## Fluid response to heat transfer with a phase change

When heat is transferred to a liquid that can vaporize, the phase change is usually the most significant contributor to the overall change in density, and any individual phase expansions are typically ignored. One key parameter in the evaluation of the phase change is the latent heat of vaporization – for multi-component liquids, this is not as straight-forward as for pure liquids, and various methods can be employed to estimate this parameter. The fluid response to heat transfer discussed below is one of three elements in the evaluation of relief requirements for overpressure scenarios based on heating or cooling of a constant volume container:^{1}

- the characterization of the heat transfer to the container
- the fluid behavior in response to that heat transfer
- the hydrodynamics within the container

**Fluid response with a phase change**. As noted in the CCPS Guidelines 2nd Edition, “For systems containing a fluid that undergoes a phase change (that is, boiling systems), the phase change is the significant contribution to the density change and the expansion of the individual phases is usually ignored.” The Guidelines then proceeds to provide a differential energy balance and discusses how to determine the input:

The density of the phases and the specific enthalpy required to create the phase change (that is, the latent heat for single component fluids) are usually required for the calculations involved in characterizing the relieving requirements for boiling systems. The specific enthalpy required to create the phase change for a multi-component mixture can be complex, and five different approaches were proposed for the update to the Guidelines. In the end, the 1st edition’s *Single-component venting* and *Dynamic simulation* were retained, while the more common approach of generating an effective heat of vaporization was not included.

The five different approaches to determining relieving requirements for these boiling systems that we have encountered over the years are presented, in the order of the typical degree of detail in the computations and the results.

*Single-component venting*: Determine the single-component venting requirement for each component alone (as if that component comprised the entire charge). Use the highest single-component venting requirement as the design requirement of the mixture.*Bubblepoint latent heat*: Develop the vapor-liquid equilibrium relationship (VLE) and calculate the initial equilibrium phase compositions. Note that this step is quite simple for ideal solutions; however, most mixtures are not ideal solutions. Use applicable mixing rules to obtain mixture properties for use in the single-component equations of the previous section.*Effective heat of vaporization*: Estimate an effective heat of vaporization by specifying the fraction to be vaporized, effectively bypassing the time dependent nature of the event by assuming the maximum venting rate occurs while vaporizing the fraction specified.*Multicomponent batch vaporization*: Obtain the vaporization rate over the course of the venting incident from a multicomponent batch vaporization routine using the given heat input rate. Use the observed maximum rate for design.*Dynamic simulation*: Simulate the incident using a multicomponent pressure relief computer routine such as SuperChemsTM for DIERS or other acceptable dynamic process simulation software. Vary the vent area to match the computed maximum venting pressure to the design maximum accumulation. Use the maximum venting rate as the design value.

**Effective heat of vaporization**. We usually promote the effective heat of vaporization as an efficient means of calculating required relief rates in response to heat input for multi-component mixtures, a balance between dealing with the effects of multiple components without being too computationally intensive. Please refer to our Fireside Chat Multi-component effective heat of vaporization for details on calculating this parameter.

**Multi-component batch vaporization**. The batch vaporization approach has the added capability of detecting a maximum in the venting requirement, but requires a time-dependent batch vaporization simulation, usually performed using process simulation software. One potential algorithm for performing this time-dependent batch vaporization was proposed:

- Initialize the calculation by establishing the mass, compositions, densities and specific enthalpies of liquid and gas phases in the constant-volume container for an initial pressure and temperature. The initial bubblepoint temperature at the relieving pressure is a convenient starting point, and the vapor composition at this point can be used as an initial gas phase composition in the event the container does not have gas phase initially.
- For each step of calculation, establish a fraction of the liquid flashed. Calculate the vaporization of that fraction of liquid flashed at constant pressure subject to the following constraints: constant mass and constant overall composition. Establish the new temperature associated with that vapor/liquid distribution, and then establish the densities and specific enthalpies of liquid and gas phases in the constant-volume container.
- Calculate the heat input rate, potentially accounting for the changes in the heat input rate (for example, the change in wetted surface area that occurs as a result of the vaporization of that liquid). Using this heat input rate, calculate the time of vaporization from a heat balance equation, with time being the energy required to change the enthalpy of the fluids divided by the heat input rate. Note that the change in enthalpy of either the liquid or the gas phases over the step are non-zero both due to temperature rise across the step and due to liquid and gas phase composition change.
- Using volume balance, calculate average mass flow rate to be relieved during the step. The required cross-sectional area of the pressure relief device can be determined using sizing techniques.
- This process is repeated until a significant portion of the liquid is vaporized (for example, 90% of the liquid phase), and the relief requirement is based on that step that resulted in the maximum required cross-sectional area.

We will note the similarities in this approach outlined above with the methodology of Ouderkirk^{2}, only with the additional accounting for the boiling of the liquid.

**Blog series information**. This blog is part of a series on the proposed updates to the CCPS Guidelines 2nd edition §3.3Venting Requirements for Nonreacting Cases that were removed during final editing. See the general CCPS Guidelines for Pressure Relief and Effluent Handling 2nd Edition review for more information.

[1] AIChE Center for Chemical Process Safety. “CCPS Guidelines for Pressure Relief and Effluent Handling Systems”. 2nd Edition, 2017; New Jersey: John Wiley & Sons, Inc.

[2] Ouderkirk R. “Rigorously Size Relief Valves for Supercritical Fluids”.

*Chemical Engineering Progress*. 2002 August; 98(8): 34-43.

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