Applied Process Control E-Book

Michael Mulholland

• Herausgeber: Wiley-VCH Verlag GmbH & Co. KGaA
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 309

Veröffentlichungsjahr: 2016

Beschreibung

Bridging theory and practice, this book contains over 200 practical exercises and their solutions, to develop the problem-solving abilities of process engineers.
The problems were developed by the author during his many years of teaching at university and are kept brief, taken from the fields of instrumentation, modelling, plant control, control strategy design and stability of control. The algorithm flows and codes, which are mostly based on MATLAB?, are given in many cases and allow for easy translation into applications.
Since the text is structured according to "Applied Process Control: Essential Methods", all of the necessary background information on the underlying methods can be easily and quickly found in this accompanying book.

Leseprobe

Contents

Cover

Related Titles

Title Page

Copyright

Preface

Acknowledgements

Abbreviations

Part I: Problems

Chapter 1: Problems – Introduction

Chapter 2: Problems – Instrumentation

P_2.1 2.4.1.1

P_2.2 2.2

P_2.3 2.2

P_2.4 2.4.1.1

P_2.5 2.4.1.1

P_2.6 2.4.1.1

P_2.7 2.4.1.1

P_2.8 2.4.1.1

P_2.9 2.4.2.1

P_2.10 2.4.4

P_2.11 2.6.1.1

P_2.12 2.6.1.2

P_2.13 2.6.1.2

P_2.14 2.6.1.2

P_2.15 2.6.1.4

P_2.16 2.6.1.4

P_2.17 2.6.1.4

P_2.18 2.6.1.4

P_2.19 2.6.1.4

P_2.20 2.6.1.4

P_2.21 2.6.1.4

P_2.22 2.6.1.4

P_2.23 2.6.1.4

P_2.24 2.6.1.4

P_2.25 2.6.1.4

P_2.26 2.6.1.4

P_2.27 2.6.1.4

P_2.28 2.6.1.5

P_2.29 2.7

P_2.30 2.8

P_2.31 2.9

P_2.32 2.9

P_2.33 2.9

P_2.34 2.9

P_2.35 2.9

P_2.36 2.9

P_2.37 2.9

P_2.38 2.9

P_2.39 2.9

Chapter 3: Problems – Modelling

P_3.1 3.3

P_3.2 3.3

P_3.3 3.3

P_3.4 3.3

P_3.5 3.3

P_3.6 3.3

P_3.7 3.3

P_3.8 3.3

P_3.9 3.3

P_3.10 3.3

P_3.11 3.3

P_3.12 3.3

P_3.13 3.4

P_3.14 3.4

P_3.15 3.5

P_3.16 3.5

P_3.17 3.7

P_3.18 3.7

P_3.19 3.7

P_3.20 3.7

P_3.21 3.7

P_3.22 3.7

P_3.23 3.7

P_3.24 3.9.1

P_3.25 3.9.2

P_3.26 3.9.2.1

P_3.27 3.9.2.2

P_3.28 3.9.2.2

P_3.29 3.9.2.2

P_3.30 3.9.2.2

P_3.31 3.9.2.2

P_3.32 3.9.2.2

P_3.33 3.9.2.2

P_3.34 3.9.2.3

P_3.35 3.9.3.1

P_3.36 3.9.3.1

P_3.37 3.9.3.1

P_3.38 3.9.3.2

P_3.39 3.9.3.2

P_3.40 3.9.3.2

P_3.41 3.9.3.2

P_3.42 3.9.3.2

P_3.43 3.9.3.3

P_3.44 3.9.3.3

P_3.45 3.9.3.4

P_3.46 3.9.3.4

P_3.47 3.9.3.5

P_3.48 3.9.3.5

P_3.49 3.9.4.1

P_3.50 3.9.4.1-3.7

P_3.51 3.9.4.1

P_3.52 3.9.4.2

P_3.53 3.9.4.2

P_3.54 3.9.5.1

P_3.55 3.9.5.1

P_3.56 3.9.5.1

P_3.57 3.9.5.2

P_3.58 3.9.5.2

P_3.59 3.9.7

P_3.60 3.10

P_3.61 3.11

Chapter 4: Problems – Basic Elements Used in Plant Control Schemes

P_4.1 4.1

P_4.2 4.2.1

P_4.3 4.2.2

P_4.4 4.2.3

P_4.5 4.2.4

P_4.6 4.2.4–4.12.1

P_4.7 4.2.6.1–4.2.6.2–4.12.1

P_4.8 4.2.8.1

P_4.9 4.3

P_4.10 4.4–4.10

P_4.11 4.5–4.7

P_4.12 4.6–4.10

P_4.13 4.8

P_4.14 4.8

P_4.15 4.8–4.10

P_4.16 4.10

P_4.17 4.11

P_4.18 4.12.2

P_4.19 4.12.2

P_4.20 4.12.2

P_4.21 4.12.2

P_4.22 4.12.2

Chapter 5: Problems – Control Strategy Design for Processing Plants

P_5.1 5.1

P_5.2 5.1

P_5.3 5.1

P_5.4 5.1

P_5.5 5.1

P_5.6 5.1

P_5.7 5.1

P_5.8 5.1

P_5.9 5.1

P_5.10 5.1

P_5.11 5.1

P_5.12 5.1

P_5.13 5.1

P_5.14 5.1

P_5.15 5.1

P_5.16 5.2.1

P_5.17 5.2.1

P_5.18 5.2.2

P_5.19 5.2.2

P_5.20 5.2.3

P_5.21 5.2.3

P_5.22 5.2.4

P_5.23 5.2.4

P_5.24 5.2.4

P_5.25 5.3.1

P_5.26 5.3.2–5.3.3

P_5.27 5.3.3

P_5.28 5.3.3

P_5.29 5.3.3

P_5.30 5.3.3

Chapter 6: Problems – Estimation of Variables and Model Parameters from Plant Data

P_6.1 6.1.1

P_6.2 6.1.2

P_6.3 6.1.3

P_6.4 6.2

P_6.5 6.3

P_6.6 6.4

P_6.7 6.4.1–3.10

P_6.8 6.4.1–3.10

P_6.9 6.4.1

P_6.10 6.4.2

P_6.11 6.4.3

P_6.12 6.5.1

P_6.13 6.5.2

P_6.14 6.5.2

P_6.15 6.5.2

P_6.16 6.5.2

P_6.17 6.5.3.1

P_6.18 6.5.3.2

P_6.19 6.7.1

Chapter 7: Problems – Advanced Control Algorithms

P_7.1 7.1.1–7.1.2

P_7.2 7.4

P_7.3 7.5.1

P_7.4 7.5.2

P_7.5 7.6.1

P_7.6 7.6.2

P_7.7 7.6.4

P_7.8 7.6.5

P_7.9 7.6.5–6.4.1

P_7.10 7.8.1.1

P_7.11 7.7–7.8.2

P_7.12 7.8.2

P_7.13 7.8.2

P_7.14 7.8.2

P_7.15 7.8.2

P_7.16 7.8.2–3.9.5.1

P_7.17 7.8.2–3.9.5.1

P_7.18 7.8.2

P_7.19 7.8.2–3.9.5.1

P_7.20 7.8.2

P_7.21 7.8.2.1

P_7.22 7.8.2.1

P_7.23 7.8.3.5–7.8.3.4

P_7.24 7.13.2

P_7.25 7.14.3

Chapter 8: Problems – Stability and Quality of Control

P_8.1 8.2.1

P_8.2 8.2.1.3

P_8.3 8.2.1.5

P_8.4 8.2.1.5

P_8.5 8.2.1.5

P_8.6 8.2.1.5

P_8.7 8.2.1.5

P_8.8 8.2.1.5

P_8.9 8.3

P_8.10 8.4

P_8.11 8.5

P_8.12 8.5

P_8.13 8.5

P_8.14 8.6.3–8.6.4

P_8.15 8.6.4

P_8.16 8.6.5

P_8.17 8.6.5

P_8.18 8.7

P_8.19 8.8

Chapter 9: Problems – Optimisation

P_9.1 7.6.5-7.8.3-9.2

P_9.2 7.6.5-7.8.3-9.2

P_9.3 7.6.5-7.8.3-9.2

P_9.4 7.6.5-7.8.3-9.2

P_9.5 9.3

P_9.6 9.4

P_9.7 9.5.2

P_9.8 9.5.3-9.5.3.2

P_9.9 9.7

P_9.10 9.8.2

P_9.11 9.10

Part II: Solutions

Chapter 2: Problem Solutions – Instrumentation

S_2.1 2.4.1.1

S_2.2 2.2

S_2.3 2.2

S_2.4 2.4.1.1.2

S_2.5 2.4.1.1

S_2.6 2.4.1.1

S_2.7 2.4.1.1

S_2.8 2.4.1.1

S_2.9 2.4.2.1

S_2.10 2.4.4

S_2.11 2.6.1.1

S_2.12 2.6.1.2

S_2.13 2.6.1.2

S_2.14 2.6.1.2

S_2.15 2.6.1.4

S_2.16 2.6.1.4

S_2.17 2.6.1.4

S_2.18 2.6.1.4

S_2.19 2.6.1.4

S_2.20 2.6.1.4

S_2.21 2.6.1.4

S_2.22 2.6.1.4

S_2.23 2.6.1.4

S_2.24 2.6.1.4

S_2.25 2.6.1.4

S_2.26 2.6.1.4

S_2.27 2.6.1.4

S_2.28 2.6.1.5

S_2.29 2.7

S_2.30 2.8

S_2.31 2.9

S_2.32 2.9

S_2.33 2.9

S_2.34 2.9

S_2.35 2.9

S_2.36 2.9

S_2.37 2.9

S_2.38 2.9

S_2.39 2.9

Chapter 3: Problem Solutions – Modelling

S_3.1 3.3

S_3.2 3.3

S_3.3 3.3

S_3.4 3.3

S_3.5 3.3

S_3.6 3.3

S_3.7 3.3

S_3.8 3.3

S_3.9 3.3

S_3.10 3.3

S_3.11 3.3

S_3.12 3.3

S_3.13 3.4

S_3.14 3.4

S_3.15 3.5

S_3.16 3.5

S_3.17 3.7

S_3.18 3.7

S_3.19 3.7

S_3.20 3.7

S_3.21 3.7

S_3.22 3.7

S_3.23 3.7

S_3.24 3.9.1

S_3.25 3.9.2

S_3.26 3.9.2.1

S_3.27 3.9.2.2

S_3.28 3.9.2.2

S_3.29 3.9.2.2

S_3.30 3.9.2.2

S_3.31 3.9.2.2

S_3.32 3.9.2.2

S_3.33 3.9.2.2

S_3.34 3.9.2.3

S_3.35 3.9.3.1

S_3.36 3.9.3.1

S_3.37 3.9.3.1

S_3.38 3.9.3.2

S_3.39 3.9.3.2

S_3.40 3.9.3.2

S_3.41 3.9.3.2

S_3.42 3.9.3.2

S_3.43 3.9.3.3

S_3.44 3.9.3.3

S_3.45 3.9.3.4

S_3.46 3.9.3.4

S_3.47 3.9.3.5

S_3.48 3.9.3.5

S_3.49 3.9.4.1

S_3.50 3.9.4.1-3.7

S_3.51 3.9.4.1

S_3.52 3.9.4.2

S_3.53 3.9.4.2

S_3.54 3.9.5.1

S_3.55 3.9.5.1

S_3.56 3.9.5.1

S_3.57 3.9.5.2

S_3.58 3.9.5.2

S_3.59 3.9.7

S_3.60 3.10

S_3.61 3.11

Chapter 4: Problem Solutions – Basic Elements Used in Plant Control Schemes

S_4.1 4.1

S_4.2 4.2.1

S_4.3 4.2.2

S_4.4 4.2.3

S_4.5 4.2.4

S_4.6 4.2.4–4.12.1

S_4.7 4.2.6.1–4.2.6.2–4.12.1

S_4.8 4.2.8.1

S_4.9 4.3

S_4.10 4.4–4.10

S_4.11 4.5–4.7

S_4.12 4.6–4.10

S_4.13 4.8

S_4.14 4.8

S_4.15 4.8–4.10

S_4.16 4.10

S_4.17 4.11

S_4.18 4.12.2

S_4.19 4.12.2

S_4.20 4.12.2

S_4.21 4.12.2

S_4.22 4.12.2

Chapter 5: Problem Solutions – Control Strategy Design for Processing Plants

S_5.1 5.1

S_5.2 5.1

S_5.3 5.1

S_5.4 5.1

S_5.5 5.1

S_5.6 5.1

S_5.7 5.1

S_5.8 5.1

S_5.9 5.1

S_5.10 5.1

S_5.11 5.1

S_5.12 5.1

S_5.13 5.1

S_5.14 5.1

S_5.15 5.1

S_5.16 5.2.1

S_5.17 5.2.1

S_5.18 5.2.2

S_5.19 5.2.2

S_5.20 5.2.3

S_5.21 5.2.3

S_5.22 5.2.4

S_5.23 5.2.4

S_5.24 5.2.4

S_5.25 5.3.1

S_5.26 5.3.2–5.3.3

S_5.27 5.3.3

S_5.28 5.3.3

S_5.29 5.3.3

S_5.30 5.3.3

Chapter 6: Problem Solutions – Estimation of Variables and Model Parameters from Plant Data

S_6.1 6.1.1

S_6.2 6.1.2

S_6.3 6.1.3

S_6.4 6.2

S_6.5 6.3

S_6.6 6.4

S_6.7 6.4.1–3.10

S_6.8 6.4.1–3.10

S_6.9 6.4.1

S_6.10 6.4.2

S_6.11 6.4.3

S_6.12 6.5.1

S_6.13 6.5.2

S_6.14 6.5.2

S_6.15 6.5.2

S_6.16 6.5.2

S_6.17 6.5.3.1

S_6.18 6.5.3.2

S_6.19 6.7.1

Chapter 7: Problem Solutions – Advanced Control Algorithms

S_7.1 7.1.1–7.1.2

S_7.2 7.4

S_7.3 7.5.1

S_7.4 7.5.2

S_7.5 7.6.1

S_7.6 7.6.2

S_7.7 7.6.4

S_7.8 7.6.5

S_7.9 7.6.5–6.4.1

S_7.10 7.8.1.1

S_7.11 7.7–7.8.2

S_7.12 7.8.2

S_7.13 7.8.2

S_7.14 7.8.2

S_7.15 7.8.2

S_7.16 7.8.2–3.9.5.1

S_7.17 7.8.2–3.9.5.1

S_7.18 7.8.2

S_7.19 7.8.2–3.9.5.1

S_7.20 7.8.2

S_7.21 7.8.2.1

S_7.22 7.8.2.1

S_7.23 7.8.3.5–7.8.3.4

S_7.24 7.13.2

S_7.25 7.14.3

Chapter 8: Problem Solutions – Stability and Quality of Control

S_8.1 8.2.1

S_8.2 8.2.1.3

S_8.3 8.2.1.5

S_8.4 8.2.1.5

S_8.5 8.2.1.5

S_8.6 8.2.1.5

S_8.7 8.2.1.5

S_8.8 8.2.1.5

S_8.9 8.3

S_8.10 8.4

S_8.11 8.5

S_8.12 8.5

S_8.13 8.5

S_8.14 8.6.3–8.6.4

S_8.15 8.6.4

S_8.16 8.6.5

S_8.17 8.6.5

S_8.18 8.7

S_8.19 8.8

Chapter 9: Problem Solutions – Optimisation

S_9.1 7.6.5-7.8.3-9.2

S_9.2 7.6.5-7.8.3-9.2

S_9.3 7.6.5-7.8.3-9.2

S_9.4 7.6.5-7.8.3-9.2

S_9.5 9.3

S_9.6 9.4

S_9.7 9.5.2

S_9.8 9.5.3-9.5.3.2

S_9.9 9.7

S_9.10 9.8.2

S_9.11 9.10

End User License Agreement

List of Illustrations

Figure 1.1

Guide

Cover

Table of Contents

Begin Reading

Part 1

Chapter 1

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Buzzi-Ferraris, G., Manenti, F.

Interpolation and Regression Models for the Chemical Engineer

Solving Numerical Problems

2010

Print ISBN: 978-3-527-32652-5

Buzzi-Ferraris, G., Manenti, F.

Nonlinear Systems and Optimization for the Chemical Engineer

Solving Numerical Problems

2014

Print ISBN: 978-3-527-33274-8

Buzzi-Ferraris, G., Manenti, F.

Differential and Differential-Algebraic Systems for the Chemical Engineer

Solving Numerical Problems

2015

Print ISBN: 978-3-527-33275-5

Michael Mulholland

Applied Process Control

Efficient Problem Solving

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Print ISBN: 978-3-527-34118-4

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Preface

A series of problems is presented following the material in the accompanying book: Applied Process Control – Essential Methods. After all of the problem statements, the corresponding worked solutions are presented in the same order in the second half of this book. Many of the problems have been used in examinations for Process Engineering students, mostly at the undergraduate level, but a few also for postgraduate research students. These test problems typically require 10–30 min for their solution. Apart from such short problems, there is in addition a range of more time-consuming problems covering aspects that can only be dealt with using computer programs. The relevant book section is indicated with each problem, and in the contents.

A few additional problems and solutions may be obtained from the site https://sourceforge.net/projects/rtc-simulator/. This site also has a simple interactive simulator program which includes 20 different applications for such aspects as PID and DMC controller tuning, advanced level control, Smith prediction, Kalman filtering and control strategies for a furnace, a boiler and a hybrid system. No support is available for the simulator.

Michael Mulholland

University of KwaZulu-Natal

March, 2016

Acknowledgements

Many of the problems in this book are dealt with using the MATLAB® program, which is distributed by the MathWorks, Inc. They may be contacted at

The MathWorks, Inc.

3 Apple Hill Drive

Natick, MA 01760–2098, USA

Tel: [phone]

Fax: [phone]

E-mail:

[email protected]

Web:

mathworks.com

How to buy:

http://www.mathworks.com/store

A few problems are dealt with in the GAMS® optimisation environment, distributed by

GAMS Development Corporation

1217 Potomac Street, NW

Washington, DC 20007, USA

General Information and Sales: ([phone]

Fax: [phone]

Contact:

[email protected]

Some problems make use of the LPSOLVE mixed integer linear programming software which is hosted on the SourceForge Web site at

http://sourceforge.net/projects/lpsolve/

Abbreviations

A/D

analogue to digital

AC/FO

air to close/fail open

ANN

artificial neural network

AO/FC

air to open/fail closed

APC

advanced process control

ARIMAX

autoregressive integrated moving average exogenous

ARMAX

autoregressive moving average exogenous

ARX

autoregressive exogenous

BB

branch and bound

BFW

boiler feedwater

BIDP

backward iterative dynamic programming

CEM

cause and effect matrix

CRT

cathode ray tube

CV

controlled variable

CVP

control variable parameterisation

CW

cooling water

D/A

digital to analogue

DAE

differential and algebraic equations

DCS

distributed control system

DMC

dynamic matrix control

DP

differential pressure

DV

disturbance variable

E{ . . . }

expectation of . . .

EKF

extended Kalman filter

ES

evolutionary strategy

FFT

fast Fourier transform

FIDP

forward iterative dynamic programming

FIMC

fuzzy internal model controller

FIR

finite impulse response

FRM

fuzzy relational model

FRMBC

fuzzy relational model-based control

FSQP

feasible sequential quadratic programming

Fuzzy

fuzzy logic

GA

genetic algorithm

GAMS

General Algebraic Modelling System®

GM

gain margin

GPC

generalised predictive control

HP

high pressure (port)

HS

high select

I

identity matrix

I/O

input–output

I/P

current to pressure (pneumatic) converter

IAE

integral of absolute error

IDP

iterative dynamic programming

IMC

internal model control

INA

inverse Nyquist array

IO

input–output

IP

integer programming

ISE

integral of squared error

KO

knockout (separation drum)

LAN

local area network

LBT

lower block triangular

LCD

liquid crystal display

LDMC

linear dynamic matrix control

LP

linear programming

LP

low pressure (port)

LPG

liquefied petroleum gas

LPSOLVE

MILP program (

http://sourceforge.net/projects/lpsolve/

)

LQR

linear quadratic regulator

LS

low select

LS

least squares

MATLAB

MATLAB® program, distributed by the MathWorks, Inc.

MEK

methyl ethyl ketone

MIDO

mixed integer dynamic optimisation

MILP

mixed integer linear programming

MIMO

multi-input, multi-output

MINLP

mixed integer nonlinear programming

MIP

mixed integer programming

MIQP

mixed integer quadratic programming

MLD

mixed logical dynamical

MM

molecular mass

MPC

model predictive control

MRI

Morari resiliency index

MV

manipulated variable

NC

normally closed

NLP

nonlinear programming

NO

normally open

NSGA-II

fast non-dominated sorting genetic algorithm II

OA

outer approximation

ODE

ordinary differential equation

OHTC

overall heat transfer coefficient

P

proportional

P/I

pressure (pneumatic) to current converter

PCA

principal components analysis

PDE

partial differential equation

PI

proportional integral

PID

proportional integral derivative

PLC

programmable logic controller

PM

phase margin

PV

process variable

QDMC

quadratic dynamic matrix control

RAID

redundant array of independent discs

RGA

relative gain array (Bristol array)

RLS

recursive least squares

RTD

resistance temperature detector

RTO

real-time optimisation

SCADA

supervisory control and data acquisition

SG

specific gravity

SISO

single-input single-output

SP

setpoint

SQP

sequential quadratic programming

VPC

valve position control

WABT

weighted average bed temperature

WAN

wide area network (e.g. using telecommunication, radio)

WG

water-gauge

ZOH

zero-order hold

Part IProblems

1Problems – Introduction

Figure 1.1 maps process control development sequences as referred to in sections of Applied Process Control – Essential Methods. The problems in Chapters 2–9 are indexed with the same section references. One notes in Figure 1.1 that the main divisions are state-based systems versus input–output systems, with these two system types each again divided into linear and non-linear.

Figure 1.1 Aspects of process control related to book sections.

Recall that state-based systems are able to predict forward in time, knowing only the present state and future inputs, for example

(1.1)

(1.2)

and so on.

This idea is essential for many algorithms, including those using dynamic programming (Bellman, 1957). On the other hand, input–output systems need additional information about past inputs and outputs in order to make such a prediction, for example

(1.3)

(1.4)

and so on.

If all of the accumulation variables (i.e. states) in a system have been identified, one might attempt to fit the state-based form Equation 1.1 to measurements. Alternatively, this form will arise naturally from theoretical modelling of the physics. Conversely, if one is not sure that one has all of the states, one would try to fit the input–output form of Equation 1.3, with a guessed number of lags, to measured data. This is also the form that arises from step-tests and use of a dynamic matrix. Another option, for a theoretical model where a state cannot be measured, is to insert an observer (e.g. Kalman filter) for the missing state(s) – thus allowing state-based methods to be used.

The second division mentioned for both of these system types is linear versus non-linear. A lot of fast, powerful and robust methods have been developed for linear systems. If one's system is anywhere near linear, one wants to get access to these methods. This is often done based on a linearisation at an average operating point, or even on a roving re-linearisation, such as in the extended Kalman filter. Nonetheless, there are some methods that will take care of non-linearities – such as models that run forward in predictive control. But one should beware of non-linear systems that require optimisation – global optimisation is not a well-developed art.

Figure 1.1 does not distinguish between systems presented in a discrete form versus continuous. Applications will generally be in discrete form, but if for some reason a continuous method is used, the equations can be discretised with a sufficiently small time step.

Some further points to note regarding the problems which are presented here:

The text consistently uses bold characters to signify matrices [

A

], vectors [

x

] and matrix transfer functions [

G

(

s

),

G

(

z

)]. Non-bold characters are used for scalars.

2Problems – Instrumentation

P_2.1 2.4.1.1

Furnace draught systems are typically low pressure, for example 1″ water gauge. The airflow is to be monitored in order to implement air/fuel ratio control. Usually a Venturi is used in order to minimise loss of the available applied draught (see diagram). Your 30 cm diameter air intake ducting has a hood to minimise ingress of foreign material, and proceeds through a Venturi with throat diameter of 15 cm before the forced draught fan.

You have calculated a design airflow of 2 th−1 at 25 °C and 101 kPa abs. Estimate the ΔP that will be generated by the Venturi, so that you can specify a suitable DP cell.

Hint: Take universal gas constant R = 8.314 kPa m3 K−1 kmol−1; air as 78 : 21 : 1 by volume for N2 (28):O2 (32):Ar (40).

P_2.2 2.2

The flow control loop shown above has been set up for water (SG = 1) in such a way that a mid-range setpoint (12 mA) gives a flow of 10 m3 h−1.

Find the true volumetric flow in the system if an oil of SG = 0.8 is passed through the pipe, but the setpoint is left unchanged at 12 mA.

What will be the signal from the DP cell under this condition?

If the linear valve was 60% open with the water, how far open will it be with the oil (assume that the Δ

P

V

change

is negligible).

P_2.3 2.2

A flow controller uses an orifice plate to detect the flow. The plate is sized to give 0–20″ WG for a flow range of 0–10 m3 h−1. Show all of the necessary elements in the flow control loop using electronic signals, except for the valve, which must be activated pneumatically. Show the signal range on each connection, as well as the particular signals for a flow of 5 m3 h−1, with the valve half open.

P_2.4 2.4.1.1

You are setting up an electronic DP cell (4–20 mA) and orifice plate to measure a flow of alcohol (SG = 0.8) in the range of 0–20 l min−1. To check your settings, you are passing a known water flow of 10 l min−1 through the pipeline. What should the DP cell output be?

P_2.5 2.4.1.1

An orifice meter and DP cell are used to measure the flow of fuel gas onto a site:

The square-rooted output of the DP cell is used directly as a measure of the mass-flow of fuel gas according to an original calibration based on butane (MM: 58) at 3 bara and 20 °C.

It has been noted that the actual gas is a propane–butane mixture, varying from 100% butane to 100% propane (MM: 44), and that it arrives at pressures ranging from 2 to 4 bara and at temperatures from 10 to 30 °C.

For a given reading of the device, what is the worst % error (% of true mass flow below reading mass flow)? Assume incompressible flow.

P_2.6 2.4.1.1

The flow of two streams into a vessel is kept at a setpoint ratio by manipulating one of the streams. The flows are measured by means of orifice plates and DP cells. The plates are sized to give 0–20″ WG for a flow range of 0–10 m3 h−1. Show all necessary signal connections, converters and transducers on an appropriate Piping and Instrumentation diagram. Give actual values for all signals when the flow of the ‘idle’ stream is 6 m3 h−1 and that of the manipulated stream is 4 m3 h−1, for a ratio setpoint of 1.0.

P_2.7 2.4.1.1

An orifice plate has been sized to produce a differential pressure of 20″ WG for a flow of 5 m3 h−1 of cyclohexanol, which has a relative density of 0.95. A DP cell is set up to transmit the 0–20″ WG signal on an instrument range of 4–20 mA. The latter signal is processed by a square-root extractor, which re-transmits the result on a 4–20 mA range.

On a certain occasion, there is only water in the system, and the final square-root-extracted signal reads 40% of its range.

What are the two electronic signals (mA)?

What is the true flow of the water in m

3

h

−1

?

P_2.8 2.4.1.1

For the indicated signal ranging, if the flow is 7 m3 h−1, find the signals at (b), (c) and (d).

P_2.9 2.4.2.1

Use a diagram and a short explanation (4 lines) to show how you would use a DP cell to measure the liquid level in a closed vessel containing a condensable vapour.

P_2.10 2.4.4

Using simple sketches, explain the instrument differences between measurement of temperature by thermocouple and by a resistance device such as Pt100.

P_2.11 2.6.1.1

Sketch an ‘air-to-open’ globe control valve, clarifying how the diaphragm, spring, plug and seat act to vary the flow.

On your diagram show a positioner, clarifying how it relates to the valve signal.

Explain the symptom(s) and cause(s) of hysteresis which are often observed in control valve operation.

P_2.12 2.6.1.2

A control valve has the ‘equal percentage’ characteristic f(x) = 50x−1 and it has a Cv value of 12. A total of 60 psi are available to drive 10 US gallons of water per minute through a pipeline and the valve, when the valve is 50% open. Find the pressure drop across the rest of the pipeline for this flow.

P_2.13 2.6.1.2

A pipeline delivers water from a head-tank through a valve which has the ‘equal percentage’ characteristic shown.

When the valve is shut, the pressure gauge reads 3.0 barg, and when it is fully open the gauge reads 1.0 barg and a flow of 10 m3 h−1 is delivered.

What will the flow be when the valve is 50% open?

Based on any chosen design guideline, comment on the sizing of the valve.

P_2.14 2.6.1.2

A horizontal pipeline delivers a liquid between two points of fixed pressure as shown:

A control valve with the indicated ‘equal percentage’ characteristic is used to control the flow. When this valve is 50% open (i.e. x = 0.5), a flow of 6 m3 h−1 is achieved, and when it is 100% open, the flow is 10 m3 h−1.

Compare and comment on the steady-state gain of the whole system [(m3 h−1) (%open)−1] near the 50 and 100% open points.

Hint: Avoid a lot of algebra by just evaluating two more flows near the given flows.

P_2.15 2.6.1.4

Water runs down 50 m vertically from a reservoir through a fully open control valve, achieving a flow of 10 m

3

 h

−1

. If the

C

V

of the valve is 5 (m

3

water h

−1

) (m water)

−1/2

, what flow could be achieved if the valve were removed altogether?

Explain why an ‘equal percentage’ control valve can give a more linear variation of flow with valve position in some situations.

P_2.16 2.6.1.4

Fuel oil from a pressurised manifold at 150 psig is supplied through a pipeline to a furnace. Presently, there is a control valve at the furnace with Cv = 0.05, and this valve allows a flow of 2 l min−1 through the burner nozzle when fully open. Now you are required to specify a more suitable control valve such that 50% of the overall dynamic pressure loss is across the valve when it is half open.

P_2.17 2.6.1.4

The control valve to let distillate (SG = 0.8) down to a lower pressure column has been sized according to the recommendation that 50% of the dynamic ΔP should lie across the valve when it is half open, giving Cv = 3. If the valve is linear, what will the flow be when it is fully open?

P_2.18 2.6.1.4

A centrifugal pump delivers water from a settling pond through a horizontal pipeline to a second settling pond some distance away.

It is found that a flow rate of 35 US gallons per minute is sustained with no valve present.

Specify a suitable control valve for this pipeline, such that 50% of the total frictional pressure drop occurs across the valve when it is half open.

What will be the flow when the installed valve is fully open?

P_2.19 2.6.1.4

The water pumping installation shown achieves a flow of 6 m3 h−1.

Using the given pump characteristic (head across pump versus flow), specify a control valve for the pipeline such that half of the friction ΔP of the valve and pipeline together lies across the valve when it is half open.

Hint: 1 m3 = 264.2 US gal, 1 m water = 1.42 psi.

P_2.20 2.6.1.4

A boiler feedwater pump delivers at a constant pressure through a pipeline to an elevated steam drum as below:

Poor level control has been observed owing to the fact that the linear control valve is only about 5% open during normal operation. If the CV factor of the existing valve is 10, specify a replacement valve such that it will remain about 50% open during normal operation.

Why do ‘installed’ and ‘inherent’ valve characteristics differ?

P_2.21 2.6.1.4

Two distillation columns operate at a variable pressure difference, with part of the bottoms of the first being let down to the second under flow control:

When the pressure in the first column is 5 bar above that in the second, a flow setpoint of 10 tph results in the valve settling at 50% open, whilst when the first column is 4 bar above the second, the same flow requires a valve position of 70% open.

Can the required flow of 10 tph be sustained if the first column's pressure drops by a further 1 bar?

P_2.22 2.6.1.4

Two distillation columns operating at fixed pressures (2.6 and 1.8 barg) in a refinery are connected by a pipeline which transfers the bottoms of the first column as feed to the second column.

When the single linear control valve on this pipeline is fully open, a flow of 10 m3 h−1 is achieved; and when it is half open, a flow of 7 m3 h−1 is achieved.

To increase the capacity of this line, engineers plan to install a second identical control valve on a short bypass around the valve.

Determine the maximum flow that will be achieved with the proposed configuration.

P_2.23 2.6.1.4

Water is to be pumped around the system shown below:

The pipe friction losses are negligible in this system.

You are required to size a suitable control valve such that a minimum tank level difference of Δ

h

T

 = 

2m

can be achieved. (Give the specific units of your own

C

V

value.)

If the valve is linear, what valve position will be required to give a tank level difference of

10 m

?

P_2.24 2.6.1.4

Liquid is let down between two pressure vessels (P1 > P2) as in the following diagram:

Since the pipe has a large diameter, all pressure loss may be assumed to lie across the orifice plate and the valve. In fact, the system has been designed such that the drops across these two items are equal when the valve is half open.