Complete EOS Thermal Formulation for Simulation of CO2 Storage

2021 ◽  
Author(s):  
Arthur Moncorgé ◽  
Martin Petitfrère ◽  
Sylvain Thibeau
Keyword(s):  
Co2 Storage ◽  
Continuous Phase ◽  
Conservation Equation ◽  
Co2 Injection ◽  
Energy Conservation Equation ◽  
Input Variables ◽  
New Formulation ◽  
Reservoir Simulator ◽  
Primary Variable ◽  
Phase Envelope

Abstract Storage of CO2 in depleted gas reservoirs or large aquifers is one of the available solutions to reduce anthropogenic greenhouse gas emissions. Numerical modeling of these processes requires the use of large geological models with several orders of magnitude of variations in the porous media properties. Moreover, modeling the injection of highly concentrated and cold CO2 in large reservoirs with the correct physics is introducing numerical challenges that conventional reservoir simulators cannot handle. We propose a thermal formulation based on a full equation of state formalism to model pure CO2 and CO2 mixtures with the residual gas of depleted reservoirs. Most of the reservoir simulators model the phase-equilibriums with a pressure-temperature based formulation. With this usual framework, it is not possible to exhibit two phases with pure CO2 contents. Moreover, in this classical framework, the crossing of the phase envelope is associated with a large discontinuity in the enthalpy computation which can prevent the convergence of the energy conservation equation. In this work, accurate and continuous phase properties are obtained basing our formulation on enthalpy as a primary variable. We first implement a new phase-split algorithm with input variables as pressure and enthalpy instead of the usual pressure and temperature and we validate it on several test cases. This algorithm can model situations where the mixture can change rapidly from one phase to the other at constant pressure and temperature. Then treating enthalpy instead of temperature as a primary variable in both the reservoir and the well modeling algorithms, our reservoir simulator can model situations with pure or near pure components as well as crossing of the phase envelope that usual formulations implemented in reservoir simulators cannot handle. We first validate our new formulation against the usual formulation on a problem where both formulations can correctly represent the physics. Then we show situations where the usual formulations fail to represent the correct physics and that are simulated well with our new formulation. Finally, we apply our new model for the simulation of pure and cold CO2 injection in a real depleted gas reservoir from the Netherlands.

Complete Equation of State Thermal Formulation for Simulation of CO2 Storage

SPE Journal ◽  
2021 ◽  
pp. 1-15
Author(s):  
Arthur Moncorgé ◽  
Martin Petitfrère ◽  
Sylvain Thibeau
Keyword(s):  
Equation Of State ◽  
Co2 Storage ◽  
Continuous Phase ◽  
Conservation Equation ◽  
Co2 Injection ◽  
Energy Conservation Equation ◽  
Carbon Dioxide Co2 ◽  
New Formulation ◽  
Primary Variable ◽  
Phase Envelope

Summary Storage of carbon dioxide (CO2) in depleted gas reservoirs or large aquifers is one of the available solutions to reduce anthropogenic greenhouse gas emissions. Numerical modeling of these processes requires the use of large geological models with several orders of magnitude of variations in the porous media properties. Moreover, modeling the injection of highly concentrated and cold CO2 in large reservoirs with the correct physics introduces numerical challenges that conventional reservoir simulators cannot handle. We propose a thermal formulation based on a full equation of state (EoS) formalism to model pure CO2 and CO2 mixtures with the residual gas of depleted reservoirs. Most of the reservoir simulators model the phase equilibriums with a pressure-temperature-based formulation. With this usual framework, it is not possible to exhibit two phases with pure CO2 contents. Moreover, in this classical framework, the crossing of the phase envelope is associated with a large discontinuity in the enthalpy computation, which can prevent the convergence of the energy conservation equation. In this work, accurate and continuous phase properties are obtained, basing our formulation on enthalpy as a primary variable. We first implement a new phase-split algorithm with input variables as pressure and enthalpy instead of the usual pressure and temperature, and we validate it on several test cases. This algorithm can model situations in which the mixture can change rapidly from one phase to the other at constant pressure and temperature. Then, treating enthalpy instead of temperature as a primary variable in both the reservoir and the well modeling algorithms, our reservoir simulator can model situations with pure or near pure components, as well as crossing of the phase envelope that usual formulations implemented in reservoir simulators cannot handle. We first validate our new formulation against the usual formulation on a problem in which both formulations can correctly represent the physics. Then, we show situations in which the usual formulations fail to represent the correct physics and that are simulated well with our new formulation. Finally, we apply our new model for the simulation of pure and cold CO2 injection in a real depleted gas reservoir from the Netherlands.

Improving CO2 storage and oil recovery by injecting alcohol-treated CO2

2020 ◽  
Vol 60 (2) ◽  
pp. 662
Author(s):  
Saira ◽  
Furqan Le-Hussain
Keyword(s):  
Oil Recovery ◽  
Co2 Sequestration ◽  
Computer Modelling ◽  
Co2 Storage ◽  
Co2 Injection ◽  
Displacement Efficiency ◽  
Sweep Efficiency ◽  
Numerical Studies ◽  
Reservoir Simulator ◽  
Enhance Oil Recovery

Oil recovery and CO2 storage related to CO2 enhance oil recovery are dependent on CO2 miscibility. In case of a depleted oil reservoir, reservoir pressure is not sufficient to achieve miscible or near-miscible condition. This extended abstract presents numerical studies to delineate the effect of alcohol-treated CO2 injection on enhancing miscibility, CO2 storage and oil recovery at immiscible and near-miscible conditions. A compositional reservoir simulator from Computer Modelling Group Ltd. was used to examine the effect of alcohol-treated CO2 on the recovery mechanism. A SPE-5 3D model was used to simulate oil recovery and CO2 storage at field scale for two sets of fluid pairs: (1) pure CO2 and decane and (2) alcohol-treated CO2 and decane. Alcohol-treated CO2 consisted of a mixture of 4 wt% of ethanol and 96 wt% of CO2. All simulations were run at constant temperature (70°C), whereas pressures were determined using a pressure-volume-temperature simulator for immiscible (1400 psi) and near-miscible (1780 psi) conditions. Simulation results reveal that alcohol-treated CO2 injection is found superior to pure CO2 injection in oil recovery (5–9%) and CO2 storage efficiency (4–6%). It shows that alcohol-treated CO2 improves CO2 sweep efficiency. However, improvement in sweep efficiency with alcohol-treated CO2 is more pronounced at higher pressures, whereas improvement in displacement efficiency is more pronounced at lower pressures. The proposed methodology has potential to enhance the feasibility of CO2 sequestration in depleted oil reservoirs and improve both displacement and sweep efficiency of CO2.

Experimental and Modeling Study of Salt Precipitation During Injection of CO2 Contaminated With H2S Into Depleted Gas Fields in the Northeast of the Netherlands

SPE Journal ◽  
2014 ◽  
Vol 19 (06) ◽  
pp. 1058-1068 ◽  
Author(s):  
P.. Bolourinejad ◽  
R.. Herber
Keyword(s):  
The Netherlands ◽  
Carbonic Acid ◽  
Co2 Storage ◽  
Mineral Dissolution ◽  
Co2 Injection ◽  
Salt Precipitation ◽  
Geological Time ◽  
Core Samples ◽  
Carbon Dioxide Co2 ◽  
Gas Fields

Summary Depleted gas fields are among the most probable candidates for subsurface storage of carbon dioxide (CO2). With proven reservoir and qualified seal, these fields have retained gas over geological time scales. However, unlike methane, injection of CO2 changes the pH of the brine because of the formation of carbonic acid. Subsequent dissolution/precipitation of minerals changes the porosity/permeability of reservoir and caprock. Thus, for adequate, safe, and effective CO2 storage, the subsurface system needs to be fully understood. An important aspect for subsurface storage of CO2 is purity of this gas, which influences risk and cost of the process. To investigate the effects of CO2 plus impurities in a real case example, we have carried out medium-term (30-day) laboratory experiments (300 bar, 100°C) on reservoir and caprock core samples from gas fields in the northeast of the Netherlands. In addition, we attempted to determine the maximum allowable concentration of one of the possible impurities in the CO2 stream [hydrogen sulfide (H2S)] in these fields. The injected gases—CO2, CO2+100 ppm H2S, and CO2+5,000 ppm H2S—were reacting with core samples and brine (81 g/L Na+, 173 g/L Cl−, 22 g/L Ca2+, 23 g/L Mg2+, 1.5 g/L K+, and 0.2 g/L SO42−). Before and after the experiments, the core samples were analyzed by scanning electron microscope (SEM) and X-ray diffraction (XRD) for mineralogical variations. The permeability of the samples was also measured. After the experiments, dissolution of feldspars, carbonates, and kaolinite was observed as expected. In addition, we observed fresh precipitation of kaolinite. However, two significant results were obtained when adding H2S to the CO2 stream. First, we observed precipitation of sulfate minerals (anhydrite and pyrite). This differs from results after pure CO2 injection, where dissolution of anhydrite was dominant in the samples. Second, severe salt precipitation took place in the presence of H2S. This is mainly caused by the nucleation of anhydrite and pyrite, which enabled halite precipitation, and to a lesser degree by the higher solubility of H2S in water and higher water content of the gas phase in the presence of H2S. This was confirmed by the use of CMG-GEM (CMG 2011) modeling software. The precipitation of halite, anhydrite, and pyrite affects the permeability of the samples in different ways. After pure CO2 and CO2+100 ppm H2S injection, permeability of the reservoir samples increased by 10–30% and ≤3%, respectively. In caprock samples, permeability increased by a factor of 3–10 and 1.3, respectively. However, after addition of 5,000 ppm H2S, the permeability of all samples decreased significantly. In the case of CO2+100 ppm H2S, halite, anhydrite, and pyrite precipitation did balance mineral dissolution, causing minimal variation in the permeability of samples.

scholarly journals Numerical Simulation and Optimization of CO2 Sequestration in Saline Aquifers

2012 ◽  
Author(s):  
Zheming Zhang ◽  
Ramesh Agarwal
Keyword(s):  
Numerical Simulation ◽  
Co2 Sequestration ◽  
Storage Capacity ◽  
Co2 Storage ◽  
Injection Well ◽  
Co2 Injection ◽  
Great Promise ◽  
Saline Aquifer ◽  
Simulation And Optimization ◽  
Co2 Plume

With recent concerns on CO2 emissions from coal fired electricity generation plants; there has been major emphasis on the development of safe and economical Carbon Dioxide Capture and Sequestration (CCS) technology worldwide. Saline reservoirs are attractive geological sites for CO2 sequestration because of their huge capacity for sequestration. Over the last decade, numerical simulation codes have been developed in U.S, Europe and Japan to determine a priori the CO2 storage capacity of a saline aquifer and provide risk assessment with reasonable confidence before the actual deployment of CO2 sequestration can proceed with enormous investment. In U.S, TOUGH2 numerical simulator has been widely used for this purpose. However at present it does not have the capability to determine optimal parameters such as injection rate, injection pressure, injection depth for vertical and horizontal wells etc. for optimization of the CO2 storage capacity and for minimizing the leakage potential by confining the plume migration. This paper describes the development of a “Genetic Algorithm (GA)” based optimizer for TOUGH2 that can be used by the industry with good confidence to optimize the CO2 storage capacity in a saline aquifer of interest. This new code including the TOUGH2 and the GA optimizer is designated as “GATOUGH2”. It has been validated by conducting simulations of three widely used benchmark problems by the CCS researchers worldwide: (a) Study of CO2 plume evolution and leakage through an abandoned well, (b) Study of enhanced CH4 recovery in combination with CO2 storage in depleted gas reservoirs, and (c) Study of CO2 injection into a heterogeneous geological formation. Our results of these simulations are in excellent agreement with those of other researchers obtained with different codes. The validated code has been employed to optimize the proposed water-alternating-gas (WAG) injection scheme for (a) a vertical CO2 injection well and (b) a horizontal CO2 injection well, for optimizing the CO2 sequestration capacity of an aquifer. These optimized calculations are compared with the brute force nearly optimized results obtained by performing a large number of calculations. These comparisons demonstrate the significant efficiency and accuracy of GATOUGH2 as an optimizer for TOUGH2. This capability holds a great promise in studying a host of other problems in CO2 sequestration such as how to optimally accelerate the capillary trapping, accelerate the dissolution of CO2 in water or brine, and immobilize the CO2 plume.

Heat Transfer Analysis of a Novel Pressurized Air Receiver for Concentrated Solar Power via Combined Cycles

2009 ◽  
Vol 1 (4) ◽  
Author(s):  
I. Hischier ◽  
D. Hess ◽  
W. Lipiński ◽  
M. Modest ◽  
A. Steinfeld
Keyword(s):  
Heat Transfer ◽  
Thermal Efficiency ◽  
Porous Ceramic ◽  
Conservation Equation ◽  
Heat Transfer Analysis ◽  
Operational Parameters ◽  
Small Aperture ◽  
Solar Absorber ◽  
Energy Conservation Equation ◽  
Combined Cycles

A novel design of a high-temperature pressurized solar air receiver for power generation via combined Brayton–Rankine cycles is proposed. It consists of an annular reticulate porous ceramic (RPC) bounded by two concentric cylinders. The inner cylinder, which serves as the solar absorber, has a cavity-type configuration and a small aperture for the access of concentrated solar radiation. Absorbed heat is transferred by conduction, radiation, and convection to the pressurized air flowing across the RPC. A 2D steady-state energy conservation equation coupling the three modes of heat transfer is formulated and solved by the finite volume technique and by applying the Rosseland diffusion, P1, and Monte Carlo radiation methods. Key results include the temperature distribution and thermal efficiency as a function of the geometrical and operational parameters. For a solar concentration ratio of 3000 suns, the outlet air temperature reaches 1000°C at 10 bars, yielding a thermal efficiency of 78%.

Energy conservation, time-reversal invariance and reciprocity in ducts with flow

2001 ◽  
Vol 431 ◽  
pp. 223-237 ◽  
Author(s):  
WILLI MÖHRING
Keyword(s):  
Energy Conservation ◽  
Sound Wave ◽  
Conservation Equation ◽  
Smooth Transition ◽  
Rotational Flow ◽  
Flow Energy ◽  
Energy Conservation Equation ◽  
Reversal Invariance ◽  
Edge Conditions ◽  
Piecewise Continuous

A sound wave propagating in an inhomogeneous duct consisting of two semi-infinite uniform ducts with a smooth transition region in between and which carries a steady flow is considered. The duct walls may be rigid or compliant. For an irrotational sound wave it is shown that the three properties of the title are closely related, such that the validity of any two implies the validity of the third. Furthermore it is shown that the three properties are fulfilled for lossless locally reacting duct walls provided the impedance varies at most continuously. For piecewise-continuous wall properties edge conditions are essential. By an analytic continuation argument it is shown that reciprocity remains true for walls with loss. For rotational flow, energy conservation theorems have been derived only with the help of additional potential-like variables. The inter-relation between the three properties remains valid if one considers these additional variables to be known. If only the basic gasdynamic variables in both half-ducts are known, one cannot formulate an energy conservation equation; however, reciprocity is fulfilled.

scholarly journals Managing Uncertainty in Geological CO2 Storage Using Bayesian Evidential Learning

Energies ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1557
Author(s):  
Amine Tadjer ◽  
Reidar B. Bratvold
Keyword(s):  
Uncertainty Quantification ◽  
History Matching ◽  
Co2 Storage ◽  
Carbon Capture And Storage ◽  
Monitoring Program ◽  
Co2 Injection ◽  
Drinking Water Contamination ◽  
Model Inversion ◽  
Geological Co2 Storage ◽  
And Storage

Carbon capture and storage (CCS) has been increasingly looking like a promising strategy to reduce CO2 emissions and meet the Paris agreement’s climate target. To ensure that CCS is safe and successful, an efficient monitoring program that will prevent storage reservoir leakage and drinking water contamination in groundwater aquifers must be implemented. However, geologic CO2 sequestration (GCS) sites are not completely certain about the geological properties, which makes it difficult to predict the behavior of the injected gases, CO2 brine leakage rates through wellbores, and CO2 plume migration. Significant effort is required to observe how CO2 behaves in reservoirs. A key question is: Will the CO2 injection and storage behave as expected, and can we anticipate leakages? History matching of reservoir models can mitigate uncertainty towards a predictive strategy. It could prove challenging to develop a set of history matching models that preserve geological realism. A new Bayesian evidential learning (BEL) protocol for uncertainty quantification was released through literature, as an alternative to the model-space inversion in the history-matching approach. Consequently, an ensemble of previous geological models was developed using a prior distribution’s Monte Carlo simulation, followed by direct forecasting (DF) for joint uncertainty quantification. The goal of this work is to use prior models to identify a statistical relationship between data prediction, ensemble models, and data variables, without any explicit model inversion. The paper also introduces a new DF implementation using an ensemble smoother and shows that the new implementation can make the computation more robust than the standard method. The Utsira saline aquifer west of Norway is used to exemplify BEL’s ability to predict the CO2 mass and leakages and improve decision support regarding CO2 storage projects.

Estimation of CO2 Diffusivity in Brine by Use of the Genetic Algorithm and Mixed Kernels-Based Support Vector Machine Model

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Qihong Feng ◽  
Ronghao Cui ◽  
Sen Wang ◽  
Jin Zhang ◽  
Zhe Jiang
Keyword(s):  
Genetic Algorithm ◽  
Support Vector Machine ◽  
Diffusion Coefficient ◽  
Co2 Storage ◽  
Co2 Injection ◽  
Support Vector ◽  
Hybrid Technique ◽  
Machine Model ◽  
Proposed Model ◽  
Wide Range

Diffusion coefficient of carbon dioxide (CO2), a significant parameter describing the mass transfer process, exerts a profound influence on the safety of CO2 storage in depleted reservoirs, saline aquifers, and marine ecosystems. However, experimental determination of diffusion coefficient in CO2-brine system is time-consuming and complex because the procedure requires sophisticated laboratory equipment and reasonable interpretation methods. To facilitate the acquisition of more accurate values, an intelligent model, termed MKSVM-GA, is developed using a hybrid technique of support vector machine (SVM), mixed kernels (MK), and genetic algorithm (GA). Confirmed by the statistical evaluation indicators, our proposed model exhibits excellent performance with high accuracy and strong robustness in a wide range of temperatures (273–473.15 K), pressures (0.1–49.3 MPa), and viscosities (0.139–1.950 mPa·s). Our results show that the proposed model is more applicable than the artificial neural network (ANN) model at this sample size, which is superior to four commonly used traditional empirical correlations. The technique presented in this study can provide a fast and precise prediction of CO2 diffusivity in brine at reservoir conditions for the engineering design and the technical risk assessment during the process of CO2 injection.

scholarly journals INDOOR AIR TEMPERATURE DISTRIBUTION – AN ALTERNATIVE APPROACH TO BUILDING SIMULATION

2003 ◽  
Vol 2 (1) ◽  
Author(s):  
A. T. Franco ◽  
C. O. R. Negrão
Keyword(s):  
Temperature Distribution ◽  
Air Temperature ◽  
Indoor Air ◽  
Linear Equations ◽  
Three Dimensional ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Algebraic Equations ◽  
Conservation Of Energy ◽  
Energy Conservation Equation

The current paper presents a model to predict indoor air temperature distribution. The approach is based on the energy conservation equation which is written for a certain number of finite volumes within the flow domain. The magnitude of the flow is estimated from a scale analysis of the momentum conservation equation. Discretized two or three-dimensional domains provide a set of algebraic equations. The resulting set of non-linear equations is iteratively solved using the line-by-line Thomas Algorithm. As long as the only equation to be solved is the conservation of energy and its coefficients are not strongly dependent on the temperature field, the solution is considerably fast. Therefore, the application of such model to a whole building system is quite reasonable. Two case studies involving buoyancy driven flows were carried out and comparisons with CFD solutions were performed. The results are quite promising for cases involving relatively strong couplings between heat and airflow.

scholarly journals A Two-Layer Model for Steady-Amplitude Gravity Waves and Convection Generated by a Thermal Forcing

2018 ◽  
Vol 75 (7) ◽  
pp. 2199-2216 ◽  
Author(s):  
A. A. M. Sayed ◽  
L. J. Campbell
Keyword(s):  
Gravity Waves ◽  
Lower Layer ◽  
Stable Stratification ◽  
Internal Gravity Waves ◽  
Conservation Equation ◽  
Lower Atmosphere ◽  
Thermal Forcing ◽  
Energy Conservation Equation ◽  
Vertical Location ◽  
Convective Cells

Abstract A two-dimensional two-layer mathematical model is described representing internal gravity waves and convection generated by a thermal forcing in the lower atmosphere. The model consists of an upper layer with stable stratification, a lower layer with unstable stratification, and a thermal forcing in the form of a nonhomogeneous term in the energy conservation equation. Exact analytical solutions are derived for some simple configurations. Depending on the vertical location and depth of the thermal forcing, the model can be used to represent different configurations in which gravity waves are generated by diabatic heating. When the thermal forcing is centered in the lower layer, convective cells are generated in the lower layer, and gravity waves are forced and propagate upward from the interface between the two layers. When the thermal forcing is centered at the interface, the convection in the lower layer is weaker, and gravity waves are forced by the direct effect of the thermal forcing in the upper layer and the influence of the convective cells below. Steady-amplitude solutions for the vertical profile of the gravity waves and convection are derived and generalized to include cases where there is a spectrum of horizontal wavenumbers or vertical wavenumbers or frequencies present.

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