S2 Process Simulation Using Simulink

8/20/2019 S2 Process Simulation Using Simulink

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Process Simulation

using Simulink

Cheng-Liang ChenPSELABORATORY

Department of Chemical EngineeringNational TAIWAN University


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Chen CL 1

Process SimulationSimulation of A Gas Process

Consider the gas tank shown below. A fan blows air into a tank, and from the

tank the air flows out through a valve. Suppose the air flow delivered by the fan isgiven by

f i(t) = 0.16mi(t)

where f i(t) is gas flow in scf/min, (scf is cubic feet at standard conditions of 60oF

and 1 atm); mi(t) is signal to fan, %. The flow through the valve is expressed by

f o(t) = 0.00506mo(t)

p(t)[ p(t) − p1(t)]

where f o(t) is gas flow, scf/min; mo(t) is signal to valve, %; p(t) is pressure intank, psia; p1(t) is downstream pressure from valve, psia.


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Chen CL 2

The volume of the tank is 20 ft3, and it can be assumed that the process occursisothermally at 60oF. The initial steady-state conditions are

f̄ i = f̄ o = 8 scfm; ¯ p = 40 psia; ¯ p1 = 14.7 psia; m̄i = m̄o = 50 %

An unsteady-state mole balance around the control volume, defined as the fan,tank, and outlet valve, is

dn(t)

dt

= V

RT

dp(t)

dt

= ρ̄f i(t) − ρ̄f o(t)

ρ̄ = 0.00263 lbmoles/scf is molar density of gas at standard conditions; R = 10.73

psia-ft3/lbmoles-oR is ideal gas law constant; T = 520oR is gas temperature.

Please construct a Simulink model to simulate this process, and shows the

response of the pressure to a step change of 5% in the signal to the inlet fan

(starts from time =5 min.)


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Chen CL 3

Process SimulationSimulation of A Gas Process

V

RT

dp(t)

dt = ρ̄f i(t)− ρ̄f o(t)f i(t) = 0.16mi(t) (ρ̄ = 0.00263 lbmole/scf , V = 20 ft

3)

f o(t) = 0.00506mo(t)

p(t)[ p(t)− p1(t)]

mi(0) = m̄i = 50%, mo(0) = m̄o = 50%, p1(0) = ¯ p1 = 14.7psia

⇒ f o(0) = f i(0) = 0.16mi(0) = (0.16)(50) = 8.0 scf/min

f o(0) = 0.00506mo(0)

p(0)[ p(0)− p1(0)]

⇒ p(0) = 39.8 psia

⇒ dp(t)dt

= ρ̄RT V

[f i(t)− f o(t)]

= (0.00263)(10.73)(520)

20 [f i(t)− f o(t)]

= 0.734[f i(t)− f o(t)] (now: mi = 55% at t = 5)


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Chen CL 4

f i(t) = 0.16mi(t), dp(t)

dt = 0.734[f i(t) − f o(t)]

f o(t) = 0.00506mo(t) p(t)[ p(t) − p1(t)] f o(0) = 39.8 mi : 50 → 55%

C C


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Chen CL 5

subplot(2,1,1)

plot(dt,p,’m’,’linewidth’,2)

ylabel(’\bf p(t)’,’Fontsize’,14);

title(’\bf Gas pressure response to step fan change’,’Fontsize’,14)subplot(2,1,2)

plot(dt,mi,’b’,’linewidth’,2)

ylabel(’\bf m_i(t)’,’Fontsize’,14);

xlabel(’\bf t (min)’,’Fontsize’,14);

set(gca,’linewidth’,3);

% set(gca,’Fontsize’,14);

Ch CL 6


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Chen CL 6

Process SimulationSimulation of A Stirred Tank Heater

The stirred tank is used to heat a process stream so that its premixed componentsachieve a uniform composition. Temperature control is important in this processbecause a high temperature tends to decompose the product while a lowtemperature results in incomplete mixing. The tank is heated by steam condensing

inside a coil. A proportional-integral-derivative (PID) controller is used to control

Ch CL 7


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Chen CL 7

the temperature in the tank by manipulating the steam valve position.The feed has a density ρ of 68.0 lb/ft3, a heat capacity c p of 0.80 Btu/lb-

oF. Thevolume V of liquid in the reactor is maintained at 120 ft3. The coil consists of 205ft of 4-in. schedule 40 steel pipe, weighting 10.8 lb/ft with a heat capacity of 0.12

Btu/lb-o

F and an outside parameter of 4.500 in. The overall heat transfercoefficient U , based on the outside area of the coil, has been estimated as 2.1Btu/min-ft2-oF. The steam available is saturated at a pressure of 30 psia; it canbe assumed that its latent heat of condensation λ is constant at 966 Btu/lb. Itcan also be assumed that the inlet temperature T i is constant.An energy balance on the liquid in the tank, assume negligible heat losses, perfect

mixing, and constant volume and physical properties, results in the equation

V ρcvdT (t)

dt = f (t)ρc pT i(t) + U A[T s(t) − T (t)]− f (t)ρc pT (t)

An energy balance on the coil, assuming that the coil metal is at the same

temperature as the condensing steam, results in (C M : heat capacitance of coilmetal, Btu/oF; w(t): steam rate, lb/min)

C M dT s(t)

dt = w(t)λ− U A[T s(t) − T (t)]

The initial steady-state conditions are T (0) = 150oF and T s(0) = 230oF. Also the

Ch CL 8


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Chen CL 8

initial design conditions are f (0) = 15 ft3/min, T i(0) = 100oF, and w(0) = 42.2

lb/min.

Construct a Simulink diagram for the simulation of the heater. shows the

responses of the temperatures to a step changes in process flow.

Ch CL 9


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Chen CL 9


dT (t)dt =

1V f (t)[T i(t) − T (t)] +

UAV ρc

v

[T s(t) − T (t)], T (0) = 150oF

dT s(t)dt =

1C M {λw(t)− U A[T s(t) − T (t)]} T s(0) = 230

oF

T i(0) = 100oF, f (0) = 15ft3/min, w(0) = 42.2lb/min

Chen CL 10


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Chen CL 10


Response of heater outlet temperature and steam chest temperature

to a step change in process flow

Chen CL 11


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Chen CL 11


Subsystem Block for The Stirred Tank Heater

Chen CL 12


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Chen CL 12

Transfer Function SimulationTemperature Control of A Stirred Tank Heater (p.201)

Chen CL 13


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Chen CL 13

Transfer Function SimulationTemperature Control of A Stirred Tank Heater (p.201)

Chen CL 14


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Chen CL 14

Process SimulationSimulation of A Batch Bioreactor

Many important specialty chemical products are produced in bioreactors byprocesses such as fermentation. Most of these processes are carried out in batchmode by filling a tank with a substrate solution and inoculating it with a smallamount of biomass. The biomass, feeding on the substrate, reproduces to producethe desired product, until the substrate is consumed. This example is presentedhere to show some of the special characteristics of biochemical processes.

A dynamic model of the growth of the biomass concentration x(t) and of theconsumption of the substrate concentration, s(t), is given on a per unit volumebsis as follows:

dx(t)dt = µ(t)x(t)

ds(t)dt = −

1y(t)µ(t)x(t)

where y is the yield in biomass per unit mass of substrate and µ(t) is the biomassgrowth rate function (h−1). This growth rate function is analogous to the kineticmodels used to model chemical reactors. It is designed to match experimentaldata. Here we will use the Monod model with adaptability wich has the followingform:

dµ(t)

dt = α µ

m

s(t)

k + s(t)− µ(t)

Chen CL 15


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Chen CL 15

where α is the adaptability parameter, and k and µm are the parameters of the

model. Please use Simulink to simulate the model with the following data:

α = 15h−1, k = 0.5g/liter, s(0) = 2.5g/liter, µ(0) = µm = 1.2h−1, and

x(0) = 0.001g/liter.

Chen CL 16


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Chen CL 16

Process SimulationSimulation of A Batch Bioreactor

dx(t)dt = µ(t)x(t)

ds(t)dt = −

1yµ(t)x(t)

dµ(t)dt = α

µm

s(t)k+s(t) − µ(t)

α = 15 h−1, µ(0) = µm = 1.2

k = 0.5 g/liter, s(0) = 2.5 g/liter, x(0) = 0.001 g/liter

Chen CL 17


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Chen CL 17

Chen CL 18


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Chen CL 18

Process SimulationSimulation of A Pressure Tank

A stray bullet fired by a careless robber punctures the compressed air tank at a gasstation. The mass balance of air in the tank is

V dρ(t)

dt = wi(t) −Ao

2ρ(t)[ p(t) − po]

where

ρ(t) = M

RT p(t)

wi(t) kg/s, is the inlet flow from the air compressor, V = 1.5 m3, is the volume of

the tank, Ao = 0.785 cm2, is the area of the bullet hole, M = 29 kg/kmole, is the

molecular weight of air, R = 8.314 kPa-m3/kmole-K, is the ideal gas law

constant, and temperature T is assumed constant at 70oC, po = 500 kPa gauge.

Use Simulink to simulate the process and plot the response of the pressure in the

tank.

Chen CL 19


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Chen CL 19

Process SimulationSimulation of A Pressure Tank

Chen CL 20


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Chen CL 20

Chen CL 21


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Process SimulationSimulation of A Mixing Tank

Computer-room ExerciseConsider the mixing process shown below. Assume

that the density of the input and output streams

are very similar and that the flow rates f 1 and

f 2 are constant. It is desired to understand

how each inlet concentration affects the outlet

concentration. Develop the mathematical model.

Use Simulink to simulate the mixing process

and plot the response of the outlet concentration to a step change of 5

gallon/minute (gpm) in flow f 1. At the initial steady-state conditions the flow

from the tank is 100 gpm, and its concentration is 0.025 moles/cm3. The tank

volume is 200 gallons, and the feed compositions are 0.010 and 0.05 moles/cm3.

Assume a tight level controller keeps the volume in the tank constant.

Chen CL 22


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Process SimulationSimulation of A Nonisothermal Chemical Reaction

Computer-room ExerciseConsider a stirred-tank reactor with reaction A → B

as shown below. To remove the heat of reaction the

reactor is surrounded by a jacket through which a

cooling liquid flows. Let us assume that the heat

loss to the surroundings are negligible, and that

the thermodynamic properties, densities, and heat

capacities of the reactants and products are both

equal and constant. The heat of reaction is constant and is given by ∆H r inBtu/lbmole of A reacted. Let us also assume that the level of liquid in the reactortank is constant; that is, the rate of mass into the tank is equal to the rate of mass out of the tank. Finally, the rate of reaction is given by

rA(t) = koe−E/RT (t)

c

2

A(t)

lbmoles of A reacted

ft3-min

Chen CL 23


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where the frequency factor ko and energy of activation E are constants. Thefollowing Table gives the steady-state values of the variables and other processspecifications. It is desired to find out how the outlet concentrations of A and B,and the outlet temperature respond to changes in the inlet concentration of A,

cAi(t); the inlet temperature of the reactant T i(t); the inlet temperature of cooling liquid T ci(t); and the flows f (t) and f c(t).

Process information

V = 13.26 ft3 ko = 8.33 × 108 ft3/(lbmole-min)

E = 27, 820 Btu/lbmole R = 1.987 Btu/(lbmole-o

R)ρ = 55 lbm/ft3 C p = 0.88 Btu/(lbm-

oF)

∆H r = −12, 000 Btu/lbmole U = 75 Btu/(h-ft2-oF)

A = 36 ft2 C pc = 1.0 Btu/(lbm-oF)

V c = 1.56 ft3

Steady-state values

C Ai(t) = 0.5975 lbmole/ft3 T i(t) = 635

oR

T c = 602.7oR f = 1.3364 ft3/min

cA(t) = 0.2068 lbmole/ft3 T (t) = 678.9oR

T ci(t) = 540o

R f c(t) = 0.8771 ft3

/min

Chen CL 24


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Assume the reactor is initially at the design conditions. Use Simulink to simulatethe process and plot the response of the reactor temperature to a step change of 0.25 ft3/min in process flow, and of 0.1 ft3/min in coolant flow.

f (t)cAi(t)− f (t)cA(t) − V rA(t) = V dcA(t)dt

rA(t) = koe−E/RT (t)c2A(t)

f (t)ρC pT i(t) − U A[T (t) − T c(t)]− f (t)ρC pT (t) − V rA(∆H r) = V ρC vdT (t)

dt

f c(t)ρ

cC

pcT

ci(t) + U A[T (t) − T

c(t)]− f

c(t)ρ

cC

pcT

c(t) = V

cρ

cC

vc

dT c(t)

dt

S2 Process Simulation Using Simulink

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