Spreadsheet Optimization for Parameter Estimation of Pressure–Saturation Equations Used for Two-Phase Groundwater Flow

2006 ◽  
Vol 179 (1-4) ◽  
pp. 57-65 ◽  
Author(s):  
Lizette R. Chevalier ◽  
Jemil N. Yesuf
Keyword(s):  
Parameter Estimation ◽  
Groundwater Flow ◽  
Two Phase

History Matching in Two-Phase Petroleum Reservoirs

1980 ◽  
Vol 20 (06) ◽  
pp. 521-532 ◽  
Author(s):  
A.T. Watson ◽  
J.H. Seinfeld ◽  
G.R. Gavalas ◽  
P.T. Woo
Keyword(s):  
Optimal Control ◽  
Parameter Estimation ◽  
Objective Function ◽  
History Matching ◽  
Computing Time ◽  
Absolute Permeability ◽  
Two Phase ◽  
Automatic History Matching ◽  
Control Approach ◽  
First Order

Abstract An automatic history-matching algorithm based onan optimal control approach has been formulated forjoint estimation of spatially varying permeability andporosity and coefficients of relative permeabilityfunctions in two-phase reservoirs. The algorithm usespressure and production rate data simultaneously. The performance of the algorithm for thewaterflooding of one- and two-dimensional hypotheticalreservoirs is examined, and properties associatedwith the parameter estimation problem are discussed. Introduction There has been considerable interest in thedevelopment of automatic history-matchingalgorithms. Most of the published work to date onautomatic history matching has been devoted tosingle-phase reservoirs in which the unknownparameters to be estimated are often the reservoirporosity (or storage) and absolute permeability (ortransmissibility). In the single-phase problem, theobjective function usually consists of the deviationsbetween the predicted and measured reservoirpressures at the wells. Parameter estimation, orhistory matching, in multiphase reservoirs isfundamentally more difficult than in single-phasereservoirs. The multiphase equations are nonlinear, and in addition to the porosity and absolutepermeability, the relative permeabilities of each phasemay be unknown and subject to estimation. Measurements of the relative rates of flow of oil, water, and gas at the wells also may be available forthe objective function. The aspect of the reservoir history-matchingproblem that distinguishes it from other parameterestimation problems in science and engineering is thelarge dimensionality of both the system state and theunknown parameters. As a result of this largedimensionality, computational efficiency becomes aprime consideration in the implementation of anautomatic history-matching method. In all parameterestimation methods, a trade-off exists between theamount of computation performed per iteration andthe speed of convergence of the method. Animportant saving in computing time was realized insingle-phase automatic history matching through theintroduction of optimal control theory as a methodfor calculating the gradient of the objective functionwith respect to the unknown parameters. Thistechnique currently is limited to first-order gradientmethods. First-order gradient methods generallyconverge more slowly than those of higher order.Nevertheless, the amount of computation requiredper iteration is significantly less than that requiredfor higher-order optimization methods; thus, first-order methods are attractive for automatic historymatching. The optimal control algorithm forautomatic history matching has been shown toproduce excellent results when applied to field problems. Therefore, the first approach to thedevelopment of a general automatic history-matchingalgorithm for multiphase reservoirs wouldseem to proceed through the development of anoptimal control approach for calculating the gradientof the objective function with respect to theparameters for use in a first-order method. SPEJ P. 521＾

scholarly journals Solution of the 3D density-driven groundwater flow problem with uncertain porosity and permeability

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Alexander Litvinenko ◽  
Dmitry Logashenko ◽  
Raul Tempone ◽  
Gabriel Wittum ◽  
David Keyes
Keyword(s):  
Groundwater Flow ◽  
Flow Problem ◽  
Two Phase ◽  
Contaminant Plumes ◽  
Quasi Monte Carlo ◽  
Strongly Nonlinear ◽  
Groundwater Aquifers ◽  
Porosity And Permeability ◽  
Liquid Flows ◽  
Computational Resources

AbstractThe pollution of groundwater, essential for supporting populations and agriculture, can have catastrophic consequences. Thus, accurate modeling of water pollution at the surface and in groundwater aquifers is vital. Here, we consider a density-driven groundwater flow problem with uncertain porosity and permeability. Addressing this problem is relevant for geothermal reservoir simulations, natural saline-disposal basins, modeling of contaminant plumes and subsurface flow predictions. This strongly nonlinear time-dependent problem describes the convection of a two-phase flow, whereby a liquid flows and propagates into groundwater reservoirs under the force of gravity to form so-called “fingers”. To achieve an accurate numerical solution, fine spatial resolution with an unstructured mesh and, therefore, high computational resources are required. Here we run a parallelized simulation toolbox ug4 with a geometric multigrid solver on a parallel cluster, and the parallelization is carried out in physical and stochastic spaces. Additionally, we demonstrate how the ug4 toolbox can be run in a black-box fashion for testing different scenarios in the density-driven flow. As a benchmark, we solve the Elder-like problem in a 3D domain. For approximations in the stochastic space, we use the generalized polynomial chaos expansion. We compute the mean, variance, and exceedance probabilities for the mass fraction. We use the solution obtained from the quasi-Monte Carlo method as a reference solution.

Sensorless parameter estimation and current‐sharing strategy in two‐phase and multiphase IPOP DAB DC–DC converters

2018 ◽  
Vol 11 (6) ◽  
pp. 1135-1142 ◽  
Author(s):  
Yubin Wang ◽  
Fan Wang ◽  
Yifei Lin ◽  
Tianqu Hao
Keyword(s):  
Parameter Estimation ◽  
Two Phase ◽  
Current Sharing ◽  
Sharing Strategy

scholarly journals Parameter estimation of kinetic models from metabolic profiles: two-phase dynamic decoupling method

2011 ◽  
Vol 27 (14) ◽  
pp. 1964-1970 ◽  
Author(s):  
Gengjie Jia ◽  
Gregory N. Stephanopoulos ◽  
Rudiyanto Gunawan
Keyword(s):  
Parameter Estimation ◽  
Kinetic Models ◽  
Metabolic Profiles ◽  
Two Phase ◽  
Decoupling Method ◽  
Phase Dynamic ◽  
Dynamic Decoupling

Groundwater flow parameter estimation using refinement and coarsening indicators for adaptive downscaling parameterization

2017 ◽  
Vol 100 ◽  
pp. 139-152 ◽  
Author(s):  
Mamadou Maina F.Z. Hassane ◽  
P. Ackerer
Keyword(s):  
Parameter Estimation ◽  
Groundwater Flow ◽  
Flow Parameter

Two-phase CO 2 migration in tilted aquifers in the presence of groundwater flow

2014 ◽  
Vol 77 ◽  
pp. 717-729 ◽  
Author(s):  
Shujuan Wang ◽  
Kambiz Vafai ◽  
Sumit Mukhopadhyay
Keyword(s):  
Groundwater Flow ◽  
Two Phase

scholarly journals A Parameter Estimation Technique for a Groundwater Flow Model

2020 ◽  
Vol 5 (4) ◽  
pp. 202
Author(s):  
Joseph Acquah ◽  
Francis Benyah ◽  
Jerry Samuel Yao-Kuma
Keyword(s):  
Parameter Estimation ◽  
Groundwater Flow ◽  
Flow Model ◽  
Groundwater Flow Model ◽  
Estimation Technique

scholarly journals Groundwater Parameter Inversion Using Topographic Constraints and a Zonal Adaptive Multiscale Procedure: A Case Study of an Alluvial Aquifer

Water ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1899 ◽  
Author(s):  
Dimitri Rambourg ◽  
Philippe Ackerer ◽  
Olivier Bildstein
Keyword(s):  
Parameter Estimation ◽  
Groundwater Flow ◽  
Unconfined Aquifer ◽  
Water Levels ◽  
Specific Yield ◽  
Local Minima ◽  
Diffusion Type ◽  
Aquifer Parameters ◽  
Water Head ◽  
Verification Period

The identification of aquifer parameters (i.e., specific yield and hydraulic conductivity) and forcing terms (recharge) is crucial for the process of modeling groundwater flow and contamination. Inversion techniques allow the unravelling of complex systems’ heterogeneity with more ease than manual calibration by computing parameter fields through an automated minimization between simulated and measured data (i.e., water head or measured aquifer parameters). It also allows the iterative search of multiple, equally plausible solutions, depending on system complexity (e.g., aquifer heterogeneity and variability of the forcing terms such as recharge). A Zoned Adaptive Multiscale Triangulation (ZAMT) is used for parameter estimation. ZAMT is the extension of an adaptive multiscale parameter estimation procedure already applied on different field cases. This extension consists of adding constraints varying over the domain. The ZAMT dissociates the parameter grid from the calculation mesh and allows local parameter grid refinement depending on local criteria, addressing the ill-posedness of inversion problems, decreasing computation time by reducing the amount of possible solutions and local minima, and ensuring flexibility in the parameter’s distribution. Each parameter is defined per vertex of the parameter grid; it can be set with a different range of values in order to integrate more pedo-geological information and help the optimization process by reducing the number of local minima. For the same purpose, a plausibility term based on topological characteristics of the aquifer or minimal and maximal water levels is added to the objective function. Groundwater flow is described by a classical nonlinear diffusion-type equation (unconfined aquifer), which is discretized with a two-dimensional nonconforming finite element method because water head data is unsuitable to invert three-dimensional parameter fields. Therefore, flow is considered mainly horizontal, and the parameters are obtained as average values on the saturated thickness. The study area is an alluvial (unconfined) aquifer of 6.64 km², situated in the southern, Mediterranean part of France. The simulation runs with a chronicle of 191 piezometers over 7 years (2012–2019), using a calibration period of 5 years (2012–2016). The optimization threshold is set to ensure a mean absolute error below 40 cm. The ZAMT and the additional plausibility criterion were found to produce an ensemble of realistic parameter sets with low parameter standard deviation. The model is considered robust as the water head error remains at the same level during the verification period, which includes an exceptionally dry year (2017). Overall, the calibration is best near the rivers (Dirichlet boundaries), while the terraced portion of the site challenges the limits of the 2D approach and the inversion procedure.

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