Oil & Natural Gas Projects
Exploration and Production Technologies
Direct Quantification of Uncertainties Associated with Reservoir Performance
This project was funded through DOE's Natural Gas and Oil Technology Partnership
Program. The program establishes alliances that combine the resources and experience
of the nation's petroleum industry with the capabilities of the national laboratories
to expedite research, development, and demonstration of advanced technologies
for improved natural gas and oil recovery.
The goal of this project was to develop an efficient and accurate approach to
quantify uncertainty for flow in randomly heterogeneous reservoirs.
Los Alamos National Laboratory
Los Alamos, NM
University of Oklahoma
San Ramon, CA
Researchers developed a completely new approach to quantify uncertainties associated
with resevoir performance simulations-a moment-equation method based on Kahunen-Loeve
decomposition (KLME), which is much more efficient and accurate than the moment-equation
method they originally proposed. The KLME approach makes it possible to evaluate
higher-order terms that are needed for highly heterogeneous reservoirs. The
KLME method enables the simulation of flow and transport in large-scale heterogeneous
reservoirs and may revolutionize the way of quantifying uncertainty in reservoir
Performance predictions obtained from reservoir flow simulations are the primary
tool for managing existing operations and planning future developments. The
study provides a general, computationally efficient and accurate tool for quantifying
uncertainties for flow in heterogeneous porous media. It couuld have a significant
impact on a wide range of fields, including energy security (nuclear waste repository
sciences), contaminant transport (DOE's site cleanup), oil/gas recovery (energy
security), and geological carbon sequestration (global warming).
Accurate modeling of reservoir flows requires a detailed spatial description
of reservoir properties such as permeability and porosity. However, oil and
gas reservoirs exhibit a high degree of spatial variability in medium properties,
which are usually measured only at a few locations. This leads to uncertainty
about the values of reservoir properties and in turn to uncertainty in predicting
flow in such reservoirs. The common tool in quantifying this uncertainty in
industry has been the Monte Carlo method, which is computationally expensive.
Researchers originally proposed to develop a direct method based on the moment
approach. During the course of this study, they developed a completely new approach,
a moment-equation method based on KLME, which is much more efficient and accurate
than the Monte Carlo method and the moment-equation method originally proposed.
Project researchers have:
- Developed a moment approach based on KLME for solving stochastic flow in
randomly heterogeneous reservoirs.
- Extended the KLME method to a number of different flow conditions, such
as multiphase flow.
Because of heterogeneity in reservoir properties such as permeability, the
flow equations are treated as stochastic partial differential equations. Researchers
first decomposed the log permeability using the Karhunen-Loéve (KL) decomposition,
which is of mean square convergence. They then wrote the pressure head as an
infinite series whose terms h(n) represent the head contribution at the nth
order in terms Y, the standard deviation of log permeability, and derived a
set of recursive equations for h(n). This assumes that h(n) can be expressed
as infinite series in terms of the products of n Gaussian random variables.
In short, using the new approach, with a much lower computational cost, the
project performers are able to evaluate the mean pressure head up to fourth
order in Y and the pressure head variance to the third order in Y2.
Researchers compared the results from the KLME approach against those from
Monte Carlo simulations and the first-order moment method originally proposed.
It is evident that the KLME approach, with higher-order corrections, is superior
to the first-order approximations and is computationally more efficient than
both the Monte Carlo simulations and the first-order moment method. The KLME
approach has been extended to simulate water flow in unsaturated soils (Yang
et al.), in conditional fields (Lu and Zhang), and two-phase (water and oil
phases) flow problems (Chen et al.).
Current Status (October 2005)
This method is being combined with a Kalman filter to efficiently characterize
geological reservoirs and incorporated into MODFLOW, the most popular groundwater
Publications (partial list)
Lu, Z., and Zhang, D., Stochastic studies of well capture zones in bounded heterogeneous
media, Water Resour. Res., 39(4), 1100, doi:10.1029/2001WR 001633, 2003.
Lu, Z., and Zhang, D., Solute spreading in nonstationary flows in bounded,
heterogeneous unsaturated-saturated media, Water Resour. Res., 39(3), 1049,
doi:10. 1029/2001WR000908, 2003.
Li, L., Tchelepi, H.A., and Zhang, D., Perturbation-based moment equation approach
for flow in heterogeneous porous media: applicability range and analysis of
high-order terms, Journal of Comput. Physics, v.188 n.1, p.296-317, 2003.
Lu, Z., and Zhang, D., Conditional simulations of flow in randomly heterogeneous
porous media using a KL-based moment-equation approach, Advances in Water Resources,
27(9), 859-874, 2004.
Project Start: May 3, 2002
Project End: May 2, 2005
Anticipated DOE Contribution: $500,000
Performer Contribution: $600,000 (55% of total)
NETL - Dan Gurney (email@example.com or 918-699-2063)
LANL - Zhiming Lu (firstname.lastname@example.org or 505-665-2126)