Process Instrumentation, Control, and Dynamics First Edition

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Process Instrumentation,Control, and DynamicsFirst Edition

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Process Instrumentation,Control, and Dynamics

First Edition

By Kal Renganathan SharmaPrairie View A&M University


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Bassim Hamadeh, Publisher

Michael Simpson, Vice President o Acquisitions

Christopher Foster, Vice President o Marketing

Jessica Knott, Managing Editor

Stephen Milano, Creative Director

Kevin Fahey, Cognella Marketing Program ManagerRose Tawy, Acquisitions Editor

Jamie Giganti, Project Editor

Erin Escobar, Licensing Associate

Copyright 2012 by University Readers, Inc. All rights reserved. No part o this publication may be

reprinted, reproduced, transmitted, or utilized in any orm or by any electronic, mechanical, or other

means, now known or hereater invented, including photocopying, microflming, and recording, or in

any inormation retrieval system without the written permission o University Readers, Inc.

First published in the United States o America in 2012 by University Readers, Inc.

Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are

used only or identifcation and explanation without intent to inringe.

16 15 14 13 12 1 2 3 4 5

Printed in the United States o America

ISBN: 978-1-60927-508-2


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This book is dedicated to my eldest son R. Hari Subrahmanyan Sharma (alias

Ramkishan) who turns 10 this August 13th

2011.


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Contents

Preface

Chapter 1.0: Introduction

1.1 Overview 1

1.2 Motivation and Examples of Control Applications 21.3 Control Strategy 11

1.4 Control Types 12

1.5 Summary 16

1.6 References 19

1.7 Exercises 20

Chapter 2.0: Process Models

2.1 Overview 23

2.2 Semi-Empirical Models 24

2.3 Mechanistic Models 29

2.4 Models From Shell Balance and Equations of Momentum, Energy, and Continuity 44

2.5 State Space Models 54

2.6 Multiplicity in Model Solutions 67

2.7 Dimensionless Groups 74

2.8 Stochastic Models 93

2.9 Summary 100

2.10 Nomenclature 104

2.11 References 105

2.12 Exercises 108

Chapter 3.0: Process Dynamics

3.1 Transient Conversion in Isothermal CSTR 143

3.2 Transient Temperature in Mixing Tank 150

3.3 State Space Model Development of CTSR with Jacket Temperature 154

3.4 State Space Representation and Stability 157

3.5 Free Radical Polymerization in CSTR 161

3.6 Prototypical First Order Process 168


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3.7 Prototypical Second Order Process 169

3.8 Disappearance of Overshoot During Damped Wave Conduction 170

3.9 Two-Dimensional Trajectory of Accelerating Particles in Rectangular

Sedimentation Tank 187

3.10 Summary 202

3.11 References 205

3.12 Exercises 209

Chapter 4.0: Feedback Control

4.0 Control Systems 247

4.1 On-Off Control 248

4.2 Proportional Control 250

4.3 Control Block Diagrams 250

4.4 Offset Using Proportional Only Controllers 253

4.5 Proportional-Integral, PI Control 255

4.6 Conditions for Underdamped Response of PI Control of Prototypical First

Order Process 2624.7 PD, Proportional Derivative Control, and PID, Proportional Integral

Derivative Control 264

4.8 Tyreus-Luyben Oscillation Based Tuning 277

4.9 Summary 278

4.10 References 281

4.11 Exercises 282

Chapter 5.0: Frequency Response Analysis

5.1 Motivation 303

5.2 Output Response of a Prototypical First Order System to a Periodic Input 3045.3 Bode and Nyquist Diagrams 307

5.4 Frequency Analysis of Second Order Systems 316

5.5 Closed Loop StabilityBode and Nyquist Criterion 317

5.6 Summary 320

5.7 References 322

5.8 Exercises 323

Chapter 6.0: Refresher in Distillation, Thermodynamics,and Fluid Mechanics

Nomenclature 338

6.0 Overview 342

6.1 Vapor Distillation 342

6.2 Five Laws of Thermodynamics 435

6.3 Fluid Mechanics 450

6.4 "Yield Stress Fluids" 461

6.5 Equation of Conservation of Mass 462

6.6 Equation of Motion 464


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6.7 Navier-Stokes, Euler and Bernoulli Equations 465

6.8 References 467

6.9 Exercises 471

Chapter 7.0: Pharmacokinetic Analysis

7.1 Overview 473

7.2 Renal Clearance 475

7.3 Single Compartment Models 476

7.4 Analysis of Simple Reactions in Circle 492

7.5 Subcritical Damped Oscillations 498

7.6 Two Compartment Models 502

7.7 Computer Simulation 504

7.8 Summary 508

7.9 References 513

7.10 Exercises 515

Chapter 8.0: Advanced Control Methods

8.1 Ratio Control 528

8.2 SPC, Statistical Process Control 532

8.3 IMC, Internal Model Control 542

8.4 Feedforward Control 557

8.5 Estimation and Control of Polymerization Reactors 560

8.6 Neural Networks 572

8.7 Summary 580

8.8 References 584

8.9 Exercises 585

Chapter 9.0: Instrumentation

9.1 Precision and Accuracy 593

9.2 Sensors and Probes 594

9.3 Temperature Measurements 594

9.4 Viscosity Measurements 599

9.5 Biochips 608

9.6 Pressure Measurements 610

9.7 Summary 6139.8 References 614

9.9 Exercises 615

Chapter 10.0: Nanorobots for Use in Nanomedicine

10.1 Introduction 621

10.2 FullerenesDiscovery and Synthesis Methods 627

10.3 Summary of Nanostructuring Methods 628


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10.4 Thermodynamic Stability of Nanostructures 632

10.5 Nanorobots in Nanomedicine 636

10.6 Molecular Computing 636

10.7 Molecular Machines 638

10.8 Supramolecular Chemistry 640

10.9 CNRs, Collectives of Nanorobots 644

10.10 Developments in Nanorobot Applications 64910.11 CNTs, Carbon Nanotubes 651

10.12 Characterization of Nanostructures 652

10.13 Summary 655

10.14 References 658

Appendix A 667


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PREFACE

This textbook is developed for use in the instruction of undergraduate one-semesterprocess dynamics and control course. I instruct CHEG 4033 Process Dynamics and Controlto juniors/seniors in chemical engineering and MCEG 3073, Automatic Controls tojuniors/seniors in mechanical engineering at Prairie View A & M University, Prairie View,TX. Automation came about after mechanization in the industry. Chemical process controlis a subset of the field of automation theory and practice. AIChE, American Institute ofChemical Engineers, New York, NY recently celebrated their centennial or 100 thanniversary. Process Control as required courses in the chemical engineering degree plan ina number of US universities came out in the late 60s or 70s.

There are three goals in writing this textbook: (i) modern textbook that keeps pacewith the progress made in desktop computer hardware and software; (ii) more relevant to the

industrial practioner; (iii) compliance with second law of thermodynamics. No machine canbe devised; no process can be designed where the heat flows from low temperature to a hightemperature in a spontaneous manner. The current books over emphasize concepts such asovershoot and PID control. Overshoot often times is a mathematical artifact and in realsystems is equivalent of heat flowing from a low temperature to a high temperature. IdealPID control, Proportional, Integral and Derivative control is not physically realizable. Itappears as a natural next line on the black board after P control and PI control and PDcontrol! The current textbooks in vogue place too much druthers on tuning parameters andclosed form analytical solutions and inversion of Laplace transform expressions.Pedagogical studies across the nation have shown that student learning outcomes are betterwhen examples from life sciences are used. In this textbook an entire chapter is devoted to

Pharmacokinetic study. Single and multiple compartment models for zeroth order, firstorder, second order are discussed in detail. Kinetics of Reactions in circle scheme isintroduced de no vo. Michaelis and Menten kinetics are also discussed.

Use of numerical solution to differential equations such as the fourth order RungeKutta method is invoked when necessary in the textbook. Adherence to closed formanalytical solutions only is now an ancient method common among previous generation ofengineers. The next millennium is going to see the use of desktop computer spreadsheets,differential equation solvers, development of control block diagrams using SIMULINK in thefront end and MATLAB in the back end is discussed. Nonlinear systems can also be handledwith the same software used for linear systems.

Stability issues are made more student friendly. Stability types and character arespelled out clearly. The BZ reaction, limit cycles, chaos and oscillatory behaviors in someprocesses are touched upon. Dynamics of reactors is discussed in detail. Second law ofthermodynamics and entropy analysis is introduced to save time and energy for the engineereager to scale-up novel chemistry from the laboratory to the pilot plant to the manufacturingplant. Examples of real case occurrences of instability such as a polymerization kettle settingbecause of Tormsdorff effect, vibration of FBC, fluidized bed combustors tried by DOE in


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the 70s with coarse particles, the three mile island and Chernobyl nuclear accident, the BPAmericas oil spill of 2010 are discussed in detail. There are plenty of lessons in control anddynamics in these incidents. Examples from patent literature such as torque control and noisecontrol of a Toshiba washing machine with an agitator and rotating tub are discussed indetail. For the first time non-Fourier heat conduction and relaxation, transient PFR plug flow

reactor, CSTR with recycle are discussed. SPC , statistical process control concepts arediscussed in detail. Feedback and feedforward control strategies are discussed in detail withnumber of illustrations from the industry.

Dimensionless numbers introduced into the literature by this author such as frequencynumber, Sharma number (mass), Sharma number (heat)/storage number are discussed. Thesignificance of Damkohler number is discussed in detail. Other dimensionless groups such asFourier number, Fick number, Newton number, Reynolds number, Prandtl number, Stantonnumber, Peclect number etc can greatly simplify matters in process modeling. The differentregimes can be delineated and control action designed suitably. The interactions betweenprocess and control action intended are discussed in detail. Bode Plots, Nyquist diagrams,Routh arrays are demonstrated clearly. Feedforward controllers such as ratio control made an

interesting discussion point. A separate chapter is devoted to instrumentation.


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Introduction | 1

Chapter 1.0

INTRODUCTION

Chapter Overview

Motivation Feed forward Control Feedback Control Ratio Control Examples Types of Control

1.1 OVERVIEW

Process Dynamics, Process Control and Process Instrumentation are important in the design,

construction, operation and maintenance of chemical manufacturing plants world over. Plant

start-up, Plant Shut-down operations gets the attention of the technical leader(s) more than

during steady-state operation of the plant. Lip service is paid to the importance of transient

studies. Transient behavior of chemical reactors, distillation columns, absorption towers and

other unit operations need be better studied during collegiate education. Moores law states

that computing speed of microprocessors double every 18 months. Mathematical methods for

model development have been refined over centuries. The methods and means available tothe engineer need be better utilized.

Computer simulation and model development can be an integral part of an engineers

endeavors. The days when the effect of professionals who do mathematical modeling and

computer simulation on the bottom line of the enterprise is only indirect are over. The

coming era is when the PW of chemical plants are better for having an army of engineers and


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2 | Process Instrumentation, Control, and Dynamics

PhD scholars, who perform process dynamics studies, develop process control block

diagrams, instrument the chemical plant with sensors hooked with data acquisition to the

desktop computer.

1.2 MOTIVATION AND EXAMPLES OF CONTROL APPLICATIONS

Here are some examples of why process dynamics, control and instrumentation are

important.

Example 1-1 Trommsdorff Effect during Free Radical Polymerization

The suspension kettle in Muscatine, IA ofPonsanto Plastics, has been set-up.

Granite is needed to break the reaction-mass and get on with the polymer production. The

suspected reason is Trommsdorff effect[1].

During free-radical polymerizations there are three important sets of reactions: (i) Initiation;

(ii) Propagation and; (iii) Termination. As the polymerization reaction proceeds in

suspension kettles, the viscosity of the polymer mass increases. The termination reactions are

hindered. The polymer chain grows unbounded in size. This has set-up the reactor. This

effect is also called auto acceleration effect. It can be considered as a runaway reaction.

The action taken to prevent such occurrences during continuous polymerization of styrene or

copolymer of styrene and acrylonitrile a solvent is added.

A viscometer may be added to measure the viscosity of the reaction mass. The control action

can be to decrease the flow of the monomer supply or decreasing the reactor temperature etc

should the viscosity of the mass be high.


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Introduction | 3

Example 1-2 Centralized Heating and Cooling

The modern homes are equipped with a thermostat to set the desired temperature of the

residence (Tsp). Valves to the furnace and air conditioner can be controlled by using

measurement of temperature in the residence (Tm ). When the measured temperature, Tm < Tsp

the furnace is turned on and cooling shut-off. When Tm > Tsp the furnace is shut-off and the

air conditioner is turned on. Such a control method is calledfeedback control.

Figure 1.1 Centralized Heating and Cooling System in Homes using Feedback Control

This shall be discussed in more detail later. The block diagram for such control action is

shown below in Figure 1.1. Air from the blower is heated by the furnace or cooled by the air-

conditioner as the case may be. The heating or cooling action depends on the error signal and

whether the measured temperature, Tm is lower or higher compared with the set point

temperature, Tsp. Thermocouples are used to measure the temperature in the room.

Comparison of measured room temperature to set-point is performed by a comparator. The

feedbackstep is the measurement of actual room temperature using temperature sensor

Air from

Blower

ACTUAL

TEMPERATUREFURNACE

Control

Valve

AIR

CONDITIONER

Tm

Control Valve

Controller

Error e(t)

Comparator

+

T

sp


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(output) with the input (set-point). Figure 1-1 contains the essential elements of a block flow

diagram. These are:

Comparators Blocks Reference sensor Output sensor Controller Input/reference signals Plant OS system Feedback loop Disturbance signal Output signal

Example 1-3 Regulation of Body Temperature

Figure 1.2 Heat Conduction through Skin, Fat, Muscle and Bone Layers from

Surroundings to Blood Flow in Human Anatomy

The body temperature in humans can be seen to be held in dynamic balance by;

(i) the generation of heat by metabolic activities within the human anatomy and(ii) by transfer of heat outside the human anatomy to the surroundings.

SkinMuscle Bone

Fat


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Introduction | 5

(iii) The heat gain, heat storage and heat transfer mechanism coexist in humananatomy. As can be seen from Figure 1.2 there are five layers between the

surroundings and the blood [2].

The thermo physical properties of the blood, skin, fat and bone are different from

each other. The modes of heat transfer can be molecular heat conduction, heat convection,

heat radiation and by a fourth mode of heat transfer called damped wave conduction.

Metabolism in one word includes all the chemical reactions taking place within the human

anatomy. Energy is liberated from chemical reactions that are exothermic. This is used to

sustain life and to perform the various functions, basic and chosen. Work is done by human

anatomy.

The minimal rate of metabolism needed to sustain life is referred to as basic rate of

metabolism. This rate is obtained while the patient is awake and resting and is at a stress-less

state. Digestive activities should cease, the external hot weather does not cause any heat

exchange or thermoregulation. There is enough energy generated at this state, for the heart to

pump blood throughout the human anatomy, retain normal electrical activity in the nervous

system and generate calories of energy. The basic rate of metabolism can be measured using

the rate at which oxygen is consumed and the energy generated from metabolism of oxygen.

Some work done by human anatomy is allowed. The energy needed for metabolic activity is

obtained from chemical reactions that get coupled resulting in a net decrease in free energy.

The basic rate of metabolism in an average patient is roughly 75 watts. The major organs

such as brain, skeletal muscle, liver, heart, gastrointestinal tract, kidneys, lungs, etc,

participate in the base metabolism. The muscles in the human skeleton require less energy at

the rest state compared with the state of exercise. When the patient is asleep the metabolic

rate falls below the basic rate of metabolism. The metabolic rate at all other activities such aswalking, sitting, mating, eating, cooking, growing, etc are higher than the basic rate of

metabolism. The rate of metabolic rate can exceed the basic rate of metabolism by a factor of

10-20 during strenuous exercise.


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The basic rate of metabolism in Homo sapiens varies with the body mass m, as ..The relationship between the basic rate of metabolism and human anatomical parameters can

be expressed in terms of the surface to volume ration of the patient as .

.

Within the human anatomy, mechanisms are in place that will take effect to cool the

anatomy when the average temperature reaches 350

C. The average temperature within the

human anatomy is usually, 37 0 C. Au contraire, when the skin temperature reaches below

22.5 0 C cellular mechanisms will take effect that will result in generation of heat. The core

human anatomical temperature is maintained within a narrow range by use of insulation and

heat production.

Figure 1-3 Regulation of Human Anatomical Temperature seen as Feed forward

Control

Two mechanisms that can cause cooling within the human anatomy are: i)

vasodilatation and; ii) evaporative cooling affected by sweat. After strenuous exercise, on

account of vasodilatation, the skin exterior appears a bit reddish. The blood near the skin

surface gets refrigerated and flows back to the veins and arteries thereby affecting energy

transfer. The human anatomy reduces heat loss in the temperature range of 24 32 0 C by

reduced blood flow to the dermis. Below 24 0 C, vasoconstriction mechanism is not sufficient

Feedforward Control

(Disturbance)

Core

BodyTemp.

+

heat formation

heat absorption

heat dissipation

heat resistance Central

Nervous

System

Controller

Set Point

37 C


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Introduction | 7

and the heat production is by shivering or physical activity. There appears a set point in

thermoregulation. Regulatory process is a bit more complicated than a first order feed

forward control process. Transient receptor potential ion channels are sensitive to hot and

cold temperatures. TRP channels get activated upon control action from the hypothalamus

and stimulate the nerves. Nerve signals and hormone signals result in

vasodilatation/vasoconstriction or blood flow regulation and changes in metabolism and heat

generation. Block flow diagram of regulation of human anatomical temperature is shown in

Figure 1.3.

Example 1-4 Feedback Control of 3 Arm Robotic Manipulator with End Effector

Consider a 3 arm robotic manipulator with end effector. This can be programmed to perform

tasks such as to pick a bolt from the Table as shown in Figure 1-4. The manipulator is

instrumented with sensors at each joint to measure the joint angle. The joints are revolute [3].

Figure 1.4 3 Arm Manipulator with End Effector Picking a Bolt from Table

Each joint has an actuator that can be made to apply a torque on the neighboring link. Each

joint has a position sensor. Velocity sensors or tachometers are also present at these joints.

(S)

(G)

(T)

(W)

(B)


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The manipulator joints follow a prescribed position trajectory. The actuators are commanded

in terms of torque. A feedback control system can be deployed. The appropriate actuator

commands that will realize the desired motion can be given. The feedback from the sensors

in the joints is used to accomplish this task. The torque required is computed. This feedback

control loop is shown in Figure 1.5.

A vector of joint torques, , is given as input into the robot from the control system. The

sensors from the joints measure the joint angles, , and joint velocities. . This is sent as

signal to the control box. The number of parameters sent as a vector depends on the number

of joints, N in the system. The torque is calculated in the control box from the information

input from the trajectory generator and by comparison with the measurements received from

the sensors in the joints. A dynamic model can be used if necessary. The feedback is used to

detect any servo error. The control action taken has to be in such as fashion that the robotic

system is stable.

Figure 1.5 Block Diagram of Feedback Control of Robot Picking a Bolt

Trajectory

Generator

Control System

Robot


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Introduction | 9

Example 1-5 Nuclear Meltdown in Japan after the Tsunami and Earthquake

On March 11th 2011 the earth shook for more than 2 minutes [4] in Iwaki, Japan. Skyscrapers

began to oscillate and buildings collapsed. Tsunami came in. Earthquake of the order of 8.9

on the Richter scale is the most severe earthquake Japan has suffered in seismic history. The

ocean floors heaved and the water came all the way into the living areas. Floods and fires

came about. Four tectonic plates are near the island nation of Japan. This tsunami was even

of a bigger magnitude compared with the one in Indian ocean in 2004. Electric power was

completely cut off.

Figure 1-6 Fukushima Nuclear Power Plant

The Fukushima nuclear power plant (Figure 1.6) was damaged during the earthquake.

Seawater was directed onto the fuel during the meltdown of the nuclear power plants. There

was no better control action in place. Called The Fukushima 50 the firefighters were risking

death and were braving 250 millisieverts of radioactivity. This is five times more than the

permissible dose.


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The damaged nuclear reactors spewed radiation. There are no controls in place although that

geographical area is prone to earthquakes.

Example 1-6 Deepwater Horizon Oil Spill

The disaster that changed the price at the gasoline pumps in summer of 2010 did not have

better control and sensors in place than it did. The explosion of the Deepwater Horizon

drilling rig claimed 11 lives. The Gulf region lost its economic engine and left thousands

with mental and physical problems due to stress and pollution. Five million barrels of oil

gushed into the ocean for 86 days. Tourism dropped in the Gulf of Mexico. Off-shore drilling

can be better instrumented and have alarms in place and better controlled.

Deepwater Horizon was a semi-submersible, ultra-deepwater offshore oil drilling rig built in

2001 by Hyandai Heavy Industries, South Korea. The rig was used to drill the deepest oil

well in history at a vertical depth of 10,683 m in Gulf of Mexico 250 miles southeast of

Houston, TX. An explosion on the rig caused by a blowout [6] ignited a fireball visible from

a distance of 56 km. The fire was inextinguishable and the Deepwater Horizon sank. The oil

well was gushing at the sea floor and caused the largest offshore oil spill in the history of

United States. The oil spill causes a lot of damage to the environment and fisheries industry.

Transocean received an early partial settlement of $401 million for the loss of Deepwater

Horizon. The gushing of oil was at about 62,000 barrels per day on the average and 162,000

barrels a day on the worst case. The spewing went on for three months. The gush rate

decreased as the oil reservoir was depleted. The amount of Louisiana shoreline affected by

oil grew to 510 km by November 2010. The oil spill amounted to about 4.9 million barrels.

The blow-out preventer valves were not closed. Remotely operated underwater vehicles were

used to attempt to close the blowout preventer valves on the well head. A containment dome

that was 125 tons in weight was tried and failed when gas leaking from the pipe combined

with cold water formed methane hydrate crystals that blocked the opening at the top of the

dome. The top kill was a procedure where heavy drilling fluids were pumped into the

blowout preventer in order to restrict the gushing of oil before sealing it forever with cement.

This also failed.

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Process Instrumentation, Control, and Dynamics First Edition

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