Uncertainty Quantification of Allen-Cahn Phase Field Parameters in Multiphysics Simulation of Oil Shale Radio Frequency Heating

2021 ◽  
Author(s):  
Travis Ramsay
Keyword(s):  
Finite Element ◽  
Phase Field ◽  
Oil Shale ◽  
Polynomial Chaos ◽  
Rock Type ◽  
Reaction Diffusion ◽  
Chaos Expansion ◽  
Summary Statistics ◽  
Rf Heating ◽  
Simulation Results

Abstract Radio frequency (RF) heating represents a dielectric heating technique for converting kerogen-rich oil shale into liquid oil through in-situ pyrolysis. This process can be modeled using a multiphysics finite element based coupled thermal, phase field, mechanical and electromagnetic (TPME) numerical framework. This work focuses on the combination of a two-dimensional (2D) TPME multiphysics simulation with uncertainty quantification (UQ) that incorporates the Allen-Cahn phase field parameters, specifically those which describe the associated reaction-diffusion process as electromagnetic energy being converted to thermal energy in the RF heating process. The breadth of UQ performed in this study includes not only the Allen-Cahn parameters but also selected thermal, statistical rock-type distribution in the geological model, as well as electromagnetic parameters of the applied quasi-static Maxwell equation. A Non-Intrusive Polynomial Chaos (NIPC) is used for: considering the affect of Allen-Cahn phase field parameters on the evaluation of plausible conversion timelines of TPME simulation and the evaluation of summary statistics to predict the order of Polynomial Chaos Expansion (PCE) that is representative of full kerogen-rich zonal conversion response in a geologically descriptive finite element model. A sparse representation of polynomial chaos coefficients is highlighted in the process of computing summary statistics for the complex stochastically-driven TPME simulation results. Additionally, Monte Carlo (MC) simulations were performed in order to validate the results of the sparse NIPC representation. This is done considering MC is a widely recognized stochastic simulation process. Additionally, NIPC was used to illustrate the potential performance improvement that are possible, with a sparse polynomial chaos expansion enhanced by the incorporation of Least Angle Regression (LAR), as compared to MC simulation. Although the parametic uncertainty of the reaction-diffusion parameters of the Allen-Cahn was comprehensive, they did not accelerate the conversion timelines associated with the full zonal conversion of the kerogen-rich rock type in the statistical simulation results. By executing the stochastic simulations for a greater length of time the extent of full zonal conversion is examined in the RF modeling.

scholarly journals Stochastic Analysis of the Eigenvalue Problem for Mechanical Systems Using Polynomial Chaos Expansion— Application to a Finite Element Rotor

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
E. Sarrouy ◽  
O. Dessombz ◽  
J.-J. Sinou
Keyword(s):  
Finite Element ◽  
Stochastic Analysis ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Eigenvalues And Eigenvectors ◽  
Campbell Diagram ◽  
Complex Eigenvalues ◽  
Gyroscopic Effects ◽  
Rotor Model

This paper proposes to use a polynomial chaos expansion approach to compute stochastic complex eigenvalues and eigenvectors of structures including damping or gyroscopic effects. Its application to a finite element rotor model is compared to Monte Carlo simulations. This lets us validate the method and emphasize its advantages. Three different uncertain configurations are studied. For each, a stochastic Campbell diagram is proposed and interpreted and critical speeds dispersion is evaluated. Furthermore, an adaptation of the Modal Accordance Criterion (MAC) is proposed in order to monitor the eigenvectors dispersion.

Stochastic Finite Element Method Using Polynomial Chaos Expansion

2011 ◽  
Vol 199-200 ◽  
pp. 500-504 ◽  
Author(s):  
Wei Zhao ◽  
Ji Ke Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Polynomial Chaos ◽  
Expansion Method ◽  
Polynomial Chaos Expansion ◽  
Polynomial Expansion ◽  
Stochastic Finite Element Method ◽  
Chaos Expansion ◽  
Stochastic Finite Element ◽  
Element Method

We present a new response surface based stochastic finite element method to obtain solutions for general random uncertainty problems using the polynomial chaos expansion. The approach is general but here a typical elastostatics example only with the random field of Young's modulus is presented to illustrate the stress analysis, and computational comparison with the traditional polynomial expansion approach is also performed. It shows that the results of the polynomial chaos expansion are improved compared with that of the second polynomial expansion method.

Uncertainty Quantification of an Explicitly Coupled Multiphysics Simulation of In-Situ Pyrolysis by Radio Frequency Heating in Oil Shale

SPE Journal ◽  
2020 ◽  
Vol 25 (03) ◽  
pp. 1443-1461
Author(s):  
Travis Ramsay
Keyword(s):  
Radio Frequency ◽  
Uncertainty Quantification ◽  
Oil Shale ◽  
Oil And Gas ◽  
Polynomial Chaos ◽  
Epistemic Uncertainty ◽  
Rf Heating ◽  
Commercial Development ◽  
Mc Simulation

Summary In-situ pyrolysis provides an enhanced oil recovery (EOR) technique for exploiting oil and gas from oil shale by converting in-place solid kerogen into liquid oil and gas. Radio-frequency (RF) heating of the in-place oil shale has previously been proposed as a method by which the electromagnetic energy gets converted to thermal energy, thereby heating in-situ kerogen so that it converts to oil and gas. In order to numerically model the RF heating of the in-situ oil shale, a novel explicitly coupled thermal, phase field, mechanical, and electromagnetic (TPME) framework is devised using the finite element method in a 2D domain. Contemporaneous efforts in the commercial development of oil shale by in-situ pyrolysis have largely focused on pilot methodologies intended to validate specific corporate or esoteric EOR strategies. This work focuses on addressing efficient epistemic uncertainty quantification (UQ) of select thermal, oil shale distribution, electromagnetic, and mechanical characteristics of oil shale in the RF heating process, comparing a spectral methodology to a Monte Carlo (MC) simulation for validation. Attempts were made to parameterize the stochastic simulation models using the characteristic properties of Green River oil shale. The geologic environment being investigated is devised as a kerogen-poor under- and overburden separated by a layer of heterogeneous yet kerogen-rich oil shale in a target formation. The objective of this work is the quantification of plausible oil shale conversion using TPME simulation under parametric uncertainty; this, while considering a referenced conversion timeline of 1.0 × 107 seconds. Nonintrusive polynomial chaos (NIPC) and MC simulation were used to evaluate complex stochastically driven TPME simulations of RF heating. The least angle regression (LAR) method was specifically used to determine a sparse set of polynomial chaos coefficients leading to the determination of summary statistics that describe the TPME results. Given the existing broad use of MC simulation methods for UQ in the oil and gas industry, the combined LAR and NIPC is suggested to provide a distinguishable performance improvement to UQ compared to MC methods.

An Efficient Sampling Method for Regression-Based Polynomial Chaos Expansion

2013 ◽  
Vol 13 (4) ◽  
pp. 1173-1188 ◽  
Author(s):  
Samih Zein ◽  
Benoît Colson ◽  
François Glineur
Keyword(s):  
Finite Element ◽  
Design Of Experiments ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Computational Time ◽  
Chaos Expansion ◽  
Analysis Model ◽  
Element Analysis ◽  
Analytical Functions ◽  
The Cost

AbstractThe polynomial chaos expansion (PCE) is an efficient numerical method for performing a reliability analysis. It relates the output of a nonlinear system with the uncertainty in its input parameters using a multidimensional polynomial approximation (the so-called PCE). Numerically, such an approximation can be obtained by using a regression method with a suitable design of experiments. The cost of this approximation depends on the size of the design of experiments. If the design of experiments is large and the system is modeled with a computationally expensive FEA (Finite Element Analysis) model, the PCE approximation becomes unfeasible. The aim of this work is to propose an algorithm that generates efficiently a design of experiments of a size defined by the user, in order to make the PCE approximation computationally feasible. It is an optimization algorithm that seeks to find the best design of experiments in the D-optimal sense for the PCE. This algorithm is a coupling between genetic algorithms and the Fedorov exchange algorithm. The efficiency of our approach in terms of accuracy and computational time reduction is compared with other existing methods in the case of analytical functions and finite element based functions.

scholarly journals Stochastic Finite Element Analysis using Polynomial Chaos

2016 ◽  
Vol 38 (1) ◽  
pp. 33-43 ◽  
Author(s):  
S. Drakos ◽  
G.N. Pande
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Stochastic Analysis ◽  
Polynomial Chaos ◽  
Computational Time ◽  
Chaos Expansion ◽  
Stochastic Finite Element ◽  
Element Analysis ◽  
Stochastic Finite Element Analysis ◽  
Random Finite Element

Abstract This paper presents a procedure of conducting Stochastic Finite Element Analysis using Polynomial Chaos. It eliminates the need for a large number of Monte Carlo simulations thus reducing computational time and making stochastic analysis of practical problems feasible. This is achieved by polynomial chaos expansion of the displacement field. An example of a plane-strain strip load on a semi-infinite elastic foundation is presented and results of settlement are compared to those obtained from Random Finite Element Analysis. A close matching of the two is observed.

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