed reactor setup. The fluxes of the reaction fluid and the heat-carrying flow are decoupled in order to overcome limitations due to heat conduction in the reactive bulk material. The fixed bed represents a porous medium where Darcy-type flow conditions can be assumed. Here, a numerical model for such a reactor concept is presented, which has been implemented in the software DuMux. An attempt to calibrate and validate it with experimental results from the literature is discussed in detail. This allows for the identification of a deficient insulation of the experimental setup. Accordingly, heat-loss mechanisms are included in the model. However, it can be shown that heat losses alone are not sufficient to explain the experimental results. It is evident that another effect plays a role here. Using Bayesian inference, this effect is identified as the reaction rate decreasing with progressing conversion of reactive material. The calibrated model reveals that more heat is lost over the reactor surface than transported in the heat transfer channel, which causes a considerable speed-up of the discharge reaction. An observed deceleration of the reaction rate at progressed conversion is attributed to the presence of agglomerates of the bulk material in the fixed bed. This retardation is represented phenomenologically by mofifying the reaction kinetics. After the calibration, the model is validated with a second set of experimental results. To speed up the calculations for the calibration, the numerical model is replaced by a surrogate model based on Polynomial Chaos Expansion and Principal Component Analysis.

Abstract

A variety of empirical formulas to predict river bed evolution with hydro-morphodynamic river models exists. Modelers lack objective guidance of how to select the most appropriate one for a specific application. Such guidance can be provided by Bayesian model selection (BMS). Its applicability is however limited by high computational costs. To transfer it to computationally expensive river modeling tasks, we propose to combine BMS with model reduction based on arbitrary Polynomial Chaos Expansion. To account for approximation errors in the reduced models, we introduce a novel correction factor that yields a reliable model ranking even under strong computational time constraints. We demonstrate our proposed approach on a case study for a 10-km stretch of the lower Rhine river. The correction factor may shield us from misleading model ranking results. In our case, the correction factor was shown to increase the confidence in model selection.