# Heat Exchanger (HX)

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This sub model is part of the Tank Model.

## General Description

The Tank model allows the user to insert a heat exchanger into the unit. If the user checks the heat exchanger tick box, the model then requires connections to the HX streams. Normally the specific purpose Shell and Tube Heat Exchanger model would be used. The heat exchanger sub-model used in a tank simulates a shell and tube unit, with the contents of the unit as the shell side, while the heat exchanger acts as the tube side.

A full description of the heat exchanger theory is given in the model description.

NOTE: The heat exchanger will only transfer sensible heat to the contents of the tank, i.e. the fluid in the heat exchanger will NOT boil or condense.

## Model Theory

The following equation describes the energy transfer to each of the two individual streams:

$\mathbf{\mathit{Q=m(H_{in}-H_{out})}}$
where
Q - Energy Transfer - this is calculated either using the Log Mean Temperature Difference or the Effectiveness method, which are described below.
m - Mass flow of the stream
Hin - Enthalpy of entering stream
Hout - Enthalpy of leaving stream - this is the value that is then used to determine the temperature of the outgoing streams.

Using the stream enthalpies in the energy transfer calculations ensures that the variation of specific heat with temperature is taken into consideration.

### Log Mean Temperature Difference Method

This method uses the following equation to calculate the energy transfer between the tank contents and the heat exchange fluid:

$\mathbf{\mathit{Q=UA\boldsymbol{\Delta}T_{LM}}}$
where
Q - Energy Transfer
U - Overall coefficient of Heat Transfer
A - Area available for Energy Transfer
$\mathbf{\mathit{\boldsymbol{\Delta}T_{LM} = \frac{\Delta T_2 -\Delta T_1}{ln(\frac{\Delta T_2}{\Delta T_1})}}}$ - Log Mean Temperature Difference (LMTD)
For Counter Current Flow $\Delta T_2 = T_{H_{in}} - T_{C_{out}}$ and $\Delta T_1 = T_{H_{out}} - T_{C_{in}}$

For Co-Current, or Parallel, Flow $\Delta T_2 = T_{H_{out}} - T_{C_{out}}$ and $\Delta T_1 = T_{H_{in}} - T_{C_{in}}$

Notes:

1. The user may input a LMTD correction factor to correct for the different Heat Exchanger flow geometries. These correction factors are available in most references on Heat Transfer theory, and should be available from specific heat exchanger suppliers. Alternatively, the user may use the Effectiveness method to determine the heat transfer.

The unit uses an iterative technique to determine the LTMD of the unit. This is then used to calculate the energy transfer between the two streams.

Reference

Perry, R.H., Perry's Chemical Engineers' Handbook, McGraw Hill Inc, 6th Edition, 1984.

### Effectiveness Method

In this method Heat Exchanger Effectiveness, ε, is defined by the following equation:

$\epsilon = \frac{Q_{actual}}{Q_{maximum}}$

Where:

Qactual is the Actual amount of energy transferred between the streams; and
Qmaximum is the Maximum possible energy transferred if the fluid with Cmin = Mass * Cp experienced a temperature change equal to the difference between the temperature of the entering hot and cold fluids:
$Q_{maximum} = C_{min} * (T_{H_{in}} - T_{C_{in}})$

Therefore, to obtain the Actual energy transferred in the heat exchange, the value for ε must be found. This varies depending on the heat exchanger layout and can be determined from two dimensionless ratios:

Number of Transfer Units (NTU)

The Number of Transfer Units is indicative of the size of the heat exchanger and is defined as:

$NTU = \frac{UA}{C_{min}}$
U - Overall Heat Transfer coefficient;
A - Heat Transfer Area; and
Cmin = Mass * Cp for the fluid with the lowest value for this value.

Note: The maximum value of NTU allowed within SysCAD is 5.5, as this corresponds to the limit of the correlations.

Energy Capacity Ratio

Both fluids involved in the energy transfer have a value for Energy Capacity, C = Mass * Cp. We define Cmin and Cmax as the values with the minimum and maximum Energy Capacity values. Please note that Cmin is not necessarily the fluid the smallest value of Cp.

Then $C = \frac{C_{min}}{C_{max}}$

Using these 2 ratios a number of Heat Exchanger Effectiveness relations have been derived for heat exchangers with various flow geometries. These are described in the table below:

Flow Geometry Heat Exchanger Effectiveness Relation
Parallel Flow $\epsilon = \frac{1-e^{-NTU(1+C)}}{1+C}$
Counter Flow $\epsilon = \frac{1-e^{-NTU(1-C)}}{1-C*e^{-NTU(1-C)}}$
Cross Flow - Mixed $\epsilon = [A + B - \frac{1}{NTU}]^{-1}$ where $A = \frac{1}{1 - e^{-NTU}}$ and $B = \frac{C}{1 - e^{-NTU * C}}$
Cross Flow - Unmixed $\epsilon = 1 - e^{\frac{e^{-NTU*C*n} - 1}{C*n}}$ and $n = NTU^{-0.22}$
Shell and Tube
One shell pass, 2,4,6, etc tube passes.
$\epsilon = 2 * \frac{1 - B}{(1 + C)(1 - B) + A(1 + B)}$

where $A = \sqrt{1 + C^2}$

and $B = e^{-NTU * A}$

Reference

Holman,J.P., Heat Transfer, McGraw Hill Inc, SI Metric Edition, 1989.

### Assumptions

1. The overall heat transfer coefficient remains constant throughout the unit.
2. The system is adiabatic - heat exchange only takes place between the 2 fluids.
3. The temperatures of both fluids are constant over a given cross section and can be represented by bulk temperatures.

## Data Sections

The default access window consists of several sections,

1. HX tab - This tab contains general information relating to the sub model.
2. Calc tab - Optional second tab which allows the user to perform some flow calculations.

### HX Page

Symbol / Tag Input / Calc Description

### Requirements

On Tick Box This enables the Heat Exchanger sub-model in the tank. If this is disabled, then no heat exchange will occur.
Mode Log_Mean_Temp_Diff The duty is calculated using the Log Mean Temperature Difference, LMTD. If this method is used, then the user does not have to select a Flow Geometry for the unit. However, if a Flow Geometry is selected, then SysCAD will calculate the Effectiveness of the unit.
Effectiveness_NTU The duty is calculated using Effectiveness based on the heat exchanger configuration. If the user chooses this Mode of operation, then they must set the actual Heat Exchange configuration in the field Flow Geometry.
Simple-FixedDuty The duty is a user input value, this heat flow value can be defined for the Tank OR HX Element side. SysCAD will balance the heat values by applying the equal but opposite heat flow to the "unspecified" side. Negative value for heat loss and Positive value for heat addition. Available in SysCAD 9.2 Build 135.14140 or newer.
Simple-ProductTemp The product temperature is a user input value, this can be the Tank Mixture Temperature leaving the Tank OR HX Element outlet stream stream temperature. SysCAD will balance the heat values by applying the equal but opposite heat flow (needed to achieve the required temperature) to the "unspecified" side. Available in SysCAD 9.2 Build 135.14140 or newer.
Simple-TempRise The product Temperature Rise is a user input value, this can be the Tank Mixture Temperature leaving the Tank OR HX Element outlet stream stream temperature. SysCAD will balance the heat values by applying the equal but opposite heat flow (needed to achieve the required temperature rise) to the "unspecified" side. Available in SysCAD 9.2 Build 135.14140 or newer.
Simple-TempDrop The product Temperature Drop is a user input value, this can be the Tank Mixture Temperature leaving the Tank OR HX Element outlet stream stream temperature. SysCAD will balance the heat values by applying the equal but opposite heat flow (needed to achieve the required temperature drop) to the "unspecified" side. Available in SysCAD 9.2 Build 135.14140 or newer.
The following fields are only visible with the Log_Mean_Temp_Diff and Effectiveness_NTU Modes.
FlowGeometry Unspecified This option may only be selected if the Log Mean Temperature Difference Method is chosen. In this case the flow geometry of the heat exchanger is not used, and the unit is assumed to have counter current flow.
ParallelFlow A parallel flow heat exchanger is used. This means that the flow though the 2 sides of the Heat Exchange is co-current.
CounterFlow A counter current flow heat exchanger.
CrossFlow - Mixed A cross flow heat exchanger, with both sides mixed.
CrossFlow - Unmixed A cross flow heat exchanger, with both sides unmixed.
Shell/Tube A conventional Shell and Tube heat exchanger with a single shell and 2n tubes, where n is any integer.
HTC Input The overall Heat Transfer Coefficient for the heat exchanger, U.
Area Input The Heat Exchanger Area available for heat transfer.
LMTDFact Input The LMTD factor. The default value is 100%. Note: This field is only visible if the Mode chosen is Log_Mean_Temp_Diff.
The following fields are only visible with the Simple Temperature/duty Modes. Available in SysCAD 9.2 Build 135.14140 or newer.
SideDefinition Tank The temperature or duty requirements can be specified for the Tank side only.
HX Element The temperature or duty requirements can be specified for the HX Element side only.
Tank /HX Element Thermal requirements (only visible with the Simple Temperature/duty Modes. Available in SysCAD 9.2 Build 135.14140 or newer.)
ReqdDuty Input Visible when Mode is set to Simple-FixedDuty. User specifies the required heat duty of the chosen side.
Note: a positive duty is used for heating (rise in temperature), while a negative duty is used for cooling.
ReqdProdT Input Visible when Mode is set to Simple-ProductTemp. User specifies the required product temperature of the chosen side.
RqdTempRise Input Visible when Mode is set to Simple-TempRise. User specifies the required temperature rise across the chosen side.
Note: a negative rise can be used to define a temperature drop.
RqdTempDrop Input Visible when Mode is set to Simple-TempDrop. User specifies the required temperature drop across the chosen side.
Note: a negative drop can be used to define a temperature rise.
Options (only visible with the Simple Temperature/duty Modes. Available in SysCAD 9.2 Build 135.14140 or newer.)
Other.CalcFlow Tick Box If this option is selected, the Calc tab page will appear with some options for calculating the required flow on the unspecified side.
TrackOneSideFlow Tick Box If this option is selected, warning messages will be given if one side of the heat exchanger (but not both) has no flow and hence no heat exchange can occur.

### Results

Duty Calc The calculated duty of the heat exchange.
The following fields are only visible with the Log_Mean_Temp_Diff and Effectiveness_NTU Modes.
U * A Calc HTC * Area
LMTD Calc The calculated Log Mean Temperature Difference across the heat exchanger.
FlowMode Display This will display if the Heat Exchanger is operating in Counter Current or CoCurrent flow mode. The Flow Geometry chosen by the user will determine this mode. (Currently only the Parallel Flow geometry will result in a CoCurrent flow mode).
NTU Calc The Number of Transfer Units for the Heat Exchanger - please see the Effectiveness theory for a description. This value is indicative of the size of the Heat Exchanger.
Effectiveness Calc The calculated effectiveness of the unit, based on the user defined configuration, heat transfer coefficient U, Area A and energy transfer coefficients, as described in the Model theory.
LMTDFactEff Calc If the Effectiveness method is chosen, then this is the calculated Log Mean Temperature Difference Factor for the heat exchanger. If the Log Mean Difference Method is used, then this value is the user defined LMTD Factor.
HX.Pri... - Tank Side: All Tank Input streams combined.
Mode Output The heat exchange mode - heat exchange always takes place via Sensible heat exchange, i.e. no boiling or condensing is supported with this sub-model.
Qm Display The mass flow through the primary side (the tank) of the heat exchanger.
Cp Calc The Specific Heat, Cp, of the material in the tank.
Ti Display The temperature of the material in the tank entering the heat exchange sub-model.
To Calc The temperature of the material leaving the heat exchanger sub-model.
Pi Calc The pressure prior to heat exchange.
Po Calc The pressure after heat exchange.
dT Calc The temperature change of the material in the tank across the heat exchanger.
SatT@P/SatT Calc The Saturated temperature of the material in the tank at the tank pressure.
SatP@T/SatP Calc The Saturated pressure of the material in the tank at the exit temperature.
SatPP@T/SatPP Calc The saturated partial pressure of the material in the tank at the exit temperature.
PPFrac Calc The partial pressure fraction.
Duty Calc The heat exchanger duty of the primary, or tank, side.
HX.Sec... - HX Element Side: Stream connected to the Heat Exchange Element.
Mode Output The heat exchange mode - heat exchange always takes place via Sensible heat exchange, i.e. no boiling or condensing is supported with this sub-model.
Qm Display The mass flow through the secondary side of the heat exchanger.
Cp Calc The Cp of the material flowing through the secondary side of the heat exchanger.
Ti Display The temperature of the HX input stream.
To Calc The temperature of the HX output stream.
Pi Calc The stream pressure prior to heat exchange. This is not normally relevant for ProBal Mode.
Po Calc The stream pressure after heat exchange. This is not normally relevant for ProBal Mode.
dT Calc The temperature change of the secondary stream across the heat exchanger.
SatT@P/SatT Calc The Saturated temperature of the material in the stream at the stream pressure.
SatP@T/SatP Calc The Saturated pressure at the exit temperature from the tubes.
SatPP@T/SatPP Calc The Saturated partial pressure at the exit temperature from the tubes.
PPFrac Calc The partial pressure fraction.
Duty Calc The heat exchanger duty for the secondary, or tube, side.

### Calc

This page is only visible if the Other.CalcFlow option is chosen on the HX tab page.

 Tag / Symbol Input / Calc Description/Calculated Variables / Options Other (Tank/HX Element) side flow calculation This section is only visible if the Other.CalcFlow option is chosen on the HX tab page This section deals with the "unspecified side", the specified side is set on the HX tab page The flowrate of the "unspecified side" is calculated using: $\mathbf{\mathit{m=Q/(Cp\boldsymbol{\Delta}T})}$ Where Q = -1 * Duty of "specified side" and dT can be specified or calculated using the method list box in this section: DemandConnection None (Manual) The required flow (DemandQm) will be calculated but not used by the model. It is up to the user to use an external controller to fetch this value. General Demand The required flow (DemandQm) will be passed back through the feed streams using the General Demand functionality. Method ProductTemp This allows the user to specify the required outlet temperature. TempDrop This allows the user to specify the required temperature drop across the heat exchanger. TempRise This allows the user to specify the required temperature rise across the heat exchanger. TemperatureReqd / TReqd Input This field is only visible if ProductTemp is chosen for Method. The required product temperature. TempDropReqd / TDropReqd Input This field is only visible if TempDrop is chosen for Method. The required temperature drop across this side. Note: a negative drop can be used to define a temperature rise. TempRiseReqd / TRiseReqd Input This field is only visible if TempRise is chosen for Method. The required temperature rise across this side. Note: a negative rise can be used to define a temperature drop. QmTarget Tick Box If this option is ticked, then the required flow (DemandQm) will be considered a target and the user will not receive any warning messages if the ActualQm does not equal DemandQm. TargetTemperature / TargetT Calc The actual Target Temperature. This is determined based on the actual feed temperature and the preceding temperature requirement. If this side is being heated, the TargetT can not be less than the feed temperature. If this side is being cooled, the TargetT can not be greater than the feed temperature. ActualTemperature / ActualT Calc The actual outlet temperature. This will be the same as shown on the first tab page and is just shown here for comparison. DemandMassFlow / DemandQm Calc The required mass flow in order to achieve the Target Temperature. ActualMassFlow / ActualQm Calc The actual mass flow. This will be the same as shown on the first tab page and is just shown here for comparison. DemandQmErr Calc The difference between the required mass flow and the actual mass flow (DemandQm - ActualQm).