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ACCURATE AND EFFICIENT UNCERTAINTY QUANTIFICATION OF
SUBSURFACE FLUID FLOW VIA THE PROBABILISTIC COLLOCATION
METHOD
by
Heng Li
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(PETROLEUM ENGINEERING)
December 2010
Copyright 2010 Heng Li
Object Description
| Title | Accurate and efficient uncertainty quantification of subsurface fluid flow via the probabilistic collocation method |
| Author | Li, Heng |
| Author email | hengli@usc.edu; liheng2005@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Petroleum Engineering |
| School | Viterbi School of Engineering |
| Date submitted | 2010 |
| Restricted until | Unrestricted |
| Date published | 2010-10-12 |
| Advisor (committee chair) | Zhang, Dongxiao |
| Advisor (committee member) |
Ershaghi, Iraj Ghanem, Roger |
| Abstract | Uncertainty quantification of subsurface flow has recently attracted a significant amount of attention. The uncertainty can result from the combination of the formation heterogeneity and the incomplete knowledge of its properties. Traditional flow simulations treat the geological formation deterministic, thus resulting in deterministic predictions. However, taking uncertainty into account necessitates a stochastic description of the formation properties and hence stochastic approaches to flow simulations.; This dissertation explores an efficient approach, i.e., the probabilistic collocation method (PCM) for uncertainty quantification of flow in random porous media. In this approach, the dependent random variables are represented by employing the orthogonal polynomial functions (polynomial chaos expansions) as the bases of the random space. Utilizing the collocation technique in the random space directly results in a set of independent simulations. This independence feature of this stochastic approach allows us to directly employ existing flow simulators. Random fields such as heterogeneous permeability (or porosity) fields are parameterized using some dimension reduction techniques such as the Karhunen-Loeve expansion. Applications to both single-phase and multi-phase flows are performed. Other than the typical log-normal probability distribution, other non-Gaussian probability distributions are also considered for characterizing the formation properties that are treated as random fields. Conditional simulations of both Gaussian and non-Gaussian random fields when measurements of hydraulic conductivity are available are discussed in this dissertation.; This dissertation also considers uncertainty analysis of petroleum reservoir simulations, where the uncertain parameters have arbitrary probability distributions. The experimental design methods are widely used for uncertainty analysis in the oil industry. However, the traditional experimental design methods usually have an inherent assumption of uniform distributions for the random inputs and they do not take into account the full probability density functions (PDFs) of the input random parameters consistently.; In this dissertation, orthogonal polynomials for arbitrary PDFs are constructed numerically and the PCM is utilized for uncertainty propagation. Each collocation point captures a different weight of the random variables for a given PDF and thus yields optimal approximation of the responses. Various studied cases reveal that, while the computational efforts are greatly reduced compared to Monte Carlo simulation, the PCM is able to accurately quantify uncertainty of the reservoir performance. Results also reveal that the PCM is more robust, accurate, and efficient than experimental design methods for uncertainty analysis. |
| Keyword | uncertainty quantification; random field; porous media; probabilistic collocation method |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m3504 |
| Rights | Li, Heng |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | http://www.usc.edu/isd/libraries/services/ask_a_librarian/email/ |
| Filename | etd-Li-4164 |
| Archival file | uscthesesreloadpub_Volume51/etd-Li-4164.pdf |
Description
| Title | Page 1 |
| Full text | ACCURATE AND EFFICIENT UNCERTAINTY QUANTIFICATION OF SUBSURFACE FLUID FLOW VIA THE PROBABILISTIC COLLOCATION METHOD by Heng Li A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful llment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (PETROLEUM ENGINEERING) December 2010 Copyright 2010 Heng Li |
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