Numerical study of the effect of heat transfer on solid phase formation during decompression of CO2 in pipelines

CO2 solid phase formation accompanying rapid decompression of high-pressure CO2 pipelines may lead to blockage of the flow and safety valves, presenting significant hazard for safe operation of the high-pressure CO2 storage and transportation facilities. In this study, a homogeneous equilibrium flow model, accounting for conjugate heat transfer between the flow and the pipe wall, is applied to study the CO2 solid formation in a 50 mm internal diameter and 37 m long pipe for various initial thermodynamic states of CO2 fluid and wide range of discharge orifice diameters. The results show that the rate of CO2 solid formation in the pipe is limited by heat transfer at the pipe wall. The predicted amounts of solid CO2 are discussed in the context of venting of CO2 pipelines.


Introduction
Despite the fact that carbon dioxide (CO2) at low concentrations is commonly considered as a safe substance, accidental failure of facilities transporting large quantities of CO2 at high pressures for carbon capture and storage or utilization [1,2] may cause significant harm to personnel and local populations as a result of explosion overpressure and the asphyxiate nature of the CO2 in the ensuing dispersion cloud [3,4].
Blockage of safety valves by solid CO2 which may form as a result of near-isentropic decompression of highpressure CO2 to the level below 5.18 bar (triple point of CO2) is considered as one of major causes of failure of CO2 storage and transport facilities [5,6]. Also, accumulation of solid CO2 in pipelines and vessels may increase the risk of blockage and overfilling of units at later stages of operation [7][8][9][10][11]. In particular, our recent studies showed that solid CO2 may form during decompression of pipelines initially filled with CO2 at 60-80 bar pressures [12,13]. Given that solid CO2 accumulation in safety valves and vented sections of pipelines presents a risk for the system integrity, designing venting equipment and procedures that minimize the amounts of solid phase formed becomes critically important. This requires development and application of mathematical models of pipeline decompression accounting for multiphase nature of the decompression flow and thermodynamic properties of CO2 fluid in various states, including the triple point.
Recent studies showed that Homogeneous Equilibrium Mixture (HEM) model predicts well the pressure and temperature measured in the pipeline Full Bore Rupture test [13] and amounts of solid CO2 formed in the pipeline in the orifice discharge tests [12]. Using this model it was demonstrated that duration of the pipeline decompression to the triple point where CO2 solids can form in the pipe, scales with the pipeline length [14], while the amount of solid CO2 formed depends on the history of decompression flow [12]. The latter depends on a number of factors, including the initial thermodynamic state of the fluid, the discharge hole diameter, and the rate of heat transfer at the pipe wall. Despite the fact that understanding the above effects is crucial for preventing/minimizing the CO2 solids formation in process equipment, they have not been systematically studied. The present study is focused on the application of the HEM flow model to quantify the amount of CO2 solid phase that may form under various scenarios of pipeline decompression..
In the present study, in order to predict the history of decompression of a CO2 pipeline ( Figure 1) accounting for spatial variations in the flow along the pipe, a set of quasione-dimensional HEM-based mass, momentum and energy conservation equations, is applied [15]: where p is the pressure, u is the velocity, D and are respectively the pipe diameter and crosssectional area of the flow; f is the Fanning friction factor, calculated using Chen's correlation [16], and q is the heat flux at the pipe wall.
In the above equations, the HEM density and specific internal energy are calculated knowing the fluid phase composition and properties of saturated vapor, liquid and solid phases as functions of pressure. The thermodynamic properties of CO2 in liquid and vapor states are calculated using the GERG 2004 equation of state (EoS) [17], while properties of solid CO2 are predicted using the extended Peng-Robinson EoS [18].
The heat flux, q , is defined by Newton's cooling law for single-phase and solid-vapor turbulent flows (with the Dittus-Boelter correlation [19] adopted to predict the heat transfer coefficient), and using Rohsenow's correlation for nucleate boiling [20] for vapor-liquid flows.
The set of equations (1) -(3) is closed by the boundary conditions specified at both ends of the pipeline (Figure 1), and using a lumped heat capacity model predicting evolution of the pipe wall temperature [14].
For the numerical solution of the governing equations of the model, Godunov's finite volume method combined with a fractional stepping time-integration scheme is applied [21].
At any time level, the total amount of CO2 solid phase formed in the pipe is obtained by numerically integrating the resolved solid phase density profiles along the pipeline. The time integration procedure is terminated when the pressure at the discharge end of the pipe reaches 1 bar.

Results and discussion
This section is aimed at evaluation of the impact of key parameters of decompression process on the solid CO2 formation in pipelines. For this purpose, the above described model is applied to predict the amount of solid CO2 formed in a pipe for various initial states of CO2 fluid and various discharge orifice diameters. For the sake of example, the study is performed for a medium-scale mild steel pipeline of 50 mm internal diameter, 5 mm wall thickness and 37 m length (http://www.co2quest.eu/). In order to demonstrate the impact of initial conditions on the amount of solid CO2 that could form in the pipe, the study was performed for two cases involving depressurization of the pipeline, initially at 54.4 bar pressure and 18 o C, via 6 mm orifice. In the first case the pipeline was initially filled with saturated liquid, while in the second case the pipe contained compressed saturated gas.

The effect of initial conditions
In Figure 2 evolution of the fluid pressure and temperature predicted by the model at location in the middle of the pipe, are plotted in the phase diagram of CO2. As can be seen in Figure 2, the liquid phase decompression path (trajectory 3-4) crosses the triple point, and hence corresponds to a scenario where CO2 solids can be expected to form in the pipe. At ca. 2 bar, the model predicts complete sublimation of the solid phase, and the trajectory deviates from the sublimation line into the vapor phase region. On the other hand, the decompression from the compressed gas state (trajectory 1-2) follows the saturation line only till ca. 12 bar pressure, where the fluid turns to vapor, as can be explained by heating from the pipe wall. As such, the model indicates that decompression of a compressed CO2 gas state doesn't lead to CO2 solids forming in the pipe. Figure 3 shows the effect of d/D ratio on the mass of solid CO2 formed in the pipe upon its decompression to the triple point, obtained based on the HEM flow model predictions, in comparison with estimates using the thermodynamic method assuming isentropic decompression [12]. As can be seen in Figure 3, predictions by the thermodynamic method are insensitive to the orifice diameter. Also, the thermodynamic method systematically (by ca. 15-50 %) overestimates the mass of solid phase in comparison with the predictions by the decompression flow model. This discrepancy can be directly attributed to nonisentropic nature of the fluid expansion process, involving conjugate heat transfer between the fluid and the pipe wall. Figure 3 also shows that the mass of solid CO2 predicted by the outflow model scales nearly linearly with D d / in the range from 0.1 to 0.4. This indicates that using small ratios D d /

The effect of release orifice diameter
can be more advantageous for use in design of decompression systems where the solid CO2 pose hazard for the system operation and integrity.

Conclusions
The results obtained using the HEM pipeline outflow model showed that decompression of CO2 from initial vapor state is characterized by significant heating of the flow by the pipe wall. This heating may result in complete evaporation of liquid phase before the fluid decompression to the triple point, leading to no CO2 solids formed in the pipe. This contrasts to scenarios of decompression of pipes containing CO2 in a form of compressed liquid, which evaporates only partially upon decompression to the triple point, potentially leading to large amount of solid CO2 forming in the pipe, creating a hazard for the system operation and integrity. The amounts of solid CO2 calculated based on the simulations using the HEM flow model were compared with predictions using the thermodynamic model. While the latter gives conservative estimate of the amount of solid CO2, the HEM decompression flow model resolves the effect of the orifice diameter and hence can become useful, e.g. for design of CO2 venting systems.