HCO-TERNARY: A FORTRAN code for calculating P–V–T–X properties and liquid vapor equilibria of fluids in the system H2O–CO2–CH4

The equation of state (EOS) for the system H₂O–CO₂–CH₄ was programmed in a FORTRAN code which allows for its utilization in several modes. In one mode, specifically designed for mathematical modeling of two-phase, two-component flow, the code accepts as independent variables (1) pressure and (2) the composition of the gas phase. Other modes allow for the calculation of phase equilibria and/or the molar volumes of H₂O and binary mixtures, with pressure and temperature as the input variables (just pressure in the case of H₂O). Another mode is used to calculate phase equilibria for ternary mixtures, with pressure, temperature and the mole fraction of water in the gas phase as input variables. The algorithms for automatic convergence utilized in each mode are described.The code was tested extensively against experimental data from the literature. Some of these data were applied in the development of the EOS, and others were published subsequently. Analyses of the performance of the code and EOS for the modes described above, in the range 50–1000°C, 0–1000 bar, are presented. P–T–X regions of best applicability of the code and EOS are also identified.     

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).     

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 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.     

FORTRAN programs for calculation of fluid properties from microthermometric data on fluid inclusions

Four FORTRAN programs for the calculation of fluid properties from observational data on fluid inclusions are described along with instructions for their implementation. The primary data from fluid inclusion studies are phase identifications, phase transition temperatures, and estimates of relative phase volumes. From these data the programs calculate densities, compositions and isochores for H₂O, CO₂, H₂OCO₂, H₂ONaCl and H₂OCO₂NaCL mixtures.     

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.     

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.     

Numerical investigation of formation and dissolution of CO<Subscript>2</Subscript> bubbles within silicone oil in a cross-junction microchannel

In this paper, a numerical investigation is conducted to study the formation and dissolution process of CO₂ bubbles within silicone oil in a cross-junction microchannel. A coupled multiphase–multicomponent computational fluid dynamics model based on the volume-of-fluid method is used, which is able to capture the physics of the multiphase bubble formation, dissolution mass transfer, and the tracking of the dissolved CO₂ species. The computational model is firstly validated with experimental results where good agreement is attained. Next, the model is used to investigate the bubble formation process at the cross-junction in the presence of dissolution and also the bubble evolution as it is transported along the downstream channel. It is revealed that during bubble formation, there is a high concentration of CO₂ solute around the cross-junction walls, as silicone oil flow to this region is minimal. As the CO₂ bubble travels downstream, the transport of the CO₂ solute is largely driven by the local flow currents of the silicone oil within the vicinity of the bubble. An extensive parametric study is also conducted, looking at the effects of varying the surface tension, diffusion coefficient and flow rates. The results demonstrate that the initial CO₂ bubble length and period of bubble formation are most affected by the flow rate, while the mass transfer is most strongly governed by the diffusion coefficient.     

Status of the TOUGH-FLAC simulator and recent applications related to coupled fluid flow and crustal deformations

This paper presents recent advancement in and applications of TOUGH-FLAC, a simulator for multiphase fluid flow and geomechanics. The TOUGH-FLAC simulator links the TOUGH family multiphase fluid and heat transport codes with the commercial FLAC^3D geomechanical simulator. The most significant new TOUGH-FLAC development in the past few years is a revised architecture, enabling a more rigorous and tight coupling procedure with improved computational efficiency. The applications presented in this paper are related to modeling of crustal deformations caused by deep underground fluid movements and pressure changes as a result of both industrial activities (the In Salah CO₂ Storage Project and the Geysers Geothermal Field) and natural events (the 1960s Matsushiro Earthquake Swarm). Finally, the paper provides some perspectives on the future of TOUGH-FLAC in light of its applicability to practical problems and the need for high-performance computing capabilities for field-scale problems, such as industrial-scale CO₂ storage and enhanced geothermal systems. It is concluded that despite some limitations to fully adapting a commercial code such as FLAC^3D for some specialized research and computational needs, TOUGH-FLAC is likely to remain a pragmatic simulation approach, with an increasing number of users in both academia and industry.     

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.     

APL and FORTRAN programs for a new equation of state for H2O,CO2, and their mixtures at supercritical conditions

APL and FORTRAN programs utilizing a new modified hard-sphere Redlich-Kwong equation calculate volumes and fugacity coefficients for pure H₂O and CO₂, and activities in H₂O-CO₂ mixtures, throughout most of the crustal and upper mantle P?T conditions. The new modification allows the term of the equation representing attractive intermolecular forces to vary as a function of both temperature and pressure, in contrast to earlier versions where this term was considered a function of temperature only. Compared with previous modified Redlich-Kwong (MRK) equations, this equation predicts thermodynamic properties for pure H₂O and CO₂ which are in better agreement with those derived from experimental P?V?T data. These programs are versatile and can be incorporated into existing routines which calculate mixed-volatile (H₂O–CO₂) phase equilibria for petrologic systems.     

Connectionist approaches for solubility prediction of n-alkanes in supercritical carbon dioxide

Carbon dioxide injection is a known promising and economical technology for improving oil recovery. Despite its immense effect on oil recovery, the application of this technique in modern recovery industry has been limited due to poor solubility of n-alkanes in supercritical CO₂. Therefore, it is very consequential to investigate the solubility of different n-alkanes in supercritical CO₂. Since experimental methods for measuring the solubility of n-alkanes in supercritical CO₂ at different temperatures and pressures are not economical and usually take a long time, feasibility of applying intelligent tools in the solubility prediction of different n-alkanes in supercritical CO₂ at pressures up to 45.9 MPa was conducted in this study. For this purpose, two models including an artificial neural network and an adaptive neuro-fuzzy interference system (ANFIS) both trained with particle swarm optimization (PSO) algorithm were used for simulating this process. Calculated mole fractions of n-alkanes in supercritical CO₂ from ANFIS–PSO model were excellently consistent with actual measured values. Moreover, comparison between these models and Chrastil semiempirical correlation show superiority and accuracy of the proposed ANFIS–PSO approach. Results of this study indicate that ANFIS–PSO method is a powerful technique for predicting solubility of n-alkanes in supercritical CO₂.

     

Fast and inexpensive method for the fabrication of transparent pressure-resistant microfluidic chips

The recent rise of high-pressure applications in microfluidics has led to the development of different types of pressure-resistant microfluidic chips. For the most part, however, the fabrication methods require clean room facilities, as well as specific equipment and expertise. Furthermore, the resulting microfluidic chips are not always well suited to flow visualization and optical measurements. Herein, we present a method that allows rapid and inexpensive prototyping of optically transparent microfluidic chips that resist pressures of at least 200 bar. The fabrication method is based on UV-curable off-stoichiometry thiol-ene epoxy (OSTE+) polymer, which is chemically bonded to glass. The reliability of the device was verified by pressure tests using CO₂, showing resistance without failure up to at least 200 bar at ambient temperature. The microchips also resisted operation at high pressure for several hours at a temperature of 40 °C. These results show that the polymer structure and the chemical bond with the glass are not affected by high-pressure CO₂. Opportunities for flow visualization are illustrated by high-pressure two-phase flow shadowgraphy experiments. These microfluidic chips are of specific interest for use with supercritical CO₂ and for optical characterization of phase transitions and multiphase flow under near-critical and critical CO₂ conditions.     

Separation of CO2 by single and mixed aqueous amine solvents in membrane contactors: fluid flow and mass transfer modeling

Removal of carbon dioxide from gas mixtures is of vital importance for the control of greenhouse gas emission. This study presents a numerical simulation using computational fluid dynamics of mass and momentum transfer in hollow-fiber membrane contactors. The simulation was conducted for physical and chemical absorption of CO₂. A mass transfer model was developed to study CO₂ transport through hollow-fiber membrane contactors. The model considers axial and radial diffusions in the contactor. It also considers convection in the tube and shell side with chemical reaction. The model equations were solved by numerical method based on finite element method. Moreover, the simulation results were validated with the experimental data obtained from literature for absorption of CO₂ in amine aqueous solutions as solvent. The simulation results were in good agreement with the experimental data for different values of gas and liquid velocities. The simulation results indicated that the removal of CO₂ increased with increasing liquid velocity in the tube side. Simulation results also showed that hollow-fiber membrane contactors have a great potential in the area of gas separation specially CO₂ separation from gas mixtures.     

Flow of CO<Subscript>2</Subscript>–ethanol and of CO<Subscript>2</Subscript>–methanol in a non-adiabatic microfluidic T-junction at high pressures

In this work, an experimental investigation of the single- and multiphase flows of two sets of fluids, CO₂–ethanol and CO₂–methanol, in a non-adiabatic microfluidic T-junction is presented. The operating conditions ranged from 7 to 18 MPa, and from 294 to 474 K. The feed mass fraction of CO₂ in the mixtures was 0.95 and 0.87, respectively. Under these operating conditions, CO₂ was either in liquid, gas or supercritical state; and the mixtures experienced a miscible single phase or a vapour–liquid equilibrium (VLE), with two separated phases. Taylor, annular and wavy were the two-phase flow regimes obtained in the VLE region. In the single phase region, the observed flows were classified into standard single-phase flows, “pseudo” two-phase flows and local phenomena in the T-junction. Flow regime maps were generated, based on temperature and pressure conditions. Two-phase flow void fractions and several parameters of Taylor flow were analysed. They showed a clear dependency on temperature, but were mostly insensitive to pressure. A continuous accumulation of liquid, either in the CO₂ channel or at the CO₂-side wall after the T-junction, disturbed most of the experiments in VLE conditions by randomly generating liquid plugs. This phenomenon is analysed, and capillary and wetting effects due to local Marangoni stresses are suggested as possible causes.     

Direct and Indirect Estimation of Leaf Area Index,fAPAR, and Net Primary Production of Terrestrial Ecosystems

A primary objective of the Earth Observing System (EOS) is to develop and validate algorithms to estimate leaf area index (L), fraction of absorbed photosynthetically active radiation (f_APAR), and net primary production (NPP) from remotely sensed products. These three products are important because they relate to or are components of the metabolism of the biosphere and can be determined for terrestrial ecosystems from satellite-borne sensors. The importance of these products in the EOS program necessitates the need to use standard methods to obtain accurate ground truth estimates of L, f_APAR, and NPP that are correlated to satellite-derived estimates. The objective of this article is to review direct and indirect methods used to estimate L, f_APAR, and NPP in terrestrial ecosystems. Direct estimates of L, biomass, and NPP can be obtained by harvesting individual plants, developing allometric equations, and applying these equations to all individuals in the stand. Using non-site-specific allometric equations to estimate L and foliage production can cause large errors because carbon allocation to foliage is influenced by numerous environmental and ecological factors. All of the optical instruments that indirectly estimate L actually estimate “effective” leaf area index (L_E) and underestimate L when foliage in the canopy is nonrandomly distributed (i.e., clumped). We discuss several methods, ranging from simple to complex in terms of data needs, that can be used to correct estimates of L when foliage is clumped. Direct estimates of above-ground and below-ground net primary production (NPP_A and NPP_B, respectively) are laborious, expensive and can only be carried out for small plots, yet there is a great need to obtain global estimates of NPP. Process models, driven by remotely sensed input parameters, are useful tools to examine the influence of global change on the metabolism of terrestrial ecosystems, but an incomplete understanding of carbon allocation continues to hamper development of more accurate NPP models. We summarize carbon allocation patterns for major terrestrial biomes and discuss emerging allocation patterns that can be incorporated into global NPP models. One common process model, light use efficiency or epsilon model, uses remotely sensed f_APAR, light use efficiency (LUE) and carbon allocation coefficients, and other meteorological data to estimates NPP. Such models require reliable estimates of LUE. We summarize the literature and provide LUE coefficients for the major biomes, being careful to correct for inconsistencies in radiation, dry matter and carbon allocation units.     

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.     

A new equation of state and Fortran 77 program to calculate vapor–liquid phase equilibria of CH4–H2O system at low temperatures

A new equation of state (EOS) and the corresponding computer program package VLEWM are developed to calculate vapor–liquid phase equilibria and volumetric properties of CH₄–H₂O system at low temperatures. The EOS can predict vapor–liquid equilibria and volumetric properties of CH₄–H₂O system accurately at temperatures 273–383 K, and at pressures 0–1000 bar. The program package VLEWM is written in FORTRAN 77. It provides two main functions: (1) to calculate the composition in vapor phase and liquid phase of CH₄–H₂O system at equilibrium and (2) to judge the phase and to calculate molar volume of CH₄–H₂O mixture.     

Calibration of remotely sensed, coarse resolution NDVI to CO2 fluxes in a sagebrush-steppe ecosystem

The net ecosystem exchange (NEE) of carbon flux can be partitioned into gross primary productivity (GPP) and respiration (R). The contribution of remote sensing and modeling holds the potential to predict these components and map them spatially and temporally. This has obvious utility to quantify carbon sink and source relationships and to identify improved land management strategies for optimizing carbon sequestration. The objective of our study was to evaluate prediction of 14-day average daytime CO₂ fluxes (F_day) and nighttime CO₂ fluxes (R_n) using remote sensing and other data. F_day and R_n were measured with a Bowen ratio-energy balance (BREB) technique in a sagebrush (Artemisia spp.)-steppe ecosystem in northeast Idaho, USA, during 1996-1999. Micrometeorological variables aggregated across 14-day periods and time-integrated Advanced Very High Resolution Radiometer (AVHRR) Normalized Difference Vegetation Index (iNDVI) were determined during four growing seasons (1996-1999) and used to predict F_day and R_n. We found that iNDVI was a strong predictor of F_day (R²=0.79, n=66, P<0.0001). Inclusion of evapotranspiration in the predictive equation led to improved predictions of F_day (R²=0.82, n=66, P<0.0001). Crossvalidation indicated that regression tree predictions of F_day were prone to overfitting and that linear regression models were more robust. Multiple regression and regression tree models predicted R_n quite well (R²=0.75-0.77, n=66) with the regression tree model being slightly more robust in crossvalidation. Temporal mapping of F_day and R_n is possible with these techniques and would allow the assessment of NEE in sagebrush-steppe ecosystems. Simulations of periodic F_day measurements, as might be provided by a mobile flux tower, indicated that such measurements could be used in combination with iNDVI to accurately predict F_day. These periodic measurements could maximize the utility of expensive flux towers for evaluating various carbon management strategies, carbon certification, and validation and calibration of carbon flux models.     

Application of satellite remote sensing techniques for estimating air–sea CO2 fluxes in Hudson Bay,Canada during the ice-free season

The role of coastal seas as either a sink or a source of CO₂ is subject to a great deal of uncertainty. This uncertainty largely arises from a lack of observations in the coastal zones. Remote sensing offers an avenue for expanding these observations by allowing for the extrapolation of relatively limited data sets of dissolved CO₂ (pCO_2sw). In this paper, predictive algorithms for pCO_2sw that could be applied to remote sensing products were created from a field data set collected from September–October, 2005 in Hudson Bay, Canada. The field data showed that an effective pCO_2sw interpolation algorithm could be created using sea surface temperature (SST) as a predictor, and that a slight improvement of the algorithm could be achieved if measurements of absorption due to coloured dissolved organic material (a_CDOM) were included. Unfortunately, satellite retrievals of a_CDOM did not match well with in situ observations, and so only SST (obtained from the MODIS Aqua sensor) was used to create monthly maps of pCO_2sw for the period of August–October. To estimate fluxes of CO₂, constructed surfaces of pCO_2sw were combined with estimates of gas transfer velocity derived from QuikSCAT wind retrievals, and pCO_2air based on field observations. The results of these calculations revealed that Hudson Bay acts as a source of CO₂ during August and September, but reverts to a sink of CO₂ in October as the water temperature decreases. Overall, a positive flux of 1.60 TgC was estimated for the region during the ice-free season. This result is in contrast to most Arctic or sub-Arctic continental shelf seas, where usually strong absorptions of CO₂ are observed.