458.401 Process & Product Design
13
Jong Min Lee
School of Chemical and Biological Engineering Seoul National University
Synthesis of a Process Using a Simulator and
Simulator Troubleshooting
Simulator Troubleshooting 13
Introduction
• A process simulator typically handles batch, semi-batch, and continuous processes
• Blind use of simulators can be potentially dangerous
• This lecture emphasizes the general approach to setting up processes and
• Highlights some of the common problems that process
simulator users encounter and offers solutions to these
problems
3
Select Thermodynamic Model
Select Units and Select Feed Stream Properties
Select Equipment Parameters
Select Convergence Criteria and Run Sim.
Select Output Display Options
Component Database Thermodynamic
Model Solver Flowsheet
Builder Unit Operation
Block Solver Data Output Generator
Flowsheet Solver
Select Chemical Components
Input Topology of Flowsheet Basic Computational Elements
in Process Simulator Simulation Problem
Simulator Troubleshooting 13
Sequential Modular Approach
• Groups the equations describing the performance of equipment units and solves them in modules
• Most widely used, e.g., Aspen Plus
• Each piece of equipment is solved in sequence
• The output from a given piece of equipment, along with
specific information on the equipment, becomes the input to the next piece of equipment
• For a process with recycle streams, tearing of recycle
streams and iterations are involved
5
A B C D E F
1 2 3 4 5 6 7
8 9 r
A B C D E F
1 2 3 4 5 6 7
8 9
r2 r1
Tear Recycle Streams
Simulator Troubleshooting 13
Input Data: Chemical Components
• Simulators will have a databank of many components
• All components (inerts, reactants, products, by-products, utilities, and waste chemicals) should be identified
• Chemicals unavailable in the databank can be added (user-
added components)
• Simulators use both pure component and mixture properties
- viscosity, thermal conductivity, diffusivity, enthalpy, fugacity, K-factors, critical constants, density, M.W., surface tension, etc.
• Expert systems to help the user select the appropriate model
- But, not recommended
• A moderately complex simulation will use at least two
different thermodynamic packages for different parts of the flowsheet
7
Simulator Troubleshooting 13
Example 13.1 HCl absorber (T-602)
13
12 11
10
lps E-607
10a
T-602
Propylene, HCl H 2 O
H + , Cl - , H 2 O
Phase Component Flows (kmol/h)
SRK Model PPAQ Model
Stream 12 Liquid
Stream 13 Vapor
Stream 12 Liquid
Stream 13 Vapor
Propylene 0.05 57.48 — 57.53
Ally Chloride 0.01 — 0.01 —
Hydrogen Chloride 0.91 18.78 19.11 0.58
Water 81.37 0.63 81.88 0.12
Total 82.34 76.89 101.00 58.23
Input Data: Topology and Feed Stream
• Selection and Input of Flowsheet Topology
- Every time a stream splits or several streams combine, a simulator equipment module (splitter or mixer) must be included
- Care must be taken when connecting batch and continuous unit operations
• Feed Stream Properties
- Feed with n components, 1 or 2 phases: n + 2 specifications
- If the feed is a single component and contains 2 phases
‣ T and P are not independent
‣ Vapor fraction (vf) and T or P are specified
- Vf can be used to specify a two-phase multicomponent system, but not recommended
- Use the vf to define feed stream only for saturated vapor (vf = 1), saturated liquid (vf = 0), and two-phase, single-component (0 < vf < 1) streams; All other streams should be specified using the T and P
9
Simulator Troubleshooting 13
Input Data: Equipment Parameters
• Level 1 Simulation
- Minimum data are supplied to solve material and energy balances
• Level 2 Simulation
- Do as many of the design calculations as possible; more input data than Level 1
Heat Exchanger
Process Stream In Process Stream Out
Outlet Condition of Process Stream
Duty
Heat Exchanger
Process Stream In Process Stream Out
Outlet Condition of Process Stream Utility Conditions
Heat Transfer Coefficients Exchanger Effectiveness Factor
Duty
Heat Exchanger Area
Utility Flowrate
• Pumps
- Desired P of the fluid leaving the pump or desired +△P
• Compressors and Turbines
- Desired P of the fluid leaving the pump or desired +△P
- Mode of compression or expansion: adiabatic, isothermal, or polytropic
• Heat Exchangers
- Single process stream, Fired Heaters
‣ Exit process stream (exit P and T - single phase exit condition or exit P and vf - two phase exit condition)
- Two or multiple process streams (e.g., heat integration)
‣ Exit conditions for both streams
‣ Be aware of the possibility of temperature crosses: check the T profiles
11
Simulator Troubleshooting 13
Input Data: Equipment Parameters
• Mixers: simple tees in pipes
- Outlet pressure or pressure drop at the mixing point (very small)
- If feed streams enter the mixer at different pressures, the outlet stream is assumed to be at the lowest pressure of the feed streams (little error in MEBs) — correct analysis in Section 22.4
• Splitters
- Outlet pressure or pressure drop across the device
- Relative flows of the output streams
• Valves
- Either the outlet pressure or pressure drop
Input Data: Equipment Parameters
• Reactors
- Stoichiometric Reactor
‣ # and stoichiometry of the reactions, T, P, conversion of the limiting reactant
‣ Reactor configuration (PFR, CSTR) is not required because no estimate of reactor volume is made. Only basic MEBs are performed
- Kinetic (Plug Flow and CSTR) Reactor
‣ Kinetic expressions are known
‣ # and stoichiometry of the reactions,
‣ Kinetic constants (Arrhenius rate constants, Langmuir-Hinshelwood, etc.), and
‣ Reactor configuration (PFR, CSTR) is required
‣ Cooling and heating of reactants may be available to generate T profiles in the reactor
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Simulator Troubleshooting 13
Input Data: Equipment Parameters
• Reactors
- Equilibrium Reactor
‣ # and stoichiometry of the reactions and
‣ Fractional approach to equilibrium are required
‣ Equilibrium constants as f(T) may be required for each reaction or may be calculated directly from information in the DB
- Minimum Gibbs Free Energy Reactor
‣ Another common form of the equilibrium reactor
‣ Outlet stream composition is calculated by a free energy minimization technique
‣ Usually data are available from the DB
‣ The only input data: list of components that one anticipates in the output from the reactor
‣ Equilibrium conversion: infinite residence time
• Reactors
- Batch Reactor
‣ Similar to kinetic reactor (requires the same kinetic input)
‣ The volume of the reactor is specified
‣ The feeds, outlet flows, and reactor T (or heat duty) are scheduled (i.e., specified as time series)
• Which reactor to choose?
- Start with the least complicated reactor that will allow the heat and material balance to be established
- The reactor module can always be substituted later with a more complex one
- Make sure you choose a correct ________ reactant when specifying a desired conversion
15
Simulator Troubleshooting 13
Input Data: Equipment Parameters
• Flash Units: single-stage VLE calculation
- In order to specify completely condition of the two output streams (liquid and vapor), two parameters must be input
- Many possible combinations
‣ T and P, T and heat load, or P and mole ratio of vapor to liquid in exit streams
- The flash module is a combination of two pieces of physical equipment: phase separator and heat exchanger
- Can serve as a surge or storage vessel for batch operation
Input Data: Equipment Parameters
• Distillation Column
- Rigorous methods: ________________ calculations
- Shortcut methods: Fenske and Underwood relationships using key components
‣ DSTWU (Aspen Plus)
• Winn method for N min
• Underwood method for R min
• Gilliland to relate actual # of stages and RR
- Use shortcut first to get preliminary design calculations
- In both methods, duties of the reboiler and condenser are carried out. Detailed design of these heat exchangers (area calculations) often cannot be carried out during the column simulation
17
Simulator Troubleshooting 13
Input Data: Equipment Parameters
• Distillation Column: Shortcut (e.g., DSTWU in Aspen Plus)
- Inputs
‣ Identification of the key components to be separated
‣ Fractional recoveries of each key component in the overhead product
‣ Column pressure and pressure drop
‣ The ratio of actual to minimum reflux ratio
- The simulator will estimate the number of theoretical plates
required, the exit stream conditions (bottom and overhead
products), optimum feed location, and the reboiler and
condenser duties
• Distillation Column: Rigorous (e.g., RADFRAC in Aspen Plus)
- Inputs: total # of specs = # of products (top, bottom, and side streams)
‣ # of theoretical plates
‣ Condenser and reboiler type
‣ Column pressure and pressure drop
‣ Feed tray location and side product locations (if needed)
- Tray-to-tray equilibrium calculations can be handled for several hundred stages
- This can be used to simulate accurately other equilibrium staged devices, for example, absorbers and strippers
• Batch distillation: similar to the rigorous module, except that feeds and product draws are on a schedule
19
Simulator Troubleshooting 13
12
11 10
19
mps
P-102 A/B E-104
42 20 1
V-102 cw
13 T-101
15
E-106
Benzene 99.6 mol%
Component Stream 10 Stream 15 Stream 19 Stream 11
Hydrogen 0.02 — 0.02 —
Methane 0.88 — 0.88 —
Benzene 106.3 105.2 — 1.1
Toluene 35.0 0.4 — 34.6
Example 13.2 Benzene Recovery Column
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Specification 1
Key components: Benzene and Toluene Top composition: Benzene 99.6 mol%
Recovery of toluene in the bottoms is 0.98
Specification 2
Top composition: Benzene 99.6 mol%
Recovery of benzene in the bottoms is 0.01
Violates the MB
Do not violate the MB
Make sure your specifications do not violate the MB
Simulator Troubleshooting 13
Input Data: Equipment Parameters
• Absorbers and Strippers
- Usually simulated using the rigorous distillation module
- Condensers and reboilers are not normally used
- Two feeds
• Liquid-Liquid Extractors
- A rigorous tray-by-tray module is used to simulate this multistage equipment
- Thermodynamic model for two liquid phases (appropriate
liquid-phase activity coefficients)
• Ill-posed problem. This normally means that an equipment specification has been given incorrectly .
• Too tight tolerance
• The number of iterations is not sufficient for convergence.
This occurs most often with many recycle streams.
- Remove as many recycle streams as possible and add the recycle streams back, one by one, using the results from the preceding simulation as the starting point for the new one.
(Read 13.3)
23
Simulator Troubleshooting 13
Physical Properties Estimation - Pure Component Properties
• 3 Most Fundamental Fixed Properties
- Molecular weight
- Standard liquid density
- Normal boiling point
• Benzene, Toluene
Pure Component Properties - Critical Point
25
What is a critical point?
A maximum point at which vapor and liquid phases coexist with each other
Gas vs. Vapor
Gas: H2, O2, N2, CO, CO2, or CH4
Vapor (증기 - 증발된 기체): Water, Benzene, Toluene, Xylenes, …
액상이 base에 있어야 함
(임계점이 매우 낮은 온도, 일반 온도에서 대부분 초임계 상태. 기상-액상 공존 X)
Z c = v real
v ideal = p c v c RT c
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임계압축인자
Simulator Troubleshooting 13
Critical Properties of CO 2
Tc: 304.21 K
Pc: 7,383 kPa
Vc: 0.094 m 3 /kmol
Zc: 0.274
27
Estimated overhead vapor product compositions at column top are: CH 4
65 mol%, C 2 H 6 15 mol%, C 3 H 8 15 mol%, and i-C 4 H 10 5 mol%
If reflux drum operating temperature is 45℃, estimate reflux drum
operating pressure. Use Peng-Robinson EOS model for your simulation
If you cannot get a converged solution, explain the reason
Estimate pseudo critical temperature for the above 4 component mixture
Example-01
Simulator Troubleshooting 13
Peng-Robinson
NRTL
29
Simulator Troubleshooting 13
Components Tc [℃] Mole Fraction
C1 -82.59 0.65
C2 32.17 0.15
C3 96.68 0.15
iC4 134.99 0.05
Tcm -27.61
Pseudo Critical Temperature = -27.6039 ℃
Pseudo Critical Pressure = 45.3975 bar
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Simulator Troubleshooting 13
Pure Component Properties
Standard heat of reaction from heat of formation Heats of formation
Enthalpy of formation: Standard heat of formation Gibbs free energy of formation
From the standard heat of formation of each component, estimate standard heat of reaction
CH 4 + 2O 2 = CO 2 + 2H 2 O
Heat of Formation
33
Simulator Troubleshooting 13
Heat of Reaction
35
Component 𝛥H f [kJ/kmol]
CH 4 -74,520
O 2 0
CO 2 -393,510
H 2 O -241,810
𝛥H 0R (25℃) CH 4 + 2O 2 = CO 2 + 2H 2 O -802,610
Simulator Troubleshooting 13
Physical Properties Estimation - Pure Component Properties
• Temperature-Dependent Properties (열역학적 물성)
- Vapor pressure (liquid phase property)
- Enthalpy (열함량) for gas, liquid, and solid
- Idea gas heat capacity (열용량, 비열) (function of temperature)
- Heat of vaporization (증발 잠열)
- Densities for gas, liquid, and solid
• Transport Properties (전달 물성)
- Viscosity, thermal conductivity, diffusion coefficient, surface
tension (역시 온도 의존)
Vapor Pressure (액체의 증기압)
• Method 1: Clausius-Clapeyron Equation
• Method 2: Equation of state - ⍵ (accentric factor) or Twu’s Alpha Function 이용
• Method 3: Antoine Equation (매개변수 개수가 simulator에 따라 다를 수 있음)
37
ln
✓ P vap P 0
◆
= H vap R
✓ 1 T
1 T b
◆
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_______________
Simulator Troubleshooting 13
Choosing Thermodynamic Model
• If Tc and Pc are known for each pure component, the parameters for simple, cubic equations of state can be estimated.
• Pure-Component Properties
- Density, viscosity, thermal conductivity, and heat capacities are generally available in simulator.
- GCM is reasonably good for estimation
• Enthalpy
- Although the pure-component heat capacities are calculated with acceptable accuracy, the enthalpies of phase changes often are not.
- If △Hvap is an important part of a calculation, simple EOS should not be used. In fact, “latent heat” or “ideal” options would be better.
- If the substance is above or near its Tc, EOS must be used. However,
the user must beware, especially if polar substances such as water are
present
39
of 500 kg/h of water entering at 70℉. Assume atmospheric pressure
H2 22.72 kg/h
N2 272.24
CO 268.40
HCl 26.84
Perform a simulation to determine the final temperature of the cooled gas stream with the default thermodynamic model and with the ideal model.
PR or SRK gives an outlet temp of 480℉. The ideal model gives an outlet temp of 348℉. The value calculated by the ideal model is closer to reality in this case because the EOS do a poor job of estimating the enthalpy of vaporization of water, which is the most important property for the energy balance.
The ideal model uses the experimentally determined value of this enthalpy of vaporization (from the DB)
Simulator Troubleshooting 13
Phase Equilibria
• PE is sometimes called the fugacity coefficient, K-factor, or fluid model.
• Whenever possible, phase-equilibrium data should be used to regress the
parameters in the model, and the deviation between the model predictions and the experimental data should be studied.
• EOS: an algebraic equation
- Pressure of mixture = f (composition, volume, temperature)
- Through standard thermodynamic relationships, the fugacity, enthalpy, etc. for the mixture can be determined
- These properties can be calculated for any density; therefore, both liquid and vapor properties, as well as supercritical phenomena, can be determined
f i v = v i y i P
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f l i = l i x i P
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Phase Equilibria
• Activity-coefficient models: can only be used to calculate liquid-state nugacities and enthalpies of mixing
- 𝛾 i = f (composition, temperature)
- Cannot be used for supercritical or non condensable
components because it is a correction factor for ideal-solution model (Raoult’s law)
41
f i l = i x i f i 0
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Simulator Troubleshooting 13
Equations of State
• Recommended for simple systems (nonpolar, small molecules) and in regions where activity-coeff. models are inappropriate.
• Default fugacity model: Soave-Redlich-Kwong (SRK) or Peng- Robinson (PR)
- Normally use three pure-component parameters per
substance and one binary-interaction parameter per binary pair
- Give qualitatively correct results even in the supercritical region
- Poor predictors of enthalpy changes except for light hydrocarbons and they are not quantitatively accurate for phase equilibria
- Good for systems containing hydrocarbons and light gases
43
The simplest EOS is an ideal gas law, a combination of Boyle and Charle’s law
P v = RT
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(pressure-explicit form)
Why pressure-explicit form?
ln ˆ v i = 1 RT
Z v v 1
"✓
@P
@n i
◆
T,V,n j 6=i
RT V
#
dV ln Z v
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ln ˆ l i = 1 RT
Z v l 1
"✓
@P
@n i
◆
T,V,n j6=i
RT V
#
dV ln Z l
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Simulator Troubleshooting 13
Ideal Gas Law
• Assumptions
- 1st assumption
‣ Molecules have no size
‣ As T approaches zero or P approaches infinity, V equals zero
- 2nd assumption
‣ Molecules do not interact with each other
‣ They never condense to liquefy
van der Waals EOS
45
https://ko.wikipedia.org/wiki/요하너스_디데릭_판데르발스
The van der Waals theory (1873) assumes
molecules have finite limiting volume b and attract one another according to a/v 2
• Molecules have finite size
• ‘b’: Liquid molar volume
• Molecules to interact with each other
• ‘a/V 2 ’: attractive pressure (a: energy parameter) (b: size parameter)
1910 노벨상 수상
Simulator Troubleshooting 13
Step 1
Real gas has finite size since it liquefies whereas ideal gas has no size when the pressure approaches infinity or temperature goes to
absolute zero point
v real = v ideal + b = RT P + b
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P = RT v b
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47
Pressure exerted by real gas is less than P = RT/(v-b) by a/v 2 due to the existence of intermolecular forces
P = RT
v b C 1 ⇥ C 2
<latexit sha1_base64="8bCxjK0IOMIq6JTjn5EPRr3uds0=">AAACDnicbVDLSsNAFJ3UV62vqEs3g6XgxpJUQRcKhW5cVukLmhAm00k7dDIJM5NCCfkCN/6KGxeKuHXtzr9x2mahrQfucDhnLvfe48eMSmVZ30ZhbX1jc6u4XdrZ3ds/MA+POjJKBCZtHLFI9HwkCaOctBVVjPRiQVDoM9L1x42Z350QIWnEW2oaEzdEQ04DipHSkmdWmvAWOoFAOH1oZekEnkM/00/Ds6GjaEikpjXPLFtVaw64SuyclEGOpmd+OYMIJyHhCjMkZd+2YuWmSCiKGclKTiJJjPAYDUlfU470IDedn5PBilYGMIiELq7gXP3dkaJQymmo96yESI3ksjcT//P6iQqu3ZTyOFGE48WgIGFQRXCWDRxQQbBiU00QFlTvCvEI6WyUTrCkQ7CXT14lnVrVvqjW7i/L9Zs8jiI4AafgDNjgCtTBHWiCNsDgETyDV/BmPBkvxrvxsfhaMPKeY/AHxucPCVCZjQ==</latexit>
공간 내 분자 밀도와 관련
/ n 1
v ⇥ n 2
v = a v 2
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논문 제목: On the continuity of vapor phase into condensed liquid phase with a same tool; equation of state
증기상, 액상, 증기+액상 공존을 모두 ___________으로!
Simulator Troubleshooting 13
Vapor Pressure of CH 3 Cl at 322K with vdw EOS
Terms Value
Tc (K) 416.3
Pc (atm) 65.9
P vap (322K) 10.49
R 0.08206
T (k) 322
a = 27
64 ⇥ R 2 T c 2 P c
= 27
64 ⇥ (0.08206) 2 (416.3) 2
65.9 = 7.4709
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b = RT c
8P c
= (0.08206)(416.3)
(8)(65.9) = 0.0648
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P = RT v b
a
v 2 = (0.08206)(322) v 0.0648
7.4709
v 2 = 26.42 v 0.0648
7.4709 v 2
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49
Pressure
Volume
v vap
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v
<latexit sha1_base64="AFlBHlAZN6hmZ9SpWxZYLSn0k/Y=">AAAB7nicbVDLSgNBEOyNrxhfUY9eBoPgKexGQfEU8OIxgnlAsobZySQZMju7zvQGwpKP8OJBEa9+jzf/xkmyB00saCiquunuCmIpDLrut5NbW9/Y3MpvF3Z29/YPiodHDRMlmvE6i2SkWwE1XArF6yhQ8lasOQ0DyZvB6HbmN8dcGxGpB5zE3A/pQIm+YBSt1Bw/plI8TbvFklt25yCrxMtICTLUusWvTi9iScgVMkmNaXtujH5KNQom+bTQSQyPKRvRAW9bqmjIjZ/Oz52SM6v0SD/SthSSufp7IqWhMZMwsJ0hxaFZ9mbif147wf61nwoVJ8gVWyzqJ5JgRGa/k57QnKGcWEKZFvZWwoZUU4Y2oYINwVt+eZU0KmXvoly5vyxVb7I48nACp3AOHlxBFe6gBnVgMIJneIU3J3ZenHfnY9Gac7KZY/gD5/MHvVWPzg==</latexit>liq
P vap = 21.9 atm > 10.4 atm
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21.9
Simulator Troubleshooting 13
Equations of State
Peng-Robinson EOS
P = RT V b
a
V (V + b) + b(V b)
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with the van der Waals mixing rules,
a = X
i
X
j
z i z j p a i a j (1 k ij )
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b = X
i
x i b i
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BIP (Binary Interaction Parameters)
fugacity for phase equilibrium dG = V dP
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ln f 2 f 1 =
Z p 2
p 1
V RT dP
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e.g.) @ constant T
There are usually six to ten EOS choices, and a few mixing-rule choices
51
Temperature: 225K, Pressure: 60.78 bar Feed flowrates:
Carbon dioxide 6 kmol/h Hydrogen sulfide 24 kmol/h
Methane 66 kmol/h Ethane 3 kmol/h Propane 1 kmol/h
DB BIPs Zero BIPs
Peng-Robinson 52.0 kmol/h 32.5 kmol/h
SRK 60.1 kmol/h 50.5 kmol/h
Simulator Troubleshooting 13
Liquid-State Activity-Coefficient Models
If the conditions are far from the critical region of the mixture or that of the major component, and if experimental data are available for the VLE or LLE, a liquid-state activity-coefficient model is a reasonable choice
ˆ v
i y i P = P i ⇤ x i i ⇤ i exp 1 RT
Z P
P i ⇤
v l i dP
!
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The most frequently-used activity coefficient models are the Wilson, NRTL, and UNIQUAC
i = ˆ a i x i 6= 1
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