Distributed Parameter Systems

Size: px
Start display at page:

Download "Distributed Parameter Systems"

Transcription

1 Distributed Parameter Systems Introduction All the apparatus dynamic experiments in the laboratory exhibit the effect known as "minimum phase dynamics". Process control loops are often based on simulations or assumptions of first-order and second-order processes. Perfect mixing is assumed in each unit operation. The text discusses these as lumped parameter type processes. What do we mean when we say a process exhibits "Non Minimum Phase" characteristics? Phase is one of the terms plotted with the Bode plots. If the process has dead time the phase is calculated as: Φ = 57.3ωτ Where phi is in degrees for a time delay of τ seconds. ω = 2πf. One can see that as the frequency increases the phase lag becomes more negative, hence "Non Minimum Phase" When the dynamic elements in the process do not shift phase beyond 90 (first-order), the resulting closed loop cannot exhibit a damped oscillation under proportional only control. The proportional gain in this case is purely arbitrary. This is the case of the lambda method, the dynamics are approximated as a single first order and the reset setting is based on that time constant. Stable control is assured in this case, but not necessarily the optimum control. True second order systems do not occur frequently in chemical and process applications, and process dead time is usually assumed to be attributed to transportation delay, such as the fluid transport time we experienced in the heat exchanger experiment with the added tubing. In our lab, the experiments all have lumped parameters. Lumped parameters occur where these is back mixing. Even the heat exchanger has back mixing because of the passes and tube baffles. However, most industrial control systems exhibit more complex behavior. (Sorry about that, but the real world functions quite different than most texts describe.) Many industrial processes have distributed parameters, the process variable are a function of distance as well as time. This requires us to view the dynamics in an additional dimension of length. There are two ways of viewing this, one as multiple interacting lags, and the second as non-interacting lags. The lags can be either discrete or operate as a continium. Examples of these from the fuel ethanol plants are, double pipe exchangers cool the mash before fermentation, falling film evaporators concentrate the syrup, distillation column to separate ethanol from water and molecular sieves; which are packed columns used to reduce the water content from the ethanol beyond the azeotrope concentration.

2 All these continuum processes result in the dynamic effects being expressed as a function of distance as well as time in the form of a partial differential equation or PDE. k d + k 2 t A process could have both interactive and non-interactive lags, as an example, a distillation column tray levels are non-interactive while the composition in interactive. This has been confirmed. The hydraulic time constant (non-interactive) is faster than the composition (interactive). Discrete Multiple Interacting Lags Although dead time added to a first-order lag provides a dynamic model that demonstrates realistic behavior for many industrial control simulations, some processes require more accurate dynamic modeling. An example is a distillation column, where many equilibrium stages or trays interact; the exiting compositions are a function of the interacting stages. Each tray can be represented by a first-order lag whose time constant is the familiar V/F or volume divided by the flow rate. The column cannot be represented by nth order lags where n is the number of column trays. The compositions on the trays interact with each other, and frequently the feed point is somewhere in the mid section of the column, further complicating the problem. These processes are frequently simulated as a series on first order function blocks, the resultant step response is frequently assumed to be a second order plus dead time or SOPDT. The following interactive lag example is a simulation of 4 first order lags where the V/F or volume divided by the flow time constants increase as the flow increases.

3 Multiple Interactive Lags PV time Distributed Lags Adding additional first order blocks does not noticeably affect the shape of the response curve; the 20-lag simulation can even be used to represent a packed column that has no discrete stages, i.e., a distributed lag. Another common process of this type is the heat exchanger, consisting of a distribution of heat-transfer surface and heat capacity. However, heat exchangers have an added complication: with a fixed volume but variable flow, their totaled time constants vary inversely with flow-rate, the familiar V/F term. Let us look at the dynamics of these processes from the viewpoint of heat transfer.

4 First Order Example T L Tamb Consider the thermo well example. In this case we had heat flowing from one end of the well to the other as well as heat being transferred along the well length. We can model the fundamental equation is Fourier's law of heat transfer where: A - area of heat transfer surface h heat transfer coefficient P well perimeter surface k - thermal conductivity of the material 2 T ka = hpt 2 x While this process does exhibit distributed dynamics, the temperature along the well is a function of time as well as distance, the solution of the dynamic behavior of the tip of the well, where the temperature is measured is a simple first order, calculated based on the well dimensions, thermal conductivity of the material and the heat transfer coefficient at the well surface. The thermo well first order time constant can be calculated by the following formula: τ = 560GC Uf d P f d D = 2 3( D d 2 ) Where t is the time constant in minutes G is the specific gravity of the thermowell Cp is the specific heat of the thermowell material BTU/lb-degF U is the heat transfer coefficient in BUT/hr-ft^2-degF fd is a dimension factor D is the outside diameter in inches k thermal conductivity d is the inside diameter in inches a well cross sectional area

5 Thermowell Response Temp, DegF time, minutes This is to show that even processes that have PDEs the resultant dynamic behavior can be simplified.

6 Process Identification For non-interactive lags, the total lag is the sum of each lag or Στ = nτ, 2 n + n For interactive lags the total response is τ = τ 2 We can identify the process dynamics by using the Ziegler-Nichols open loop testing method. Two times are noted once the slope is drawn on the output step response, τ de and τ e. τ e is the time for the PV to respond to the same percentage change, along the slope, as the output step change, m, in percent. These two times can be used to define the controller time constants for either interactive or non-interactive distributed process. The process gain is calculated as K p = de.5 and Σ τ = 7. 0τ de e 7 τ τ Tuning constants can be calculated for a non-interacting PID controller: for the interacting version are: Popt = 0K p Iopt = 0.30Σt Dopt = 0.09 t Popt = 5K p Iopt = 0.25 t Dopt = 0.0 t Popt is Proportional Band in percent, Iopt and Dopt are in time units. Using the ultimate period method will produce better results than the graphical method.

7 Ziegler and Nichols found that closed-loop testing under proportional control can produce still more-accurate estimates of controller settings. In this method, they reduced the controller to effectively proportional-only action by setting derivative time to zero and integral time to maximum (using a DeltaV system this will require a PD controller with no reset). Increase the gain until a uniform oscillation was produced. From this test obtained two pieces of information are found: the gain that produced the sustained oscillation and the period of the oscillation. Under these conditions, a distributed process will oscillate uniformly with the proportional band in percent set at 8.5Kp, and the resulting period of oscillation is observed to be 0.643Στ. The process parameters are then: Pu K p = Σ τ =. 55τ u 8.5 Where Pu is the un-damped proportional band and τu is the period of the un-damped cycle. It is often possible to calculate these parameters from known process information, when available, which can avoid testing, and even give valuable insight into the potential for parameter variations.

8 Distributed Lag Example A double pipe heat exchanger and a packed bed are examples of these distributed lags. The transient response is influenced by the nature of the heat transfer fluid as well as the relative flow patterns with respect to the transferred material. For the double pipe exchanger, we will discuss the heat being transferred in three ways. The first is assuming the outer jacket heat media is operating at a constant temperature while the fluid is flowing through the second pipe. The heating media could be either condensing steam or Dowtherm. In either case the supply temperature is assumed to be constant. This mass energy balance is written as partial differential equation or PDE. t L = v z L + τ ( T T ) W L τ = πdihi A ρc i i t W = τ 22 ( T T ) ( T T ) S W τ 2 W The wall temperature, T W and the liquid temperature, T L, vary across the length of the exchanger. If we assume the fluid flows through the outer jacket pipe and looses heat through the pipe to the inner fluid, the outer fluid can flow in either co-current or counter current flow. The co and counter flows refer to the flow pattern relative to the inner flow. In either of these cases, the supply temperature will also change both as a function of time and length through the exchanger. This is the simulated process you will control in Experiment 6 L τ 2 πdihi = A ρ C w w w τ 22 πdo ho = A ρ C w w w

9 Double Pipe Response Temp constant supply counter current cocurrent Time Double Pipe Heat Exchanger Simulated Outlet Temperature Response Note that in the case of the constant supply temperature, the result is the most responsive design. This is because the supply temperature is constant along the entire length of the outlet jacket. The dead time is the transportation time. Except for the knee at the bottom, the response appears to behave like a first order with dead time. Note the comparison with the interactive lag response. The constant supply and interactive lags examples are processes that have a smaller dead time to time constant ratio, these are easier to control. Processes multiple interactive variable time constants are more difficult to control because the apparent dead time will vary as the load. Tuning is difficult because different tuning settings will be required as the load varies Cascade Control If steam is supplied to a jacket or outer pipe in the double pipe exchanger, it is better to cascade to a pressure controller than a flow controller. Consider the following example: Assume a double pipe exchanger is temperature controlled by cascading a flow control loop. If a disturbance is introduced, that is an increase in load, the pressure in the steam cavity will decrease. This will cause the flow to increase. However that flow loop, typically 5 times faster than the temperature loop, will sense the increased flow and begin

10 to close the valve. This is not the right direction for valve travel. If, on the other hand, the inner loop is a pressure controller, the increased load will decrease the pressure in the cavity. The pressure controller will open the steam valve, which is the correct action for an increased load. Interactive Lags Distributive Lags PV constant supply interactive lags time In the case of the counter current design, the apparent dead time is increased and the response curve appears to behave more like a second order behavior. The counter current design had more dead time and it too appears to have a shape that appears to be second order. Simulated second order behavior response will not truly demonstrate this behavior. Double Pipe Exchanger Flow Patterns Constant Temperature Supply Ts Tin T L

11 Counter Current Flow Tin T L Ts Co-current Flow Ts Tin T L

12 Packed Bed Distribution Pattern Tin T L g t g s s = c c2 = c3 ( Tg Ts ) t L t In this case a fluid flows through a packed bed, interaction occurs with the particles in the bed. This interchange can be either thermal, such as heating or cooling the bed contents or adsorption of some material in the fluid stream, such as drying a compressed air stream. The above equations show that the exiting gas temperature is a function of the length as well as the solids temperature. The resultant response curve is shown below. There is an obvious dead time due to the transportation delay through the bed. However the transient response is obviously much more complicated than a second order. The shape is similar to the co-current double pipe heat exchanger

13 ODE PDE Simulations Frequently distributed parameter systems are simulated as multiple interactive lags. This can lead to modeling errors and if these models are used to predict control behavior, incorrect results will be obtained. Consider the double pipe exchanger, with steam as the outer heating media and Therminol-55 as the inner fluid. Two separate simulations were developed, one simulating 00 feet of jacketed pipe as 0 first order segments, two differential equations were used to simulate each segment. The term L v z in the partial differential equation L L = v + ( TW TL ) t z τ is approximated as and the partial derivatives with respect to time are TL v z evaluated as full time derivatives. This model is considered an ordinary differential equation model or ODE. An exact solution requires the integration of partial differential equations or PDE. The differences between these methods can be illustrated by comparing a step response for both solutions. A comparison of the two methods is shown as: ODE-PDE Step Response Temperature, DegF ODE PDE time, seconds

14 Note that during the first few seconds both methods appear to agree, however during the final approach, the PDE model appears to lag the ODE estimation, even though the both appear to reach the final value at about the same time. The exact inverse transform, to the time domain, of the Laplace transform of the equations has a delay element, the familiar exponential term exp(-av/l) where v is the inner fluid velocity, L is the pipe length and a is a Laplace transform. In this case the exact transform is not easily inverted. The function does take on the form of a Bessel function of the first kind, zeroth order. This follows closely with the findings of the original transport work done by Schumann and Furnas. While this ODE assumption appears to show the approximate behavior, this modeling error is magnified when controlled in a closed loop. In these simulations, both the ODE and PDE models are used to simulate the exit fluid temperature. A proportional plus integral controller is used to control the exiting fluid temperature by varying the steam condensation temperature. The same controller and settings was used for both models and yielded the following result: ODE PDE Control Comparisons Temperature, DegF ODE PDE Time, seconds Note that it takes much longer to stabilize the control even though the initial overshoots are almost equal. One way to avoid overshoot with a distributed parameter system is to use an external reset function, with the reset term delayed. Refer to the Shinskey article, The power of external-reset feedback.

15 Conclusions Control engineers should avoid making control simulations of distributed systems as a series of first order systems. The process dynamics for distributed parameter systems should include terms to simulate the distance dimension as well as the time dimension. References: Francis G. Shinskey, "Process Control: As Taught vs as Practiced" Industrial & Engineering Chemistry Research, 4(6), pp Francis G. Shinskey, The power of external reset feedback Copyright Control Global Coughanower, D. R., Process System Analysis and Control, Boston, MA: McGraw-Hill, 99. Furnas, C. C., "Heat Transfer from a Gas Stream to a Bed of Broken Solids" Trans. AIChE 24:42 (930). Schumann, T. E. W., "Heat Transfer: a Liquid Flowing Through a Porous Prism," Jour. Franklin Inst., vol 208, 929, pp

Solutions for Tutorial 10 Stability Analysis

Solutions for Tutorial 10 Stability Analysis Solutions for Tutorial 1 Stability Analysis 1.1 In this question, you will analyze the series of three isothermal CSTR s show in Figure 1.1. The model for each reactor is the same at presented in Textbook

More information

Dynamic Characteristics of Double-Pipe Heat Exchangers

Dynamic Characteristics of Double-Pipe Heat Exchangers Dynamic Characteristics of Double-Pipe Heat Exchangers WILLIAM C. COHEN AND ERNEST F. JOHNSON Princeton University, Princeton, N. J. The performance of automatically controlled process plants depends on

More information

Feedforward Control Feedforward Compensation

Feedforward Control Feedforward Compensation Feedforward Control Feedforward Compensation Compensation Feedforward Control Feedforward Control of a Heat Exchanger Implementation Issues Comments Nomenclature The inherent limitation of feedback control

More information

SRI VENKATESWARA COLLEGE OF ENGINEERING

SRI VENKATESWARA COLLEGE OF ENGINEERING COURSE DELIVERY PLAN - THEORY Page 1 of 7 Department of Chemical Engineering B.E/B.Tech/M.E/M.Tech : Chemical Engineering Regulation:2013 PG Specialisation : NA Sub. Code / Sub. Name : CH 6605 - Process

More information

CM 3310 Process Control, Spring Lecture 21

CM 3310 Process Control, Spring Lecture 21 CM 331 Process Control, Spring 217 Instructor: Dr. om Co Lecture 21 (Back to Process Control opics ) General Control Configurations and Schemes. a) Basic Single-Input/Single-Output (SISO) Feedback Figure

More information

Analyzing Mass and Heat Transfer Equipment

Analyzing Mass and Heat Transfer Equipment Analyzing Mass and Heat Transfer Equipment (MHE) Analyzing Mass and Heat Transfer Equipment Scaling up to solving problems using process equipment requires both continuum and macroscopic knowledge of transport,

More information

Process Control, 3P4 Assignment 6

Process Control, 3P4 Assignment 6 Process Control, 3P4 Assignment 6 Kevin Dunn, kevin.dunn@mcmaster.ca Due date: 28 March 204 This assignment gives you practice with cascade control and feedforward control. Question [0 = 6 + 4] The outlet

More information

Design and analysis of the prototype of boiler for steam pressure control

Design and analysis of the prototype of boiler for steam pressure control Design and analysis of the prototype of boiler for steam pressure control Akanksha Bhoursae, 2 Jalpa Shah, 3 Nishith Bhatt Institute of Technology, Nirma University, SG highway, Ahmedabad-38248,India 3

More information

Feedback Control of Linear SISO systems. Process Dynamics and Control

Feedback Control of Linear SISO systems. Process Dynamics and Control Feedback Control of Linear SISO systems Process Dynamics and Control 1 Open-Loop Process The study of dynamics was limited to open-loop systems Observe process behavior as a result of specific input signals

More information

Index. INDEX_p /15/02 3:08 PM Page 765

Index. INDEX_p /15/02 3:08 PM Page 765 INDEX_p.765-770 11/15/02 3:08 PM Page 765 Index N A Adaptive control, 144 Adiabatic reactors, 465 Algorithm, control, 5 All-pass factorization, 257 All-pass, frequency response, 225 Amplitude, 216 Amplitude

More information

Index Accumulation, 53 Accuracy: numerical integration, sensor, 383, Adaptive tuning: expert system, 528 gain scheduling, 518, 529, 709,

Index Accumulation, 53 Accuracy: numerical integration, sensor, 383, Adaptive tuning: expert system, 528 gain scheduling, 518, 529, 709, Accumulation, 53 Accuracy: numerical integration, 83-84 sensor, 383, 772-773 Adaptive tuning: expert system, 528 gain scheduling, 518, 529, 709, 715 input conversion, 519 reasons for, 512-517 relay auto-tuning,

More information

Process Solutions. Process Dynamics. The Fundamental Principle of Process Control. APC Techniques Dynamics 2-1. Page 2-1

Process Solutions. Process Dynamics. The Fundamental Principle of Process Control. APC Techniques Dynamics 2-1. Page 2-1 Process Dynamics The Fundamental Principle of Process Control APC Techniques Dynamics 2-1 Page 2-1 Process Dynamics (1) All Processes are dynamic i.e. they change with time. If a plant were totally static

More information

Process Control, 3P4 Assignment 5

Process Control, 3P4 Assignment 5 Process Control, 3P4 Assignment 5 Kevin Dunn, kevin.dunn@mcmaster.ca Due date: 12 March 2014 This assignment is due on Wednesday, 12 March 2014. Late hand-ins are not allowed. Since it is posted mainly

More information

Solutions for Tutorial 5 Dynamic Behavior of Typical Dynamic Systems

Solutions for Tutorial 5 Dynamic Behavior of Typical Dynamic Systems olutions for Tutorial 5 Dynamic Behavior of Typical Dynamic ystems 5.1 First order ystem: A model for a first order system is given in the following equation. dy dt X in X out (5.1.1) What conditions have

More information

ESRL Module 8. Heat Transfer - Heat Recovery Steam Generator Numerical Analysis

ESRL Module 8. Heat Transfer - Heat Recovery Steam Generator Numerical Analysis ESRL Module 8. Heat Transfer - Heat Recovery Steam Generator Numerical Analysis Prepared by F. Carl Knopf, Chemical Engineering Department, Louisiana State University Documentation Module Use Expected

More information

CHBE320 LECTURE XI CONTROLLER DESIGN AND PID CONTOLLER TUNING. Professor Dae Ryook Yang

CHBE320 LECTURE XI CONTROLLER DESIGN AND PID CONTOLLER TUNING. Professor Dae Ryook Yang CHBE320 LECTURE XI CONTROLLER DESIGN AND PID CONTOLLER TUNING Professor Dae Ryook Yang Spring 2018 Dept. of Chemical and Biological Engineering 11-1 Road Map of the Lecture XI Controller Design and PID

More information

IMPROVED TECHNIQUE OF MULTI-STAGE COMPENSATION. K. M. Yanev A. Obok Opok

IMPROVED TECHNIQUE OF MULTI-STAGE COMPENSATION. K. M. Yanev A. Obok Opok IMPROVED TECHNIQUE OF MULTI-STAGE COMPENSATION K. M. Yanev A. Obok Opok Considering marginal control systems, a useful technique, contributing to the method of multi-stage compensation is suggested. A

More information

PROCESS CONTROL TUTORIAL

PROCESS CONTROL TUTORIAL PROCESS CONTROL TUTORIAL An overview of engineering mathematics, process dynamics and PID control Jon Monsen, Ph.D., P.E. Process Control Tutorial An overview of engineering mathematics, process dynamics

More information

Design and Tuning of Fractional-order PID Controllers for Time-delayed Processes

Design and Tuning of Fractional-order PID Controllers for Time-delayed Processes Design and Tuning of Fractional-order PID Controllers for Time-delayed Processes Emmanuel Edet Technology and Innovation Centre University of Strathclyde 99 George Street Glasgow, United Kingdom emmanuel.edet@strath.ac.uk

More information

Enhanced Single-Loop Control Strategies Chapter 16

Enhanced Single-Loop Control Strategies Chapter 16 Enhanced Single-Loop Control Strategies Chapter 16 1. Cascade control 2. Time-delay compensation 3. Inferential control 4. Selective and override control 5. Nonlinear control 6. Adaptive control 1 Chapter

More information

Analysis and Design of Control Systems in the Time Domain

Analysis and Design of Control Systems in the Time Domain Chapter 6 Analysis and Design of Control Systems in the Time Domain 6. Concepts of feedback control Given a system, we can classify it as an open loop or a closed loop depends on the usage of the feedback.

More information

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Applied Thermodynamics for Marine Systems Prof. P. K. Das Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture No - 03 First Law of Thermodynamics (Open System) Good afternoon,

More information

SIMULATION SUITE CHEMCAD SOFTWARE PROCESS CONTROL SYSTEMS PROCESS CONTROL SYSTEMS COURSE WITH CHEMCAD MODELS. Application > Design > Adjustment

SIMULATION SUITE CHEMCAD SOFTWARE PROCESS CONTROL SYSTEMS PROCESS CONTROL SYSTEMS COURSE WITH CHEMCAD MODELS. Application > Design > Adjustment COURSE WITH CHEMCAD MODELS PROCESS CONTROL SYSTEMS Application > Design > Adjustment Based on F.G. Shinskey s 1967 Edition Presenter John Edwards P & I Design Ltd, UK Contact: jee@pidesign.co.uk COURSE

More information

PROCESS CONTROL (IT62) SEMESTER: VI BRANCH: INSTRUMENTATION TECHNOLOGY

PROCESS CONTROL (IT62) SEMESTER: VI BRANCH: INSTRUMENTATION TECHNOLOGY PROCESS CONTROL (IT62) SEMESTER: VI BRANCH: INSTRUMENTATION TECHNOLOGY by, Dr. Mallikarjun S. Holi Professor & Head Department of Biomedical Engineering Bapuji Institute of Engineering & Technology Davangere-577004

More information

Ben Wolfe 11/3/14. Figure 1: Theoretical diagram showing the each step of heat loss.

Ben Wolfe 11/3/14. Figure 1: Theoretical diagram showing the each step of heat loss. Condenser Analysis Water Cooled Model: For this condenser design there will be a coil of stainless steel tubing suspended in a bath of cold water. The cold water will be stationary and begin at an ambient

More information

Cascade Control of a Continuous Stirred Tank Reactor (CSTR)

Cascade Control of a Continuous Stirred Tank Reactor (CSTR) Journal of Applied and Industrial Sciences, 213, 1 (4): 16-23, ISSN: 2328-4595 (PRINT), ISSN: 2328-469 (ONLINE) Research Article Cascade Control of a Continuous Stirred Tank Reactor (CSTR) 16 A. O. Ahmed

More information

Incorporating Reality Into Process Simulation. Nathan Massey Chemstations, Inc. January 10, 2002

Incorporating Reality Into Process Simulation. Nathan Massey Chemstations, Inc. January 10, 2002 Incorporating Reality Into Process Simulation Nathan Massey Chemstations, Inc. January 10, 2002 Levels of Reality in Process Simulation 1. Data Accuracy and Comprehensiveness Physical Properties Phase

More information

Guide to Selected Process Examples :ili3g eil;]iil

Guide to Selected Process Examples :ili3g eil;]iil Guide to Selected Process Examples :ili3g eil;]iil Because of the strong interplay between process dynamics and control perfor mance, examples should begin with process equipment and operating conditions.

More information

If there is convective heat transfer from outer surface to fluid maintained at T W.

If there is convective heat transfer from outer surface to fluid maintained at T W. Heat Transfer 1. What are the different modes of heat transfer? Explain with examples. 2. State Fourier s Law of heat conduction? Write some of their applications. 3. State the effect of variation of temperature

More information

Plantwide Control of Chemical Processes Prof. Nitin Kaistha Department of Chemical Engineering Indian Institute of Technology, Kanpur

Plantwide Control of Chemical Processes Prof. Nitin Kaistha Department of Chemical Engineering Indian Institute of Technology, Kanpur Plantwide Control of Chemical Processes Prof. Nitin Kaistha Department of Chemical Engineering Indian Institute of Technology, Kanpur Lecture - 41 Cumene Process Plantwide Control (Refer Slide Time: 00:18)

More information

Dynamics and Control of Double-Pipe Heat Exchanger

Dynamics and Control of Double-Pipe Heat Exchanger Nahrain University, College of Engineering Journal (NUCEJ) Vol.13 No.2, 21 pp.129-14 Dynamics and Control of Double-Pipe Heat Exchanger Dr.Khalid.M.Mousa Chemical engineering Department Nahrain University

More information

Dynamic Characteristics of Counter-Current Flow Processes

Dynamic Characteristics of Counter-Current Flow Processes Dynamic Characteristics of Counter-Current Flow Processes Jennifer Puschke a, Heinz Preisig b arwth achen, Templergraben 55, 52062 achen, Germany b Chemical Engineering, NTNU, N 7491 Trondheim, Norway,

More information

Improved Identification and Control of 2-by-2 MIMO System using Relay Feedback

Improved Identification and Control of 2-by-2 MIMO System using Relay Feedback CEAI, Vol.17, No.4 pp. 23-32, 2015 Printed in Romania Improved Identification and Control of 2-by-2 MIMO System using Relay Feedback D.Kalpana, T.Thyagarajan, R.Thenral Department of Instrumentation Engineering,

More information

Innovative Solutions from the Process Control Professionals

Innovative Solutions from the Process Control Professionals Control Station Innovative Solutions from the Process Control Professionals Software For Process Control Analysis, Tuning & Training Control Station Software For Process Control Analysis, Tuning & Training

More information

Competences. The smart choice of Fluid Control Systems

Competences. The smart choice of Fluid Control Systems Competences The smart choice of Fluid Control Systems Contents 1. Open-loop and closed-loop control Page 4 1.1. Function and sequence of an open-loop control system Page 4 1.2. Function and sequence of

More information

Subject: BT6008 Process Measurement and Control. The General Control System

Subject: BT6008 Process Measurement and Control. The General Control System WALJAT COLLEGES OF APPLIED SCIENCES In academic partnership with BIRLA INSTITUTE OF TECHNOLOGY Question Bank Course: Biotechnology Session: 005-006 Subject: BT6008 Process Measurement and Control Semester:

More information

DESIGN AND CONTROL OF BUTYL ACRYLATE REACTIVE DISTILLATION COLUMN SYSTEM. I-Lung Chien and Kai-Luen Zeng

DESIGN AND CONTROL OF BUTYL ACRYLATE REACTIVE DISTILLATION COLUMN SYSTEM. I-Lung Chien and Kai-Luen Zeng DESIGN AND CONTROL OF BUTYL ACRYLATE REACTIVE DISTILLATION COLUMN SYSTEM I-Lung Chien and Kai-Luen Zeng Department of Chemical Engineering, National Taiwan University of Science and Technology, Taipei

More information

Name of Course: B.Tech. (Chemical Technology/Leather Technology)

Name of Course: B.Tech. (Chemical Technology/Leather Technology) Name of : B.Tech. (Chemical Technology/Leather Technology) Harcourt Butler Technological Institute, Kanpur Study and [Effective from the Session 201-1] B. Tech. (Chemical Technology/Leather Technology)

More information

ABB PSPG-E7 SteamTMax Precise control of main and reheat ST. ABB Group May 8, 2014 Slide 1 ABB

ABB PSPG-E7 SteamTMax Precise control of main and reheat ST. ABB Group May 8, 2014 Slide 1 ABB ABB PSPG-E7 SteamTMax Precise control of main and reheat ST May 8, 2014 Slide 1 Challenge m S m att T in T out Live steam and reheated steam temperatures are controlled process variables critical in steam

More information

Index. Index. More information. in this web service Cambridge University Press

Index. Index. More information.  in this web service Cambridge University Press A-type elements, 4 7, 18, 31, 168, 198, 202, 219, 220, 222, 225 A-type variables. See Across variable ac current, 172, 251 ac induction motor, 251 Acceleration rotational, 30 translational, 16 Accumulator,

More information

8.1 Technically Feasible Design of a Heat Exchanger

8.1 Technically Feasible Design of a Heat Exchanger 328 Technically Feasible Design Case Studies T 2 q 2 ρ 2 C p2 T F q ρ C p T q ρ C p T 2F q 2 ρ 2 C p2 Figure 3.5. Countercurrent double-pipe exchanger. 8. Technically Feasible Design of a Heat Exchanger

More information

GENERAL PHYSICS (3) LABORATORY PHYS 203 LAB STUDENT MANUAL

GENERAL PHYSICS (3) LABORATORY PHYS 203 LAB STUDENT MANUAL Haifaa altoumah& Rabab Alfaraj By Haifaa altoumah& Rabab Alfaraj GENERAL PHYSICS (3) LABORATORY PHYS 203 LAB STUDENT MANUAL Name:-. ID# KING ABDULAZIZ UNIVERSITY PHYSICS DEPARMENT 1st semester 1430H Contents

More information

Process Dynamics, Operations, and Control Lecture Notes 2

Process Dynamics, Operations, and Control Lecture Notes 2 Chapter. Dynamic system.45 Process Dynamics, Operations, and Control. Context In this chapter, we define the term 'system' and how it relates to 'process' and 'control'. We will also show how a simple

More information

CHAPTER 3 TUNING METHODS OF CONTROLLER

CHAPTER 3 TUNING METHODS OF CONTROLLER 57 CHAPTER 3 TUNING METHODS OF CONTROLLER 3.1 INTRODUCTION This chapter deals with a simple method of designing PI and PID controllers for first order plus time delay with integrator systems (FOPTDI).

More information

Introduction to Heat and Mass Transfer

Introduction to Heat and Mass Transfer Introduction to Heat and Mass Transfer Week 16 Merry X mas! Happy New Year 2019! Final Exam When? Thursday, January 10th What time? 3:10-5 pm Where? 91203 What? Lecture materials from Week 1 to 16 (before

More information

= A x (t) + B utt), by d{ _-=-=-

= A x (t) + B utt), by d{ _-=-=- M.Tech. [ 24 103 ] Degree Examination ndustrial Process nstrumentation First Semester COMPUTER CONTROL OF PROCESSES (Effective from the Admitted Batch of2003-2004) Time: 3 Hours Maximum marks: 100 Answer

More information

Tutorial 1. Where Nu=(hl/k); Reynolds number Re=(Vlρ/µ) and Prandtl number Pr=(µCp/k)

Tutorial 1. Where Nu=(hl/k); Reynolds number Re=(Vlρ/µ) and Prandtl number Pr=(µCp/k) Tutorial 1 1. Explain in detail the mechanism of forced convection. Show by dimensional analysis (Rayleigh method) that data for forced convection may be correlated by an equation of the form Nu = φ (Re,

More information

EE3CL4: Introduction to Linear Control Systems

EE3CL4: Introduction to Linear Control Systems 1 / 17 EE3CL4: Introduction to Linear Control Systems Section 7: McMaster University Winter 2018 2 / 17 Outline 1 4 / 17 Cascade compensation Throughout this lecture we consider the case of H(s) = 1. We

More information

B1-1. Closed-loop control. Chapter 1. Fundamentals of closed-loop control technology. Festo Didactic Process Control System

B1-1. Closed-loop control. Chapter 1. Fundamentals of closed-loop control technology. Festo Didactic Process Control System B1-1 Chapter 1 Fundamentals of closed-loop control technology B1-2 This chapter outlines the differences between closed-loop and openloop control and gives an introduction to closed-loop control technology.

More information

Control System Design

Control System Design ELEC ENG 4CL4: Control System Design Notes for Lecture #13 Monday, February 3, 2003 Dr. Ian C. Bruce Room: CRL-229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca (3) Cohen-Coon Reaction Curve Method

More information

CONTROL MODE SETTINGS. The quality of control obtained from a particular system depends largely on the adj ustments made to the various mode

CONTROL MODE SETTINGS. The quality of control obtained from a particular system depends largely on the adj ustments made to the various mode Instrumentation & Control - Course 136 CONTROL MODE SETTINGS The quality of control obtained from a particular system depends largely on the adj ustments made to the various mode settings. Many control

More information

Modeling and Control of Chemical Reactor Using Model Reference Adaptive Control

Modeling and Control of Chemical Reactor Using Model Reference Adaptive Control Modeling and Control of Chemical Reactor Using Model Reference Adaptive Control Padmayoga.R, Shanthi.M 2, Yuvapriya.T 3 PG student, Dept. of Electronics and Instrumentation, Valliammai Engineering College,

More information

University of Science and Technology, Sudan Department of Chemical Engineering.

University of Science and Technology, Sudan Department of Chemical Engineering. ISO 91:28 Certified Volume 3, Issue 6, November 214 Design and Decoupling of Control System for a Continuous Stirred Tank Reactor (CSTR) Georgeous, N.B *1 and Gasmalseed, G.A, Abdalla, B.K (1-2) University

More information

Lecture 5 Classical Control Overview III. Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore

Lecture 5 Classical Control Overview III. Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore Lecture 5 Classical Control Overview III Dr. Radhakant Padhi Asst. Professor Dept. of Aerospace Engineering Indian Institute of Science - Bangalore A Fundamental Problem in Control Systems Poles of open

More information

CHAPTER 10: STABILITY &TUNING

CHAPTER 10: STABILITY &TUNING When I complete this chapter, I want to be able to do the following. Determine the stability of a process without control Determine the stability of a closed-loop feedback control system Use these approaches

More information

HEAT TRANSFER 1 INTRODUCTION AND BASIC CONCEPTS 5 2 CONDUCTION

HEAT TRANSFER 1 INTRODUCTION AND BASIC CONCEPTS 5 2 CONDUCTION HEAT TRANSFER 1 INTRODUCTION AND BASIC CONCEPTS 5 2 CONDUCTION 11 Fourier s Law of Heat Conduction, General Conduction Equation Based on Cartesian Coordinates, Heat Transfer Through a Wall, Composite Wall

More information

Objective: To study P, PI, and PID temperature controller for an oven and compare their performance. Name of the apparatus Range Quantity

Objective: To study P, PI, and PID temperature controller for an oven and compare their performance. Name of the apparatus Range Quantity Objective: To study P, PI, and PID temperature controller for an oven and compare their. Apparatus Used: Name of the apparatus Range Quantity 1. Temperature Controller System 1 PID Kp (0-10) Kd(0-20) Ki(0-0.02)

More information

Distillation is a method of separating mixtures based

Distillation is a method of separating mixtures based Distillation Distillation is a method of separating mixtures based on differences in their volatilities in a boiling liquid mixture. Distillation is a unit operation, or a physical separation process,

More information

Introduction to Process Control

Introduction to Process Control Introduction to Process Control For more visit :- www.mpgirnari.in By: M. P. Girnari (SSEC, Bhavnagar) For more visit:- www.mpgirnari.in 1 Contents: Introduction Process control Dynamics Stability The

More information

Chapter 7 Control. Part Classical Control. Mobile Robotics - Prof Alonzo Kelly, CMU RI

Chapter 7 Control. Part Classical Control. Mobile Robotics - Prof Alonzo Kelly, CMU RI Chapter 7 Control 7.1 Classical Control Part 1 1 7.1 Classical Control Outline 7.1.1 Introduction 7.1.2 Virtual Spring Damper 7.1.3 Feedback Control 7.1.4 Model Referenced and Feedforward Control Summary

More information

Lesson 19: Process Characteristics- 1 st Order Lag & Dead-Time Processes

Lesson 19: Process Characteristics- 1 st Order Lag & Dead-Time Processes 1 Lesson 19: Process Characteristics- 1 st Order Lag & Dead-Time Processes ET 438a Automatic Control Systems Technology 2 Learning Objectives After this series of presentations you will be able to: Describe

More information

EC CONTROL SYSTEM UNIT I- CONTROL SYSTEM MODELING

EC CONTROL SYSTEM UNIT I- CONTROL SYSTEM MODELING EC 2255 - CONTROL SYSTEM UNIT I- CONTROL SYSTEM MODELING 1. What is meant by a system? It is an arrangement of physical components related in such a manner as to form an entire unit. 2. List the two types

More information

reality is complex process

reality is complex process ISS0080 Automation and Process Control Lecture 5 1 Process models the desire to describe reality Model of the process, model simplication, identication. model reality is complex process Replaces the original;

More information

Countercurrent heat exchanger

Countercurrent heat exchanger Countercurrent heat exchanger 1. Theoretical summary The basic operating principles and the simplified calculations regarding the counter current heat exchanger were discussed in the subject Chemical Unit

More information

ECE 388 Automatic Control

ECE 388 Automatic Control Lead Compensator and PID Control Associate Prof. Dr. of Mechatronics Engineeering Çankaya University Compulsory Course in Electronic and Communication Engineering Credits (2/2/3) Course Webpage: http://ece388.cankaya.edu.tr

More information

Basic Analysis of Data

Basic Analysis of Data Basic Analysis of Data Department of Chemical Engineering Prof. Geoff Silcox Fall 008 1.0 Reporting the Uncertainty in a Measured Quantity At the request of your supervisor, you have ventured out into

More information

Dr Ian R. Manchester

Dr Ian R. Manchester Week Content Notes 1 Introduction 2 Frequency Domain Modelling 3 Transient Performance and the s-plane 4 Block Diagrams 5 Feedback System Characteristics Assign 1 Due 6 Root Locus 7 Root Locus 2 Assign

More information

Level 7 Post Graduate Diploma in Engineering Heat and mass transfer

Level 7 Post Graduate Diploma in Engineering Heat and mass transfer 9210-221 Level 7 Post Graduate Diploma in Engineering Heat and mass transfer 0 You should have the following for this examination one answer book non programmable calculator pen, pencil, drawing instruments

More information

BME-A PREVIOUS YEAR QUESTIONS

BME-A PREVIOUS YEAR QUESTIONS BME-A PREVIOUS YEAR QUESTIONS CREDITS CHANGE ACCHA HAI TEAM UNIT-1 Introduction: Introduction to Thermodynamics, Concepts of systems, control volume, state, properties, equilibrium, quasi-static process,

More information

Memorial University of Newfoundland Faculty of Engineering and Applied Science

Memorial University of Newfoundland Faculty of Engineering and Applied Science Memorial University of Newfoundl Faculty of Engineering Applied Science ENGI-7903, Mechanical Equipment, Spring 20 Assignment 2 Vad Talimi Attempt all questions. The assignment may be done individually

More information

Solutions for Tutorial 4 Modelling of Non-Linear Systems

Solutions for Tutorial 4 Modelling of Non-Linear Systems Solutions for Tutorial 4 Modelling of Non-Linear Systems 4.1 Isothermal CSTR: The chemical reactor shown in textbook igure 3.1 and repeated in the following is considered in this question. The reaction

More information

Basic Models of Simultaneous Heat and Mass Transfer

Basic Models of Simultaneous Heat and Mass Transfer 20 Basic Models of Simultaneous Heat and Mass Transfer Keywords: Unit Models, Evaporator, Vaporizer A chemical process invariably involves energy transfer simultaneously with mass transfer. So in this

More information

Control System Design

Control System Design ELEC ENG 4CL4: Control System Design Notes for Lecture #15 Friday, February 6, 2004 Dr. Ian C. Bruce Room: CRL-229 Phone ext.: 26984 Email: ibruce@mail.ece.mcmaster.ca (3) Cohen-Coon Reaction Curve Method

More information

CONTENTS. Introduction LHP Library Examples Future Improvements CARMEN GREGORI DE LA MALLA EAI. ESTEC, October 2004

CONTENTS. Introduction LHP Library Examples Future Improvements CARMEN GREGORI DE LA MALLA EAI. ESTEC, October 2004 CARMEN GREGORI DE LA MALLA EAI CONTENTS Introduction LHP Library Examples Future Improvements INTRODUCTION (1) Loop heat pipes (LHP) are two-phase capillary heat transfer devices that are becoming very

More information

RELAY AUTOTUNING OF MULTIVARIABLE SYSTEMS: APPLICATION TO AN EXPERIMENTAL PILOT-SCALE DISTILLATION COLUMN

RELAY AUTOTUNING OF MULTIVARIABLE SYSTEMS: APPLICATION TO AN EXPERIMENTAL PILOT-SCALE DISTILLATION COLUMN Copyright 2002 IFAC 15th Triennial World Congress, Barcelona, Spain RELAY AUTOTUNING OF MULTIVARIABLE SYSTEMS: APPLICATION TO AN EXPERIMENTAL PILOT-SCALE DISTILLATION COLUMN G. Marchetti 1, C. Scali 1,

More information

Distillation. Senior Design CHE 396 Andreas Linninger. Innovative Solutions. Michael Redel Alycia Novoa Tanya Goldina Michelle Englert

Distillation. Senior Design CHE 396 Andreas Linninger. Innovative Solutions. Michael Redel Alycia Novoa Tanya Goldina Michelle Englert Distillation Senior Design CHE 396 Andreas Linninger Innovative Solutions Michael Redel Alycia Novoa Tanya Goldina Michelle Englert Table of Contents Introduction 3 Flowsheet 4 Limitations 5 Applicability

More information

Model-based PID tuning for high-order processes: when to approximate

Model-based PID tuning for high-order processes: when to approximate Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 25 Seville, Spain, December 2-5, 25 ThB5. Model-based PID tuning for high-order processes: when to approximate

More information

SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT B.Tech. [SEM V (ME-51, 52, 53, 54)] QUIZ TEST-1 (Session: )

SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT B.Tech. [SEM V (ME-51, 52, 53, 54)] QUIZ TEST-1 (Session: ) QUIZ TEST-1 Time: 1 Hour HEAT AND MASS TRANSFER Note: All questions are compulsory. Q1) The inside temperature of a furnace wall ( k=1.35w/m.k), 200mm thick, is 1400 0 C. The heat transfer coefficient

More information

MODULE 5: DISTILLATION

MODULE 5: DISTILLATION MOULE 5: ISTILLATION LECTURE NO. 3 5.2.2. Continuous distillation columns In contrast, continuous columns process a continuous feed stream. No interruptions occur unless there is a problem with the column

More information

Making Decisions with Insulation

Making Decisions with Insulation More on Heat Transfer from Cheresources.com: FREE Resources Making Decisions with Insulation Article: Basics of Vaporization Questions and Answers: Heat Transfer Experienced-Based Rules for Heat Exchangers

More information

Chapter 5. Mass and Energy Analysis of Control Volumes

Chapter 5. Mass and Energy Analysis of Control Volumes Chapter 5 Mass and Energy Analysis of Control Volumes Conservation Principles for Control volumes The conservation of mass and the conservation of energy principles for open systems (or control volumes)

More information

Robust QFT-based PI controller for a feedforward control scheme

Robust QFT-based PI controller for a feedforward control scheme Integral-Derivative Control, Ghent, Belgium, May 9-11, 218 ThAT4.4 Robust QFT-based PI controller for a feedforward control scheme Ángeles Hoyo José Carlos Moreno José Luis Guzmán Tore Hägglund Dep. of

More information

Process Unit Control System Design

Process Unit Control System Design Process Unit Control System Design 1. Introduction 2. Influence of process design 3. Control degrees of freedom 4. Selection of control system variables 5. Process safety Introduction Control system requirements»

More information

Design and Comparative Analysis of Controller for Non Linear Tank System

Design and Comparative Analysis of Controller for Non Linear Tank System Design and Comparative Analysis of for Non Linear Tank System Janaki.M 1, Soniya.V 2, Arunkumar.E 3 12 Assistant professor, Department of EIE, Karpagam College of Engineering, Coimbatore, India 3 Associate

More information

Lesson 7: Thermal and Mechanical Element Math Models in Control Systems. 1 lesson7et438a.pptx. After this presentation you will be able to:

Lesson 7: Thermal and Mechanical Element Math Models in Control Systems. 1 lesson7et438a.pptx. After this presentation you will be able to: Lesson 7: Thermal and Mechanical Element Math Models in Control Systems ET 438a Automatic Control Systems Technology Learning Objectives After this presentation you will be able to: Explain how heat flows

More information

Fuzzy-PID Methods for Controlling Evaporator Superheat

Fuzzy-PID Methods for Controlling Evaporator Superheat Purdue University Purdue e-pubs International Refrigeration and Air Conditioning Conference School of Mechanical Engineering 2000 Fuzzy-PID Methods for Controlling Evaporator Superheat R. Q. Zhu Xi an

More information

CHAPTER 13: FEEDBACK PERFORMANCE

CHAPTER 13: FEEDBACK PERFORMANCE When I complete this chapter, I want to be able to do the following. Apply two methods for evaluating control performance: simulation and frequency response Apply general guidelines for the effect of -

More information

Advanced Power Plant Modeling with Applications to an Advanced Boiling Water Reactor and a Heat Exchanger

Advanced Power Plant Modeling with Applications to an Advanced Boiling Water Reactor and a Heat Exchanger Advanced Power Plant Modeling with Applications to an Advanced Boiling Water Reactor and a Heat Exchanger Thomas D Younkins Former Member, ASME Prasanna Kumar Muralimanohar Joe H Chow 21 Advanced methods

More information

Process Control & Design

Process Control & Design 458.308 Process Control & Design Lecture 5: Feedback Control System Jong Min Lee Chemical & Biomolecular Engineering Seoul National University 1 / 29 Feedback Control Scheme: The Continuous Blending Process.1

More information

Intermediate Process Control CHE576 Lecture Notes # 2

Intermediate Process Control CHE576 Lecture Notes # 2 Intermediate Process Control CHE576 Lecture Notes # 2 B. Huang Department of Chemical & Materials Engineering University of Alberta, Edmonton, Alberta, Canada February 4, 2008 2 Chapter 2 Introduction

More information

Appendix A: Exercise Problems on Classical Feedback Control Theory (Chaps. 1 and 2)

Appendix A: Exercise Problems on Classical Feedback Control Theory (Chaps. 1 and 2) Appendix A: Exercise Problems on Classical Feedback Control Theory (Chaps. 1 and 2) For all calculations in this book, you can use the MathCad software or any other mathematical software that you are familiar

More information

To increase the concentration of product formed in a PFR, what should we do?

To increase the concentration of product formed in a PFR, what should we do? To produce more moles of product per time in a flow reactor system, what can we do? a) Use less catalyst b) Make the reactor bigger c) Make the flow rate through the reactor smaller To increase the concentration

More information

Design of de-coupler for an interacting tanks system

Design of de-coupler for an interacting tanks system IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE) e-issn: 78-1676,p-ISSN: 3-3331, Volume 7, Issue 4 (Sep. - Oct. 13), PP 48-53 Design of de-coupler for an interacting tanks system Parag

More information

SECOND ENGINEER REG. III/2 APPLIED HEAT

SECOND ENGINEER REG. III/2 APPLIED HEAT SECOND ENGINEER REG. III/2 APPLIED HEAT LIST OF TOPICS A B C D E F G H I J K Pressure, Temperature, Energy Heat Transfer Internal Energy, Thermodynamic systems. First Law of Thermodynamics Gas Laws, Displacement

More information

Theoretical Models of Chemical Processes

Theoretical Models of Chemical Processes Theoretical Models of Chemical Processes Dr. M. A. A. Shoukat Choudhury 1 Rationale for Dynamic Models 1. Improve understanding of the process 2. Train Plant operating personnel 3. Develop control strategy

More information

ECH 4224L Unit Operations Lab I Thin Film Evaporator. Introduction. Objective

ECH 4224L Unit Operations Lab I Thin Film Evaporator. Introduction. Objective Introduction In this experiment, you will use thin-film evaporator (TFE) to separate a mixture of water and ethylene glycol (EG). In a TFE a mixture of two fluids runs down a heated inner wall of a cylindrical

More information

DYNAMIC SIMULATOR-BASED APC DESIGN FOR A NAPHTHA REDISTILLATION COLUMN

DYNAMIC SIMULATOR-BASED APC DESIGN FOR A NAPHTHA REDISTILLATION COLUMN HUNGARIAN JOURNAL OF INDUSTRY AND CHEMISTRY Vol. 45(1) pp. 17 22 (2017) hjic.mk.uni-pannon.hu DOI: 10.1515/hjic-2017-0004 DYNAMIC SIMULATOR-BASED APC DESIGN FOR A NAPHTHA REDISTILLATION COLUMN LÁSZLÓ SZABÓ,

More information

7.2 Controller tuning from specified characteristic polynomial

7.2 Controller tuning from specified characteristic polynomial 192 Finn Haugen: PID Control 7.2 Controller tuning from specified characteristic polynomial 7.2.1 Introduction The subsequent sections explain controller tuning based on specifications of the characteristic

More information

Designing Steps for a Heat Exchanger ABSTRACT

Designing Steps for a Heat Exchanger ABSTRACT Designing Steps for a Heat Exchanger Reetika Saxena M.Tech. Student in I.F.T.M. University, Moradabad Sanjay Yadav 2 Asst. Prof. in I.F.T.M. University, Moradabad ABSTRACT Distillation is a common method

More information

Process Design Decisions and Project Economics Prof. Dr. V. S. Moholkar Department of Chemical Engineering Indian Institute of Technology, Guwahati

Process Design Decisions and Project Economics Prof. Dr. V. S. Moholkar Department of Chemical Engineering Indian Institute of Technology, Guwahati Process Design Decisions and Project Economics Prof. Dr. V. S. Moholkar Department of Chemical Engineering Indian Institute of Technology, Guwahati Module - 2 Flowsheet Synthesis (Conceptual Design of

More information