Nonlinear model identification and adaptive control of CO2 sequestration process in saline aquifers using artificial neural networks

In recent years, storage of carbon dioxide (CO₂) in saline aquifers has gained intensive research interest. The implementation, however, requires further research studies to ensure it is safe and secure operation. The primary objective is to secure the CO₂ which relies on a leak-proof formation. Reservoir pressure is a key aspect for assessment of the cap rock integrity. This work presents a new pressure control methodology based on a nonlinear model predictive control (NMPC) scheme to diminishing risk of carbon dioxide (CO₂) back leakage to the atmosphere due to a fail in the integrity of the formation cap rock. The CO₂ sequestration process in saline aquifers is simulated using ECLIPSE-100 as black oil reservoir simulator while the proposed control scheme is realized in MATLAB software package to prevent over-pressurization. A modified form of growing and pruning radial basis function (MGAP-RBF) neural network model is identified online for prediction of reservoir pressure behaviors. MGAP-RBF is recursively trained via extended Kalman filter (EKF) and unscented Kalman filter (UKF) algorithms. A set of miscellaneous test scenarios has been conducted using an interface program to exchange ECLIPSE and MATLAB in order to demonstrate the capabilities of the proposed methodology in guiding saline aquifer to follow some desired time-dependent pressure profiles during the CO₂ injection process.     

TOUGH+CO2: A multiphase fluid-flow simulator for CO2 geologic sequestration in saline aquifers

TOUGH+CO₂ is a new simulator for modeling of CO₂ geologic sequestration in saline aquifers. It is a member of TOUGH+, the successor to the TOUGH2 family of codes for multicomponent, multiphase fluid and heat flow simulation. The code accounts for heat and up to 3 mass components, which are partitioned into three possible phases. In the code, the thermodynamics and thermophysical properties of H₂O-NaCl-CO₂ mixtures are determined based on system status and subdivided into six different phase combinations. By solving coupled mass and heat balance equations, TOUGH+CO₂ can model non-isothermal or isothermal CO₂ injection, phase behavior and flow of fluids and heat under typical conditions of temperature, pressure and salinity in CO₂ geologic storage projects. The code takes into account effects of salt precipitation on porosity and permeability changes, and the wettability phenomena. The new simulator inherits all capabilities of TOUGH2 in handling fractured media and using unstructured meshes for complex simulation domains. The code adds additional relative permeability and capillary pressure functions. The FORTRAN 95 OOP architecture and other new language features have been extensively used to enhance memory use and computing efficiency. In addition, a domain decomposition approach has been implemented for parallel simulation. All these features lead to increased computational efficiency, and allow applicability of the code to multi-core/processor parallel computing platforms with excellent scalability.     

TOUGHREACT—A simulation program for non-isothermal multiphase reactive geochemical transport in variably saturated geologic media: Applications to geothermal injectivity and CO2 geological sequestration

TOUGHREACT is a numerical simulation program for chemically reactive non-isothermal flows of multiphase fluids in porous and fractured media. The program was written in Fortran 77 and developed by introducing reactive geochemistry into the multiphase fluid and heat flow simulator TOUGH2. A variety of subsurface thermo-physical–chemical processes are considered under a wide range of conditions of pressure, temperature, water saturation, ionic strength, and pH and Eh. Interactions between mineral assemblages and fluids can occur under local equilibrium or kinetic rates. The gas phase can be chemically active. Precipitation and dissolution reactions can change formation porosity and permeability. The program can be applied to many geologic systems and environmental problems, including geothermal systems, diagenetic, and weathering processes, subsurface waste disposal, acid mine drainage remediation, contaminant transport, and groundwater quality. Here we present two examples to illustrate applicability of the program. The first example deals with injectivity effects of mineral scaling in a fractured geothermal reservoir. A major concern in the development of hot dry rock and hot fractured rock reservoirs is achieving and maintaining adequate injectivity, while avoiding the development of preferential short-circuiting flow paths. Rock–fluid interactions and associated mineral dissolution and precipitation effects could have a major impact on the long-term performance of these reservoirs. We used recent European studies as a starting point to explore chemically induced effects of fluid circulation in the geothermal systems. We examine ways in which the chemical composition of reinjected waters can be modified to improve reservoir performance by maintaining or even enhancing injectivity. The second TOUGHREACT application example is related to CO₂ geologic sequestration in a saline aquifer. We performed numerical simulations for a commonly encountered Gulf Coast sediment under CO₂ injection conditions in order to analyze the impact of CO₂ immobilization through carbonate precipitation. Using the data presented in this paper, the CO₂ mineral-trapping capability after 10,000 years can reach 60 kg/m³ of sandstone by secondary carbonate mineral precipitation such as siderite, ankerite, and dawsonite. Most of the simulated mineral alteration pattern is consistent with the field observations of natural CO₂ reservoirs.     

Experimental study of drying effects during supercritical CO<Subscript>2</Subscript> displacement in a pore network

Underground storage in geological aquifers is one of the most important options for large-scale mitigation of CO₂. During the supercritical CO₂ (scCO₂) injection process, water dissolved in scCO₂ may have significant impact on the displacement process. In this study, a series of wet scCO₂ (WscCO₂, 100% water saturation) and dry scCO₂ (DscCO₂, 0% water saturation) displacement experiments were conducted in micromodels for a large range of flow rates. The displacement was visualized using fluorescence microscopy. Results showed that DscCO₂ saturations were up to 3.3 times larger than WscCO₂ saturations when the capillary fingering dominated the displacement. The specific interfacial areas and mobile fractions for the DscCO₂ displacements were also much larger than those for WscCO₂. The capillary forces combined with drying effects are identified as the leading causes for the considerably higher DscCO₂ sweep efficiency. Results from this study showed the important impact of mutual solubility of scCO₂ and water on the displacement process and saturation of scCO₂ (S_scCO2), suggesting that the conventional model describing the relationship between capillary pressure and S_scCO2 needs to be modified for the effect of the mutual dissolution of multiple phases to more adequately describe the scCO₂ displacement process in saline aquifer formation.     

A workflow for handling heterogeneous 3D models with the TOUGH2 family of codes: Applications to numerical modeling of CO2 geological storage

This paper is addressed to the TOUGH2 user community. It presents a new tool for handling simulations run with the TOUGH2 code with specific application to CO₂ geological storage. This tool is composed of separate FORTRAN subroutines (or modules) that can be run independently, using input and output files in ASCII format for TOUGH2. These modules have been developed specifically for modeling of carbon dioxide geological storage and their use with TOUGH2 and the Equation of State module ECO2N, dedicated to CO₂-water-salt mixture systems, with TOUGHREACT, which is an adaptation of TOUGH2 with ECO2N and geochemical fluid-rock interactions, and with TOUGH2 and the EOS7C module dedicated to CO₂-CH₄ gas mixture is described. The objective is to save time for the pre-processing, execution and visualization of complex geometry for geological system representation. The workflow is rapid and user-friendly and future implementation to other TOUGH2 EOS modules for other contexts (e.g. nuclear waste disposal, geothermal production) is straightforward. Three examples are shown for validation: (i) leakage of CO₂ up through an abandoned well; (ii) 3D reactive transport modeling of CO₂ in a sandy aquifer formation in the Sleipner gas Field, (North Sea, Norway); and (iii) an estimation of enhanced gas recovery technology using CO₂ as the injected and stored gas to produce methane in the K12B Gas Field (North Sea, Denmark).     

Tidal breathing model describing end-tidal, alveolar, arterial and mixed venous CO2 and O2

Thermodilution is the current standard for determination of cardiac output. The method is invasive and constitutes a risk for the patient. As an alternative CO₂ rebreathing allows non-invasive cardiac output estimation using Ficks principle. The method relies on estimation of arterial CO₂ partial pressure from end-tidal CO₂ pressure and estimation of mixed venous CO₂ partial pressure from end-tidal CO₂ during rebreathing. Presumably the oxygenation of blood in the lung capillaries increases lung capillary CO₂ pressure due to the Haldane effect, which during rebreathing may result in overestimation of the mixed venous CO₂ pressure. However, the Haldane effect is not discussed in the current literature describing cardiac output estimation using CO₂ rebreathing. The purpose of this study is to construct and verify a compartmental tidal breathing lung model to investigate the physiological mechanisms that influence the CO₂ rebreathing technique. The model simulations show agreement with previous studies describing end-tidal to arterial differences in CO₂ pressure and rebreathing with high and low O₂ fractions in the rebreathing bag. In conclusion the simulations show that caution has to be taken when using end-tidal measurements to estimate CO₂ pressures, especially during rebreathing where the Haldane effect causes mixed venous CO₂ partial pressure to be substantially overestimated.     

Spatially-explicit water balance implications of carbon capture and sequestration

Implementation of carbon capture and sequestration (CCS) will increase water demand due to the cooling water requirements of CO₂ capture equipment. If the captured CO₂ is injected into saline aquifers for sequestration, brine may be extracted to manage the aquifer pressure, and can be desalinated to provide additional freshwater supply. We conduct a geospatial analysis to determine how CCS may affect local water supply and demand across the contiguous United States. We calculate baseline indices for each county in the year 2005, and project future water supply and demand with and without CCS through 2030. We conduct sensitivity analyses to identify the system parameters that most significantly affect water balance. Water supply changes due to inter-annual variability and projected climate change are overwhelmingly the most significant sources of variation. CCS can have strong local effects on water supply and demand, but overall it has a modest effect on water balances.     

Mixed H2/H∞ distributed robust model predictive control for polytopic uncertain systems subject to actuator saturation and missing measurements

In this paper, we discuss the mixed H₂/H_∞ distributed robust model predictive control problem for polytopic uncertain systems subject to randomly occurring actuator saturation and packet loss. The global system is decomposed into several subsystems, and all the subsystems are connected by a fixed topology network, which is the definition for the packet loss among the subsystems. To better use the successfully transmitted information via Internet, both the phenomena of actuator saturation and packet loss resulting from the limitation of the communication bandwidth are taken into consideration. A novel distributed controller model is established to account for the actuator saturation and packet loss in a unified representation by using two sets of Bernoulli distributed white sequences with known conditional probabilities. With the nonlinear feedback control law represented by the convex hull of a group of linear feedback laws, the distributed controllers for subsystems are obtained by solving an linear matrix inequality (LMI) optimisation problem. Finally, numerical studies demonstrate the effectiveness of the proposed techniques.     

Experimental study of thermodynamic properties and phase equilibria in Na2CO3–K2CO3 system

Sodium and potassium carbonates and their mixtures are important for different applications, e.g. for latent thermal energy storage, die-casting processes and molten carbonate fuel cells. In this work the phase diagram and thermodynamic properties of Na₂CO₃–K₂CO₃ system were studied by differential thermal analysis, differential scanning calorimetry and high temperature X-ray diffraction. Three carbonate mixtures (56, 25 and 75 mol% of Na₂CO₃) have solid-solid transition in a wide temperature range between 648 K and 823 K. The high temperature XRD analysis has shown that this transition is a continuous process of changing of the unit cell volume without structural changing of the hexagonal lattice. This phenomenon has also been observed on the measured heat capacity curves. The obtained experimental results were compared with calculations performed using the previous thermodynamic datasets. The comparison of these results shows that further thermochemical assessment of this system needs to be performed to achieve better agreement with the available experimental data.     

Designing cyclic pressure pulsing in naturally fractured reservoirs using an inverse looking recurrent neural network

In this paper, an inverse looking approach is presented to efficiently design cyclic pressure pulsing (huff ‘n’ puff) with N₂ and CO₂, which is an effective improved oil recovery method in naturally fractured reservoirs. A numerical flow simulation model with compositional, dual-porosity formulation is constructed. The model characteristics are from the Big Andy Field, which is a depleted, naturally fractured oil reservoir in Kentucky. A set of cyclic pulsing design scenarios is created and run using this model. These scenarios and corresponding performance indicators are fed into the recurrent neural network for training. In order to capture the cyclic, time-dependent behavior of the process, recurrent neural networks are used to develop proxy models that can mimic the reservoir simulation model in an inverse looking manner. Two separate inverse looking proxy models for N₂ and CO₂ injections are constructed to predict the corresponding design scenarios, given a set of desired performance characteristics. Predictive capabilities of developed proxy models are evaluated by comparing simulation outputs with neural-network outputs. It is observed that networks are able to accurately predict the design parameters, such as the injection rate and the duration of injection, soaking and production periods.     

Modeling of the carbon dioxide capture process system using machine intelligence approaches

Improving the efficiency of the carbon dioxide (CO₂) capture process requires a good understanding of the intricate relationships among parameters involved in the process. The objective of this paper is to study the relationships among the significant parameters impacting CO₂ production. An enhanced understanding of the intricate relationships among the process parameters supports prediction and optimization, thereby improving efficiency of the CO₂ capture process. Our modeling study used the 3-year operational data collected from the amine-based post combustion CO₂ capture process system at the International Test Centre (ITC) of CO₂ Capture located in Regina, Saskatchewan of Canada. This paper describes the data modeling process using the approaches of (1) neural network modeling combined with sensitivity analysis and (2) neuro-fuzzy modeling technique. The results from the two modeling processes were compared from the perspectives of predictive accuracy, inclusion of parameters, and support for explication of problem space. We conclude from the study that the neuro-fuzzy modeling technique was able to achieve higher accuracy in predicting the CO₂ production rate than the combined approach of neural network modeling and sensitivity analysis.     

Numerical simulation of two-phase flow in deformable porous media: Application to carbon dioxide storage in the subsurface

In this paper, conceptual modeling as well as numerical simulation of two-phase flow in deep, deformable geological formations induced by CO₂ injection are presented. The conceptual approach is based on balance equations for mass, momentum and energy completed by appropriate constitutive relations for the fluid phases as well as the solid matrix. Within the context of the primary effects under consideration, the fluid motion will be expressed by the extended Darcy's law for two phase flow. Additionally, constraint conditions for the partial saturations and the pressure fractions of carbon dioxide and brine are defined. To characterize the stress state in the solid matrix, the effective stress principle is applied. Furthermore, the interaction of fluid and solid phases is illustrated by constitutive models for capillary pressure, porosity and permeability as functions of saturation. Based on this conceptual model, a coupled system of nonlinear differential equations for two-phase flow in a deformable porous matrix (H²M model) is formulated. As the displacement vector acts as primary variable for the solid matrix, multiphase flow is simulated using both pressure/pressure or pressure/saturation formulations. An object-oriented finite element method is used to solve the multi-field problem numerically. The capabilities of the model and the numerical tools to treat complex processes during CO₂ sequestration are demonstrated on three benchmark examples: (1) a 1-D case to investigate the influence of variable fluid properties, (2) 2-D vertical axi-symmetric cross-section to study the interaction between hydraulic and deformation processes, and (3) 3-D to test the stability and computational costs of the H²M model for real applications.     

H∞ output tracking control of uncertain and disturbed nonlinear systems based on neural network model

The work presented in this paper seeks to address the tracking problem for uncertain continuous nonlinear systems with external disturbances. The objective is to obtain a model that uses a reference-based output feedback tracking control law. The control scheme is based on neural networks and a linear difference inclusion (LDI) model, and a PDC structure and H_∞ performance criterion are used to attenuate external disturbances. The stability of the whole closed-loop model is investigated using the well-known quadratic Lyapunov function. The key principles of the proposed approach are as follows: neural networks are first used to approximate nonlinearities, to enable a nonlinear system to then be represented as a linearised LDI model. An LMI (linear matrix inequality) formula is obtained for uncertain and disturbed linear systems. This formula enables a solution to be obtained through an interior point optimisation method for some nonlinear output tracking control problems. Finally, simulations and comparisons are provided on two practical examples to illustrate the validity and effectiveness of the proposed method.     

Evaluation of two alternative carbon capture and storage technologies: A stochastic model

In this paper we evaluate two alternative CCS technologies at a coal-fired power plant from an investor's point of view. The first technology uses CO₂ for enhanced oil recovery (EOR) paired with storage in deep saline formations (DSF) and the second merely stores CO₂ in DSF. The paper updates and improves on an earlier publication by Tzimas et al. (2005). For projects of this type there are many sources of risk, three of which stand out: the price of electricity, the price of oil and the price of carbon allowances. In this paper we develop a general stochastic model that can be adapted to other projects such as enhanced gas recovery (EGR) or industrial plants that use CO₂ for either EOR or EGR with CCS. The model is calibrated with UK data and applied to help understand the conditions that generate the incentives needed for early investments in these technologies. Additionally, we analyse the risks of these investments. Investments with EOR and secondary DSF storage can only be profitable (NPV > 0) when there is a high long-term equilibrium price for oil of more than $56.38/barrel. When the investment decision can be made at any time, i.e. there is an option value, then the trigger value for optimal investment is significantly higher.     

Generating candidate networks for optimization: The CO2 capture and storage optimization problem

We develop a new framework for spatially optimizing infrastructure for CO₂ capture and storage (CCS). CCS is a complex and challenging problem: domestically deploying CCS at a meaningful scale will require linking hundreds of coal-fired power plants with CO₂ sequestration reservoirs through a dedicated and extensive (many tens-of-thousands of miles) CO₂ pipeline network. We introduce a unique method for generating a candidate network from scratch, from which the optimization model selects the optimal set of arcs to form the pipeline network. This new generation method can be applied to any network optimization problem including transmission line, roads, and telecommunication applications. We demonstrate the model and candidate network methodology using a real example of capturing CO₂ from coal-fired power plants in the US Midwest and storing the CO₂ in depleted oil and gas fields. Results illustrate the critical need to balance CCS investments with generating a candidate network of arcs.     

Model predictive control of pH in tubular photobioreactors

This paper presents the development and implementation of a branch-and-bound on–off model-based predictive control (MPC) strategy aimed at controlling pH and minimising CO₂ losses in a microalgal tubular photobioreactor. These kinds of photobioreactors are usually controlled by means of an on–off valve and thus classical on–off switching controllers are implemented, without taking into account plant dynamics. In the considered operating range, the nonlinearity of the system is not severe and thus a linear model of the pH evolution in spite of changes in CO₂ injection and in solar radiation has been obtained and used within a MPC framework to achieve desired regulation properties trying to minimise CO₂ losses, as one of the major costs in this installation is the supply of carbon dioxide and its transfer to the culture, amounting to about one-third the cost of the largest scale systems. The paper also shows the results obtained when applying the technique to the real photobioreactor.     

Numerical simulation of mass transfer in gas–liquid hollow fiber membrane contactors for laminar flow conditions

This study presents a numerical simulation using computational fluid dynamics (CFD) of momentum and mass transfer in a hollow fiber membrane contactor for laminar flow conditions. Axial and radial diffusion inside the fiber, through the membrane, and within the shell side of the membrane contactor were considered in the mass transfer equations. The simulation results were compared with the experimental data obtained from literature for CO₂ absorption in pure water. The simulation results indicated that the removal of CO₂ increased with increasing liquid flow rate in the shell side. On the other hand, increasing temperature and gas flow rate in the tube side have an opposite effect.     

TOUGHREACT Version 2.0: A simulator for subsurface reactive transport under non-isothermal multiphase flow conditions

TOUGHREACT is a numerical simulation program for chemically reactive non-isothermal flows of multiphase fluids in porous and fractured media, and was developed by introducing reactive chemistry into the multiphase fluid and heat flow simulator TOUGH2 V2. The first version of TOUGHREACT was released to the public through the U.S. Department of Energy's Energy Science and Technology Software Center (ESTSC) in August 2004. It is among the most frequently requested of ESTSC's codes. The code has been widely used for studies in CO₂ geological sequestration, nuclear waste isolation, geothermal energy development, environmental remediation, and increasingly for petroleum applications. Over the past several years, many new capabilities have been developed, which were incorporated into Version 2 of TOUGHREACT. Major additions and improvements in Version 2 are discussed here, and two application examples are presented: (1) long-term fate of injected CO₂ in a storage reservoir and (2) biogeochemical cycling of metals in mining-impacted lake sediments.     

Modeling gross primary production of temperate deciduous broadleaf forest using satellite images and climate data

Net ecosystem exchange (NEE) of CO₂ between the atmosphere and forest ecosystems is determined by gross primary production (GPP) of vegetation and ecosystem respiration. CO₂ flux measurements at individual CO₂ eddy flux sites provide valuable information on the seasonal dynamics of GPP. In this paper, we developed and validated the satellite-based Vegetation Photosynthesis Model (VPM), using site-specific CO₂ flux and climate data from a temperate deciduous broadleaf forest at Harvard Forest, Massachusetts, USA. The VPM model is built upon the conceptual partitioning of photosynthetically active vegetation and non-photosynthetic vegetation (NPV) within the leaf and canopy. It estimates GPP, using satellite-derived Enhanced Vegetation Index (EVI), Land Surface Water Index (LSWI), air temperature and photosynthetically active radiation (PAR). Multi-year (1998-2001) data analyses have shown that EVI had a stronger linear relationship with GPP than did the Normalized Difference Vegetation Index (NDVI). Two simulations of the VPM model were conducted, using vegetation indices from the VEGETATION (VGT) sensor onboard the SPOT-4 satellite and the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor onboard the Terra satellite. The predicted GPP values agreed reasonably well with observed GPP of the deciduous broadleaf forest at Harvard Forest, Massachusetts. This study highlighted the biophysical performance of improved vegetation indices in relation to GPP and demonstrated the potential of the VPM model for scaling-up of GPP of deciduous broadleaf forests.     

Development of SAW-based multi-gas sensor for simultaneous detection of CO2 and NO2

A 440 MHz wireless and passive surface acoustic wave (SAW)-based multi-gas sensor integrated with a temperature sensor was developed on a 41° YX LiNbO₃ piezoelectric substrate for the simultaneous detection of CO₂, NO₂, and temperature. The developed sensor was composed of a SAW reflective delay lines structured by an interdigital transducer (IDT), ten reflectors, a CO₂ sensitive film (Teflon AF 2400), and a NO₂ sensitive film (indium tin oxide). Teflon AF 2400 was used for the CO₂ sensitive film because it provides a high CO₂ solubility, with good permeability and selectivity. For the NO₂ sensitive film, indium tin oxide (ITO) was used. Coupling of mode (COM) modeling was conducted to determine the optimal device parameters prior to fabrication. Using the parameters determined by the simulation results, the device was fabricated and then wirelessly measured using a network analyzer. The measured reflective coefficient S₁₁ in the time domain showed high signal/noise (S/N) ratio, small signal attenuation, and few spurious peaks. The time positions of the reflection peaks were well matched with the predicted values from the simulation. High sensitivity and selectivity were observed at each target gas testing. The obtained sensitivity was 2.12°/ppm for CO₂ and 51.5°/ppm for NO₂, respectively. With the integrated temperature sensor, temperature compensation was also performed during gas sensitivity evaluation process.