Predicting PVT data for CO2–brine mixtures for black-oil simulation of CO2 geological storage

doi:10.1016/S1750-5836(07)00010-2

International Journal of Greenhouse Gas Control

Volume 2, Issue 1, January 2008, Pages 65-77

https://doi.org/10.1016/S1750-5836(07)00010-2 Get rights and content

Abstract

Accurate modeling of the storage or sequestration of CO₂ injected into subsurface formations requires an accurate fluid model. This can be achieved using compositional reservoir simulations. However, sophisticated equations of state (EOS) approaches used in current compositional simulators are computationally expensive. It is advantageous and possible to use a simple, but accurate fluid model for the very specific case of geological CO₂ storage. Using a black-oil simulation approach, the computational burden of flow simulation can be reduced significantly. In this work, an efficient and simple algorithm is developed for converting compositional data from EOS into black-oil PVT data. Our algorithm is capable of predicting CO₂–brine density, solubility, and formation volume factor, which are all necessary for black-oil flow simulations of CO₂ storage in geological formations. Numerical simulations for a simple CO₂ storage case demonstrate that the black-oil simulation runs are at least four times faster than the compositional ones without loss of accuracy. The accuracy in prediction of CO₂–brine black-oil PVT properties and higher computational efficiency of the black-oil approach promote application of black-oil simulation for large-scale geological storage of CO₂ in saline aquifers.

Introduction

The sequestration of anthropogenic CO₂ into geological formations has been considered as a potential method to mitigate climate change. Accurate evaluation of the capacity of a saline aquifer for CO₂ sequestration, and the fate of the injected fluids in sedimentary basins needs precise representation of brine and CO₂ PVT data (Adams and Bachu, 2002, Bachu and Adams, 2003). Experimental data reported in the literature show that the density of an aqueous solution of CO₂ could be slightly greater than that of pure water (Blair and Quinn, 1968, Sayegh and Najman, 1987, Hnedovsky et al., 1996). This density variation might cause free convection motion, which in turn causes increased dissolution over a larger distance and shorter time scales compared to pure diffusive flow (Lindeberg and Wessel-Berg, 1996, Ennis-King and Paterson, 2003, Ennis-King and Paterson, 2005, Ennis-King et al., 2005, Hassanzadeh et al., 2005). Therefore, accurate description of the thermodynamic and transport properties of CO₂ and brine are very important for evaluating the capacity of saline aquifers to sequester CO₂ by a solubility trapping mechanism.

In the petroleum industry, compositional reservoir simulators use EOS thermodynamic models to calculate the phase equilibrium properties of fluid mixtures (Chang et al., 1998). Although these kinds of thermodynamic models are well suited for compositional modeling of enhanced oil recovery (EOR) processes, such as miscible gas injection, the disadvantage of such models for the specific case of large-scale flow simulation of geological CO₂ storage in aquifers is that they represent computational “overkill” and are inappropriately expensive. Therefore, it would be helpful if we were able to use a simple thermodynamic model that can predict the CO₂–brine equilibrium properties accurately with less computational overhead. Indeed, there are a large number of experimental equilibrium data on the CO₂–brine system that have been used to develop correlations and tune the equations of state for CO₂ and water under subsurface conditions. Such experimental and EOS data are used in this paper to develop a black-oil PVT module needed for flow simulation geological storage of CO₂ in saline aquifers. The novelty of this work is in presenting a PVT module for converting compositional data into black-oil that provides accurate PVT data required for black-oil flow simulation of CO₂ storage in saline aquifers. The black-oil PVT module developed in this work is validated with experimental data available in the literature. Furthermore, our numerical flow simulations of CO₂ storage reveal that the black-oil simulation approach is computationally more efficient than the compositional approach. The accuracy in prediction of CO₂–brine PVT properties and superior computational efficiency encourages application of black-oil simulation approach for large-scale geological storage of CO₂ in saline aquifers.

The thermodynamic model used in this work is based on a combination of the Duan and Sun (2003) and Spycher et al. (2003) models. Similar models have recently appeared in the literature (Spycher and Pruess, 2005, Portier and Rochelle, 2005, Duan et al., 2006). In this paper, in addition to presentation of our thermodynamic module, we use it to generate CO₂–brine PVT properties as required for black-oil flow simulation. For completeness, we also present the correlations of transport properties of the CO₂ and brine system required for black-oil reservoir simulation.

This paper is organized as follows. First a brief review of the literature on thermodynamic modeling of CO₂–brine equilibrium is presented. Then, the thermodynamic model used in this study is described and its results are compared with experimental data available in the literature. This is followed by the main contribution of the paper; representation of the CO₂–brine PVT properties suitable for black-oil simulation and a comparison of black-oil and compositional simulator computational performances for simulation of CO₂ injection into saline aquifers.

Section snippets

Review of CO₂–brine solubility data

The CO₂–water equilibrium phenomenon has been studied extensively in literature. The interested reader might consult more exhaustive reviews from Diamond and Akinfiev (2003), Duan and Sun (2003), and Spycher et al. (2003) among others. In this section, a brief review of some of the studies is presented. Wiebe and Gaddy (1939) and Wiebe (1941) reported experimental solubility of CO₂ in water at temperatures up to 100 °C and pressures up to 700 atm. Dodds et al. (1956) have used available

Thermodynamic model

From the definition of fugacity, we have: $f_{i} = φ_{i} y_{i} p$ where f denotes fugacity; φ fugacity coefficient; p total pressure; y is the mole fraction in the gaseous phase. At equilibrium, the following equilibrium relationship holds (Spycher et al., 2003): $κ_{H_{2} O} = \frac{f_{H_{2} O (g)}}{a_{H_{2} O (aq)}}$ $κ_{C O_{2}} = \frac{f_{C O_{2} (g)}}{a_{C O_{2} (aq)}}$ where κ parameters are true equilibrium constants and a is the activity of a component in the aqueous phase. The κ parameters are functions of pressure and temperature as given by the following expression (Spycher

Comparison with experimental data

Chang et al. (1998), Diamond and Akinfiev (2003), Duan and Sun (2003), Spycher et al. (2003), Spycher and Pruess (2005), Portier and Rochelle (2005), and Duan et al. (2006) reviewed and used CO₂–brine mixture data available in the literature to develop their solubility model. In this section, we compare the calculated CO₂–water properties with such experimental data from the literature. These experimental data are taken from King et al. (1992), Wiebe and Gaddy, 1939, Wiebe and Gaddy, 1940,

Representation of CO₂–brine equations of state predictions in a black-oil simulator

The choice of the fluid model is very important in any flow simulation including simulation of CO₂ storage in saline aquifers. Black-oil flow simulators have been used for modeling fluid flow in petroleum reservoirs, when the reservoir fluids can be lumped into three components, oil, gas and water (Aziz and Settari, 1979). In such simulators, these three components can be partitioned in three phases generically called oil, gas and water. In this system, the gas component is usually partitioned

Performance comparison of black-oil and compositional simulations

Compositional reservoir simulators are well known to be more time consuming than black-oil simulators. This is due to the fact that compositional simulators perform frequent phase equilibrium and flash calculations at each time step. Furthermore, the formulation in compositional simulators is more complicated. Very often, this results in a larger number of time-steps used by the compositional simulator. Compositional simulators may have stability limitations resulting from the time

Discussion

This paper proposes the use of black-oil models for simulation studies of CO₂ storage in deep aquifers, and presents a simple and efficient algorithm for computing the necessary PVT data. For this purpose, the gaseous phase in the black-oil formulation was used to represent the super-critical CO₂ phase. This is appropriate for most scenarios of geological storage of CO₂, where the aquifer depth is more than 800–1000 m and the pressure and temperature conditions are above the CO₂ critical point.

Summary and conclusions

Flow modeling of CO₂ sequestration in saline aquifers has been treated in the literature since the early 1990s. Accurate evaluation of capacity of a saline aquifer to sequester CO₂ by solubility trapping needs precise representation of PVT data for the CO₂–brine system. Compositional reservoir simulators that account for complex phase behavior and very compositionally dependent systems are computationally expensive compared to traditional black-oil simulators. Although such compositional models

Acknowledgements

The authors would like to thank Nicolas Spycher for his review and constructive comments. Useful comments from the journal associate editor Stefan Bachu and two anonymous reviewers that improved the original version of the paper are acknowledged. The financial support for this work was provided by the National Science and Engineering Research Council of Canada (NSERC) and the Alberta Department of Energy. This support is gratefully acknowledged. The first author also thanks the National Iranian

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Predicting PVT data for CO2–brine mixtures for black-oil simulation of CO2 geological storage

Abstract

Introduction

Section snippets

Review of CO2–brine solubility data

Thermodynamic model

Comparison with experimental data

Representation of CO2–brine equations of state predictions in a black-oil simulator

Performance comparison of black-oil and compositional simulations

Discussion

Summary and conclusions

Acknowledgements

Energy Conv. Manage.

Geothermics

Fluid Phase Equilib.

Fluid Phase Equilib.

Fluid Phase Equilib.

Chem. Geol.

Mar. Chem.

J. Supercrit. Fluids

Chem. Geol.

Geochim. Cosmochim. Acta

Geochim. Cosmochim. Acta

J. Chem. Thermodyn.

Equations of state for basin geofluids: algorithm review and intercomparison for brines

Geofluids

Petroleum Reservoir Engineering—Physical Properties

Petroleum Reservoir Simulation

High-pressure (vapour + liquid) equilibrium in binary mixtures of (carbon dioxide + water or acetic acid) at temperatures from 313 to 353 K

J. Supercrit. Fluids

Seismic properties of pore fluids

Geophysics

Measurement of small density differences: solubility of slightly soluble gases

Rev. Sci. Instrum.

A compositional model for CO2 floods including CO2 solubility in water

SPE Reser. Evaluat. Eng.

Applied Petroleum Reservoir Engineering

Carbon dioxide solubility in water

Ind. Eng. Chem., Chem. Eng. Data Ser.

High pressure phase equilibria in the carbon dioxide–n-hexadecane and carbon dioxide water systems

Can. J. Chem. Eng.

CO2 solubility in water and brine under reservoir conditions

Chem. Eng. Commun.

Effects of CO2 solubility in brine on the compositional simulation of CO2 floods

SPE Reser. Eng. J.

Role of convective mixing in the long-term storage of carbon dioxide in deep saline formations

SPE J.

Onset of convection in anisotropic porous media subject to a rapid change in boundary conditions

Phys. Fluids

The viscosity of carbon dioxide

J. Phys. Chem. Ref. Data

Predicting PVT data for CO₂–brine mixtures for black-oil simulation of CO₂ geological storage

Review of CO₂–brine solubility data

Representation of CO₂–brine equations of state predictions in a black-oil simulator

A compositional model for CO₂ floods including CO₂ solubility in water

CO₂ solubility in water and brine under reservoir conditions

Effects of CO₂ solubility in brine on the compositional simulation of CO₂ floods