Method Using a Density–Energy State Function with a Reference Equation of State for Fluid-Dynamics Simulation of Vapor–Liquid–Solid Carbon Dioxide

Abstract

With the advent of CO 2 capture and storage (CCS) as an important remedy for reducing atmospheric CO 2 emissions, it has become necessary to develop accurate and efficient simulation tools. Among other things, such tools should handle the depressurization from supercritical pressures down to atmospheric conditions. This might involve the formation of solid CO 2 (dry ice) as the state passes the triple point. In this work, we propose a dynamic simulation method that handles the dry-ice formation. The method uses the Span-Wagner reference equation of state, with additional relations for thermodynamic properties along the sublimation line. A density-energy state function formulation is employed, which naturally follows from mass and energy conservation. To illustrate the method's capabilities, demanding test cases are considered, both for the depressurization of a vessel and for fluid dynamics in a pipeline, where phase change occurs due to changing boundary conditions.

A method for simulating two-phase pipe flow with real equations of state

“…Thermodynamically, the equilibrium condition of this isochoric-isoenergetic (ρe) problem represents a global maximum in the entropy of the system [26]. The numerical algorithm used to solve the ρe problem are based on the method of Giljarhus et al [27], and discussed in more detail in Hammer et al [28].…”

Computation of three-dimensional three-phase flow of carbon dioxide using a high-order WENO scheme

“…To avoid spurious oscillations, however, it will often be necessary to reconstruct in another set of variables than the state variables Q [30,Sec. 14.4.3] Hammer et al [6] performed reconstruction in flow velocity, density and internal energy when performing 1D simulations with second-order MUSCL reconstruction and the Span-Wagner reference EOS for CO 2 . For simulations with high-order WENO reconstruction and the ideal gas or stiffened-gas EOS, Titarev and Toro [11] and Coralic and Colonius [13] performed reconstruction in the local characteristic variables.…”

“…Depressurization of CO 2 from supercritical pressures typically involves complex three-phase (gas-liquid-solid) flow. Describing this kind of flow necessitates a multiphase flow model and an equation of state (EOS) that is accurate and capable of capturing the three-phase behaviour [6,7]. For high vessel pressures, the CO 2 jet resulting from a leak will form a shock, which the numerical method must be able to capture.…”

Simulation of two-phase flow through ducts with discontinuous cross-section

“…Where the fluid is a two-phase mixture equations (4), and (5), utilising equations (8) and (7), are solved by iterating the mixture pressure, P giving the saturated temperature T , calculated from equation (7) (see example Hammer et al, 2013, for a full description).…”