349 research outputs found
Modeling two-phase flow of immiscible fluids in porous media: Buckley-Leverett theory with explicit coupling terms
Continuum models that describe two-phase flow of immiscible fluids in porous media often treat momentum exchange between the two phases by simply generalizing the single-phase Darcy law and introducing saturation-dependent permeabilities. Here we study models of creeping flows that include an explicit coupling between both phases via the addition of cross terms in the generalized Darcy law. Using an extension of the Buckley-Leverett theory, we analyze the impact of these cross terms on saturation profiles and pressure drops for different couples of fluids and closure relations of the effective parameters. We show that these cross terms in the macroscale models may significantly impact the flow compared to results obtained with the generalized Darcy laws without cross terms. Analytical solutions, validated against experimental data, suggest that the effect of this coupling on the dynamics of saturation fronts and the steady-state profiles is very sensitive to gravitational effects, the ratio of viscosity between the two phases, and the permeability. Our results indicate that the effects of momentum exchange on two-phase flow may increase with the permeability of the porous medium when the influence of the fluid-fluid interfaces become similar to that of the solid-fluid interfaces
Physics-informed machine learning for solving partial differential equations in porous media
Physical phenomenon in nature is generally simulated by partial differential equations. Among different sorts of partial differential equations, the problem of two-phase flow in porous media has been paid intense attention. As a promising direction, physics-informed neural networks shed new light on the solution of partial differential equations. However, current physics-informed neural networks’ ability to learn partial differential equations relies on adding artificial diffusion or using prior knowledge to increase the number of training points along the shock trajectory, or adaptive activation functions. To address these issues, this study proposes a physics-informed neural network with long short-term memory and attention mechanism, an ingenious method to solve the Buckley-Leverett partial differential equations representing two-phase flow in porous media. The designed network structure overcomes the dependency on artificial diffusion terms and enhances the importance of shallow features. The experimental results show that the proposed method is in good agreement with analytical solutions. Accurate approximations are shown even when encountering shock points in saturated fields of porous media. Furthermore, experiments show our innovative method outperforms existing traditional physics-informed machine learning approaches.Cited as: Shan, L., Liu, C., Liu, Y., Tu, Y., Dong, L., Hei, X. Physics-informed machine learning for solving partial differential equations in porous media. Advances in Geo-Energy Research, 2023, 8(1): 37-44. https://doi.org/10.46690/ager.2023.04.0
Application of multilevel concepts for uncertainty quantification in reservoir simulation
Uncertainty quantification is an important task in reservoir simulation and is an
active area of research. The main idea of uncertainty quantification is to compute
the distribution of a quantity of interest, for example oil rate. That uncertainty,
then feeds into the decision making process.
A statistically valid way of quantifying the uncertainty is a Markov Chain Monte
Carlo (MCMC) method, such as Random Walk Metropolis (RWM). MCMC is a
robust technique for estimating the distribution of the quantity of interest. RWM is
can be prohibitively expensive, due to the need to run a huge number of realizations,
45% - 70% of these may be rejected and, even for a simple reservoir model it
may take 15 minutes for each realization. Hamiltonian Monte Carlo accelerates the
convergence for RWM but may lead to a large increase computational cost because
it requires the gradient.
In this thesis, we present how to use the multilevel concept to accelerate convergence
for RWM. The thesis discusses how to apply Multilevel Markov Chain Monte
Carlo (MLMCMC) to uncertainty quantification. It proposes two new techniques,
one for improving the proxy based on multilevel idea called Multilevel proxy (MLproxy)
and the second one for accelerating the convergence of Hamiltonian Monte
Carlo is called Multilevel Hamiltonian Monte Carlo (MLHMC).
The idea behind the multilevel concept is a simple telescoping sum: which represents
the expensive solution (e.g., estimating the distribution for oil rate on finest
grid) in terms of a cheap solution (e.g., estimating the distribution for oil rate on
coarse grid) and `correction terms', which are the difference between the high resolution
solution and a low resolution solution. A small fraction of realizations is then
run on the finer grids to compute correction terms. This reduces the computational
cost and simulation errors significantly.
MLMCMC is a combination between RWM and multilevel concept, it greatly reduces
the computational cost compared to the RWM for uncertainty quantification.
It makes Monte Carlo estimation a feasible technique for uncertainty quantification
in reservoir simulation applications. In this thesis, MLMCMC has been implemented
on two reservoir models based on real fields in the central Gulf of Mexico and in
North Sea.
MLproxy is another way for decreasing the computational cost based on constructing
an emulator and then improving it by adding the correction term between
the proxy and simulated results.
MLHMC is a combination of Multilevel Monte Carlo method with a Hamiltonian
Monte Carlo algorithm. It accelerates Hamiltonian Monte Carlo (HMC) and is faster
than HMC. In the thesis, it has been implemented on a real field called Teal South
to assess the uncertainty
Learning Generic Solutions for Multiphase Transport in Porous Media via the Flux Functions Operator
Traditional numerical schemes for simulating fluid flow and transport in
porous media can be computationally expensive. Advances in machine learning for
scientific computing have the potential to help speed up the simulation time in
many scientific and engineering fields. DeepONet has recently emerged as a
powerful tool for accelerating the solution of partial differential equations
(PDEs) by learning operators (mapping between function spaces) of PDEs. In this
work, we learn the mapping between the space of flux functions of the
Buckley-Leverett PDE and the space of solutions (saturations). We use
Physics-Informed DeepONets (PI-DeepONets) to achieve this mapping without any
paired input-output observations, except for a set of given initial or boundary
conditions; ergo, eliminating the expensive data generation process. By
leveraging the underlying physical laws via soft penalty constraints during
model training, in a manner similar to Physics-Informed Neural Networks
(PINNs), and a unique deep neural network architecture, the proposed
PI-DeepONet model can predict the solution accurately given any type of flux
function (concave, convex, or non-convex) while achieving up to four orders of
magnitude improvements in speed over traditional numerical solvers. Moreover,
the trained PI-DeepONet model demonstrates excellent generalization qualities,
rendering it a promising tool for accelerating the solution of transport
problems in porous media.Comment: 23 pages, 11 figure
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