Liquid Load Charge Material Heat Required Calculator

Detailed Description

The following formulas describe the calculation of total heat required for a liquid load/charge material, including sensible heat, latent heat, vaporization, reaction heat, and additional heat. Each step is documented with its own formula and symbol table.

The calculation follows a top-down approach:

1. Total Heat Required - Sum of liquid heating/vaporization, reaction heat, and additional heat
2. Liquid Heating - Heat required to raise temperature of liquid (varies based on vaporization)
   • Below vaporizing temp: Sensible heat only
   • Above vaporizing temp: Sensible heat to vaporizing + latent heat + sensible heat of vapor and remaining liquid
3. Heat of Reaction - Endothermic reaction heat if applicable

Total Heat Required

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\begin{equation}\label{eq:liquid-load-charge-material-total-heat-required-cpp} Q_{total} = Q_{liq} + Q_{reaction} + Q_{additional}\end{equation}

Symbols

\(Q_{total}\)	Total heat required \([\unit{ \btu\per\hour}]\)
\(Q_{liq}\)	Heat required for liquid heating/vaporization \([\unit{ \btu\per\hour}]\)
\(Q_{reaction}\)	Heat of reaction \([\unit{ \btu\per\hour}]\)
\(Q_{additional}\)	Additional heat required \([\unit{ \btu\per\hour}]\)

Sensible Heat (Below Vaporizing Temp)

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The total heat required when discharge temperature is below vaporizing temperature.

\begin{equation}\label{eq:liquid-load-charge-material-sensible-heat-cpp} Q_{liq} = m_{feed} \cdot C_{p,liq} \cdot (T_{discharge} - T_{initial})\end{equation}

Symbols

\(Q_{liq}\)	Heat required for liquid heating \([\unit{ \btu\per\hour}]\)
\(m_{feed}\)	Charge (liquid) feed rate \([\unit{ \pound\per\hour}]\)
\(C_{p,liq}\)	Specific heat of liquid \([\unit{ \btu\per\pound\degreeFahrenheit}]\)
\(T_{discharge}\)	Discharge temperature \([\unit{ \degreeFahrenheit}]\)
\(T_{initial}\)	Initial temperature \([\unit{ \degreeFahrenheit}]\)

Full Heating (Above Vaporizing Temp)

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The total heat required when discharge temperature is above vaporizing temperature.

\begin{equation}\label{eq:liquid-load-charge-material-full-heat-cpp} Q_{liq} = Q_{sens,liq} + Q_{vap} + Q_{sens,vapor} + Q_{sens,remliq}\end{equation}

\begin{equation}\label{eq:liquid-load-charge-material-sensible-heat-to-vaporizing-cpp} Q_{sens,liq} = m_{feed} \cdot C_{p,liq} \cdot (T_{vaporizing} - T_{initial})\end{equation}

\begin{equation}\label{eq:liquid-load-charge-material-vaporization-heat-cpp} Q_{vap} = m_{feed} \cdot f_{vaporized} \cdot H_{latent}\end{equation}

\begin{equation}\label{eq:liquid-load-charge-material-sensible-heat-vapor-cpp} Q_{sens,vapor} = m_{feed} \cdot f_{vaporized} \cdot C_{p,vapor} \cdot (T_{discharge} - T_{vaporizing})\end{equation}

\begin{equation}\label{eq:liquid-load-charge-material-sensible-heat-remaining-liq-cpp} Q_{sens,remliq} = m_{feed} \cdot (1-f_{vaporized}) \cdot C_{p,liq} \cdot (T_{discharge} - T_{vaporizing})\end{equation}

Symbols

\(Q_{liq}\)	Heat required for liquid heating/vaporization \([\unit{ \btu\per\hour}]\)
\(Q_{sens,liq}\)	Sensible heat to vaporizing temperature \([\unit{ \btu\per\hour}]\)
\(Q_{vap}\)	Vaporization heat \([\unit{ \btu\per\hour}]\)
\(Q_{sens,vapor}\)	Sensible heat for vaporized fraction \([\unit{ \btu\per\hour}]\)
\(Q_{sens,remliq}\)	Sensible heat for remaining liquid \([\unit{ \btu\per\hour}]\)
\(m_{feed}\)	Charge (liquid) feed rate \([\unit{ \pound\per\hour}]\)
\(C_{p,liq}\)	Specific heat of liquid \([\unit{ \btu\per\pound\degreeFahrenheit}]\)
\(T_{vaporizing}\)	Vaporizing temperature \([\unit{ \degreeFahrenheit}]\)
\(T_{initial}\)	Initial temperature \([\unit{ \degreeFahrenheit}]\)
\(f_{vaporized}\)	Fraction of charge vaporized \([\unit{ \unitless}]\)
\(H_{latent}\)	Latent heat of vaporization \([\unit{ \btu\per\pound}]\)
\(C_{p,vapor}\)	Specific heat of vapor \([\unit{ \btu\per\pound\degreeFahrenheit}]\)
\(T_{discharge}\)	Discharge temperature \([\unit{ \degreeFahrenheit}]\)

Heat of Reaction

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\begin{equation}\label{eq:liquid-load-charge-material-heat-of-reaction-cpp} Q_{reaction} = \begin{cases} m_{feed} \cdot f_{reacted} \cdot H_{reaction} & \text{if endothermic} \\ 0 & \text{if exothermic or none} \end{cases}\end{equation}

Symbols

\(Q_{reaction}\)	Heat of reaction \([\unit{ \btu\per\hour}]\)
\(m_{feed}\)	Charge (liquid) feed rate \([\unit{ \pound\per\hour}]\)
\(f_{reacted}\)	Fraction of charge reacted \([\unit{ \unitless}]\)
\(H_{reaction}\)	Heat of reaction \([\unit{ \btu\per\pound}]\)

See also

Liquid Load Charge Material Database

Modules
	Total Heat Required Formula
	Sensible Heat (Below Vaporizing Temp) Formula
	Full Heating (Above Vaporizing Temp) Formula
	Heat of Reaction Formula

Files
file	liquid_load_charge_material_heat_required.h

Namespaces
namespace	liquid_load_charge_material_heat_required
	Namespace for liquid load/charge material heat required calculation.

Functions
double	liquid_load_charge_material_heat_required::totalHeatRequired (LoadChargeMaterial::ThermicReactionType thermic_reaction_type, double specific_heat_liquid, double vaporizing_temperature, double latent_heat, double specific_heat_vapor, double charge_feed_rate, double initial_temperature, double discharge_temperature, double percent_vaporized, double percent_reacted, double reaction_heat, double additional_heat)
	Calculates the total heat required for a liquid load/charge material.

Function Documentation

totalHeatRequired()

double liquid_load_charge_material_heat_required::totalHeatRequired	(	LoadChargeMaterial::ThermicReactionType	thermic_reaction_type,
		double	specific_heat_liquid,
		double	vaporizing_temperature,
		double	latent_heat,
		double	specific_heat_vapor,
		double	charge_feed_rate,
		double	initial_temperature,
		double	discharge_temperature,
		double	percent_vaporized,
		double	percent_reacted,
		double	reaction_heat,
		double	additional_heat
	)

Parameters

[in]	thermic_reaction_type	Thermic reaction type (endothermic, exothermic, or none)
[in]	specific_heat_liquid	Specific heat of liquid \([\unit{\btu\per\pound\degreeFahrenheit}]\)
[in]	vaporizing_temperature	Vaporizing temperature \([\unit{\degreeFahrenheit}]\)
[in]	latent_heat	Latent heat of vaporization \([\unit{\btu\per\pound}]\)
[in]	specific_heat_vapor	Specific heat of vapor \([\unit{\btu\per\pound\degreeFahrenheit}]\)
[in]	charge_feed_rate	Charge (liquid) feed rate \([\unit{\pound\per\hour}]\)
[in]	initial_temperature	Initial temperature \([\unit{\degreeFahrenheit}]\)
[in]	discharge_temperature	Discharge temperature \([\unit{\degreeFahrenheit}]\)
[in]	percent_vaporized	Percent of charge vaporized (as percent, e.g., 10 for 10%)
[in]	percent_reacted	Percent of charge reacted (as percent, e.g., 5 for 5%)
[in]	reaction_heat	Heat of reaction \([\unit{\btu\per\pound}]\)
[in]	additional_heat	Additional heat required \([\unit{\btu\per\hour}]\)

Returns

Total heat required \([\unit{\btu\per\hour}]\).