View source for Heat Exchanger (HX)

[[Category:Sub-Models]] [[Category:Energy]]
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'''Related Links:''' [[Tank]]
----
{{TOC}}
== General Description ==

This sub-model is part of the '''[[Tank]]''' Model. The Tank model allows the user to insert a heat exchanger into the unit. 
*When HeatXChg is set to On, the model requires connections to the Heat Exchange inlet and outlet streams. 
*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.
*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.
*Heat exchange will be limited if H2O(l) in the tank would reach a temperature above the critical point.
*If user needs to use steam - condensing as the heating media, then please consider using the '''[[Shell and Tube Heat Exchanger 2]]''' model.
A full description of the heat exchanger theory is given in the model description.

== Model Theory ==

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

:<math>\mathbf{\mathit{Q=\dot{m}(H_{in}-H_{out})}}</math>
:where
:Q - Energy Transfer - this is calculated either using the ''Log Mean Temperature Difference'' or the ''Effectiveness'' method, which are described below.
:<math>\dot{m}</math> - Mass flow of the stream
:H<sub>in</sub> - Enthalpy of entering stream
:H<sub>out</sub> - 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:

:<math>\mathbf{\mathit{Q=UA\boldsymbol{\Delta}T_{LM}}}</math>
:where
:Q - Energy Transfer
:U - Overall coefficient of Heat Transfer
:A - Area available for Energy Transfer

:<math>\mathbf{\mathit{\boldsymbol{\Delta}T_{LM} = \cfrac{\Delta T_2 -\Delta T_1}{ln \left( \cfrac{\Delta T_2}{\Delta T_1} \right)}}}</math> - Log Mean Temperature Difference (LMTD)
:: For Counter Current Flow <math> \Delta T_2 = T_{H_{in}} \; - T_{C_{out}} \; </math> and <math> \Delta T_1 = T_{H_{out}} \; - T_{C_{in}} \; </math>
:: For Co-Current, or Parallel, Flow <math> \Delta T_2 = T_{H_{out}} \; - T_{C_{out}} \; </math> and <math> \Delta T_1 = T_{H_{in}} \; - T_{C_{in}} \; </math>

Notes:
# 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, 6<sup>th</sup> Edition, 1984.

=== Effectiveness Method ===

In this method Heat Exchanger Effectiveness, &epsilon;, is defined by the following equation:

<math> \epsilon = \cfrac{Q_{actual}}{Q_{maximum}}</math>

Where:
: Q<sub>actual</sub> is the Actual amount of energy transferred between the streams; and
: Q<sub>maximum</sub> is the Maximum possible energy transferred if the fluid with C<sub>min</sub> = Mass * C<sub>p</sub> experienced a temperature change equal to the difference between the temperature of the entering hot and cold fluids:
:: <math> Q_{maximum} = C_{min} * (T_{H_{in}} - T_{C_{in}}) </math>

Therefore, to obtain the Actual energy transferred in the heat exchange, the value for &epsilon; 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:

:<math> NTU = \cfrac{UA}{C_{min}}</math>

:: U - Overall Heat Transfer coefficient;
:: A - Heat Transfer Area; and
:: C<sub>min</sub> = Mass * C<sub>p</sub> 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 * C<sub>p</sub>.  We define C<sub>min</sub> and C<sub>max</sub> as the values with the minimum and maximum Energy Capacity values.  Please note that C<sub>min</sub> is not necessarily the fluid the smallest value of C<sub>p</sub>.

Then <math> C = \cfrac{C_{min}}{C_{max}}</math>

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:

{| class="wikitable"
|-
! Flow Geometry     || Heat Exchanger Effectiveness Relation
|-
| Parallel Flow || <math> \epsilon = \cfrac{1-e^{-NTU(1+C)}}{1+C} \quad</math>
|-
| Counter Flow || <math> \epsilon = \cfrac{1-e^{-NTU(1-C)}}{1-C*e^{-NTU(1-C)}} \quad</math>
|-
| Cross Flow - Mixed || <math> \epsilon = \left[ A + B - \cfrac{1}{NTU} \right]^{-1} \quad</math> where <math> \quad A = \cfrac{1}{1 - e^{-NTU}} \quad</math> and <math> \quad B = \cfrac{C}{1 - e^{-NTU * C}} \quad</math>
|-
| Cross Flow - Unmixed || <math> \epsilon = 1 - e^{\cfrac{e^{-NTU*C*n} - 1}{C*n}} \quad </math> and <math> \quad n = NTU^{-0.22} \quad </math>
|-
| Shell and Tube <br> One shell pass, 2,4,6, etc. tube passes. || <math> \epsilon = 2 * \cfrac{1 - B}{(1 + C)(1 - B) + A(1 + B)} \quad</math> where <math>\quad A = \sqrt{1 + C^2} \quad </math>  and <math>\quad B = e^{-NTU * A} \quad</math>
|}

''' Reference '''

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

=== Assumptions ===

# The overall heat transfer coefficient remains constant throughout the unit.
# The system is adiabatic - heat exchange only takes place between the 2 fluids.
# 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, 

# '''[[#HX Page|HX]]''' tab - This tab contains general information relating to the sub model.
# '''[[#Calc|Calc]]''' tab - Optional second tab which allows the user to perform some flow calculations.

=== HX Page===

NOTE: HX is for sensible heat transfer only, not phase change (i.e. boiling or condensing) will occur.

{|   border="1" cellpadding="5" cellspacing="0"
|width=200|'''Tag (Long/Short)'''||width=120|'''Input / Calc'''||'''Description/Calculated Variables / Options'''
|-
|  colspan="3" font style="background: #ebebeb"    |
=== Requirements === 
|-
|On || Tick Box || This enables the Heat Exchanger sub-model in the tank.  If this is disabled, then no heat exchange will occur.
|-
|rowspan = "6" valign="top"|Mode || Log_Mean_Temp_Diff || The duty is calculated using the [[Heat Exchanger (HX)#Log Mean Temperature Difference Method|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.
|-
|  valign="top"  |Effectiveness_NTU || The duty is calculated using [[Heat Exchanger (HX)#Effectiveness Method|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''.
|-
|  valign="top"  |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.
|-
|  valign="top"  |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.
|-
|  valign="top"  |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.
|-
|  valign="top"  |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.
|-
|  colspan="3" font style="background: #ebebeb"    |The following fields are only visible with the ''Log_Mean_Temp_Diff'' and ''Effectiveness_NTU'' Modes.
|-
|rowspan = "6" valign="top"|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.
|-
| LMTDFactor / 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''.
|-
|  colspan="3" font style="background: #ebebeb"    |The following fields are only visible with the Simple Temperature/duty Modes.
|- 
|  valign="top" rowspan="2"  |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.
|- 
|  colspan="3" font style="background: #ebebeb"    | '''''Tank /HX Element Thermal requirements''''' (only visible with the Simple Temperature/duty Modes.)
|- 
|ReqdDuty || Input ||Visible when Mode is set to '''Simple-FixedDuty'''. User specifies the required heat duty of the chosen side.<br> '''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.<br> '''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.<br> '''Note:''' a negative drop can be used to define a temperature rise.
|- 
|  colspan="3" font style="background: #ebebeb"    | '''''Options''''' (only visible with the Simple Temperature/duty Modes.)
|-
|Other.CalcFlow || Tick Box || If this option is selected, the [[#Calc|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.
|-
|  colspan="3" font style="background: #ebebeb"    |

=== Results ===
|-
| Duty||font style="background: #ebebeb"  |Calc|| The calculated duty of the heat exchange.
|-
|  colspan="3" font style="background: #ebebeb"    |The following fields are only visible with the ''Log_Mean_Temp_Diff'' and ''Effectiveness_NTU'' Modes.
|-
|U * A||font style="background: #ebebeb"  |Calc|| HTC * Area
|-
| LMTD||font style="background: #ebebeb"  |Calc|| The calculated Log Mean Temperature Difference across the heat exchanger.
|-
|FlowMode||  font style="background: #ebebeb"  |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||font style="background: #ebebeb"  |Calc|| The Number of Transfer Units for the Heat Exchanger - please see the [[Heat Exchanger (HX)#Effectiveness Method|Effectiveness]] theory for a description.  This value is indicative of the size of the Heat Exchanger.
|-
|Effectiveness||font style="background: #ebebeb"  |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||font style="background: #ebebeb"  |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.
|-
|  font style="background: #ebebeb"  colspan="3" |'''''HX.Pri...''''' - Tank Side: All Tank Input streams combined.
|-
|Mode|| font style="background: #ebebeb"   |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.
|-
|MassFlow / Qm||font style="background: #ebebeb"  |Display|| The mass flow through the primary side (the tank) of the heat exchanger.
|-
|Cp||font style="background: #ebebeb"  |Calc|| The Specific Heat, Cp, of the material in the tank.
|-
|TemperatureIn / Ti||font style="background: #ebebeb"  |Display|| The temperature of the material in the tank entering the heat exchange sub-model.
|-
|TemperatureOut / To||font style="background: #ebebeb"  |Calc|| The temperature of the material leaving the heat exchanger sub-model.
|-
|DeltaT / dT||font style="background: #ebebeb"  |Calc|| The temperature change of the material in the tank across the heat exchanger.
|-
|PressureIn / Pi||font style="background: #ebebeb"  |Calc|| The pressure prior to heat exchange.
|-
|PressureOut /  Po||font style="background: #ebebeb"  |Calc|| The pressure after heat exchange.
<!---
|-
|SatT@P/SatT||font style="background: #ebebeb"  |Calc|| The Saturated temperature of the material in the tank at the tank pressure.
|-
|SatP@T/SatP||font style="background: #ebebeb"  |Calc|| The Saturated pressure of the material in the tank at the exit temperature.
|-
|SatPP@T/SatPP||font style="background: #ebebeb"  |Calc|| The saturated partial pressure of the material in the tank at the exit temperature.
|- 
|PPFrac ||  font style="background: #ebebeb" |Calc ||The partial pressure fraction.
-->
|-
|Duty||font style="background: #ebebeb"  |Calc||The heat exchanger duty of the primary, or tank, side.
|-
|  font style="background: #ebebeb" colspan="3"   |'''''HX.Sec...''''' - HX Element Side:  Stream connected to the Heat Exchange Element.
|-
|Mode|| font style="background: #ebebeb"   |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.
|-
|MassFlow / Qm||font style="background: #ebebeb"  |Display|| The mass flow through the secondary side of the heat exchanger.
|-
|Cp||font style="background: #ebebeb"  |Calc|| The Cp of the material flowing through the secondary side of the heat exchanger.
|-
|TemperatureIn / Ti||font style="background: #ebebeb"  |Display|| The temperature of the HX input stream.
|-
|TemperatureOut / To||font style="background: #ebebeb"  |Calc|| The temperature of the HX output stream.
|-
|DeltaT / dT||font style="background: #ebebeb"  |Calc|| The temperature change of the secondary stream across the heat exchanger.
|-
|PressureIn / Pi||font style="background: #ebebeb"  |Calc|| The stream pressure prior to heat exchange. This is not normally relevant for ProBal Mode.
|-
|PressureOut / Po||font style="background: #ebebeb"  |Calc|| The stream pressure after heat exchange. This is not normally relevant for ProBal Mode.
<!---
|-
|SatT@P/SatT||font style="background: #ebebeb"  |Calc|| The Saturated temperature of the material in the stream at the stream pressure.
|-
|SatP@T/SatP||font style="background: #ebebeb"  |Calc|| The Saturated pressure at the exit temperature from the tubes.
|-
|SatPP@T/SatPP||font style="background: #ebebeb"  |Calc|| The Saturated partial pressure at the exit temperature from the tubes.
|- 
|PPFrac ||  font style="background: #ebebeb" |Calc ||The partial pressure fraction.
-->
|-
|Duty||font style="background: #ebebeb"  |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.

{|   border="1" cellpadding="5" cellspacing="0"
|width=200|'''Tag (Long/Short)'''||width=120|'''Input / Calc'''||'''Description/Calculated Variables / Options'''
|-
|  colspan="3" font style="background: #ebebeb"    |
'''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: <math>\mathbf{\mathit{\dot{m}=Q/(Cp\boldsymbol{\Delta}T})}</math><br>
* Where Q = -1 * Duty of "specified side" and dT can be specified or calculated using the method list box in this section:
|-
|  valign="top" rowspan="2"  | 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 [[Demand|General Demand]] functionality.
|- 
|  valign="top" rowspan="3"  | 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.<br> '''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.<br> '''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||  font style="background: #ebebeb"|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 || font style="background: #ebebeb" |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|| font style="background: #ebebeb" |Calc || The required mass flow in order to achieve the Target Temperature.
|-
|ActualMassFlow / ActualQm|| font style="background: #ebebeb" |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|| font style="background: #ebebeb" |Calc || The difference between the required mass flow and the actual mass flow (DemandQm - ActualQm).
|}