SAJJAD KHUDHUR ABBASCeo , Founder & Head of SHacademyChemical Engineering , Al-Muthanna University, IraqOil & Gas Safety and Health Professional – OSHACADEMYTrainer of Trainers (TOT) - Canadian Center of Human Development

Episode 48 : Computer Aided Process Engineering Simulation Problem

Flowsheet for cyclohexane production - What are we solving?

C6 H6 = 100

C-1T=422.2 K P = 33.3 atm

Recycle H2

T=330 K P = 34 atm

M-1

T=322 K P = 31.6 atm Purge gas

D-1

SP-1

E-2Isothermal reactor

T=497.2 K

P=1 atm

E-3Other data: R-1 (heat of reaction, conversion,

reference compound), E-1 (U & A), SP-1 (purge rate)

Condition: H2/C6H6 in reactor feed=12 methane/H2 balance for purge

R-1

E-1

mixer

T=322 K

P=0.5 atmH2 = 97.5CH =2.54

Cyclohexane product

The objective is to fill-out all the stream summary table!

All stream is defined by NC+2 variables (component flows, T & P)

Variables Streams

S1 S2 S3 S4 S5 ……. S13f1

f2

f3

f4

T

P

The objective is to fill-out the stream summary table! Which stream variables are known? x indicate a specified variable.

Number of equations = 11 (NC+2); number of variables = 13 (NC+2); degree of freedom = 2 (NC+2)

Variables Streams

S1 S2 S3 S4 S5 ……. S13f1 x x

f2 x x

f3 x x

f4 x x

T x x

P x x

Steady State Simulation Approaches

E-1

E-2

E-3

R-1

SP-1

D-1

C-1

variables Solvex

M-1

x

x Equation Oriented

x

equations

x

x represents variables of the connecting streamsx

x

x

M-1 E-1 E-2 R-1 E-3 D-1 SP-1 C-1

Flowsheet Decomposition

* Identify partitions* Identify recycle-loops

* Determine tear-streams* Determine calculation order

Equation Ordering* Rearrange model equations

* Identify partitions* Determine sparse pattern

Flowsheet decomposition & equation ordering

E-1

E-2

E-3

R-1

SP-1

D-1

C-1

variables Convergence procedure*

M-1

x k+1 = x k -F / J*

*

*

equations*

the connecting streams*

*

Calculation order*

M-1 E-1 E-2 R-1 E-3 D-1 SP-1 C-1

How many partitions ?

How many recycle loops ?

How many tear streams and which are they ?

Flowsheet Decomposition

Flowsheet Decomposition

How many partitions ? 2

How many recycle loops ? 1

How many tear streams and which are they ? 1 ; any stream from 2,3,4,7

Solve, for tear-stream = 2, unit 2, unit 3, unit 4,unit 1; after convergence,solve unit 5

Modul ar approach versus equation orient ed approach

Sequential Modular Approach EquationOrientedApproachSimulate one unit model at a time

Solve all unit models together

Decompose flowsheet Order equationsIterate in tear streams Update all unknown

variables simultaneously

Less flexible but more robust More flexible but less robustInitialization is important Initialization is very important

Storage requirement not high Storage requirement can be very high

Flow-diagram for Sequential Modular Approach

Simultaneous Modular Approach

Generate linear model parameters

Solve with rigorous model

Generate new model parameters

Check results from inner-loop with outer-loop

Determination of recycle-loops and partitions

The first step is to determine the existence of recycle loops and partitions (algorithm of Sargent and Westerberg) –

1) Trace from one unit to the next by following the direction of the unit output streams, one after the other. Stop when,a) A unit reappears. In this case, collect all the units traced so far into one

group.b) A unit with no linked output is encountered

2) Count the number of different groups of units. Each group of units represents a partition.

3) Identify groups with a single unit. Add each of these groups to the list of partitions.

Tear-stream determination and calculation order

•Algorithm2(Gundersen)

•Foreachpartition, performthefollowing,

1. Removeall streamsthat arenot includedinrecycleloops.2. Calculatetheratioofnumberofvariablesper(output streams)/(input

streams).3. Tear all input streams tothe unit (node) whichhas the largest ratioof

number of variablesper(output streams)/(input streams).4. Repeat fromstep1until everyloophasbeentorn.

Convergence Techniques (Modular)Method

JSuccessivesubstitution

IWegstein

D=diag{d}; djj =(yj –yj

)/(hj –hj )

i i -1 i i -1

Dominant Eigen-value

1/(1-) I; =(wi –wi -1)/( yi

–yi -1)Broydon’s rule

Full matrixQN–update(see3.2.3.3)Newt

on[F( yi )/ y] –1

Table 3.1: The formof Jthat canbeusedinequations 3.35–3.36for different convergence techniques.

Equation for tear-h (y) = y - w = 0

y i+l = y i – J h (y i)

stream convergence

Update method

Choice of the method defines J

Convergence Techniques (Equation Oriented)

Method

JSuccessivesubstitution

IWegstein

D=diag{d}; djj =(yj –yj

)/(hj –hj )

i i -1 i i -1

Dominant Eigen-value

1/(1-) I; =(wi –wi -1)/( yi

–yi -1)Broydon’s rule

Full matrixQN–update(see3.2.3.3)Newt

on[F( yi )/ y] –1

Table 3.1: The formof Jthat canbeusedinequations 3.35–3.36for different convergence techniques.

Mathematical modelF A y - b = 0

y i+l = y i – J h (y i)

of process flowsheet

Update method

Choice of the method defines J

Thanks for Watching Please follow me / SAJJAD KHUDHUR ABBAS