Heat exchanger - Revision history

Cindyxchen: /* Linear Programming */

2016-02-19T21:08:52Z

Linear Programming

← Older revision		Revision as of 21:08, 19 February 2016
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	This linear program set up could be solved using the General Algebraic Modeling System (GAMS), as shown below.		This linear program set up could be solved using the General Algebraic Modeling System (GAMS), as shown below.

			[[File: Gams_problem.png\|375px\|center\|GAMS problem input (Seider, 2004)]]

			The GAMS Program first names the variables used in the program, stating the Z is the objective variable that will be minimized and the other variables are "positive variables," satisfying the final condition stated in Equation LP.6 that all utilities and residual values must be greater than zero. The linear program model is named HEAT and is solved using LP (signifying linear program algorithms) to minimize the Z variable.

	[[File: Gams.PNG\|375px\|center\|GAMS problem input (Seider, 2004)]]		[[File: Gams.PNG\|375px\|center\|GAMS problem input (Seider, 2004)]]

Cindyxchen: /* References */

2016-02-19T21:01:01Z

References

← Older revision		Revision as of 21:01, 19 February 2016
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	# W.D. Seider, J.D. Seader, D.R. Lewin, ''Process Design Principles: Synthesis, Analysis, and Evaluation'', Wiley: New York, 2004.		# W.D. Seider, J.D. Seader, D.R. Lewin, ''Process Design Principles: Synthesis, Analysis, and Evaluation'', Wiley: New York, 2004.
	# Aspen Technology, Inc. Aspen Energy Analyzer: Tutorial Guide. (2011)		# Aspen Technology, Inc. Aspen Energy Analyzer: Tutorial Guide. (2011)
	# M.J. Bagajewicz. "Heat Integration." Chemical Engineering PanAmerican Collaboration. 2008.		# M.J. Bagajewicz. ''Heat Integration'' Chemical Engineering PanAmerican Collaboration. 2008.
	# F. Maréchal, D. Favrat. ''Combined Exergy and Pinch Analysis for Optimal Energy Conversion Technologies Integration''. 2005.		# F. Maréchal, D. Favrat. ''Combined Exergy and Pinch Analysis for Optimal Energy Conversion Technologies Integration''. 2005.
			# L.T. Biegler, I.E. Grossmann, A.W. Westerberg. ''Systematic Methods of Chemical Process Design'', Prentice Hall: New Jersey, 1999.

Cindyxchen: /* Future Developments */

2016-02-19T20:59:33Z

Future Developments

← Older revision		Revision as of 20:59, 19 February 2016
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	As seen in the figure above, a loop may cross the pinch point. These loops can be broken by transferring heat across the pinch point. This, however, violates the heuristic that heat should not be transferred across the pinch point and at least one violation of the specific Δ<math>T_{min}</math> will also occur. To restore Δ<math>T_{min}</math>, heat can be shifted along a path, which increases the energy consumption of the process. From this dilemma, it is clear that there are pros and cons to the attempt to minimize any heat exchanger network.		As seen in the figure above, a loop may cross the pinch point. These loops can be broken by transferring heat across the pinch point. This, however, violates the heuristic that heat should not be transferred across the pinch point and at least one violation of the specific Δ<math>T_{min}</math> will also occur. To restore Δ<math>T_{min}</math>, heat can be shifted along a path, which increases the energy consumption of the process. From this dilemma, it is clear that there are pros and cons to the attempt to minimize any heat exchanger network.

	Analysis with the incorporation of capital costs can be done by assessing the heat exchanger network as a [https://en.wikipedia.org/wiki/Linear_programming#Integer_unknowns mixed integer non-linear programming] (MINLP) problem. MINLP problems are typically solved using numerical solvers. But large scale MINLP problems, such as the ones that may be generated for a process plant, may be difficult to solve using available numerical algorithms and solvers.		Analysis with the incorporation of capital costs can be done by assessing the heat exchanger network as a [https://en.wikipedia.org/wiki/Linear_programming#Integer_unknowns mixed integer non-linear programming] (MINLP) problem. MINLP problems are typically solved using numerical solvers. But large scale MINLP problems, such as the ones that may be generated for a process plant, may be difficult to solve using available numerical algorithms and solvers (Biegler, 1999).

	=References=		=References=

Cindyxchen: /* Modify Heat Exchanger Network Diagrams */

2016-02-19T20:55:52Z

Modify Heat Exchanger Network Diagrams

← Older revision		Revision as of 20:55, 19 February 2016
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	* Add a heat exchanger: right click and hold the Add Heat Exchanger icon from the Design Tools palette. Once the mouse is released, a solid red dot will appear on the desired stream. Click and hold the red dot to the new stream. The heat exchanger will appear once the mouse is released. Double click either end of the heat exchanger to open the Heat Exchanger Editor view. On the Data tab, click the Tied checkbox by the appropriate streams and enter other temperatures as needed.		* Add a heat exchanger: right click and hold the Add Heat Exchanger icon from the Design Tools palette. Once the mouse is released, a solid red dot will appear on the desired stream. Click and hold the red dot to the new stream. The heat exchanger will appear once the mouse is released. Double click either end of the heat exchanger to open the Heat Exchanger Editor view. On the Data tab, click the Tied checkbox by the appropriate streams and enter other temperatures as needed.

	[[File: HX2.jpg\|~~300px~~\|center\|Heat exchanger windows (Aspen, 2011)]]		[[File: HX2.jpg\|500px\|center\|Heat exchanger windows (Aspen, 2011)]]

	* Adjust the split ratio: open HEN Diagram Properties View and click the New button. Input Split Ratio into the Name field. Select Edit >> Annotations tab >> Streams group >> Segments drop-down list >> Split Fraction. Double-click on either end of the heat exchanger to observe the changes in the hot stream inlet temperature. Double-click on either end of the splitter to open the splitter view. Adjust the split ratio accordingly.		* Adjust the split ratio: open HEN Diagram Properties View and click the New button. Input Split Ratio into the Name field. Select Edit >> Annotations tab >> Streams group >> Segments drop-down list >> Split Fraction. Double-click on either end of the heat exchanger to observe the changes in the hot stream inlet temperature. Double-click on either end of the splitter to open the splitter view. Adjust the split ratio accordingly.

Cindyxchen: /* Modify Heat Exchanger Network Diagrams */

2016-02-19T20:54:55Z

Modify Heat Exchanger Network Diagrams

← Older revision		Revision as of 20:54, 19 February 2016
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	* Add a heat exchanger: right click and hold the Add Heat Exchanger icon from the Design Tools palette. Once the mouse is released, a solid red dot will appear on the desired stream. Click and hold the red dot to the new stream. The heat exchanger will appear once the mouse is released. Double click either end of the heat exchanger to open the Heat Exchanger Editor view. On the Data tab, click the Tied checkbox by the appropriate streams and enter other temperatures as needed.		* Add a heat exchanger: right click and hold the Add Heat Exchanger icon from the Design Tools palette. Once the mouse is released, a solid red dot will appear on the desired stream. Click and hold the red dot to the new stream. The heat exchanger will appear once the mouse is released. Double click either end of the heat exchanger to open the Heat Exchanger Editor view. On the Data tab, click the Tied checkbox by the appropriate streams and enter other temperatures as needed.

	[[File: HX2.~~JPG~~\|300px\|center\|Heat exchanger windows (Aspen, 2011)]]		[[File: HX2.jpg\|300px\|center\|Heat exchanger windows (Aspen, 2011)]]

	* Adjust the split ratio: open HEN Diagram Properties View and click the New button. Input Split Ratio into the Name field. Select Edit >> Annotations tab >> Streams group >> Segments drop-down list >> Split Fraction. Double-click on either end of the heat exchanger to observe the changes in the hot stream inlet temperature. Double-click on either end of the splitter to open the splitter view. Adjust the split ratio accordingly.		* Adjust the split ratio: open HEN Diagram Properties View and click the New button. Input Split Ratio into the Name field. Select Edit >> Annotations tab >> Streams group >> Segments drop-down list >> Split Fraction. Double-click on either end of the heat exchanger to observe the changes in the hot stream inlet temperature. Double-click on either end of the splitter to open the splitter view. Adjust the split ratio accordingly.

Cindyxchen: /* Linear Programming */

2016-02-19T20:54:36Z

Linear Programming

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	<br>		<br>
	::Minimize <math>Q_{steam}</math>		::Minimize <math>Q_{steam}</math>
	::<with respect to (w.r.t.): <math>Q_{steam}</math>		::with respect to (w.r.t.): <math>Q_{steam}</math>
	::Subject to (s.t.):		::Subject to (s.t.):
	::<math>\begin{align}		::<math>\begin{align}
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	<br>		<br>

	This LP set up could be solved using the General Algebraic Modeling System (GAMS), as shown below.		This linear program set up could be solved using the General Algebraic Modeling System (GAMS), as shown below.

	[[File: Gams.PNG\|375px\|center\|GAMS problem input (Seider, 2004)]]		[[File: Gams.PNG\|375px\|center\|GAMS problem input (Seider, 2004)]]

Cindyxchen: /* Linear Programming */

2016-02-19T20:53:41Z

Linear Programming

← Older revision		Revision as of 20:53, 19 February 2016
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	===Linear Programming===		===Linear Programming===
	Consider a system where two cold streams, C1 and C2, are to be heated and two hot streams, H1 and H2, are to be cooled without phase change. ~~Ths~~ conditions and properties of these streams are listed below.		Consider a system where two cold streams, C1 and C2, are to be heated and two hot streams, H1 and H2, are to be cooled without phase change. The conditions and properties of these streams are listed below.

	[[File:Streams24.png\|450px\|center\|Stream information table (Seider, 2004)]]		[[File:Streams24.png\|450px\|center\|Stream information table (Seider, 2004)]]

Cindyxchen: /* Linear Programming */

2016-02-19T20:53:25Z

Linear Programming

← Older revision		Revision as of 20:53, 19 February 2016
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	[[File:Enthalpy_table.PNG\|450px\|center\|Anaylsis Results (Seider, 2004)]]		[[File:Enthalpy_table.PNG\|450px\|center\|Anaylsis Results (Seider, 2004)]]

	[[File:Cascade_hen.PNG\|~~200px~~\|thumb\|right\|Figure 3. Cascade of temperature intervals, energy balances, and residuals (Seider, 2004)]]		[[File:Cascade_hen.PNG\|225px\|thumb\|right\|Figure 3. Cascade of temperature intervals, energy balances, and residuals (Seider, 2004)]]
	<br>		<br>
	The linear program can be formulated as:		The linear program can be formulated as:
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	::<math>Q_{cw}</math> is the cold utility duty		::<math>Q_{cw}</math> is the cold utility duty
	where all energy requirements should be multiplied by 10,000 Btu/hr.		where all energy requirements should be multiplied by 10,000 Btu/hr.
	<br><br>		<br><br><br>
	This program will minimize the heat entering from a hot utility. Figure 3 shows the energy flows between each interval of the system and the values of the variables calculated in the initial and final pass.		This program will minimize the heat entering from a hot utility. Figure 3 shows the energy flows between each interval of the system and the values of the variables calculated in the initial and final pass.
	<br>		<br>

Cindyxchen: /* Linear Programming */

2016-02-19T20:52:12Z

Linear Programming

← Older revision		Revision as of 20:52, 19 February 2016
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	[[File:Cascade_hen.PNG\|200px\|thumb\|right\|Figure 3. Cascade of temperature intervals, energy balances, and residuals (Seider, 2004)]]		[[File:Cascade_hen.PNG\|200px\|thumb\|right\|Figure 3. Cascade of temperature intervals, energy balances, and residuals (Seider, 2004)]]
			<br>
	The linear program can be formulated as:		The linear program can be formulated as:
	<br>		<br>

Cindyxchen: /* Linear Programming */

2016-02-19T20:50:39Z

Linear Programming

← Older revision		Revision as of 20:50, 19 February 2016
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	===Linear Programming===		===Linear Programming===
	Consider a system where two cold streams, C1 and C2, are to be heated and two hot streams, H1 and H2, are to be cooled without phase change. Ths conditions and properties of these streams are listed below.		Consider a system where two cold streams, C1 and C2, are to be heated and two hot streams, H1 and H2, are to be cooled without phase change. Ths conditions and properties of these streams are listed below.
	~~{\|class="wikitable" style="margin: auto;"~~

	~~! Stream~~		[[File:Streams24.png\|450px\|center\|Stream information table (Seider, 2004)]]
	~~! Initial Temp. °F~~
	~~! Target Temp~~. °F		Preliminary pinch analysis calculations lead to the following enthalphy changes in each interval.
	~~! Heat Capacity Flow Rate, Btu/hr°F~~
	~~! Heat Load, Btu/hr~~		[[File:Enthalpy_table.PNG\|450px\|center\|Anaylsis Results (Seider, 2004)]]
	\|-
	\|C1
	\| ~~120~~
	~~\| 235~~
	~~\| 20~~,~~000~~
	~~\| 230~~
	\|-
	~~\|C2~~
	\| ~~180~~
	\| ~~240~~
	\| 40,~~000~~
	~~\| 240~~
	\|-
	~~\|H1~~
	~~\| 260~~
	~~\| 160~~
	~~\| 30,000~~
	~~\| 300~~
	\|-
	~~\|H2~~
	~~\| 250~~
	~~\| 130~~
	~~\| 15,000~~
	~~\| 180~~
	\|}

	[[File:Cascade_hen.PNG\|200px\|thumb\|right\|Figure 3. Cascade of temperature intervals, energy balances, and residuals (Seider, 2004)]]		[[File:Cascade_hen.PNG\|200px\|thumb\|right\|Figure 3. Cascade of temperature intervals, energy balances, and residuals (Seider, 2004)]]
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	::<math>R_i</math> is the residual from interval i		::<math>R_i</math> is the residual from interval i
	::<math>Q_{cw}</math> is the cold utility duty		::<math>Q_{cw}</math> is the cold utility duty
	where all energy requirements should be multiplied by ~~<math>~~10~~^4</math>~~ Btu/hr.		where all energy requirements should be multiplied by 10,000 Btu/hr.
	<br><br>		<br><br>
	This program will minimize the heat entering from a hot utility. Figure 3 shows the energy flows between each interval of the system and the values of the variables calculated in the initial and final pass.		This program will minimize the heat entering from a hot utility. Figure 3 shows the energy flows between each interval of the system and the values of the variables calculated in the initial and final pass.
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	[[File: Gams.PNG\|375px\|center\|GAMS problem input (Seider, 2004)]]		[[File: Gams.PNG\|375px\|center\|GAMS problem input (Seider, 2004)]]

	From this result, <math>R_3 = 0</math>, signifying that the pinch is located at interval 3, as seen in Figure 3. Additionally, this result reveals that the hot utility requirement, <math>Q_{steam}</math>, is 50 and the cold utility requirement, <math>Q_{cw}</math>, is 60. However, this simulation only accounts for sensible heat changes. Additional variables, such as heat of reaction, heat of mixing, and even variable specific heat over time, should be considered in a more representative model.		From this result, <math>R_3 = 0</math>, signifying that the pinch is located at interval 3, as seen in Figure 3. Additionally, this result reveals that the hot utility requirement, <math>Q_{steam}</math>, is 500,000 Btu/hr and the cold utility requirement, <math>Q_{cw}</math>, is 600,000 Btu/hr. However, this simulation only accounts for sensible heat changes. Additional variables, such as heat of reaction, heat of mixing, and even variable specific heat over time, should be considered in a more representative model.

	This example is taken from <i>Process Design Pinciples: Synthesis, Analysis, and Evaluation</i> by Seider, Seader, and Lewin.		This example is taken from <i>Process Design Pinciples: Synthesis, Analysis, and Evaluation</i> by Seider, Seader, and Lewin.