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KWAME NKRUMAH UNIVERSITY OF SCIENCE AND TECHNOLOGY, KUMASI INSTITUTE OF DISTANCE LEARNING CHE 451 Chemical Process Design & Economics (Credits: 4)

Benjamin Afotey, PhD Chemical Engineering Department August, 2014

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Course Introduction Design is the synthesis of ideas to achieve a desired goal (product). The designer starts with an idea and proceeds to develop several alternative designs that he evaluates and finally settles on the one that satisfies his objective (goal). The search for alternative designs is important to the economic viability of the design project. CHE 451 is a fourth year core course offered in first semester in BSc. Chemical Engineering.

Course Overview Methodology of the Design Process: Constraints on a Design Problem; Fixed/Rigid constraints, Less rigid constraints, The design process; Design objectives, Data collection, Generation of possible designs,Selection, Chemical manufacturing processes, Continuous and batch processes, Organization of a chemical engineering design project. Codes and Standards, Design Factors, Variable & Mathematical Representation of Design Problems: Codes and standards, Design factors, Systems of units, Mathematical representation of the design problem, Selection of design variables. Optimization and Batch Production Process: Introduction, Simple models, Multiple variable systems, Methods of analysis, Other optimization methods, Batch production process. Process Synthesis: Introduction, Raw materials and chemical reactions, Summary of process design heuristics, Heuristics in equipment design. Process Simulation: Introduction, Process simulator, Types of process simulation, Units operation solvers, Uncertainty and sensitivity issues. Flow sheeting, Piping and Instrumentation: Introduction, Piping & instrumentation diagrams, Valve selection, Pumps, Classification of pumps, Factors to consider in pump selection, Centrifugal pumps, Effective characteristics curves, Design parameters of centrifugal pumps, Operating point, Choice of rotational speed,. Process Economics: Cost estimation, Cash flow for industrial operation, Factors affecting investment and production costs, Capital investment, Estimation of capital investment, Types of capital cost estimates, cost indices, Methods of estimating capital investment, Turnover ratio, Estimation of total product cost, Break-even point. Process Economics: Depreciation and profitability analysis, Service life, Salvage value, Present value, Methods for determining depreciation, Profitability standards, Basis for evaluating project profitability, Mathematical methods for profitability evaluation, Rate of return on investment, Discounted cash flow, Capitalized cost, Pay-back time, Sensitivity analysis.

Course Objective The following is the main course Objective 1. To enable students understand and acknowledge the importance of economic analysis in chemical process design, by way of efficiently maximizing profit.

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Course Outline The course outline is divided into eight units. Each of the eight units is broken into subtopics. Each unit addresses one or more of the course objectives. Unit 1: Methodology of the Design Process Unit 2: Codes and Standards, Design Factors, Variable &Mathematical Representation of Design Problems Unit 3: Optimization and Batch Production Process Unit 4: Process Synthesis Unit 5: Process Simulation Unit 6: Flow Sheeting, Piping and Instrumentation Unit 7: Process Economics: Cost Estimation Unit 8: Process Economics: Depreciation and Profitability Analysis

Grading Continuous Assessment: 30% End of Semester Examination: 70%

Reading List/Recommendation Textbooks/Websites/CDs 1. Plant Design and Economics for Chemical Engineers: By Peters and Timmerhaus 2. Coulson & Richardson’s Chemical Engineering Design: By Sinnot, Volume 6

Course Writer Dr. Benjamin Afotey received his BSc. Degree in Chemical Engineering in 2000 at Kwame Nkrumah University of Science and Technology, Kumasi. He received his MSc. and PhD Degrees at the University of Texas, Arlington, and U.S.A in 2003 and 2008 respectively. He worked with the Texas Commission on Environmental Quality, U.S.A between 2008 and 2009 and joined the Chemical Engineering Department in 2010.

Acknowledgement I wish to thank the Almighty God for His guidance throughout the write up. I would also like to thank my colleagues who provided encouragement of any kind. Finally, I acknowledge the effort of my Teaching Assistant who contributed in a way to the successful completion of the material.

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TABLE OF CONTENT 1.0 METHODOLOGY OF THE DESIGN PROCESS SESSION 1-1 : 1-1.1 Introduction 1-1.2.Constraint on a Design Problem 1-1.2.1 Fixed/Rigid constraint 1-1.2.2 Less rigid constraint 1-1.3 The Design Process 1-1.3.1 The design objective 1-1.3.2 Data collection 1-1.3.3 Generation of possible designs 1-1.3.4 Selection 1-1.4 Chemical Manufacturing Processes 1-1.5 Continuous and Batch Processes 1-1.5.1 Choice of continuous verses Batch processes 1-1.5.2 Organization of a chemical engineering design project 2.0 CODES AND STANDARDS, DESIGN FACTORS, VARIABLE & MATHEMATICAL REPRESENTATION OF DESIGN PROBLEMS SESSION 2-1 2-1.1 Codes and Standards 2-1.2 Factors of Safety 2-1.3 System of Units 2-1.4 Mathematical Representation of the Design Problem 2-1.5 Selection of Design Variables 3.0 OPTIMIZATION AND BATCH PRODUCTION PROCESS SEESION 3-1 3-1.1 Introduction 3-1.2 Simple Methods 3-1.3 Multiple Variable Systems 3-1.4 Methods of Analysis 3-1.5 Other Optimization Methods 3-1.6 Batch Production Process 4-0 PROCESS SYNTHESIS SESSION 4-1 4-1.1Introduction 4-1.2 Raw Materials and Chemical Reactions 4-1.3 Summary of Process Design Heuristics 4-1.4 Heuristics in Equipment Design 5.0 PROCESS SIMULATION SESSION 5-1 5-1.1 Introduction 5-1.2 Process Simulator 5-1.3 Types of Process Simulation 5-1.4 Unit Operation Solvers 5-1.5 Uncertainty and Sensitivity Issues iv

1 1 1 1 1 1 2 3 4 4 5 5 7 7 7 11 11 11 12 13 13 18 20 20 20 21 22 23 24 24 26 26 26 26 34 34 38 38 38 39 39 40 40

6.0 FLOW SHEETING, PIPING AND INSTRUMENTATION SESSION 6-1 6-1.1 Introduction 6-1.2 Piping and Instrumentation Diagrams 6-1.3 Valve Selection 6-1.3.1 Gate valves 6-1.3.2 Globe valves SESSION 6-2 6-2.1 Introduction of Pumps 6-2.2 Classification of Pumps 6-2.3 Factors to Consider in Pump Selection 6-2.4 Centrifugal Pumps 6-2.4.1 Effective characteristics curves 6-2.4.2 Design parameters of centrifugal pumps 6-2.4.3 Operating point 6-2.4.4 Q/H Curve versus Technical choices 6-2.4.5 Choice of rotation speed 6-2.4.6 Suction Conditions: Concept of NPSH 7.0 PROCESS ECONOMICS: COST ESIMATION SESSION 7-1 7-1.1 Cost Estimation 7-1.2 Cash Flow for Industrial Operations 7-1.3 Factors affecting Investment and Production Costs 7-1.4 Capital Investment 7-1.5 Estimation of Capital Investment 7-1.5.1 Introduction 7-1.5.2 Types of capital cost estimates 7-1.5.3 Cost indexes 7-1.5.4 Methods for estimating capital investment 7-1.5.4.1 Power factor applied to plant-capacity ratio 7-1.5.4.2 Detailed item estimate 7-1.5.4.3 Other Methods for Estimating Equipment or Capital Investment 7-1.5.5 Turn-over ratio SESSION 7-2 7-2.1 Estimation of Total Product Cost 7-2.2 Break-even Point 8.0 PROCESS ECONOMICS: DEPRECIATION AND PROFITABILITY ANALYSIS SESSION 8-1 8-1.1 Depreciation 8-1.2 Service Life 8-1.3 Salvage Value 8-1.4 Present Value 8-1.5 Methods for Determining Depreciation 8-1.5.1 Straight-line method 8-1.5.2 Declining – balance ( or fixed percentage) method 8-1.5.3 Other methods for determining depreciation v

42 42 42 43 44 45 46 46 46 46 47 48 48 49 49 51 52 53 57 57 57 58 59 59 61 61 61 62 63 63 66 67 68 68 68 70 75 75 75 76 76 76 77 77 77 78

SESSION 8-2 8-2.1 Profitability Analysis 8-2.2 Profitability Standards 8-2.3 Basis for Evaluating Project Profitability 8-2.4 Mathematical Methods for Profitability Evaluation 8-2.4.1 Rate of return on investment 8-2.4.2 Discounted cash flow 8-2.4.3 Capitalized cost 8-2.4.4 Payout period (or Pay-back time) 8-2.4.5 Sensitivity Analysis

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82 82 82 83 84 84 86 88 90 91

LIST OF FIGURES Figure 1-1.1 Design Constraints Figure 1-1.2 The Design Process Figure 1-1.3 Anatomy of a Chemical Process Figure 1-1.4 The Structure of a Chemical Engineering Project Figure 1-1.5 Project Organisation Figure 3-1.1 Effect of Constraints on the Optimum of a Function Figure 3-1.2 Yield as a Function of Reactor Temperature and Pressure Figure 6-1.1 Flow-sheet of Simplified Nitric Acid Production Process Figure 6-1.2 Polymer Production Diagram Figure 6-1.3 Commonly used Valves Figure 6-2.1 Approximate Range of Operation for the Three Main Types of Pump Figure 6-2.2 Basic Curves Characterizing a Centrifugal Pump Figure 6-2.3 Curve Characteristic of the System Figure 6-2.4 Variation of Operating Point by means of a Valve Figure 6-2.5 Variation in Specific Speed versus the Type of Impeller used Figure 6-2.6 Different Types of Characteristic Curves Figure 6-2.7 Variation in the Operating Point versus the Rotation Speed Figure 7-1.1 Cash Flow for an Overall Industrial Operation Figure 7-2.1 Cost Involved in Total Product Cost for a Typical Chemical Process Plant Figure 7-2.2 Break-even Chart for Chemical Processing Plant Figure 7-2.3: Project Cash Flow Diagram

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2 3 5 8 9 23 24 42 43 45 48 49 50 50 51 52 53 58 70 71 72

LIST OF TABLES Table 6-2.1 Main Types of Pumps Table 7-1.1: Cost indexes as Annual Averages Table 7-1.2 Typical Exponents for Equipment Cost vs. Capacity

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47 63 64

UNIT

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METHODOLOGY OF THE DESIGN PROCESS Introduction This unit discusses the methodology of the design process and its application to the design of chemical manufacturing processes. Learning Objectives After reading this unit, you should be able to: 1. Explain chemical process design 2. Distinguish between fixed and less rigid constraints 3. Know what constitutes the design process 4. List the basic components of a chemical manufacturing process SESSION 1-1 In this session we shall discuss what a chemical process design is, the constraints of the design problem, the components of the chemical manufacturing process and the difference between a continuous and a batch process.

1-1.1 Introduction: Design is the synthesis of ideas to achieve a desired goal (product). The designer starts with an idea and proceeds to develop several alternative designs that he evaluates and finally settles on the one that satisfies his objective (goal). The search for alternatives: this step becomes necessary because the designer will be constrained by several factors.

1-1.2 Constraints on a Design Problem 1-1.2.1 Fixed/Rigid constraints: these are constraints the designer must live with outside his influence. E.g. physical laws, government regulations and standards. The fixed constraints define the outer boundary of all possible designs.

1-1.2.2 Less rigid constraints: these are constraints the designer can manipulate inorder to arrive at the best design. E.g. materrials of construction, time. These are interrnal constraints over which the designer has some control. In summarry we have the following diagramatic sketch.

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Figure 1-1.1: Design Constraints 1-1.3 The Design Process The design process can be shown in schematic form in Figure 1-1.2.

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Figure 1-1.2: The Design Process

The diagram shows the design process as an iterative procedure because as the design proceeds the designer will be looking for information and ideas to refine the design.

1-1.3.1 The Design objective In the particular case of a chemical process plant, the objective/goal is to satisfy the public need for a product. In large commercial organizations, this need is identified by the sales/ marketing department. Before starting to work, the designer should obtain complete information/background on the need for the product and its application areas/uses.

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1-1.3.2 Data collection To proceed with the design, the designer must assemble all the relevant facts and data required. For process design, the information should include process alternatives, equipment performances, physical property data. In large design companies, they have “in house” manuals containing all the process “know how” on which the design is based and preferred methods and data for the frequently used design procedures.

1-1.3.3 Generation of possible designs At this stage the designer must come up with all possible solutions for analysis, evaluation and selection. To do this, he must rely on his own experience or that of others, using tried or tested methods. Chemical engineering projects can be divided into 3 types: 1. Modification, additions to existing plant often undertaken by the plant design group. 2. New production capacity to meet growing sales demand, and the sale of established processes by contractors. Repetition of existing designs, with only minor design changes. 3. New processes, developed from laboratory research, through pilot plant, to a commercial process. Here most of the unit operations and process equipment will use established designs.

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1-1.3.4 Selection The selection process can follow the following screening stages:

Possible designs (credible) – within the external constraints

Plausible designs (feasible)- within the internal constraints

Probable designs – likely candidates

Best designs (optimum) – judged the best solution to the problem

To select the best design from the probable designs, detailed design work and costing will be necessary.

1-1.4 Chemical Manufacturing Processes The basic components of a typical chemical process can be shown using the block diagram below.

Figure 1-1.3: Anatomy of a Chemical Process

Each block represents a stage in the overall process for producing a product from the raw materials. Each stage is a collection of equipment required to accomplish a defined task.

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Stage 1: Raw Material Storage Unless the raw materials are supplied as intermediate products from a neighboring plant, storage space is needed to hold several days or months supply. Types of storage required will depend on the nature of the raw materials, and the methods of delivery.

Stage 2: Feed Preparation Some purification of the raw materials will be necessary to render them in a form required for feed to the reaction stage.

Stage 3: Reactor In the reactor the raw materials are brought together under conditions that promote the production of the desired product. However by-products and unwanted compounds/ impurities will also be formed.

Stage 4: Product Separation After the reactor, the products and by-products are separated from any unreacted material. If in sufficient quantity, the unreacted material will be recycled to either the reactor directly or to the feed purification and preparation stage.

Stage 5: Purification Before sale, the main product is purified to meet product specification. If the by-product is also produced in sufficiently large quantities, it must also be purified for sale.

Stage 6: Product Storage Provision for product packaging and transport will be required. Besides some inventory of finished product must be held to match production with sales

Ancillary Process In addition to the main process stages/ units, provision will have to be made for the supply of utility services, process water, cooling water, compressed air, steam. Facilities are required for maintenance, firefighting, offices, laboratories and accommodation. 6

1-1.5 Continuous and Batch Processes Continuous processes are designed to operate 24 hours a day, 7 days a week, throughout the year (365 days). However down time is allowed for maintenance and process catalyst regeneration. Plant attainment: this is the percentage of the available hours in a year that the plant operates. This is usually 90-95%.

1-1.5.1 Choice of continuous versus batch production The choice will not be clear - cut, however one can use as a guide the following rules: Continuous 1. Production rate greater than 5*106 kg/h (5000tonnes/h) 2. Single product 3. No severe fouling 4. Good catalyst life 5. Proven process design 6. Established market 7. Cost can be reduced 8. Less labor Batch 1. Production rate less than 5*106 kg/h (5000tonnes/h) 2. A range of products or product specifications 3. Severe fouling 4. Short catalyst life 5. New product 6. Uncertain design

1-1.5.2 Organization of a chemical engineering design project The design work required in the engineering of a chemical manufacturing process plant can be divided into two broad phases: 7

Phase 1.Process Design This covers the steps from the initial selection of the process to be used, through to the issuing of the process flow-sheets; and includes the selection, specification, and chemical engineering design of equipment. In any organization, this phase is handled by the process design group composed of chemical engineers. The group is also responsible for the preparation of piping and instrumentation diagrams. Organization of a project group is shown in Figure 1-1.4 below.

Figure 1-1.4: The Structure of a Chemical Engineering Project

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Phase 2. The detailed mechanical design of equipment; the structural, civil and electrical design; specification and design of ancillary services. Other specialist groups will be responsible for cost estimation, and the purchase and procurement of equipment and materials.

The sequence of steps in the design, construction and start up of a chemical process plant is shown diagrammatically in Figure 1-1.5. .

Figure 1-1.5: Project Organization Project manager; a chemical engineer by training is responsible for the coordination of the project.

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SELF ASSESSMENT 1-1 (a) Distinguish between Fixed and less rigid constraints (b) List the components of a basic chemical manufacturing process and in just two sentences explain the importance of each in the manufacturing process. (c) In a tabular form, list six differences between a continuous process and a batch process.

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UNIT

2

CODES AND STANDARDS, DESIGN FACTORS, VARIABLE & MATHEMATICAL REPRESENTATION OF DESIGN PROBLEMS Introduction This unit discusses the codes & standards, design factors and variables and mathematical representation of the design problems. Learning Objectives After reading this unit, you should be able to: 1. Distinguish between codes and standards 2. Understand the importance of design factors as a margin of safety in meeting design specifications 3. Appreciate the importance of mathematical representation of the design problem SESSION 2-1 In this session we shall study the difference between codes and standards, design factors and their relation to equipment safety and the mathematical representation of the design problem.

2-1.1 Codes and Standards The terms CODE and STANDARD are used interchangeably, though CODE should be reserved for a code of practices. That is a recommended design or operating procedure. STANDARD on the other hand refers to preferred sizes, eg. pipes, composition etc. In modern engineering practice we have standards and codes that cover various functions e.g 1. Materials, properties and composition 2. Testing procedures for performance, composition and quality 3. Preferred sizes, eg tubes, plates, sections 4. Design methods, inspection, fabrication 5. Codes of practice, for plant operation and safety All developed countries have national organizations responsible for the issue and maintenance of standards for the manufacturing industries and for the protection of consumers.

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In the U.K:; British Standards Institution In the U.S; National Bureau of Standards They are responsible for coordinating information on standards. Standards are issued by the Federal State and various commercial organizations. The major ones of interest to chemical engineers are: American National Standards Institute (ANSI) American Petroleum Institute (API) American Society for Testing Materials (ASTM) American Society of Mechanical Engineers (ASME)

International Organization for Standardisation (ISO) coordinates the publication of International Standards.

In Ghana, there is no national standards organization to coordinate local standards for industries. However there are national standard organizations with standards for the protection of consumers eg. Standards Boards, Food and Drug Administration (FDA), and the Environmental Protection Agency (EPA). Equipment manufactures work together to produce standardized designs and size ranges for commonly used items; electric motors, pumps, pipes, and pipe fittings.

2-1.2 Factors of Safety (Design Factors) Design is an inexact act; errors and uncertainties can arise in the design data available and in the approximations necessary in the design calculations. To meet design specifications, factors are included to give a margin of safety in the design so that the equipment will not fail to perform satisfactorily, and that it will operate safely. e.g. in a mechanical and structural design, the magnitude of design factors used to allow for uncertainties in material properties, design methods fabrication and operating loads are well established. In process design, design factors are used to give tolerances in the design e.g. process stream average flows calculated from material balances are often increased by a factor of 10%, to give some flexibility in process operation. This factor then sets the maximum flows for equipment, instrumentation and piping design. 12

2-1.3 System of Units Chemical engineering uses a diversity of units from American and British engineering Systems, CGS (grain, centimeter, second) MKS( kilogram, meter, seconds) English and American – pound mass (lb), foot, second or hours, pound force. If working in S. I units is preferred, data expressed in the American and British engineering systems can be converted to S.I units. Conversions factors are available in the literature.

2-1.4 Mathematical Representation of the Design Problem A process unit e.g. distillation unit in a chemical process plant performs some operation on the inlet material stream to produce the desired outlet stream.

Inlet stream

Process Unit

Outlet stream

In the design of such a unit, the design calculations model the operation of the unit. Thus the flow of materials is replaced by flow of information into the unit and flow of derived information out of the unit.

Input Information

Calculation method

Output Information

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Information flows are the values of the variables which are involved in the design. Example:

Input stream

Output stream

variables

variables

Flow rate

same as the input variables.

Composition Temperature Pressure Enthalpy 

Composition, temperature, pressure are called intensive variables, i.e. independent of quantity of material flow (flow rate)(Nv).



The constraints on the design will place restrictions on the possible values that these variables can take; for example the values of some of the variables will be fixed directly by process specification. The values of other variables will be determined by design relationships arising from constraints.



Some of the design relationships will be in the form of explicit mathematical equations (design equations): such as those arising from material and energy balances, thermodynamic relationships, and equipment performance parameters.



Other relationships will be less precise such as those arising from the use of standards and preferred sizes and safety considerations (Nr).



The difference between the number of variables in the design and the number of design relationships is called the number of degrees of freedom.

If Nv – the number of possible variables in a design problem Nr – the number of design relationships Nd = Nv – Nr Nd = number of degrees of freedom

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Case 1. If Nv=Nr implies Nd = 0; this implies that there is only one unique solution to the problem. The problem is not a true design problem and no optimization is possible.

Case 2 Nv is less than Nr, Nd is less than 0; this implies that the problem is over defined, and only the trivial solution is possible.

Case 3 Nv >Nr, Nd > 0; implies there is an infinite number of possible solutions. However for a practical problem, there will be only a limited number of feasible solutions. Nd represents the number of variables which the designer must assign values to solve the problem.

EXAMPLE 2-1.1: Consider a single phase stream (liquid/vapour) containing C components.

Input

Process Unit

Output

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Note (1) The sum of the mass/mol fractions equal 1. (2) The enthalpy is a function of stream composition, temperature and pressure. Therefore, Degrees of Freedom, Nd = Nv – Nr =(C+4) – (2) = C+2 Specifying C+2 variables completely defines the stream.

EXAMPLE 2-1.2: Flash distillation / Equilibrium distillation In this process unit, a feed is passed into a still (fractionating column), where part is vaporized, and the vapour remaining in contact with the liquid. The mixture of vapor and liquid leaves the still and is separated so that the vapour is in equilibrium with the liquid.

Where, F= Stream flow rate, P= pressure, T=temperature, xi= concentration of component i, q = heat input. Surfixes, 1= inlet; 2=outlet vapor; 3 =outlet liquid

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Note: 1. given the temperature and pressure, the concentration of any component in the vapor phase can be obtained from the concentration in the liquid phase ( v-l-e data) 2. An equilibrium separation implies that the outlet streams and the still are the same pressure and temperature. This implies that

P2 = P

(1)

T2 = T

(3)

P3 = P

(2)

T3 = T

(4)

Gives 4 equations. Degrees of freedom Nd (No of degrees of freedom)=Nv - Nr= (3C + 9) - (2C + 5) = C + 4 Though the total degrees of freedom calculated is (C+4), some of the variables will be fixed by the process conditions and will not be free for the designer to select as design variables. For example: the flash distillation unit will normally be one unit in a process system and the feed composition and feed conditions will be fixed by the upstream process. Hence defining the feed, fixes (C+2) variables and the designer is left with, (C+4)-(C+2) = 2

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2-1.5 Selection of Design Variables To solve a design problem, the designer has to decide which variables are to be chosen as design variables, i.e the ones he can manipulate to produce the best design. This choice is crucial to enable the simplification of the calculations. Example: Flash distillation problem in the previous example. For a binary mixture, C=2; this implies Nd=C+4=6 If the feed stream flow, composition, temperature, pressure are fixed by upstream conditions, then the number of design variables is Nd=6-(C+2)=6-4=2. This implies, the designer is free to select 2 variables from the remaining variables to proceed with the calculation of the outlet stream composition and flows.

Scenerio 1

Suppose you select the still pressure implies for a binary system, vapour-liquid equilibrium (V-L-e) relationship is determined, and one outlet stream flow rate, then the outlet compositions can be calculated by the simultaneous solution of mass-balance and (v-l-e) relations.

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Scenerio 2

If you select the still pressure and the liquid outlet stream composition, then the simultaneous solution of the mass balance and the v-l-e relationship will not be necessary. Following the procedure below, one can calculate the stream compositions.

1. Specify P determines the v-l-e curve from experimental data 2. Knowing the outlet liquid composition, the outlet vapor composition can be calculated from the v-l-e. 3. Knowing the feed and outlet compositions, and the feed flow rate, the outlet stream flows can be calculated from a material balance. 4. An enthalpy balance gives the heat input required.

SELF ASSESSMENT 2-1 (a) List 3 American organizations responsible for coordinating information on standards. (b) List 3 national standard organizations with standards for the protection of consumers.

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UNIT OPTIMIZATION AND BATCH PRODUCTION PROCESS Introduction This unit discusses batch production processes and the importance of optimization. Learning Objectives After reading this unit, you should: 1. Appreciate the importance of optimization in plant design 2. Understand the process of batch production

SESSION 3-1 In this session we shall discuss the steps involved in optimizing the design of a chemical process plant. Further, we shall

3-1.1 Introduction Optimizing the design of a chemical process plant is a foreboding task. This can be achieved by subdividing the plant into subunits and optimizing each subunit. However this does not result in the optimal design of the whole plant because the optimization of each subunit is at the expense of the other. The general procedure for optimizing process units and equipment design: Step1: the first step is to clearly define the objective. i.e the criteria to be used for measuring the performance of the system. For a chemical process plant, the overall objective is to maximize profit. This overall objective can be broken down into sub objectives such as; minimize operating cost, minimize capital investment, maximize yield of the product, reduce labour requirements, reduce maintenance, operate safely. Step 2: the second step is to determine the objective function; the system of equations and other relationships, which relate the objectives with the variables to be manipulated to optimize the function. Step 3: this step is to find values of the variables that give the optimum value of objective function i.e maximum or minimum. The best technique to be used will depend on the complexity of the system and the type of mathematical model used to represent it.

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3-1.2 Simple Models If the objective function can be expressed as a function of one variable (single degree of freedom), the function can be differentiated or plotted to find the maximum or minimum. This situation arises only for exceptional cases. In most practical situations, the numbers of variables exceed the number of relationships. Example of a simple model: Determine the optimum proportions for a closed cylindrical container. D

L

The surface area A in terms of the dimensions is:    A   DL  2 D 2    DL  D 2 2 4  the objective function is f D, L   D  L 

D2 2

(1)

for a given volume (V) we have, V 

 D2 4V L  L 4  D2

(2)

exp res sin g the objective function in terms of one variable D, we have

f(D) 

4V D 2  D 2

differenti ating ; f ' (D) 

 4V D D

(3)

finding the optimum D, we set the above equation to zero  4V 4V  4V   D  0  D3  D  D     4V  4V  substituti ng D in (2) above  L  21     

2

3

1

3

 4V      

1

3

For a cylindrical container, the minimum surface area to enclose a given volume is obtained when the length (height) is made equal to the diameter. In practice, when the cost is the objective function; L=2D; this is because the cost must include that of forming the vessel, making the joints in addition to the cost of the material.

3-1.3 Multiple Variable Systems The general optimization problem can be represented mathematically as:

f  f (v1 , v 2 , v3 ,.......v n ) where f  objective function and v1 , v 2 , v3 ,.......v n are the variables In a design situation, there will be constraints on the possible values of the objective function due to constraints on the variables. -

Equality constraints are expressed by equations of the form

 m   m (v1 , v 2 , v3 ,.......v n )  0 -

Inequality constraints are expressed by equations of the form  p   p (v1 , v 2 , v3 ,.......v n )  Pp

Optimization of the problem involves finding values for the variables v1 , v 2 , v3 ,.......v n that will optimize the objective function ( i.e give maximum or minimum values within the constraints).

3-1.4 Methods of Analysis: a. Analytical method: objective functions can be expressed as a mathematical function; use the methods of calculations to find maximum or minimum values. -

For practical situations where the values of the variables are subject to constraints, the optimum of the constrained objective function will not necessarily occur where the partial derivatives of the objective function are zero.

e.g.

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Figure 3-1.1: Effect of Constraints on the Optimum of a Function

-

The method of Lagrange’s undetermined multipliers is a useful analytical technique for dealing with problems that have equality constraints (fixed design values).

b. Search Methods: Relationships between variables and constraints that arise in practical design problems are such that analytical methods are not feasible; hence the use of search methods. For single variable problems where the objective function is unimodal, the simplest approach is to calculate the value of the objective function at uniformly spaced values of the variable until a maximum or minimum is obtained.

Figure 3-1.2 Yield as a Function of Reactor Temperature and Pressure 23

3-1.5 Other Optimization Methods - Linear programming; a technique used when the objective function and constraints can be expressed as a linear function of the variables. - Dynamic programming; used for the optimization of large systems.

3-1.6 Batch Production Process -

Productive period: this is the period when product is being produced

-

Nonproductive period; this is the period when the product is discharged and equipment prepared for the next batch.

-

Total batch time: productive period + nonproductive period

-

The rate of production is determined by the total batch time as follows:

Batches per year = 8760 x Plant attainment Total batch time (batch cycle time)

Annual production rate = (quantities produced per batch)x(batches per year)

Cost per unit of production= annual cost of production Annual production rate

SELF ASSESSMENT 3-1 A rectangular tank with a square base is constructed from 5 mm steel plates. If the capacity required is eight cubic meters. Determine the optimum dimensions if the tank has a closed top.

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UNIT PROCESS SYNTHESIS Introduction This unit discusses the synthesis of chemical processes. Learning Objectives After reading this unit, you should be able to: 1. Explain process synthesis 2. Define and explain heuristics

SESSION 4-1 In this session we shall discuss process synthesis and the importance of heuristics in chemical process optimization.

4-1.1 Introduction: process synthesis aims at the optimization of the logical structure of a chemical process; specifically the sequence of steps; reaction, separation (distillation, extraction etc), the source and destination of recycle streams. The logical structure of a chemical process: Given the following; -

Raw materials, required products, allowed byproducts, a set of unit operations for consideration, cost factors for materials and unit operations required to generate and rank in order of preference and feasible chemical plant flow sheets.

Approach 1. Combinatorial algorithms are used to find all feasible flow sheets contained in a toolkit of raw materials and operating steps. The flow sheets are then reviewed and optimized based on performance, economic and safety criteria. Approach 2. Heuristic rules based on experiences that are used for the selection and positioning of processing operations as flow sheets are assembled.

4-1.2 Raw Materials and Chemical Reactions Heuristic 1: select raw materials and chemical reactions to avoid or reduce the handling and storage of hazardous and toxic chemicals. e.x. Manufacture of ethylene glycol

C 2 H 4  1 O2  C 2 H 4 O   2

(1)

C 2 H 4 O  H 2 O  HOCH 2  CH 2 OH   25

(2)

-

Both reactions are extremely exothermic, therefore they need to be controlled carefully. Such processes are designed with two reaction steps with storage of the intermediate, to enable continuous production, even when maintenance problems shut down the first reaction operation.

Alternative to the 2-step example process: 1. Use chlorine and caustic in a single reaction step, to avoid the intermediate:

CH 2  CH 2  Cl 2  2 NaOH (aq)  HOCH 2  CH 2 OH  2 NaCl

2. Use the 2-step reaction with the following modifications: -

As ethylene-oxide is formed, react it with carbon dioxide to form ethylene carbonate, a much less active intermediate that can be stored safely. This can then be hydrolysed to form the required ethylene glycol product

C 2 H 4  1 O2  C 2 H 4 O   2 C 2 H 4 O  CO2  C3 H 4 O3 C3 H 4 O3  H 2 O  HOCH 2  CH 2 OH  CO2

Heuristic 2: Distribution of Chemicals Use an excess of one chemical reactant in a reaction to completely consume a second valuable, toxic or hazardous reactant. e.x. use an excess of ethylene in the production of Dichloroethane.

Cl C2

C2H4Cl2 + C2H4

2H4

C2H4 26

Heuristic 3: when nearly pure products are required, eliminate the inert species before the reaction operations, when the separations are easily accomplished, or when the catalyst is adversely affected by the inert.

Heuristic 4: introduce liquid or vapour purge streams to provide exit for species that; -

Enter the process as impurities in the feed

-

Produced by irreversible side reactions

e.x. Ammonia, NH3 synthesis loop

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Heuristic 5: Do not purge valuable species or species that are toxic and hazardous, even in small concentrations -

Add separators to recover valuable species

-

Add reactors to eliminate toxic and hazardous species

e.g. catalytic converter in car exhaust

Heuristic 6: For competing series or parallel reactions, adjust temperature, pressure, and catalyst to obtain high yields of desired products. In the initial distribution of chemicals, assume that these conditions can be satisfied; obtain kinetic data, and check this assumption before developing a base-case design. e.x. Manufacture of alkyl-chloride

k1 CH 2  CHCH 3  Cl 2  CH 2  CHCH 2 Cl  HCl

 Cl 2  k2

 k3

CH 3 CHClCH 2 Cl

CHCl  CHCH 2 Cl  HCl

Dichloropropane

dichloropropene

This is a series/parallel reaction; -

for each reaction, obtain H R , K o , E

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R

For each reaction, obtain kinetic data and examine the dependency of reaction rate on temperature; implies k  k o e

E

RT

Since for multiple reactions, high temperature favors the reaction of higher activation energy and vice versa.

Heuristic 7: for reversible reactions, consider conducting them in a separation device capable of removing products, and hence driving the reaction to the right. e.g. manufacture of ethyl-acetate (ethyl ethanoate) using reactive distillation Conventionally, this will call for the reaction: EtOH + HOAc

EtOAc +H2O

followed by separation of products using a sequence of separation of towers, using a reactive distillation:

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Heuristic 8: Separations : separate liquid mixtures using distillation, stripping towers and liquid-liquid extractors.

Heuristic 9: attempt to condense vapour mixtures with cooling water, then use heuristic 8.

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Heuristic 10: Heat Transfer in reactors: to remove highly exothermic heat of reaction, consider the use of excess reactant, an inert diliuent.

Heuristic 11: For less exothermic heat of reaction, circulate reactor fluid to an external cooler, or use a jacketed vessel or cooling coils.

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Heuristic 12: Pumping and Compression: To increase the pressure of a stream, pump a liquid rather than compress a gas: i.e condense a vapor as long as refrigeration ( and compression) is not needed before pumping.

Instead of:

Compressors have large capital cost and consume a lot of power. 32

4-1.3 Summary of Process Design Heuristics The discussion focused on the following: -

understanding the importance of selecting reaction paths that do not involve toxic or hazardous chemicals.

-

Be able to distribute the chemicals in a process flowsheet, to account for the presence of inert species, to purge species that would otherwise build up to unacceptable concentrations, to achieve a high selectivity of the desired products.

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Apply heuristics in in selecting separation processes to separate liquids, vapours, and vapour-liquid mixtures.

-

Understand the advantages of pumping a liquid rather than compressing a vapor.

4-1.4 Heuristics in Equipment Design 1. Equipment Size Need information on the required throughput to determine vessel size -

General guidelines for vessel size o Height: 2-10 m o L/D: 2-5m

-

Towers/ Columns o Height: 2-50m o L/D: 2-30m

Note: Do not specify units outside these ranges

2. Heat Exchangers Several kinds are used -

Area: 10-1000m2

-

For shell and tube (tubular) o Tube diameter: 1-2 cm o Tube length: 2-6m o Shell diameter:0.3-1m

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-

Plate and frame Newer technology- thin, gasketed plates separate hot and cold fluids. Advantage: more compact and very efficient

3. Heat transfer considerations -

Minimum temperature approach: for fluids 10oC and for refrigerants, 5oC

-

Cooling water in: 30oC; Cooling water out: 45oC

-

Equipment heat transfer(overall) coefficient in decreasing order of magnitude Reboiler>Condenser>Liquid-to-Liquid>gas-to-gas

-

Heat Exchangers:Δtlm < 100oC

4. Towers/ Columns Tower operating pressure is usually determined by the temperature of condensing medium or maximum allowable reboiler temperature 

Sequencing multiple towers: typically

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Do easy separation first and leave difficult ones for last

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If relative volatilities of all species are close , remove one-by-one from overhead

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When volatilities are close but feed concentrations vary, remove high concentrations first. 

Distillation operating conditions

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Economically reflux ratio is typically 1.2-1.5 times Lmin

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Optimum number of theoretical trays trays is typically 2 times Nmin

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Find Nmin from Fenske-Underwood equation 

Tower design

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Tray spacing are typically 20-24”

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Pressure drop typically 0.1psi per tray

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Tray efficiencies: 60-90% for gas absorption and stripping

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5. Process Conditions: General Guidelines (a) High Pressure To achieve a high pressure in a process: -

For a liquid use a pump; for a vapour first condense it and pump it into an evaporatior

-

For a gas compression; P/Po