NAMP for North American Mobility In Higher Education Program PIECE NAMP Module 9 Introduction to Steady State Simulation Introducing Process integration for Environmental Control in Engineering Curricula Module 9 – Steady state simulation PIECE 1 PIECE NAMP integration for Environmental Control in Engineering Curricula Process Paprican PIECE École Polytechnique de Montréal Universidad Autónoma de San Luis Potosí University of Ottawa Universidad de Guanajuato North Carolina State University Instituto Mexicano del Petróleo Program North American Mobility in Higher Education Module 9 –for Steady state simulation Texas A&M University NAMP 2 NAMP PIECE Module 9 This module was created by: Amy Westgate North Carolina State University University of Ottawa From Host University North Carolina State University Richard Ezike Module 9 – Steady state simulation University of Ottawa 3 NAMP PIECE Project Summary Objectives Create web-based modules to assist universities to address the introduction to Process Integration into engineering curricula Make these modules widely available in each of the participating countries Participating institutions Six universities in three countries (Canada, Mexico and the USA) Two research institutes in different industry sectors: petroleum (Mexico) and pulp and paper (Canada) Each of the six universities has sponsored 7 exchange students during the period of the grant subsidised in part by each of the three countries’ governments Module 9 – Steady state simulation 4 NAMP PIECE Structure of Module 9 What is the structure of this module? All modules are divided into 3 tiers, each with a specific goal: Tier I: Background Information Tier II: Case Study Applications Tier III: Open-Ended Design Problem These tiers are intended to be completed in that particular order. In the first tier, students are quizzed at various points to measure their degree of understanding, before proceeding to the next two tiers. Module 9 – Steady state simulation 5 NAMP PIECE Purpose of Module 9 What is the purpose of this module? It is the intent of this module to cover the basic aspects of Steady State Simulation. It is identified as a prerequisite for other modules related to the learning of Steady State Simulation. This module is intended for students familiar with basic mass and energy balances and may have had some training with thermodynamics and transport processes. Module 9 – Steady state simulation 6 NAMP PIECE Tier I Background Information Module 9 – Steady state simulation 7 NAMP PIECE • Statement of Intent – Review basic chemical engineering concepts employed in steady state simulation – Understand the purpose of steady-state simulation – Learn how to develop models of processes in steady-state – Discuss problem solving techniques Module 9 – Steady state simulation 8 NAMP PIECE Steady State Process We can use steady-state processes to determine the optimum operation conditions for a process that can be limited by safety, equipment performance, and product quality constraints. • Concentration does not change with respect to time • Accumulation term in mass balance set to zero Input + Generation – Output – Consumption = 0 Module 9 – Steady state simulation 9 NAMP PIECE • Three types of processes: Batch • A process where a set amount of input enters a process, where it is removed from the process at a later time. Continuous • A process where inputs and outputs flow continuously through duration of process. Semi-batch • Neither batch or continuous, may be combination of both. In steady-state processes, we will be looking at continuous processes. Module 9 – Steady state simulation 10 NAMP PIECE Batch Example • Ammonia is produced from nitrogen and hydrogen. At time t = t0, nitrogen and hydrogen are added to the reactor. No ammonia leaves the reactor between t = t0 and t = tf. At tf, nf moles of ammonia are released. H2 N2 NH3 N 2 + 3H 2 2N H 3 t = to Module 9 – Steady state simulation t = tf 11 NAMP PIECE Semibatch Example • Helium is pressurized in large tanks for storage. When the tank valve is open, the gas diffuses out due to the difference in pressure. Module 9 – Steady state simulation 12 NAMP PIECE • Continuous Example – Pump a methanol/water mixture into a distillation column and withdraw the more volatile component (methanol) from the top of the column and the less volatile component (water) from the bottom of the column. Mostly CH3OH 50% molar CH3OH 50% molar H2O Mostly H2O Module 9 – Steady state simulation 13 NAMP PIECE Quiz #1 Classify the following processes as batch, continuous, or semibatch. • A balloon is filled with air at a steady rate of 2 m3/min. • Pump a mixture of liquids into a distillation column at a constant rate and steadily withdraw product streams from the top and bottom. • Slowly blend several liquids in a tank from which nothing is being withdrawn. Module 9 – Steady state simulation 14 NAMP PIECE Block Diagrams • When solving a problem, it is helpful to develop a Process: block diagram, such as the one below, that defines what the process looks like as well as to indicate all information about the process such as flow rates and species compositions. Carbon (C) Air (79% N2, 21% O2) Module 9 – Steady state simulation Reactor Separator 15 NAMP PIECE Degree Of Freedom Analysis • Analysis done to determine if there is enough information to solve a given problem. 1. Draw and completely label a flowchart 2. Count the unknown variables, then the independent equations relating them, 3. Subtract the number of equations from the number of variables. This gives ndf, or the number of degrees of freedom in the process. Module 9 – Steady state simulation 16 NAMP PIECE Degree of Freedom Analysis • If ndf = 0 there are n independent equations in n unknowns and the problem can be solved • If ndf >0, there are more unknowns than independent equations relating them, and at least ndf additional variable values must be specified. • If ndf <0, there are more independent equations than unknowns. The flowchart is incompletely labeled or inconsistent and redundant relations exist. Module 9 – Steady state simulation 17 NAMP PIECE Mass (Material) Balance A mass (material) balance is an essential calculation that accounts for the mass that enters and leaves a particular process. Accumulation of mass = Mass flow rate in – Mass flow rate out Module 9 – Steady state simulation 18 NAMP PIECE Mass (Material) Balance (continued) In the case of a steady-state process we are able to set the accumulation term to zero since it is a time dependent term. Since steady-state does not depend on time as it is constant, we are able to eliminate this term: Mass Flow Rate In = Mass Flow Rate Out Material Balance Procedure Module 9 – Steady state simulation 19 NAMP PIECE First Law of Thermodynamics (Energy Balance) for a Steady State Open System ΔH + ΔEk + ΔEp = Q - Ws The net rate at which energy is transferred to system as heat and/or shaft work equals the difference between rates at which (enthalpy+ kinetic energy + potential energy) is transported into and out of the system Module 9 – Steady state simulation 20 NAMP PIECE Quiz #2 1. Explain the Degree of Freedom analysis. 2. What term goes to zero in a steady-state process? 3. Is a continuous process closed or open? How about a batch process? Module 9 – Steady state simulation 21 NAMP PIECE Heat Transfer • Also classified as energy transfer • Three types of heat transfer modes: – Conduction – Convection – Radiation Module 9 – Steady state simulation 22 NAMP PIECE Conduction • Accomplished in two ways qy dT – Molecular interaction = - k A dy – “Free electrons” • Conduction equation called Fourier’s Law – qy = heat transfer area in y direction (W) – A = area normal to direction flow (m2) – dT/dy = temperature gradient (oC/m) – k = thermal conductivity (W/moC) Module 9 – Steady state simulation 23 NAMP PIECE Convection • Accomplished in two ways q = hx ΔTdA = hAΔT –Natural convection A –Forced convection • Convection equation called Newton’s Law –qy = rate of convective heat transfer (W) –A = area normal to direction flow (m2) –ΔT = temperature gradient (oC) –h = convective heat transfer coefficient (W/m2 oC) Module 9 – Steady state simulation 24 NAMP PIECE Radiation (Thermal) Exhibits same optical properties as optical light •May be absorbed, reflected, or transmitted Total radiation for unit area of opaque body of area A1, emissivity ε1, and absolute temperature T1, and a universal constant σ q A1 = 1T Module 9 – Steady state simulation 4 1 25 NAMP PIECE Radiation Between Surfaces • Simplest type occurs where each surface can see only the other and where both surfaces are black • Energy emitted by first plane is σT14; the second plane emits σT24 • if T1 > T2, then net loss energy per unit area by first plane and net gain by second are σT14- σT24, or σ(T14-T24) Cold surface Note this is only in ideal cases: no surface is exactly black, and emissivities must be considered Module 9 – Steady state simulation Hot surface 26 NAMP PIECE Mass Transfer • The transport of one constituent from a region of higher concentration to a region of lower concentration • Molecular mass transfer – Random molecular motion in quiescent fluid • Convective mass transfer – From a surface into a moving fluid or vice-versa Module 9 – Steady state simulation 27 NAMP PIECE • Flux = - (overall density)*(diffusion coefficient)*(concentration gradient) • Fick rate equation (restricted to isothermal/isobaric systems) JA = - D AB JA – mol A/m2s dC A CA- mol A/m3 dz DAB- m2/s • de Groot equation is more general J A = - cD A B Module 9 – Steady state simulation Units: dy A dz 28 NAMP PIECE • Molar flux of species A in binary system (A + B) N A cD AB y A y A (N A N B ) c = concentration DAB = diffusivity of species A in B yA = change of molar species in y with respect to a specified direction NA, NB = molar fluxes of components Module 9 – Steady state simulation 29 NAMP PIECE Quiz #3 1. What are two ways in which conduction occurs? 2. Define natural and forced convection. 3. What is the restriction to the use of Fick’s Law? Module 9 – Steady state simulation 30 NAMP PIECE Modeling • What is Modeling? • Steady-State vs. Dynamic Modeling • Empirical vs. Mechanistic Modeling • Derivation of a Steady State Model • Modeling and Process Design Implications Module 9 – Steady state simulation 31 NAMP PIECE What is a Model? A model is an depiction of a process operation used to design, change, improve or control a process. Uses of Model • Equipment Design, Size and Selection • Comparison of Different Process Configurations • Evaluation of Process Performance Against Limitations • Optimization Module 9 – Steady state simulation 32 NAMP PIECE Models vary by: – Phenomena represented • Energy, phase changes – Level of details – Assumptions (perfect mixing, heat loss) – Inputs required – Functions performed (satisfaction of constraints, optimization) – Outputs generated Module 9 – Steady state simulation 33 NAMP PIECE Requirements of a good model • Accuracy: the model should be close to the target description. • Validity: model must have a solid foundation and ability to be easily justified. • Complexity: the level of the model should be considered and easy to understand. • Computational efficiency: models should be calculable using reasonable amounts of time and computing resources. Module 9 – Steady state simulation 34 NAMP PIECE Time-based Modeling Steady State Dynamic Model Empirical Mechanistic Hybrid Level of Knowledge-based Modeling Module 9 – Steady state simulation 35 NAMP PIECE Steady – State Dynamic Balance at equilibrium condition Time dependent results Equilibrium results for all unit operations Equilibrium conditions not assumed for all units Equipment sizes not needed Equipment sizes needed Amount of information required: Amount of information required: small to medium medium to large Module 9 – Steady state simulation 36 NAMP PIECE Steady State Example Continuous Stirred Tank Reactor (CSTR) Concentration profile at one point in reactor does not change with time Module 9 – Steady state simulation Ca t 37 NAMP PIECE Dynamic Example Batch Reactor Concentration profile at one point in reactor does change with time ca t Module 9 – Steady state simulation 38 NAMP PIECE Empirical Modeling • Definition: – a model that is based on data whether it has been collected from a process or some other source. • Key Notes – – – – Derived from observation Often simple May or may not have theoretical foundation Valid only within range of observation Module 9 – Steady state simulation 39 NAMP • PIECE Procedure – Empirical Modeling 1. Obtain data from process you wish to model. – Temperature, pressure, flow, etc… 2. Perform appropriate statistical analysis and develop accurate correlations from data. 3. Develop mathematical equations to accurately represent the data and the correlations found in step 2, and determine which equations are useful in the development of the model. 4. Check for correctness in your analysis and equations, and determine if the model is satisfactory. Statistical Analysis with Excel Module 9 – Steady state simulation 40 NAMP PIECE Example: The figure below depicts a heat exchanger. Heat exchangers function as a medium to transfer energy (in the form of heat) from a hotter stream to a cooler stream. Let’s say we have a hot stream of fluid coming into the exchanger at Th1, leaves at Th2 and a cool stream coming in at Tc1 and leaving at Tc2. If the physical properties of the fluids are the same, then the temperature difference describes the amount of energy transferred. Module 9 – Steady state simulation 41 NAMP PIECE • We do not know Tc2, but we can take various measurements of Th1, Th2 and Tc1 to find Tc2 . Using certain statistical procedures, it can be determined that Tc2 is related to the other three temperatures by this equation: Tc2 = Tc1 + a(Th2-Th1) • If we knew, say, the mass flow rates and heat capacities of the two fluids, we can use them to determine the mechanistic model that relates the four temperatures for any combination of two fluids. • We have empirically determined a value for a, but only for the specific fluids and conditions tested. Module 9 – Steady state simulation 42 NAMP PIECE Mechanistic Modeling • Definition – a model that is derived from fundamental physical laws or basic principles • Key Notes – Model construction – time-consuming and costly – Most reliable, but often not enough data available Module 9 – Steady state simulation 43 NAMP • PIECE Procedure – Mechanistic Modeling 1. Know physical and chemical properties of the process. 2. Determine the appropriate process model using mass and/or heat balance. 3. Determine appropriate model run conditions and parameters 4. Complete runs and use output data to compare against the predicted model results 5. Develop an acceptable conclusion for the model. Should the conclusion not be acceptable, re-examine the assumptions, process and the physical and chemical properties made in Step 1. Make appropriate modifications and repeat Steps 2-4. Module 9 – Steady state simulation 44 NAMP PIECE Let us go back to the heat exchanger. Now we know that the empiricism a that we determined earlier is related to the mass flow and heat capacity of the two fluids. This knowledge allows us to model a heat exchanger for any two fluids. The model is determined to be: m H C p H (TH1 - TH 2 ) = m C C p C (TC 2 - TC 1 ) Module 9 – Steady state simulation 45 NAMP PIECE Steady state model derivation 1. Define Goals. a) Specific design decisions. b) Numerical values. c) Functional relationships. d) Required accuracy. 2. Prepare information. a) Sketch process. b) Identify variables of interest. c) State assumptions and data. Module 9 – Steady state simulation 46 NAMP PIECE Steady state model derivation 3. Formulate model a) Conservation balances. b) Constitutive equations. c) Rationalize (combine equations and collect terms). d) Check degrees of freedom. 4. Determine solution a) Analytical b) Numerical Module 9 – Steady state simulation 47 NAMP PIECE Steady state model derivation 5. Analyze results a) Check results for correctness Accuracy of numerical/analytical methods Plot solution Relate results to data and assumptions Answer “what if questions” Compare with experimental results Module 9 – Steady state simulation 48 NAMP PIECE Process insights resulting from modeling 1. Identification: If we know the input (I) and output (O) parameters, we can determine the structure (R) of the model. I Module 9 – Steady state simulation R? O 49 NAMP PIECE Process insights resulting from modeling 2. Simulation: If we know the structure of the model, we can simulate what the output of the process will be for a given input. I Module 9 – Steady state simulation R O? 50 NAMP PIECE Process insights resulting from modeling 3. Control/Optimization: If we know the desired output (O) and the structure (R) of the model, we can determine what the input (I) should be to optimize the process. I? Module 9 – Steady state simulation R O 51 NAMP PIECE Quiz #4 1. What are some uses of modeling? 2. Name and explain three requirements of a good model. 3. What distinguishes a steady-state model and a dynamic model? 4. Review the procedures for developing a mechanistic and empirical model. What are some differences between the two procedures? 5. Discuss the control/optimization insight of modeling. Module 9 – Steady state simulation 52 NAMP PIECE Solving Problems – Analytical Methods – Process Design – Methods • Spreadsheets • Simulation Software – Solution Determination Module 9 – Steady state simulation 53 NAMP PIECE Curve fitting – Try to find the best fit of a curve through the data such that the distribution of the data points on either side of the line is equal – Possible errors • Measurement error • Precision error • Systematic error • Calculation error • Error propagation • Curve Fitting Example Module 9 – Steady state simulation 54 NAMP PIECE Least Squares • The best curve through the data is the one that minimizes the sum of the squares of the residuals (differences between predicted and experimental values) Least Squares Method Module 9 – Steady state simulation 55 NAMP PIECE Process Design Module 9 – Steady state simulation 56 NAMP PIECE Process design The design of chemical products begins with the identification and creation of potential opportunities to satisfy societal needs and to generate profit. The scope of chemical product is extremely broad. They can be roughly classified as: 1. Basic chemical products. 2. Industrial products. 3. Consumer products. Module 9 – Steady state simulation 57 NAMP PIECE Process design Natural Resources Manufacturing Process Basic chemical Products Basic Chemical Products Manufacturing Process Industrial Products Industrial Products Manufacturing Process Consumer Products Module 9 – Steady state simulation 58 NAMP PIECE Motivation for Process Design 1. Desires of customers for chemicals with improved properties for many applications. 2. Discovery of a new inexpensive source of a raw material with comparable physical and chemical properties to the old source. 3. New markets are discovered. Module 9 – Steady state simulation 59 NAMP PIECE Steps in a Process Design 1. Process Design – Questions to Answer Is the chemical structure known? Is a process required to produce the chemicals? Is the gross profit favorable? Is the process still promising after further elaboration? Is the process and/or product feasible? Module 9 – Steady state simulation 60 NAMP PIECE Steps in a Process Design 2. Process Design – Steps Develop objective(s). Find inputs that have the desired properties and performance. Create process. Develop a base case for which to conduct initial testing on process. (does it stay stable at steady state?) Improve/maintain process Module 9 – Steady state simulation 61 NAMP PIECE Stability of the process When a process is disturbed from an initial steady state, it will generally respond in one of 3 ways. a) Proceed to a steady state and remain there. Module 9 – Steady state simulation 62 NAMP PIECE Stability of the process b) Fail to attain to a steady state condition because its output grows indefinitely. The system is unstable. Module 9 – Steady state simulation 63 NAMP PIECE Stability of the process c) Fail to attain a steady state condition because the output of the process oscillates indefinitely with a constant amplitude. The system is at the limit of stability. Module 9 – Steady state simulation 64 NAMP PIECE Quiz #5 1. What are some errors that may arise when attempting to fit a curve? 2. What are the three products developed from process design? Provide an example of each product. 3. What happens to an unstable system over time? Module 9 – Steady state simulation 65 NAMP PIECE Spreadsheet – A computer program (Microsoft Excel) used to store and calculate information in a structured array of data cells. By defining relationships between information in cells, a user can see the effects of certain data changes on other data in other parts of the spreadsheet. – Provides an easy, efficient method for solving sets of equations and other forms of data that are not too numerous but complex enough that it would be difficult to solve by hand. Module 9 – Steady state simulation 66 NAMP PIECE – Columns are designated by letters, rows by numbers http://www.instrunet.com/images/Direct%20To%20Excel%20Spreadsheet.png Module 9 – Steady state simulation 67 NAMP • Under Tools Menu PIECE Goalseek • want to know input value formula needs to determine result • Excel varies value in cell specified until dependent formula returns value you want Module 9 – Steady state simulation 68 NAMP PIECE Spreadsheet Drawbacks • Entering the equations yourself could lead to false answers as you can make a mistake. Mistakes can become unmanageable very quickly causing debugging to be difficult. • Excel can handle large amounts of data but there is a point where Excel may have difficulty in solving a system of equations. Module 9 – Steady state simulation 69 NAMP PIECE Simulation • Predicts behavior of a process by solving mathematical relationships that describe the behavior of the process components. • Involves performance of experiments with a process model Module 9 – Steady state simulation 70 NAMP PIECE • Simulation Software – Why use it? – economical way for engineers to construct or modify a process before doing a test in reality. • Can determine optimum operating conditions – Quantify equipment, raw materials required with accuracy • Can discover process problems – Make accurate changes in process without sacrificing money or safety • Determine composition of streams and simplify complex unit operations Module 9 – Steady state simulation 71 NAMP PIECE • Simulation Software – What does it allow? – Manipulation and comparison of previous data as well as for research – Manipulation of a process until a desired target is reached – Allows complex processes to be easily calculated – Can easily change conditions and see how the output is changed and the equipment behaves Module 9 – Steady state simulation 72 NAMP PIECE • Simulation Issues and Considerations – Built-in assumptions in programs – must be taken into account and validated – Can make mistakes in calculations – do mass balances over process as a check over – Number of variables involved – Physical properties of streams – Size of process being simulated Module 9 – Steady state simulation 73 NAMP PIECE Process Flowsheet (Block Diagram) A process flowsheet is a collection of icons to represent process units and arrows to represent the flow of materials to and from the units. Fresh feed Distillation steam Reactor Heater Module 9 – Steady state simulation Flash Product 74 NAMP PIECE Calculation Order In most process simulators, the units are computed one at a time. The calculation order is automatically computed to be consistent with the flow of information in the simulation flowsheet, where the information flow depends on the specifications for the chemical process. 1 Module 9 – Steady state simulation 2 3 4 75 NAMP PIECE Recycle Flows A simulation flowsheet usually contains information recycle loops. That is, there are variables that are not known which prevent the equations in the process model from being solved completely. These variables are recycled back to the initial calculation point. 1 2 3 4 For these processes, a solution technique is needed to solve the equations for all the units in the recycle loop. Module 9 – Steady state simulation 76 NAMP PIECE Iteration – Initial guess is taken at the input and a solution is determined for the system – Second, a more educated guess is made and the system is solved based on initial solution – Iterations continue until solution converges to one value Module 9 – Steady state simulation 77 NAMP PIECE Convergence Is the process to compare the guessed value with the computed value until a value is found within the tolerance range. Guessed value No Guessed value – calculated value < Tolerance Yes Convergence When the criterion is achieved, the solution is found and no more iteration needs to be done. Module 9 – Steady state simulation 78 NAMP PIECE Process synthesis methodologies Total account of an explicit process: is the most obvious. Here we generate and evaluate every alternative design. We locate the better alternative by directly comparing the evaluations. Evolution of design: follow from the generation of a good base case design. Designers can then make many small changes, a few at a time, to improve the design incrementally. Structured Decision Making: following a plan that contains all the alternatives. Design to target: we design and specify unit operations to operate according to the desired target operation of the process. Module 9 – Steady state simulation 79 NAMP PIECE Solution Determination – Sequential Solution • Work backwards from one point in a sequential order solving one equation at a time – Iterative Method – Simultaneous Solution • Have to solve multiple equations with multiple variables all at same time • Generally requires simulation software Module 9 – Steady state simulation 80 NAMP PIECE Some advice when running a simulation 1. Talk with trained professionals (chemists, vendors, other engineers in the field). 2. Beware of using estimated parameters and interaction parameters when screening process alternatives. 3. Go see the plant. Plant personnel are usually helpful. Their insight and your knowledge of modeling can help solve problems efficiently. Module 9 – Steady state simulation 81 NAMP PIECE With a simulator, one day of process operation can be simulated in just seconds, and make as many changes as you want. Fresh Feed Change composition in feed Change in Reactor Properties Distillation Reactor Steam Flash Product Heater Change in Heat Duty Module 9 – Steady state simulation Change in Column Properties 82 NAMP PIECE Commercial Simulation Software Packages There are many of them, some of them are: Excel (spreadsheet) Excel Tutorial Matlab MATLAB homepage Fortran and C++ (programming languages) Aspen AspenTech HYSYS HYSYS WinGEMS WinGEMS SuperPro Designer SuperPro Designer IDEAS (Simons) Module 9 – Steady state simulation 83 NAMP PIECE Final Quiz 1. What is a drawback of using spreadsheets? 2. What are two functions that simulation allows for? 3. How are units calculated within a simulation process? 4. Explain how iteration works and why you should use it. 5. You are an engineer who has been tabbed to design a new chemical process for a company. What are some steps you can take to help you in your design? Module 9 – Steady state simulation 84 NAMP PIECE Tier II Worked Examples Module 9 – Steady state simulation 85 NAMP PIECE • Statement of Intent – Review basic chemical engineering concepts employed in steady state simulation through examples – Understand how to develop a steady-state simulation problem in Excel Module 9 – Steady state simulation 86 NAMP PIECE First Example: A Single Effect Evaporator (to be done in Excel) Module 9 – Steady state simulation 87 NAMP PIECE Evaporation Function is to concentrate solution What affects evaporation? • Rate at which heat is transferred to the liquid • Quantity of heat required to evaporate mass of water • Maximum allowable temperature of liquid • Pressure which evaporation takes place Module 9 – Steady state simulation 88 NAMP PIECE Single Effect Vertical Evaporator Three functional sections • Heat exchanger • Evaporation section • liquid boils and evaporates • Separator • vapor leaves liquid and passes off to other equipment Three sections contained in a vertical cylinder Module 9 – Steady state simulation 89 NAMP PIECE • In the heat exchanger section (calandria), steam condenses in the outer jacket • Liquid being evaporated boils on inside of the tubes and in the space above the upper tube stack • As evaporation proceeds, the remaining liquors become more concentrated Module 9 – Steady state simulation 90 NAMP PIECE Diagram of Single Effect Evaporator Tf, xf, hf, ṁf Feed F Vapor V Tv, yv, Hv, ṁV U = J/m2 s oC P = kPa Ts, Hs, ṁs A = ? m2 Condensate S Ts, hs, ṁs Steam S Concentrated liquid L Module 9 – Steady state simulation TL, xL, hL, ṁL 91 NAMP PIECE Material and Heat Balances q = UAΔT ΔT = Ts – TL ṁF = ṁL + ṁV Heat given off by vapor λ = H s – hs ṁFxF = ṁLxL + ṁVyV ṁFhF + ṁsHs = ṁLhL + ṁVHV+ ṁshs ṁFhF + ṁsλ = ṁLhL + ṁVHV q = ṁs(Hs-hs) = ṁsλ ṁsλ – ideal heat transferred in evaporator Module 9 – Steady state simulation 92 NAMP PIECE Finding the Latent Heat of Evaporation of Solution and the Enthalpies • Using the temperature of the boiling solution TL, the latent heat of evaporation can be found; • The heat capacities of the liquid feed (CpF) and product (CpL) are used to calculate the enthalpies of the solution. Module 9 – Steady state simulation 93 NAMP PIECE Property Effects on the Evaporator • Feed Temperature – Large effect – Preheating can reduce heat transfer area requirements • Pressure – Reduction • Reduction in boiling point of solution • Increased temperature gradient • Lower heating surface area requirements • Effect of Steam Pressure – Increased temperature gradient when higher pressure steam is used. Module 9 – Steady state simulation 94 NAMP PIECE Boiling-Point Rise of Solutions • Increase in boiling point over that of water is known as the boiling point elevation (BPE) of solution • BPE is found using Duhring’s Rule – Boiling point of a given solution is a linear function of the boiling point of pure water at the same pressure Module 9 – Steady state simulation 95 NAMP PIECE Duhring lines (sodium chloride) http://www.nzifst.org.nz/unitoperations/evaporation4.htm Module 9 – Steady state simulation 96 NAMP PIECE Problem Statement (McCabe 16.1 modified) A single-effect evaporator is used to concentrate 9070 kg/h of a 5% solution of sodium chloride to 20% solids. The gauge pressure of the steam is 1.37 atm; the absolute pressure in the vapor space is 100 mm Hg. The overall heat transfer coefficient is estimated to be 1400 W/m2 oC. The feed temperature is 0oC. Calculate the amount of steam consumed, the economy, and required heating surface. First Example Excel Spreadsheet Module 9 – Steady state simulation 97 NAMP PIECE 1. Draw Diagram and Label Streams 9070 kg/h feed, 0oC, 5% solids, hF Feed F Ts, Hs, 1.37 atm gauge, ṁs Steam S Vapor V Tv, 0% solids, Hv, ṁv U = 1400 W/m2 oC P= 100 mm Hg q=? Condensate S Ts, hs, ṁs A=? Liquor L Module 9 – Steady state simulation TL, 20% solids, hL, ṁL 98 NAMP PIECE ṁF = ṁL + ṁV 2. Perform Mass Balances [9070 kg/h = ṁL kg/h+ ṁV kg/h] ṁFxF = ṁLxL + ṁVyV vapor is present, no solids) (note that yv is zero because only [0.05 * 9070 kg/h = 0.2 * ṁL kg/h + 0] • Can solve for ṁv and ṁL ṁV = 6802.5 kg/h, ṁL = 2267.5 kg/h Module 9 – Steady state simulation 99 NAMP PIECE 3. Perform Heat Balances to find the Economy The economy is defined as the mass of water evaporated per mass of steam supplied. ṁFhF + ṁSHS = ṁLhL + ṁVHV+ ṁShS ṁFhF + ṁSλ = ṁLhL + ṁVHV q = ṁS(HS- hS) = ṁSλ Module 9 – Steady state simulation 100 NAMP PIECE Needed Data • Boiling point of water at 100 mm Hg = 51oC (from steam tables) www.nzifst.org.nz/unitoperations/appendix8.htm • Boiling point of solution = 88oC (from Duhring lines) http://www.nzifst.org.nz/unitoperations/evaporation4.htm • Boiling point elevation = 88 – 51 = 37oC • Enthalpy of vapor leaving evaporator (enthalpy of superheated vapor at 88oC and 100 mm Hg [.133 bar]) = 2664 kJ/kg (F&R, p.650) – also called the latent heat of evaporation • Heat of vaporization of steam (Hs-hs = λ ) at 1.37 atm gauge [20 lbf/in2] = 939 Btu/lb = 2182 kJ/kg (McCabe, App.7, p.1073) Module 9 – Steady state simulation 101 NAMP PIECE Finding the enthalpy of the feed 1. Find the heat capacity of the liquid feed yNaCl=0.05 feed is 5% sodium chloride, 95% water ywater=0.95 C p ,m ix = x iC p i a ll m ixtu re c o m p o n e n ts Cp,water=4.18 kJ/kgoC Cp,NaCl=0.85 kJ/kgoC (Cp)F = .05*0.85 + .95*4.18 = 4.01 kJ/kgoC 2. Calculate Enthalpy (neglecting heats of dilution) h F = C p ,F (TF - Tre f ) hF = 4.01 kJ/kgoC (0 - 0 oC) = 0 kJ/kg Module 9 – Steady state simulation 102 NAMP PIECE Finding the enthalpy of the liquor yNaCl=0.20 1. Find the heat capacity of the liquor feed is 20% sodium chloride, 80% water C p ,m ix = x iC p i a ll m ixtu re c o m p o n e n ts ywater=0.80 Cp,water=4.18 kJ/kgoC Cp,NaCl=0.85 kJ/kgoC Cp,L = .20*0.85 + .80*4.18 = 3.51 kJ/kgoC 2. Calculate Enthalpy (neglecting heats of dilution) h L = C p ,L (TL - Tre f ) hL = 3.51 kJ/kgoC (88-0 oC) = 309 kJ/kg Module 9 – Steady state simulation 103 NAMP PIECE Heat Balances ṁLhL + ṁVHV - ṁFhF = ṁSHS - ṁShS = ṁS(HS- hS) = ṁSλ λ = (HS-hS) = 2182 kJ/kg (2267.5 kg/h *309.23 kJ/kg) + (6802.5 kg/h * 2664 kJ/kg) – (0) = ṁS (HS-hS) q = ṁS (2182 kJ/kg) ṁs=8626.5 kg/h q = 8626.5 kg/h*2182 kJ/kg = 1.88x107 kJ/h = 5228621 W = 5.23 MW Module 9 – Steady state simulation 104 NAMP PIECE Find the Economy = ṁV/ṁS E conom y = 6802.5 k g/h = 0.788 8626.5 k g/h Module 9 – Steady state simulation 105 NAMP PIECE 4. Calculate Required Heating Surface Condensing temperature of steam (1.37 atm gauge = 126.1oC q = UAΔT A = q/UΔT 5228621 A = 1400 W m 2 o Module 9 – Steady state simulation W = 9 8 .0 2 m 2 o C (1 2 6 .1 - 8 8 ) C 106 NAMP PIECE Click on the Hyperlink and click on the “Final Solution” tab to see the final answer for the system. First Example Final Solution Module 9 – Steady state simulation 107 NAMP PIECE Second Example: Simulation of Cyclic Process (Felder and Rousseau, Example 10.2-3, pp. 516-519) (to be done in Excel) Module 9 – Steady state simulation 108 NAMP PIECE Problem Statement The gas-phase dehydrogenation of isobutane (A) to isobutene (B) is carried out in a continuous reactor. A stream of pure isobutane (the fresh feed to the process) is mixed adiabatically with a recycle stream containing 90% mole isobutane and the balance isobutene, and the combined stream goes to a catalytic reactor. The effluent from this process goes through a multistage separation process; one product stream containing all the hydrogen (C) and 10% of the isobutane leaving the reactor as well as some isobutene is sent to another part of the plant for additional processing, and the other product stream is the recycle to the reactor. The conversion of isobutane in the reactor is 35%. Assume a fresh feed of 100 mol isobutane. Simulate the process using a spreadsheet to find the desired process variables. Module 9 – Steady state simulation C4H10 C4H8 + H2 109 NAMP PIECE Diagram of Process Second Example Cyclic Process Module 9 – Steady state simulation 110 NAMP PIECE Notes • A will denote isobutane, B denotes isobutene, C denotes hydrogen • All streams are gases, Q r is the required rate of heat transfer to the reactor and Q s is the net rate of heat transfer to the separation process • Specific enthalpies are for the gaseous species at the stream temperatures relative to 25oC - Heats of formation are taken from Table B.1, and heat capacity formulas are taken from Table B.2 in Felder and Rousseau Module 9 – Steady state simulation 111 NAMP PIECE 1. Perform Degree of Freedom Analysis Module 9 – Steady state simulation 112 NAMP PIECE Review – Degrees of Freedom 1. Draw and completely label a flowchart 2. Count the unknown variables, then the independent equations relating them, 3. Subtract the number of equations from the number of variables. This gives ndf, or the number of degrees of freedom in the process. Module 9 – Steady state simulation 113 NAMP PIECE Degree of Freedom Analysis • If ndf = 0 there are n independent equations in n unknowns and the problem can be solved • If ndf >0, there are more unknowns than independent equations relating them, and at least ndf additional variable values must be specified. • If ndf <0, there are more independent equations than unknowns. The flowchart is incompletely labeled or inconsistent and redundant relations exist. Module 9 – Steady state simulation 114 NAMP PIECE Degree of Freedom Analysis – Mixing Point 4 unknowns (ṅA1, ṅB1, ṅ4,T1) - 3 balances (2 material balances, 1 energy balance) = 1 local degree of freedom Module 9 – Steady state simulation 115 NAMP PIECE Degree of Freedom Analysis – Reactor 7 unknowns (ṅA1, ṅB1, ṅA2, ṅB2, ṅC2, T1, Qr ) - 4 balances (3 molecular species balances, 1 energy balance) - 1 additional relation (35% conversion of isobutane) + 1 independent chemical reaction = 3 local degrees of freedom Module 9 – Steady state simulation 116 NAMP PIECE Degree of Freedom Analysis – Separator 8 unknowns (ṅA2, ṅB2, ṅC2, ṅA3, ṅB3, ṅC3, ṅ4, Q s ) - 4 balances (3 material balances, 1 energy balance) - 1 additional relation (isobutane split) = 3 local degrees of freedom Module 9 – Steady state simulation 117 NAMP PIECE Net Degree of Freedom Analysis – Overall Process 7 local degrees of freedoms (1+3+3) - 7 ties (ṅA1, ṅB1, ṅA2, ṅB2, ṅC2, ṅ4, and T1 were counted twice) = 0 net degrees of freedom The problem can be solved for all labeled variables. Module 9 – Steady state simulation 118 NAMP PIECE 2. Equation Based Solution Process Module 9 – Steady state simulation 119 NAMP PIECE Tearing the Cycle • Can’t solve system in a unit-to-unit manner without trial and error • “tear” between two units - Purpose is to have the least number of variables that have to be determined by trial and error • We tear between separation process and mixing unit - Only have to determine ṅ4 by trial and error. Module 9 – Steady state simulation 120 NAMP PIECE Solution Process • Assume value of recycle flow rate (ṅ4A = 100 mol/s) • Assume mixing point outlet temperature (T1 = 50oC) • Vary ṅ4A until calculated recycle flow rate (ṅ4C*) equals assumed value in ṅ4A - Will be done by driving (ṅ4A - ṅ4C*) using Goalseek • Mixing point temperature (T1) will be varied to determine the value that drives ΔḢmix to zero (remember, the mixer is adiabatic) Module 9 – Steady state simulation 121 NAMP PIECE Known Values XA = 0.35 (fractional conversion of A) 100 mol/s (basis of calculation) Feed temperature – 20oC Reactor Effluent Temperature – 90oC Product Stream Temperature – 30oC Guess for recycle stream flow rate (ṅA4) = 100 mol/s Mole fraction of A in recycle stream = 0.9 Mole fraction of B in recycle stream = 0.1 Temperature of recycle stream – 85oC Initial guess for combined stream temperature – 50oC Module 9 – Steady state simulation 122 NAMP PIECE Mass Balances (based on initial guesses) ṅA1 = 100 mol/s feed + (100 mol/s recycle * 0.9 mol fraction = 190 mol/s) ṅB1 = 100 mol/s recycle * 0.1 mol fraction = 10 mol/s ṅA2 = ṅA1 * (1-XA) = 123.5 mol/s ṅB2 = ṅB1+ (ṅA1*XA)= 76.5 mol/s ṅC2 = ṅA1 * XA = 66.5 mol/s ṅA3 = 0.01* ṅA2 = 1.24 mol/s ṅC4 = (ṅA2- ṅA3)/0.9 mol fraction = 135.85 mol/s ṅB3 = ṅB2 – (0.1 mol fraction * ṅC4 )= 62.9 mol/s ṅC3 = ṅC2 = 66.5 mol/s Module 9 – Steady state simulation 123 NAMP PIECE Calculation of Specific Enthalpies (Tables B.1 and B.2, Felder and Rousseau) o ˆ ˆ H i = (Δ H f ) i + o ˆ (Δ H f ) i C pi dT - (heats of formation) are located in Table B.1 of F&R A (isobutane [g]) = -134.5 kJ/mol B (isobutene [g]) = 1.17 kJ/mol C (hydrogen [g])= 0 kJ/mol Module 9 – Steady state simulation 124 NAMP PIECE Calculation of Specific Enthalpies (Tables B.1 and B.2, Felder and Rousseau) oC) heat capacity of component i (kJ/mol C d T p i = a+ bT + cT-2 + dT-3 , where T is temperature in oC Chemicals A* 103 B* 105 C* 108 D* 1012 isobutane 89.46 30.13 -18.91 49.87 isobutene 82.88 25.64 -17.27 50.50 hydrogen 28.84 0.00765 0.3288 -0.8698 Module 9 – Steady state simulation 125 NAMP PIECE Heat Balances (based on initial guesses) ΔḢmix = ṅA1*ĤA1 + ṅB1*ĤB1 – 100 mol/s*ĤA0 - (ṅA4*0.9 mol A/mol *ĤA4) - (ṅA4*0.1 mol fraction*ĤB4) = -78.64 kJ/mol Q r = ṅA2*ĤA2 + ṅB2*ĤB2 + ṅC2*ĤC2 - ṅA1*ĤA1 – ṅB1*ĤB1 = 9980.4 kJ/s Q s = ṅA3*ĤA3 + ṅB3*ĤB3 + ṅC3*ĤC3+(ṅA4*0.900 mol fraction*ĤA4)+(ṅB4*0.100 mol fraction*ĤB4) – ṅA2*ĤA2 - ṅB2*ĤB2 - ṅC2*ĤC2 = -568.4 kJ/s Module 9 – Steady state simulation 126 NAMP PIECE Click on the Hyperlink and click on the “Final Solution” tab to see the final answer for the system. Second Example Final Solution Module 9 – Steady state simulation 127 NAMP PIECE Tier III Open-ended problem Approach to open-ended problem Case Study. Module 9 – Steady state simulation 128 NAMP PIECE • Statement of Intent – Learn how to approach open-ended design problems – Solve a problem on your own Module 9 – Steady state simulation 129 NAMP PIECE How to approach open–ended problems State the problem clearly, including goals, constraints, and data requirements. Define the trade-offs necessary. Define the criteria for a valid solution. Develop a set of cases to simulate possible solutions. Perform the simulation and evaluate results against solution criteria. Evaluate solutions against environmental, safety and financial considerations. Module 9 – Steady state simulation 130 NAMP PIECE The Use of Limestone Slurry Scrubbing to Remove Sulfur Dioxide from Power Plant Flue Gases Prepared by Ronald W. Rousseau and Jack Winnick, Georgia Tech Department of Chemical Engineering, and Norman Kaplan, National Risk Management Research Laboratory, United States EPA Module 9 – Steady state simulation 131 NAMP PIECE About Coal • Protection of environment through process development is an important responsibility for chemical engineers • Coal is an abundant source of energy and source of raw materials in production • Predominately carbon, but contains other elements and hydrocarbon volatile matter Module 9 – Steady state simulation 132 NAMP PIECE • burned in many of world’s power plants to produce electricity • can produce a lot of pollution if gases not treated, like soot and ash • sulfur dioxide emissions regulated in the U.S. by the Environmental Protection Agency • current regulations are no more than 520 ng SO2 per joule of heating value of the fuel fed to the furnace • plants must remove 90% of SO2 released when coal-burning Module 9 – Steady state simulation 133 NAMP PIECE About Commercial Processing • SO2 removal is classified as regenerative or throwaway • throwaway processing can be modified to produce gypsum • throwaway processing uses separating agent to remove SO2 from stack gases followed by disposal of SO2 innocuously (CaSO3 * ½ H2O) and a slurried separating agent of calcium carbonate Module 9 – Steady state simulation 134 NAMP PIECE Process Description Module 9 – Steady state simulation 135 NAMP PIECE • want to produce 500 MWe (megawatts of electricity) • properties of coal given in table on next slide • coal fed at 25oC to furnace, burned with 15% excess air • sulfur reacts to form SO2 and negligible SO3 • carbon, hydrogen oxidized completely to CO2 and water • nitrogen in coal leaves furnace as N2 • ash in coal leaves furnace in two streams • 80% leaves as fly ash in furnace flue gas • remainder as bottom ash at 900oC Module 9 – Steady state simulation 136 NAMP PIECE Component Dry Weight % Carbon 75.2 Hydrogen 5.0 Nitrogen 1.6 Sulfur 3.5 Oxygen 7.5 Ash 7.2 Moisture 4.8 kg/100 kg dry coal HHV 30780 KJ/kg dry coal Cp dry coal 1.046 kJ/(kgoC) Cp ash 0.921 KJ/(kgoC) Module 9 – Steady state simulation 137 NAMP PIECE • combustion air brought into process at 25oC, 50% RH • air sent to heat exchanger, temperature increased to 315oC • air then fed to boiler, reacts with coal • flue gas leaves furnace at 330oC, goes to electrostatic precipitator • 99.9% of particulate material removed • goes to air preheater, exchanges heat with combustion air • leaves air preheater and split into two equal streams • each stream is feed to one of two identical scrubber trains • trains sized to process 60% of flue gas Module 9 – Steady state simulation 138 NAMP PIECE • divided gas stream fed to scrubber, contacts aqueous slurry of limestone, undergoes adiabatic cooling to 53oC. • sulfur dioxide absorbed in the slurry and reacts with the limestone: • CaCO3 + SO2 + ½ H2O CaSO3 · ½ H2O + CO2 • solid/liquid slurry enters scrubber at 50oC • liquid slurry flows at 15.2 kg liquid/kg inlet gas • solid to liquid ratio in the slurry is 1:9 by weight • liquid saturated with CaCO3 and CaSO3 • cleaned flue gas • meets EPA SO2 requirements • leaves scrubber with saturated water at 53oC Module 9 – Steady state simulation 139 NAMP PIECE • cleaned flue gas contains CO2 generated in scrubbing but no fly ash • cleaned flue gas reheated to 80oC, blended with clean flue gas stream from other train, and sent to be released to atmosphere • solids in spent aqueous slurry • unreacted CaCO3, flyash from flue gas, inert materials, CaSO3 • liquid portion of slurry saturated with CaCO3, CaSO3 • specific gravity of 0.988 • spent slurry split in two • one stream sent to a blending tank, mixed with freshly ground limestone, makeup water, and recycle stream • fresh slurry stream from blending tank fed to top of scrubber Module 9 – Steady state simulation 140 NAMP PIECE • second stream sent to filter where wet solids containing fly ash, inert materials, CaSO3 and CaCO3 are separated from filtrate • filtrate saturated with CaSO3, CaCO3, and is the recycle stream fed to the blending tank • wet solids contain 50.2% liquid that has similar composition to filtrate • fresh ground limestone fed to blending tank at rate of 5.2% excess of that is required to react with SO2 absorbed from flue gas • limestone – 92.1% CaCO3 and rest is insoluble inert material Module 9 – Steady state simulation 141 NAMP PIECE • Boiler generates steam at supercritical conditions • 540oC and 24.1 MPa absolute • mechanical work derived by expanding steam through a powergenerating system of turbines • low pressure steam extracted from power system contains 27.5% liquid water at 6.55 kPa absolute • heat removed from wet low pressure steam in a condenser by cooling water • cooling water enters condenser at 25oC and leaves at 28oC • saturated condensate at 38oC is produced by condenser and pumped back to boiler Module 9 – Steady state simulation 142 NAMP PIECE Assume a basis of 100 kg dry coal/min fed to the furnace. 1. Construct a flowchart of the process and completely label the streams. Show the details of only one train in the scrubber operation. Do this in Excel. 2. Estimate the molar flow rate (kmol/min) of each element in the coal (other than those in the ash). 3. Determine the feed rate (kmol/min) of O2 required for complete combustion of the coal. Module 9 – Steady state simulation 143 NAMP PIECE 4. If 15% excess oxygen is fed to combustion furnace, estimate the following: a. The oxygen and nitrogen feed rates (kmol/min) b. The mole fraction of water in the wet air, the average molecular weight, and the molar flow rate of water in the air stream (kmol/min) c. The air feed rate (kmol/min, m3/min) 5. Estimate flow rate (kmol/min, kg/min) of each component and composition (mole frac) of furnace flue gas (ignore fly ash). At what rate (kg/min) is fly ash removed from flue gas by the electrostatic precipitator? Module 9 – Steady state simulation 144 NAMP PIECE 6. If system is assumed to meet standard 90% SO2 removal released upon combustion: a. Determine flow rate (kg/min and kmol/min) of each component in the flue gas leaving scrubber b. Determine flow rate (kg/min) of slurry entering scrubber c. Estimate solid-to-liquid mass ratio in slurry leaving scrubber. d. Estimate feed rate (kg/min) of fresh ground limestone to the blending tank. Module 9 – Steady state simulation 145 NAMP PIECE 6. (continued) e. What are flow rates (kg/min) of inerts, CaSO3, CaCO3, fly ash, and water, in the wet solids removed from the filter? f. Estimate rate (kg/min, L/min) at which filtrate is recycled to blending tank. At what rate (kg/min, L/min) is makeup water added to blending tank? 7. At what rate is heat removed from the furnace? Estimate the rate of steam generation in the power cycle, assuming all the heat removed from the furnace is used to make steam. Module 9 – Steady state simulation 146 NAMP PIECE References: • Felder, R.F. and Rousseau, R.W. Elementary Principles of Chemical Processes, Third Edition. New York, John Wiley and Sons, 2000. • Smith, J.C. and Harriott, Peter. Unit Operations of Chemical Engineering, Sixth Edition. Boston, McGraw Hill, 2001. • Earle, R.L. Unit Operations in Food Processing, Second Edition. http://www.nzifst.org.nz/unitoperations/index.htm • Thibault, Jules. Notes, CHE 4311: Unit Operations. University of Ottawa, August 2002. • Genzer, Jan. Notes, CHE 225: Chemical Process Systems. North Carolina State University, August 2002. Module 9 – Steady state simulation 147 NAMP PIECE • Source on pictures for slides 13, 41, Module 9 – Steady state simulation 148

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