Ensemble-based assimilation of non-linearly related dynamic data in reservoir models exhibiting non-Gaussian characteristics
Open Access
- Author:
- Kumar, Devesh
- Graduate Program:
- Energy and Mineral Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- February 27, 2019
- Committee Members:
- Sanjay Srinivasan, Dissertation Advisor/Co-Advisor
Sanjay Srinivasan, Committee Chair/Co-Chair
Mort Webster, Committee Member
Gregory King, Committee Member
Steven Greybush, Outside Member - Keywords:
- Data assimilation
Ensemble Kalman filter
non-Gaussian parameters
non-linear models
indicator transforms - Abstract:
- Inverse modeling techniques for estimating reservoir parameters (e.g., Transmissivity, Permeability, etc.) utilize some secondary information (e.g., hydraulic head or production data at well locations) to estimate reservoir parameters. Ensemble-based data assimilation methods are one such class of inverse modeling techniques. Ensemble Kalman filters (EnKF) in specific are built around the basic framework where modeling parameters such as transmissivity, permeability, storativity, porosity, hydraulic head, phase-saturation are included within a state vector psi^f that are updated to psi^a, based on the available dynamic data. Although EnKF presents the ability to update a large number of parameters successively as data becomes available, it suffers from some major drawbacks. It is optimal only in the case when the multivariate joint distribution describing the state vector is multi-Gaussian. Also, a linear update equation comprised of covariance values between the observed variables and update parameter and covariance between the different observed variables are used in EnKF. These assumptions and simplifications result in models that yield inaccurate predictions of reservoir performance. The aim of this research work is to propose a novel method for data assimilation which is free from the Gaussian and linear transfer function assumptions. This new method can be used to sequentially assimilate dynamic data into reservoir models using an ensemble based approach. Updating is performed in the indicator space where modeling is performed non-parametrically and the indicator transform is insensitive to non-linear operations. It is demonstrated that this indicator transform helps us achieve the desired generality which is a shortcoming of EnKF. Because the expected value of indicators directly yield the probability corresponding to an outcome, the method can be used to quantify the residual uncertainty in spatial description of reservoir properties. Because at all steps of the process an ensemble of models is available, so quantification of residual uncertainty in prediction forecasts is possible. Another advantage is that the data assimilation is sequential in nature implying that the updates can be performed in a quasi-real time sense as data becomes available.