Solution of the Span–Wagner Equation of State Using a Density–Energy State Function for Fluid-Dynamic Simulation of Carbon Dioxide

Abstract

With the introduction of carbon capture and storage (CCS) as a means to reduce carbon emissions, a need has arisen for accurate and efficient simulation tools. In this work, we propose a method for dynamic simulations of carbon dioxide using the Span-Wagner reference equation of state. The simulations are based on using the density and internal energy as states, which is a formulation naturally resulting from mass and energy balances. The proposed numerical method uses information about saturation lines to choose between single-phase and two-phase equation systems, and is capable of handling phase transitions. To illustrate the potential of the method, it is applied to simulations of tank depressurization, and to fluid-dynamic simulations of pipe transport.

Rapid depressurization of a CO2 pipeline – an experimental study

“…The thermodynamic behavior of CO 2 during a rapid depressurization of a pipeline has been experimentally studied (de Koeijer et al, 2009(de Koeijer et al, , 2011Brown et al, 2014;Håvelsrud, 2012;Huh et al, 2014) and simulated using CFD tools (de Koeijer et al, 2009(de Koeijer et al, , 2011Brown et al, 2014;Håvelsrud, 2012;Huh et al, 2014;Witlox et al, 2009;Witlox et al, 2011;Dixon et al, 2012;Calay and Holdo, 2008;Wen et al, 2011;Jie et al, 2012;Munkejord et al, 2010;Lund et al, 2011;Clausen and Munkejord, 2012;Giljarhus et al, 2012;Lund and Aursand, 2012;Munkejord et al, 2013). In order to develop accurate models for predicting the expansion behavior of CO 2 during a rapid depressurization of a CO 2 pipeline, more experimental data is required (Lund and Aursand, 2012).…”

CO2 Pipeline Integrity: Comparison of a Coupled Fluid-structure Model and Uncoupled Two-curve Methods

“…For each set of local (ρ, E) obtained from the flow equations (9), a density-energy flash routine [20] using the Span-Wagner EOS is used to find the corresponding local equilibrium state. All three possible phases are covered, as the Span-Wagner EOS of state was extended to the solid state (dry ice) using an empirical polynomial for ρ s (T ) [21].…”

Study on carbon dioxide thermodynamic behavior for the purpose of shale rock fracturing

“…The equation is an empirical representation of the fundamental equation of Helmholtz energy. Usually the dimensionless function of Helmholtz energy φ = a/(RT ) dividend of an ideal gas part φ 0 and residual part φ r [7] is used:…”

“…10-11) were determined, which represent thermal properties of liquid carbon dioxide that was transformed isochorically (volume = constants) from the temperature of 253 K to 373 K. They were calculated in REFPROP computer code. In this case the program uses a thermal conductivity of the Vesovic pure liquid model and the Span-Wagner equation of state [7]. The calculation results were implemented in LSDyna for modeling CO 2 thermal behavior.…”