Process Modeling, Simulation and Control for Chemical Engineers - Luyben
Chemical Process Simulation
Transcript of Chemical Process Simulation
![Page 1: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/1.jpg)
Chemical Process Simulation
The objective of this course is to provide the background needed by the chemical engineers to carry out computer-aided analyses of large-scale chemical processes. Major concern will fall on steady-state processes with hands on experiences on Aspen HYSYS
![Page 2: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/2.jpg)
Aspen HYSYS and the Structure of Design Process
ANALYSIS
Material &Energybalances
Equip. Sizingand
Costing
EconomicEvaluation
Final flowsheet
Societal needs
InitialFlowsheet
Parameteroptimization
StructureOptimization
FlowsheetSynthesis
Flowsheet Synthesis
1) Rxn path selection
2) Material balancing andspecies allocation
3) Separation task selectionand sequencing
4) Auxiliary task assignmentand process integration
5)Evolutionary improvementof initial flowsheet
Chemical Process Synthesis
HYS
YS HYSYS
DesignVariables
InitialValues
![Page 3: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/3.jpg)
ChE Process Analysis
![Page 4: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/4.jpg)
What is process simulation for ?
1. To interpret process flowsheets,2. To locate malfunctions, and3. To predict the performance of process.
![Page 5: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/5.jpg)
Commercial Process Simulators
• Aspen Engineering Suite of Aspen tech., Inc.– http://www.aspentech.com
• CHEMCAD 5.xx of Chemstations– http://www.chemstations.net
• Process Engineering Suite of Simulation Sciences, Inc.– http://www.simsci.com
• SUPERPRO DESIGNER 4.x of Intelligen, Inc.– http://intelligen.com/SuperPro.htm
![Page 6: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/6.jpg)
Flowsheeting
The use of computer aids to perform steady-state heat and mass balances, sizing, costing calculation for a chemical process.
![Page 7: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/7.jpg)
To perform process simulation using a process simulator
• Convert from a process flowsheet to a simulation flowsheet, i.e., replace the process units with appropriate simulation unit.
• Model and solve the process unit equations – a subroutine is written for each process unit.
![Page 8: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/8.jpg)
What are process flowsheets?• Process flowsheets are the language of
chemical processes. They describe an existing process or a hypothetical process in sufficient detail to convey the essential features.
• A process flowsheet is a collection of icons to represent process and arcs to represent the flow of material to and from the units. It emphasizes the flow of material and energy in a chemical process.
![Page 9: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/9.jpg)
A Typical Process Flow Sheet
![Page 10: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/10.jpg)
A Hypothetical process Flow sheet
![Page 11: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/11.jpg)
What is a simulation flowsheet ?
A simulation flowsheet is a collection of simulation units to represent computer program (models) that simulate the process units and arcs to represent the flow information among the simulation units.
![Page 12: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/12.jpg)
A typical simulation flow sheet
![Page 13: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/13.jpg)
A typical process simulator model
![Page 14: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/14.jpg)
Process Modeling and Simulation
![Page 15: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/15.jpg)
Chemical ProcessSimulation(I)
![Page 16: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/16.jpg)
Chemical ProcessSimulation(II)
![Page 17: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/17.jpg)
Typical Process Equipments
![Page 18: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/18.jpg)
Modeling and Simulation procedure
• Translating the description of a physical system into an appropriate mathematical form.
• Selecting a suitable computational technique.• Implementing the computational technique in
the form of a computer program.
![Page 19: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/19.jpg)
A model is the simplification of reality used to
predict system behavior.
F = ma
PhysicalModelPhysicalModel
MathematicalModelMathematicalModel
![Page 20: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/20.jpg)
Modeling and Simulation
Physical system
Mathematical model
Results and Interpretation
Laws of NatureMassEquil.Sum
H-energy+
Rate+
Others
Equation Solver Matlab
MathCadCC-5
Aspen Plus Hysysothers
![Page 21: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/21.jpg)
Define process
Develop Math model
Identify constraint
Develop computerprogram
Run simulation program
All parameterscovered?
Do model and exp.
Agree?
Determine optimumconditions
Yes
Yes
No
No
Flow chart of steps in
simulation
![Page 22: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/22.jpg)
General Process Unit Analysis1. Define system variables.
2. Write simulation equations.
3. Check degrees of freedom.
4. Choose design variables.
5. Choose appropriate math solver.
![Page 23: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/23.jpg)
Flash Analysis
An
example
![Page 24: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/24.jpg)
Flash Drum in situ.
![Page 25: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/25.jpg)
Flash Vessel (1)
![Page 26: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/26.jpg)
A Flash Vessel (2)
![Page 27: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/27.jpg)
A Flash Vessel (3)
![Page 28: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/28.jpg)
A Flash Vessel (4)
![Page 29: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/29.jpg)
Defining Process Variables
![Page 30: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/30.jpg)
Math. Model
![Page 31: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/31.jpg)
Information Flow in
Flash Calculations
![Page 32: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/32.jpg)
Information Flow (1)
![Page 33: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/33.jpg)
Information Flow (2)
![Page 34: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/34.jpg)
Information Flow (3)
![Page 35: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/35.jpg)
Information Flow (4)
![Page 36: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/36.jpg)
Information Flow (5)
![Page 37: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/37.jpg)
Information Flow (6)
![Page 38: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/38.jpg)
Information Flow (7)
![Page 39: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/39.jpg)
Information Flow (8)
![Page 40: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/40.jpg)
A typical flash example
![Page 41: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/41.jpg)
Chemical Process Simulation
•Process Flowsheet
•Simulation Flow sheet
![Page 42: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/42.jpg)
Process Flowsheet
![Page 43: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/43.jpg)
Simulation Flowsheet
![Page 44: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/44.jpg)
Nature of the Simulation Problem
1. The nature of the process streams2. The nature of the material being
processed3. The nature of each type of process unit
4. The specific process configuration
5. The feed stream property
![Page 45: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/45.jpg)
Nature of the Process Streams
1. Flow rate2. Compositions3. Temperature4. Pressure5. Others
![Page 46: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/46.jpg)
Nature of the Material Being Processed
1. A set values of the pure component properties of each chemical component in the stream.
2. Values of the stream variables for the particular stream of interest – to determine the temperature, pressure, and composition of the stream mixture.
3. A model for the thermodynamic and transport behavior of the mixture.
![Page 47: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/47.jpg)
A typical set of pure-component properties for the cal’n of thermo properties
![Page 48: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/48.jpg)
Nature of the Process Unit
1. The conservation laws: the principles of conservation of mass, energy, and momentum.
2. The rate laws: relations between rate of flow, heat transfer, mass transfer, chemical rxn, etc. and driving forces of temperature, pressure, conc., etc.
3. Physical property relations: relations between the thermodynamic and transport properties and the intensive variables of temperature, pressure, and conc.
4. Principles of thermodynamic equilibrium: limitations on the performance of physico-chemical systems imposed by the 2nd law of thermodynamics.
5. Automatic control theory: relations governing the transfer of information through the system.
![Page 49: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/49.jpg)
Process Configuration
1. The topology of the process – the description of which streams are connected to which inlet and outlet ports of which units.
2. The specifications of all design and operating parameters that are under the control of the designer.
![Page 50: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/50.jpg)
Feed / Product Streams
1. Feed stream could be treated as a process unit with an outlet and no inlet
2. Product stream could be treated as a process unit with an inlet and no outlet.
![Page 51: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/51.jpg)
Process Simulation Techniques
1. Sequential Modular Approach
2. Equation Oriented Approach
3. Simultaneous Modular Approach
![Page 52: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/52.jpg)
Methods of Analysis of System Structure –the decomposition of large system
1. Partitioning and precedence ordering• units that must be solved together are
identified in the flowsheet;• the sequence of computations of the
partitioned subsystem are determined2. Tearing : resolving a cyclic partitioned unit to
a acyclic one.3. Design variable selection : the best choice
of design variables is to render the equations most acyclic.
![Page 53: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/53.jpg)
Components of a Simulation Program
ExecutiveProgram
UnitModule Library
NumericalRoutines
PhysicalProperty
Data Bank
Thermodynami cPackage
Input Output
Solution
Optimization
EconomicAnalysis
![Page 54: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/54.jpg)
Sequential Modular Approach
1. Acyclic process – w/o recycles-Processes are solved sequentially one module
at a time.
2. Cyclic process – with recycles-need to cut streams to enable the procedure.
![Page 55: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/55.jpg)
Typical Process Modules
1. MIX - Mix several inlet streams adiabatically to form one product stream.
2. SPLIT – Split a single inlet stream into two or more product streams with the same composition and temperature.
3. COMPRESS – Raise the pressure of a gas by a specific amount.
4. PUMP - Raise the pressure of a liquid by a specific amount.
5. FLASH – Convert a liquid stream at one pressure to liquid and vapor streams in equilibrium at low pressure.
6. REACT – Simulate a chemical reactor.7. DISTILL, EXTRACT, CRYSTAL, ABSORB – Simulate the
separation processes of distillation, extraction, crystallization, and absorption, respectively.
![Page 56: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/56.jpg)
Aspen Subroutine Library(I)
![Page 57: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/57.jpg)
Aspen Subroutine Library(II)
![Page 58: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/58.jpg)
Simulation of an Acyclic Process
The flowsheet shown here depicts a hypothetical multi-unit separation process. Three liquid streams are mixed adiabatically; The product stream is pumped Through a heater to a distillation column, and the overhead product from the column is partially condensed to yield liquid and vapor products. Using blocks MIX, PUMP, HEAT, DISTILL, and CNDS, construct a block diagram for the Simulation of this process.
![Page 59: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/59.jpg)
Process for separation of ammonia and water (I)
![Page 60: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/60.jpg)
Process for separation of ammonia and water (II)
![Page 61: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/61.jpg)
Acyclic process Calculation sequence
![Page 62: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/62.jpg)
Ethylchloride production process flow sheet(I)
![Page 63: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/63.jpg)
Ethylchloride production process flow sheet(II)
![Page 64: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/64.jpg)
Recycle process calculation sequence
![Page 65: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/65.jpg)
Equation Oriented Approach
• All the equations of the whole process arecollected and solved as a large system ofnonlinear algebraic equations.
• Mathematically, the problem is formulatedas an optimization problem, i.e.,• Minimize h(x,u)
– Subject to f(x,u) = 0 ;process model eqn.g(x,u) = 0 ;process constraints.
Where x is the vector of state (dep.) variables, andu is the vector of decision (indep.) variables.
![Page 66: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/66.jpg)
Demo of Equation-Oriented approach
Simulation of an equilibrium reaction / separation process
![Page 67: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/67.jpg)
Degrees of Freedom Analysis
![Page 68: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/68.jpg)
Simulation Equations
![Page 69: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/69.jpg)
Numerical Solution
![Page 70: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/70.jpg)
Simultaneous Modular Approach
Execute Rigorous Models
Generate SimpleModel
Parameters
Solved ReducedOptimization
Problem
InsideLoop
OutsideLoop
![Page 71: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/71.jpg)
Steps of simultaneous modular approach
1. For the first iteration, make initial estimates of recycle streamvalues.
2. Solve the problem using the sequential modular approach.
3. Having obtained the first estimate of input and output values foreach unit, construct a linear relationship between them, i.e.,linearize the model equations.
4. Since the interconnection equations are already linear, solve thewhole system of model and interconnection equationssimultaneously using matrix method to obtain a new set of inletvalues.
5. If two successive iterates of assumed stream values convergewithin a preset tolerance, the simulation is complete. Otherwise,go back to step (2).
![Page 72: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/72.jpg)
The scope of a process simulator
1. Prepare process designs
2. Analyze design alternatives
3. Predict the effects of changes on plant operating conditions
4. Optimize energy consumption
5. Eliminate bottlenecks and increase throughput
![Page 73: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/73.jpg)
Running a Simulator
1. Setting up a problem
2. Creating a flowsheet3. Specifying engineering data4. Performing the simulation5. Viewing and printing results
![Page 74: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/74.jpg)
Aspen-plus demo
![Page 75: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/75.jpg)
Process Simulation with
ASPEN HYSYS
![Page 76: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/76.jpg)
Typical HYSYS Module Library
![Page 77: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/77.jpg)
Scope of Aspen HYSYS
![Page 78: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/78.jpg)
Aspen HYSYS Simulation Procedures
1. Draw flowsheet,2. Choose components,
3. Choose thermodynamic model,
4. Define feed streams,5. Provide equipment parameters,6. Run the program, and7. View, plot and output the reports and PFD.
![Page 79: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/79.jpg)
ChemCad Simulator
![Page 80: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/80.jpg)
Benzene Process Flow Sheet
![Page 81: Chemical Process Simulation](https://reader030.fdocuments.in/reader030/viewer/2022020916/61b3e149726acb06c85f7a58/html5/thumbnails/81.jpg)
References:1. Analysis, Synthesis, and Design of Chemical
Processes by Richard Turton, et al.2. Chemical Process Simulation by Asghar Husain.3. Computer Applications in ChE by H. Th. Bussemaker.4. Modeling and Simulation in ChE by R. G. E. Franks.5. Process Modeling, Simulation and Control for
Chemical Engineers by W. L. Luyben.6. Chemical Process Computations by Raghu Raman.7. Elementary Principles of Chemical Processes,
Chapter 10, by Richard M. Felder and Ronald W. Rousseau, 2nd Ed.
8. CHEMCAD (CC-5) user guide.