Chapter : Process Modelling

Question 1

what makes process modelling different from process analysis

Answer 1

the task involves process analysis with dynamics so there may be accumulation,generation and consumption terms so the models may comprise of differential equations

Question 2

derive the mass balance

Answer 2

notes

Question 3

derive volumetric balance

Answer 3

notes

Question 4

how do we find a differential equation for the level in the tank from the mass balance

Answer 4

from the mass balance we can relate mass to volume through density formula. following that we can relate volume to level through the volume formula. therefore M= Aph

Question 5

what is constant in the mass balance

Answer 5

flowrates, mass , level are not constant because they are functions of time. so density and area is the only constants

Question 6

how is mass related to volume

Answer 6

density formula M= p x V

Question 7

how is volume related to level

Answer 7

V = A x h

Question 8

how is mass related

Answer 8

M = A x p x h

Question 9

what is the control system based on for slide 7 and 8

Answer 9

the differential level equation because level is the controlled variable

Question 10

what is the rate of change of stored heat

Answer 10

heat inflow - heat outflow

Question 11

derive the heat balance

Answer 11

in notes

Question 12

why does Fin=Fout

Answer 12

because volume is constant

Question 13

why is hcond negligible compared to hst

Answer 13

the specific enthalpy of the condensate is negligible compared to the specific enthalpy of steam because the value is much smaller

Question 14

what does the final heat balance equation relate

Answer 14

it relates the temperature inside the tank with the flow rate of steak and our disturbances

Question 15

what are the potential disturbances for the heat equation

Answer 15

the temperature of steam may be subject to disturbances
the flowrate of steam may be subject to disturbances
the model may be wrong because steam can create foulingwhich leads to suboptimal performance heat exchange

Question 16

why does the component balance using mass fraction and mass flowrate not have independent equations

Answer 16

because the mass fractions both add to unity

xA+xB=1

Question 17

why does the component balance using concentrations and volumetric flow rate not have independent equations

Answer 17

becuase in a binary mixture CA+CB = p if the concentrations are in kg/m^3

Question 18

how do you convert between mass flowrate and volumetric flowrate

Answer 18

Fm=Fv * p

Question 19

how do you convert between mass and volume

Answer 19

M= V * p

Question 20

how do you convert from concentration to mass fraction

Answer 20

CA= p * xA

Question 21

what is the concentration dependence of a reaction with product inhibition

Answer 21

r = k * CA/K+CB

Question 22

what is the time delay

Answer 22

Td= L/v = L x A/ Fv

where the time delay is the time taken to travel distance l with velocity v

Question 23

what are deviation variables used for

Answer 23

continuous processes operate at steady state, deviation variables measure deviations from the steady state

Question 24

what are examples of deviation variables

Answer 24

T = Tss+∆T
L = Lss+∆L

∆T or ∆L may be positive or negative

Question 25

what are the steps for linearization

Answer 25

The steps are:
* Step 1: Formulate the appropriate balance equations
* Step 2: Find the steady state
* Step 3:
» 3.1 Define deviation variables
» 3.2 Substitute into the balance equation
» 3.3 Make linearizing approximations
* Step 4: Use the steady state relationship from the second step to simplify
the expression
End result is a linear differential equation describing the dynamics of small
deviations from the operating point

Question 26

what are examples of control system signals?

Answer 26

unit step decay, exponential decay, damped unit step, damped cosine with decaying amplitude, underdamped second order step

Question 27

why do do the graphs start from the origin

Answer 27

because we’re assuming steady state

Question 28

what happens in the unit step

Answer 28

the unit step usually represents a change to the set point e.g a control engineer changing the set point for a flow rate

Question 29

what do are control system signals functions of

Answer 29

they are all sums of exponential basis functions

Question 30

what is an example of a unit step function

Answer 30

e^0t for t>0

Question 31

what is an example of exponential decay

Answer 31

e^(-t/2) for t>0

Question 32

what is an example of damped unit step

Answer 32

1-e^(-t/2) for t>0

Question 33

what is euler’s theorem and when is it needed

Answer 33

on slide 9
it is needed for signals containing sin or cos

Question 34

what does the real and imaginary part do for the graphed function

Answer 34

the imaginary part give the oscillation
the negative real part gives the decay

Question 35

what would happen if the real part was positive

Answer 35

if the real part was positive the graph would increase to infinity with every osicalltion which would be completely unstable

Question 36

what is si

Answer 36

si values show which exponential and are called poles. complex values of si indicate the signal is oscillating. they always ome in complex conjugate pairs

Question 37

what is ai

Answer 37

ai values show how strong the signal is. the ai values are valled residues for complex and amplitudes for real.

Question 38

how do you visualize si on an s-plane

Answer 38

si values or numerical values which may be real or complex
si values show which exponential basis signals are present in f(t)

Question 39

how does si affect the signal if we’re visualizing on the s-plane

Answer 39

if we’re on the positive real axis then we have growth
if we’re on the negative real axis then we will have decay, the further along the negative axus, the faster the decay will e
if we’re on the imaginary axis then we will have some sort of oscillation
if we have a mixture of real and imaginary parts then we could have a decaying oscillation or growing oscillation which would be an unstable system

Question 40

what is the downside of the s-plane

Answer 40

we can only see si so we can;t see the amplitudes of the signals

Question 41

if the real part is less negative then what do we know

Answer 41

the decay will be slower because the larger period of oscillation means there will be fewer crossings of the x-axis so the decay will slower

Question 42

what is the period of oscillation based on

Answer 42

the frequency of oscillation/ angular frequency

Question 43

what determines the time for the signal to decay

Answer 43

the real part of the exponent

Question 44

if the imaginary part is greater what do we know about the signal

Answer 44

the greater the imaginary part, the higher the frequency of the sinusodial wave