1E202 Module 12 Computeraided balance calculations

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1E202Module 12Computer-aided balance
calculations
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This Week

• Degrees of freedom revisited...
• Single process unit
• Multiple-unit process
• Sequential modular simulation
• Cyclic systems and the converging block
• Design specifications
• Equation-based simulations
• Commercial process simulation packages
• Final comments

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Degrees of freedom revisited

• If the number of degrees of freedom ndf gt 0
• You have ndf more unknowns than equations
• Therefore you must specify ndf variable values
• These externally specified variables are called
  design variables
• The ones that are calculated from the system are
  state variables

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Single process unit
m1 kg O2 40oC 1 atm
MIXER- HEATER
m4 kg O2 m5 kg N2 50oC 1 atm
m2 kg O2 m3 kg N2 25oC 1 atm
6 variables -3 relations 3 DOF
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Is equivalent to
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Is equivalent to
m1 (kg O2) 0 kg N2 40oC 1 atm
m4 (kg O2) m5 (kg N2) 40oC 1 atm
m6 (kg O2) m7 (kg N2) T1 (oC) 1 atm
m2 (kg O2) m3 (kg N2) 25oC 1 atm
So, 3 specifications would have to be provided in
the problem statement, and only 3! For example
m1, m2, m3 or m1, m4, m5 or m2, m3, m4 or m6, m7,
T1 or
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Choosing your design variables

• It is best to choose your design variables once
  you know what your equations look like, so that
  the resulting set of equations is efficient to
  solve.
• Some sets of design variables are not allowed,
  e.g. m1, m2, m4 which would fully define the
  amount of oxygen going in, but also the amount of
  oxygen coming out. So you would over-specify some
  mass balances, and under-specify others (the
  nitrogen one).

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Multiple-unit process

• In fact, we already solved the last single-unit
  as a multi-unit process.
• So we can apply it to a more complex multi unit
  process in an identical manner!

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Example Methanol production

• Methanol produced from CO and H2 according to
  CO2H2?CH3OH
• Fresh feed contains CO and H2 in stoichiometric
  proportions
• Fresh feed enters at 2.2. m3/s at 25oC and 6 MPa
• Feed combines adiabatically with a recycle stream
• Combined stream is heated to 250oC and fed to the
  reactor
• Reactor effluent exits at same temperature, is
  cooled to 0oC at 6 MPa
• This cooling partially condenses methanol
• The gas leaving the condenser is saturated with
  methanol
• 1 of gas stream is taken off for monitoring, the
  rest is recycled.
• Overall conversion of CO 98
• The ratio of H2 to CO is 2 mol H2/1mol CO
  everywhere in the process
• Ideal gas behaviour may be assumed.

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Multiple-unit process - DOF example
CO2H2?CH3OH Overall conversion of CO 98
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Degrees of freedom - Method 1

• Mixing point
• 6 Unknown variables.
• 4 Relations.
• 2 local DOF
• Preheater
• . Unknown variables
• . Relations
• . Local DOF
• Reactor
• . Unknown variables
• . Relations
• . Local DOF

• Condenser
• . Unknown variables
• . Relations
• . Local DOF
• Purge point
• . Unknown variables
• . Relations
• . Local DOF
• Process
• . Local DOF
• . Ties (variables counted more than once)
• . Additional relation(s)
• . Total DOF

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Degrees of freedom Method 2
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Degrees of freedom Method 3
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Degrees of freedom - Method 1

• Mixing point
• 6 Unknown variables n0, n1, n2, n3, n6, Ta
• 4 Relations 2 mass, 1 energy, ideal gas eq
• 2 local DOF
• Preheater
• 4 Unknown variables n1, n2, Ta, Qh
• 1 Relation 1 energy balance
• 3 Local DOF
• Reactor
• 5 Unknown variables n1, n2, n3, n4, Qr
• 3 Relations 2 mass, 1 energy balance
• 1 Reaction (additional unknown var. xr)
• 3 Local DOF

• Condenser
• 5 Unknown variables n3, n4, n5, n6, Qc
• 3 Relations 1 mass, 1 energy, satur. cond.
• 2 Local DOF
• Purge point
• 2 Unknown variables n3, n6
• 0 Relations
• 2 Local DOF
• Process
• 12 Local DOF
• 11 Ties (variables counted more than once)
• 1 Additional relation CO conversion98
• . Total DOF

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Degrees of freedom Method 2
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Degrees of freedom Method 3
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Sequential Modular Simulation

• Process flowchart reconstructed in blocks or
  modules and connecting streams
• MIX mix several inlet streams adiabatically to
  form one product stream
• SPLIT split a single inlet into two or more
  product streams with same composition
• COMPRESS raise pressure of a gas by a specified
  amount
• PUMP raise pressure of a liquid
• REACT simulate the chemical reactor
• FLASH convert a liquid stream to liquid and
  vapor streams in equilibrium at a lower pressure
• SEPARATE separate a stream to multiple product
  streams (specify split fractions or composition),
  simulate separation according to physical laws
  for
• DISTILL
• EXTRACT
• CRYSTAL
• ABSORB

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Sequential Modular Simulation

• Balance (and other) equations for each block are
  written and solved
• simulation program contains subroutines for each
  type of block
• If no recycle streams, calculation moves from one
  unit to another
• e.g. CALL MIX (M1, S1, S2, S3)
• M1 is the label of the unit
• S1, S2 are the inlets
• S3 is the outlet
• If there is a cycle, a trial and error procedure
  is required
• values of stream variables in the cycle are
  assumed ( tear stream)
• balance equations for units in the cycle solved,
  until
• values of the assumed variables are recalculated
• new variable values are assumed
• procedure repeated until assumed and calculated
  values agree
• This tearing trial-and-error step uses a
  CONVERGENCE block

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Example structure of a mixing block

• Two streams are mixed adiabatically
• Each stream may contain 5 components
• No phase change
• Heat capacities of components may be taken as
  constants
• Heat of mixing may be neglected
• 1) Write equations for the product stream
  component flow rates and temperature
• Material balances Energy balance

2) Create a spreadsheet that would determine the
product stream variables
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Example continued
2) Create a spreadsheet that would determine the
product stream variables
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Simulation of an acyclic process

• Using the blocks MIX, HEAT, PUMP, DISTILL, CNDNS,
  PUMP construct a block diagram for the simulation
  of this process, labelling the streams and
  blocks. Indicate the sequence of subroutines with
  the inputs outputs

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Simulation of an acyclic process

• Call MIX (M1, S1, S2, SA)
• Call MIX (M2,SA, S3, S4)
• Call PUMP (P1, S4, S5, parameters)
• increases the pressure of the liquid stream by a
  specified amount
• Call HEAT (H1, S5, S6, parameters)
• calculates the heat input required to achieve the
  temperature change
• Call DISTILL (ST1, S6, S7, S8, parameters)
• solves material and energy balances to determine
  product stream flow rates, and the heat
  requirement
• Call CNDNS (S7, S9, S10, parameters)
• much the same as distill

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Cyclic systems and the convergence block

• Imagine you know all the variables for S1 and you
  want to calculate the rest.
• The procedure outlined before will not work as
  the calculation cannot start
• To solve B1 need to know S5, hence B3, hence S3,
  B2, S2, B1, ..
• Calculating the whole process by hand is possible
  (n unknowns, n equations)
• Need iterative procedure assume variable values
  for a stream within the cycle this is called
  tearing the cycle
• Solve the system if the assumed and calculated
  tear stream variables agree within a specified
  tolerance, the solution is complete
• If not use the new values, or some combination to
  initiate another iteration introduce a
  convergence block

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Simulation of a cyclic system
Example 10.2-3 FR

• Gas-phase dehydrogenation of isobutane to
  isobutene C4H10 ? C4H8 H2

Once you built the flowsheet 1) iterate n4a
until you find n4an4c (or get there using the
solver) 2) iterate T1 until you find DHmix0
(adiabatic mixing, could also use solver)
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Multiple recycle loops

• You could tear S3 and S8
• then you need two convergence blocks
• hence simultaneous solution of 2 iterative loops
• Instead you could tear S5
• this decreases computation time

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Multiple recycle loops

• Three cycles
• S2-S3-S4-S5
• S3-S4-S6-S7-S8
• S7-S9-S11
• Many ways to tear e.g. S2 and S9, S7 and S5, S4
  and S7, ..
• Techniques exist to determine systematically
• how many streams need to be torn
• which combination would give you most efficient
  calculation

Tutorial Thursday
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Design specifications

• Thusfar weve calculated output from given input
  and process parameters (P, T etc.)
• It often happens that you must design a process
  to achieve a certain output variable
• Possible through design specifications
• e.g. component specifications of an output stream
  of a Flash evaporator will provide the required
  pressure to achieve that.
• Achieved through and artificial cycle, varying P
  (the manipulated variable) until the calculated
  output variable (the sampled variable) within
  tolerance of desired value

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Design specifications
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Equation based simulation

• Disadvantages associated with sequential modular
  method
• forward calculation mode only, whereas
• engineers frequently must design feeds or process
  parameters based on product specifications
• In equation based approach
• The equations for all units are collected and
  solved simultaneously
• May be cumbersome and time consuming, but
  powerful software exists
• Maple , Mathematica , Matlab , Mathcad ,
  E-Z-Solve

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Simulation of an equilibrium reaction/separation
process

• C2H6 ? C2H4H2
• C2H6 ?C2H22H2
• Reactions take place at 977oC and 1 atm
• Equilibrium conditions are
• Separation process recycles 95 of the unreacted
  Ethane

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Equilibrium reaction/simulation process
Equations (extra unknowns extents of reaction
x1, x2 and total moles in reactor
ntot) 1) 2) 3) 4) 5) 6) 7) 8) 9) 10)
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Equilibrium reaction/simulation process
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Commercial Process Simulation Packages

• ASPEN PLUS (Aspen Tech)
• CHEMCAD (Chemstations)
• HYSYS (Hyprotech)
• DESIGN II (WinSim)
• PROVISION (Simulation Sciences)
• Frequently include physical property tables and
  equations
• May include calculation of unit size
• Some allow (size dependent) cost prediction of
  specific unit types
• Equation-based simulators not commercialised to
  same extent

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Final comments

• Whether you calculate by hand, spreadsheet,
  Fortran program or ASPEN, its only possible is
  the process has zero degrees of freedom!
• If it has more, you must select as many design
  variables as there are degrees of freedom.
• Pick design variables so as to minimise the
  number of cycles in the flow chart
• For flow charts with cycles, tear as many cycles
  as possible with minimum number of tear streams
• Dont believe the initial results of a
  simulation check some variables manually!