Joint Estimation of Hydraulic and Biochemical Parameters for Reactive Transport Modelling with a Modified ILUES Algorithm

Multicomponent reactive transport modeling is a powerful tool for the comprehensive analysis of coupled hydraulic and biochemical processes. The performance of the simulation model depends on the accuracy of related model parameters whose values are usually difficult to determine from direct measurements. In this situation, estimates of these uncertain parameters can be obtained by solving inverse problems. In this study, an efficient data assimilation method, the iterative local updating ensemble smoother (ILUES), is employed for the joint estimation of hydraulic parameters, biochemical parameters and contaminant source characteristics in the sequential biodegradation process of tetrachloroethene (PCE). In the framework of the ILUES algorithm, parameter estimation is realized by updating local ensemble with the iterative ensemble smoother (IES). To better explore the parameter space, the original ILUES algorithm is modified by determining the local ensemble partly with a linear ranking selection scheme. Numerical case studies based on the sequential biodegradation of PCE are then used to evaluate the performance of the ILUES algorithm. The results show that the ILUES algorithm is able to achieve an accurate joint estimation of related model parameters in the reactive transport model.

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Improved Estimation and Forecasting Through Residual-Based Model Error Quantification

SPE Journal ◽

10.2118/199358-pa ◽

2020 ◽

Vol 25 (02) ◽

pp. 951-968 ◽

Cited By ~ 1

Author(s):

Minjie Lu ◽

Yan Chen

Keyword(s):

History Matching ◽

Historical Data ◽

Total Error ◽

Model Error ◽

Complex Nature ◽

Model Parameters ◽

Observation Error ◽

Model Errors ◽

Ensemble Smoother ◽

Iterative Ensemble Smoother

Summary Owing to the complex nature of hydrocarbon reservoirs, the numerical model constructed by geoscientists is always a simplified version of reality: for example, it might lack resolution from discretization and lack accuracy in modeling some physical processes. This flaw in the model that causes mismatch between actual observations and simulated data when “perfect” model parameters are used as model inputs is known as “model error”. Even in a situation when the model is a perfect representation of reality, the inputs to the model are never completely known. During a typical model calibration procedure, only a subset of model inputs is adjusted to improve the agreement between model responses and historical data. The remaining model inputs that are not calibrated and are likely fixed at incorrect values result in model error in a similar manner as the imperfect model scenario. Assimilation of data without accounting for model error can result in the incorrect adjustment to model parameters, the underestimation of prediction uncertainties, and bias in forecasts. In this paper, we investigate the benefit of recognizing and accounting for model error when an iterative ensemble smoother is used to assimilate production data. The correlated “total error” (a combination of model error and observation error) is estimated from the data residual after a standard history-matching using the Levenberg-Marquardt form of iterative ensemble smoother (LM-EnRML). This total error is then used in further data assimilations to improve the estimation of model parameters and quantification of prediction uncertainty. We first illustrate the method using a synthetic 2D five-spot example, where some model errors are deliberately introduced, and the results are closely examined against the known “true” model. Then, the Norne field case is used to further evaluate the method. The Norne model has previously been history-matched using the LM-EnRML (Chen and Oliver 2014), where cell-by-cell properties (permeability, porosity, net-to-gross, vertical transmissibility) and parameters related to fault transmissibility, depths of water/oil contacts, and relative permeability function are adjusted to honor historical data. In this previous study, the authors highlighted the importance of including large amounts of model parameters, the proper use of localization, and heuristic adjustment of data noise to account for modeling error. In this paper, we improve the last aspect by quantitatively estimating model error using residual analysis.

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The Tournemire industrial analogue: reactive-transport modelling of a cement–clay interface

Clay Minerals ◽

10.1180/claymin.2013.048.2.02 ◽

2013 ◽

Vol 48 (2) ◽

pp. 167-184 ◽

Cited By ~ 10

Author(s):

C. Watson ◽

D. Savage ◽

J. Wilson ◽

S. Benbow ◽

C. Walker ◽

...

Keyword(s):

Ion Exchange ◽

Reactive Transport ◽

Transport Model ◽

Surface Complexation ◽

General Purpose ◽

Transport Modelling ◽

Mineralogical Characterization ◽

Modelling Techniques ◽

Materials Used ◽

Set Up

AbstractIn the post-closure period of a geological disposal facility for radioactive waste, leaching of cement components is likely to give rise to an alkaline plume which will be in chemical disequilibrium with the host rock (which is clay in some concepts) and other engineered barrier system materials used in the facility, such as bentonite. An industrial analogue for cement-clay interaction can be found at Tournemire, southern France, where boreholes filled with concrete and cement remained in contact with the natural mudstone for 15–20 years. The boreholes have been overcored, extracted and mineralogical characterization has been performed. In this study, a reactive-transport model of the Tournemire system has been set up using the general-purpose modelling tool QPAC. Previous modelling work has been built upon by using the most up-to-date data and modelling techniques, and by adding both ion exchange and surface complexation processes in the mudstone. The main features observed at Tournemire were replicated by the model, including porosity variations and precipitation of carbonates, K-feldspar, ettringite and calcite. It was found that ion exchange needed to be included in order for C-S-H minerals to precipitate in the mudstone, providing a better match with the mineralogical characterization. The additional inclusion of surface complexation, however, led to limited calcite growth at the concrete-mudstone interface unlike samples taken from the Tournemire site that have a visible line of crusty carbonates along the interface.

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Trace element mobility during CO2 storage: application of reactive transport modelling

E3S Web of Conferences ◽

10.1051/e3sconf/20199804007 ◽

2019 ◽

Vol 98 ◽

pp. 04007

Author(s):

Dirk Kirste ◽

Julie K. Pearce ◽

Sue D. Golding ◽

Grant K.W. Dawson

Keyword(s):

Water Quality ◽

Chemical Composition ◽

Reactive Transport ◽

Transport Model ◽

Co2 Storage ◽

Chemical Components ◽

Transport Modelling ◽

Geochemical Model ◽

Trace Element Mobility ◽

The Individual

The geologic storage of CO2 carries both physical and chemical risks to the environment. In order to reduce those risks, it is necessary to provide predictive capabilities for impacts so that strategies can be developed to monitor, identify and mitigate potential problems. One area of concern is related to water quality both in the reservoir and in overlying aquifers. In this study we report the critical steps required to develop chemically constrained reactive transport models (RTM) that can be used to address risk assessment associated with water quality. The data required to produce the RTM includes identifying the individual hydrostratigraphic units and defining the mineral and chemical composition to sufficient detail for the modelling. This includes detailed mineralogy, bulk chemical composition, reactive mineral phase chemical composition and the identification of the occurrence and mechanisms of mobilisation of any trace elements of interest. Once the required detail is achieved the next step involves conducting experiments to determine the evolution of water chemistry as reaction proceeds preferably under varying elevated CO2 fugacities with and without impurities. Geochemical modelling of the experiments is then used for characterising the reaction pathways of the different hydrostratigraphic units. The resultant geochemical model inputs can then be used to develop the chemical components of a reactive transport model.

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Flexible iterative ensemble smoother for calibration of perfect and imperfect models

Computational Geosciences ◽

10.1007/s10596-020-10008-z ◽

2020 ◽

Author(s):

Muzammil Hussain Rammay ◽

Ahmed H. Elsheikh ◽

Yan Chen

Keyword(s):

Computational Cost ◽

Model Error ◽

Physical Models ◽

Model Parameters ◽

Model Errors ◽

Estimated Parameters ◽

Ensemble Smoother ◽

Ensemble Smoothers ◽

Iterative Ensemble Smoothers ◽

Iterative Ensemble Smoother

AbstractIterative ensemble smoothers have been widely used for calibrating simulators of various physical systems due to the relatively low computational cost and the parallel nature of the algorithm. However, iterative ensemble smoothers have been designed for perfect models under the main assumption that the specified physical models and subsequent discretized mathematical models have the capability to model the reality accurately. While significant efforts are usually made to ensure the accuracy of the mathematical model, it is widely known that the physical models are only an approximation of reality. These approximations commonly introduce some type of model error which is generally unknown and when the models are calibrated, the effects of the model errors could be smeared by adjusting the model parameters to match historical observations. This results in a bias estimated parameters and as a consequence might result in predictions with questionable quality. In this paper, we formulate a flexible iterative ensemble smoother, which can be used to calibrate imperfect models where model errors cannot be neglected. We base our method on the ensemble smoother with multiple data assimilation (ES-MDA) as it is one of the most widely used iterative ensemble smoothing techniques. In the proposed algorithm, the residual (data mismatch) is split into two parts. One part is used to derive the parameter update and the second part is used to represent the model error. The proposed method is quite general and relaxes many of the assumptions commonly introduced in the literature. We observe that the proposed algorithm has the capability to reduce the effect of model bias by capturing the unknown model errors, thus improving the quality of the estimated parameters and prediction capacity of imperfect physical models.

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Data assimilation of subsurface flow via iterative ensemble smoother and physics-informed neural network

10.5194/egusphere-egu2020-12224 ◽

2020 ◽

Author(s):

Nanzhe Wang ◽

Haibin Chang

Keyword(s):

Neural Network ◽

Data Assimilation ◽

Surrogate Model ◽

Flow Problem ◽

Subsurface Flow ◽

High Accuracy ◽

Training Data ◽

Model Parameters ◽

Ensemble Smoother ◽

Iterative Ensemble Smoother

<p>Subsurface flow problems usually involve some degree of uncertainty. For reducing the uncertainty of subsurface flow prediction, data assimilation is usually necessary. Data assimilation is time consuming. In order to improve the efficiency of data assimilation, surrogate model of subsurface flow problem may be utilized. In this work, a physics-informed neural network (PINN) based surrogate model is proposed for subsurface flow with uncertain model parameters. Training data generated by solving stochastic partial differential equations (SPDEs) are utilized to train the neural network. Besides the data mismatch term, the term that incorporates physics laws is added in the loss function. The trained neural network can predict the solutions of the subsurface flow problem with new stochastic parameters, which can serve as a surrogate for approximating the relationship between model output and model input. By incorporating physics laws, PINN can achieve high accuracy. Then an iterative ensemble smoother (ES) is introduced to implement the data assimilation task based on the PINN surrogate. Several subsurface flow cases are designed to test the performance of the proposed paradigm. The results show that the PINN surrogate can significantly improve the efficiency of data assimilation task while maintaining a high accuracy.</p>

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History Matching of the Norne Full-Field Model With an Iterative Ensemble Smoother

SPE Reservoir Evaluation & Engineering ◽

10.2118/164902-pa ◽

2014 ◽

Vol 17 (02) ◽

pp. 244-256 ◽

Cited By ~ 45

Author(s):

Yan Chen ◽

Dean S. Oliver

Keyword(s):

History Matching ◽

Oil And Gas ◽

Field Model ◽

Model Parameters ◽

Data Types ◽

Full Field ◽

Ensemble Smoother ◽

Main Fault ◽

Iterative Ensemble Smoother ◽

Partial Communication

Summary Although ensemble-based data-assimilation methods such as the ensemble Kalman filter (EnKF) and the ensemble smoother have been extensively used for the history matching of synthetic models, the number of applications of ensemble-based methods for history matching of field cases is extremely limited. In most of the published field cases in which the ensemble-based methods were used, the number of wells and the types of data to be matched were relatively small. As a result, it may not be clear to practitioners how a real history-matching study would be accomplished with ensemble-based methods. In this paper, we describe the application of the iterative ensemble smoother to the history matching of the Norne field, a North Sea field, with a moderately large number of wells, a variety of data types, and a relatively long production history. Particular attention is focused on the problems of the identification of important variables, the generation of an initial ensemble, the plausibility of results, and the efficiency of minimization. We also discuss the challenges encountered in the use of the ensemble-based method for complex-field case studies that are not typically encountered in synthetic cases. The Norne field produces from an oil-and-gas reservoir discovered in 1991 offshore Norway. The full-field model consists of four main fault blocks that are in partial communication and many internal faults with uncertain connectivity in each fault block. There have been 22 producers and 9 injectors in the field. Water-alternating-gas injection is used as the depletion strategy. Production rates of oil, gas, and water of 22 producers from 1997 to 2006 and repeat-formation-tester (RFT) pressure from 14 different wells are available for model calibration. The full-field simulation model has 22 layers, each with a dimension of 46 × 112 cells. The total number of active cells is approximately 45,000. The Levenberg-Marquardt form of the iterative ensemble smoother (LM-EnRML) is used for history matching. The model parameters that are updated include permeability, porosity, and net-to-gross (ntg) ratio at each gridblock; vertical transmissibility at each gridblock for six layers; transmissibility multipliers of 53 faults; endpoint water and gas relative permeability of four different reservoir zones; depth of water/oil contacts; and transmissibility multipliers between a few main fault blocks. The total number of model parameters is approximately 150,000. Distance-based localization is used to regularize the updates from LM-EnRML. LM-EnRML is able to achieve improved data match compared with the manually history-matched model after three iterations. Updates from LM-EnRML do not introduce artifacts in the property fields as in the manually history-matched model. The automated workflow is also much less labor-intensive than that for manual history matching.

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Modelling species fate and porous media effects for landfill leachate flow

Canadian Geotechnical Journal ◽

10.1139/t05-039 ◽

2005 ◽

Vol 42 (4) ◽

pp. 1116-1132 ◽

Cited By ~ 25

Author(s):

A J Cooke ◽

R K Rowe ◽

B E Rittmann

Keyword(s):

Porous Media ◽

Landfill Leachate ◽

Reactive Transport ◽

Volatile Fatty Acids ◽

Transport Model ◽

Calcium Carbonate Precipitation ◽

Transport Modelling ◽

Inorganic Particles ◽

The Media ◽

Multiple Species

A numerical, multiple-species, reactive transport model, coupled to models of kinetic biodegradation, precipitation, and particle attachment and detachment for predicting landfill leachate-induced clogging in porous media for one-dimensional flow systems, is described. The finite-element method is used for transport modelling, with reactions incorporated into point-source or sink terms. The species modelled include three volatile fatty acids, active and inert suspended biomass, dissolved calcium, and inorganic particles. The clog matter consists of active biofilm, inert biofilm, and inorganic solids. A biofilm model is used to simulate the growth and decay of active biomass and removal of substrate. Precipitate accumulation and calcium removal are simulated by a model of calcium carbonate precipitation. Interphase movement between clog matter and fluid includes the processes of attachment and detachment. A geometric representation of the porous media allows porosity and specific surface to be estimated from the thickness of the accumulated clog matter. The porosity of the media can thus change spatially and temporally. The behaviour of the model is demonstrated with a hypothetical example.Key words: clogging, landfills, leachate collection systems, modelling, biofilms, mineral precipitation.

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C-GEM (v 1.0): a new, cost-efficient biogeochemical model for estuaries and its application to a funnel-shaped system

Geoscientific Model Development Discussions ◽

10.5194/gmdd-6-5645-2013 ◽

2013 ◽

Vol 6 (4) ◽

pp. 5645-5709 ◽

Cited By ~ 2

Author(s):

C. Volta ◽

S. Arndt ◽

H. H. G. Savenije ◽

G. G. Laruelle ◽

P. Regnier

Keyword(s):

Reactive Transport ◽

Model Comparison ◽

Transport Model ◽

Current Model ◽

Global Scale ◽

Salt Transport ◽

Biogeochemical Model ◽

Model Parameters ◽

Estuarine System ◽

Computationally Efficient

Abstract. The first part of this paper describes C-GEM (Carbon – Generic Estuary Model), a new, one-dimensional, generic reactive-transport model for the biogeochemical dynamics of carbon and associated bio-elements (N, P, Si) in estuaries. C-GEM is computationally efficient and reduces data-requirements by using an idealized representation of the estuarine geometry to quantitatively predict the dominant features of the estuarine hydrodynamics, salt transport and biogeochemistry. A protocol for the set-up of C-GEM for an estuarine system is also described. The second part of this paper presents, as a proof of concept, the application of C-GEM to the funnel-shaped Scheldt estuary (Belgium, the Netherlands), one of the best-surveyed system in the world. Steady-state and transient simulations are performed and the performance of C-GEM is evaluated through model-data and model-model comparison, using integrated measures of the estuarine biogeochemical functioning, such as system-wide estimates of the Net Ecosystem Metabolism (NEM). A sensitivity analysis is also carried out to identify model parameters that exert the most important control on biogeochemical processes and to assess the sensitivity of the NEM to uncertainties in parameter values. The paper ends by a short discussion of current model limitations with respect to local, regional and global scale applications.

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