Process Classification Before writing a material balance (MB) you must first identify the type of process in question. Batch no material (mass) is transferred into or out of the system over the time period of interest (e.g., heat a vessel of water) Continuous material (mass) is transferred into and out of the system continuously (e.g., pump liquid into a distillation column and remove the product streams from top and bottom of column) Semibatch any process that is neither batch nor continuous (e.g., slowly blend two liquids in a tank) Steady-State process variables (i.e., T, P, V, flow rates) do not change with time Transient process variables change with time CHEE 221 1
F&R 4.1 Example Classify the following processes as batch, continuous, or semibatch, and transient or steady-state. 1. A balloon is filled with air at a steady rate of 2 g/min. 2. A bottle of milk is taken from the refrigerator and left on the kitchen table. 3. Water is boiled in an open flask. 4. Carbon monoxide and steam are fed into a tubular reactor at a steady-rate and react to form carbon dioxide and hydrogen. Products and unused reactants are withdrawn at the other end. The reactor contains air when the process is started up. The temperature of the reactor is also constant, and the composition and flow rate of the entering reactant stream are also independent of time. Classify the process (a) initially and (b) after a long period of time has elapsed. CHEE 221 2
Material (Mass) Balances ( MBs )-No Reaction A material balance is simply an accounting of material. For a given system in which no reaction is occurring (you will not be told this, and will need to know this from the type of unit that is under consideration; crystallizer, evaporator, filter, furnace, etc.), a material balance can be written in terms of the following conserved quantities: 1. Total mass (or moles) 2. Mass (or moles) of a chemical compound 3. Mass (or moles) of an atomic species To apply a material balance, you need to define the system and the quantities of interest (e.g. mass of a component, total mass, moles of an atomic species). What is your system, and what are you keeping track of? System a region of space defined by a real or imaginary closed envelope (envelope = system boundary) may be a single process unit, collection of process units or an entire process CHEE 221 3
What is the System? CHEE 221 4
Some Basic Process Unit Functions Splitter divides a single input into two or more outputs of the same composition (no reaction) splitter Mixer combines two or more inputs (usually of different compositions) into a single output) (no reaction) mixer Separator separates a single input into two or more outputs of different composition (no reaction) separator CHEE 221 5
Basic Process Unit Functions cont d Reactor carries out a chemical reaction that converts atomic or molecular species in the input to different atomic or molecular species in the output Heat exchanger transfers heat from one input to a second input (no reaction) Pump changes the pressure of an input to that of the corresponding output (no reaction) reactor heat exchanger pump Actual process units can combine these different functions into a single piece of hardware, and are given different names, e.g. a separator can be a distillation column, a filter press, a centrifuge, etc. See CD that comes with your textbook for examples of process equipment. CHEE 221 6
Steam Boiler Steam Boiler Heat Exchanger (no reaction) + Reactor (reaction) CHEE 221 7
Distillation A Very Common Separator (No Reaction) Distillation Column Reflux Condenser Bottoms Reboiler Separator Heat Exchanger + Splitter Heat Exchanger + Separator CHEE 221 8
Distillation Inside the Column white = vapour blue = liquid Internal trays (or packing) are used to enhance component contact Each tray accomplishes a fraction of the separation task by transferring the more volatile species to the gas phase and the less volatile species to the liquid phase Can perform material and energy balances on: an individual tray the column, bottoms reboiler, or top condenser the entire system CHEE 221 9
Balances Depend on the Choice of System Boundary CHEE 221 10
Fractional Distillation CHEE 221 11
General Mass Balance Equation Accumulation = In Out + Generation Consumption system boundary Input streams to system System over which mass balance is made output streams from system Accumulation within the system (mass buildup) = Input through system boundary - Output through system boundary Generation within + the system - Consumption within the system CHEE 221 12
Material Balance Simplifications The following rules may be used to simplify the material balance equation: Accumulation = In Out + Generation Consumption If the system is at steady-state, set accumulation = 0 In Out + Generation Consumption = 0 If the balanced quantity is total mass, set generation = 0 and consumption = 0 (law of conservation of mass) Accumulation = In Out If the balanced substance is a nonreactive species, (neither a reactant nor a product) or for non-reacting systems in general, set generation = 0 and consumption = 0 Accumulation = In Out CHEE 221 13
Problems Involving Material Balances Initial procedures will be outlined for solving single unit processes No reaction (consumption = generation = 0) Continuous steady-state (accumulation = 0) And so the Conservation Equation becomes.. (what?) These procedures will form the foundation for more complex problems involving multiple units and processes with reaction Following a standard methodology to solve problems is the key to success. This standard methodology will be illustrated via many examples in class, and is the one used by F&R. CHEE 221 14
Material Balance Calculations All material balance calculations are variations on a single theme: Given values of some input and output stream variables (e.g. flowrates, compositions), derive and solve equations for the others Solving the equations is a matter of simple algebra (the math is easy!), however, you first need to: convert the problem statement into a process flow diagram; what are the streams in/out and what components are in each stream? label the PFD with the knowns (flows, compositions, etc.), assign variables to the unknowns (remaining flows, compositions), identify the system on which you are doing the MB, and decide on your basis (mass/moles/input/output.) derive the necessary equations from the component and/or overall MB equations, and process constraint (PC) equations follow the standard methodology to solve the problem CHEE 221 15
Sample Problem Statement Example 4.5-2 F&R Forty-five hundred kilograms per hour of a solution that is one-third K 2 CrO 4 by mass is joined by a recycle stream containing 36.4% K 2 CrO 4, and the combined stream is fed into an evaporator. The concentrated stream leaving the evaporator contains 49.4% K 2 CrO 4 ; this stream is fed into a crystallizer in which it is cooled (causing crystals of K 2 CrO 4 to come out of solution) and then filtered. The filter cake consists of K 2 CrO 4 crystals and a solution that contains 36.4% K 2 CrO 4 by mass; the crystals account for 95% of the total mass of the filter cake. The solution that passes through the filter, also 36.4% K 2 CrO 4, is the recycle stream. Calculate the rate of evaporation, the rate of production of crystalline K 2 CrO 4, the feed rates that the evaporator and the crystallizer must be designed to handle, and the recycle ratio (mass of recycle)/(mass of fresh feed). ***WHAT ARE THE UNITS (BOXES) ON YOUR PFD?*** ***WHAT ARE THE STREAMS IN/OUT, AND BETWEEN THE UNITS?*** ***WHAT COMPOUNDS ARE PRESENT IN EACH STREAM?*** CHEE 221 16
Problems Involving Material Balances Standard procedures will initially be developed for single-unit processes (F&R 4.3) No reaction (Consumption=Generation=0) Continuous steady-state (Accumulation=0) Develop good habits now, and practise. Problems will get more complex as we extend the procedures to multiple-unit processes (starting in Week 3) and processes with reaction (starting in Week 4/5) Standard procedures are summarized in F&R Section 4.3 and include: drawing/labeling a process flow diagram (4.3a) selecting a basis of calculation (4.3b) setting up material balances (4.3c) performing a degree of freedom analysis (4.3d) These are critical sections of the text and will form the basis for Quiz 1 Understanding the Concepts is not good enough. You will not be tested on Understanding the Concepts. You will be tested on your ability to solve balance problems, and to get the correct answer. CHEE 221 17
Flowcharts-Process Flow Diagrams A flowchart, or process flow diagram (PFD), is a convenient (actually, necessary) way of organizing process information for subsequent calculations. To obtain maximum benefit from the PFD in material balance calculations, you must: 1. Write the values and units of all known stream variables (flows and compositions) at the locations of the streams on the chart. 2. Assign algebraic symbols to unknown stream variables (flows and compositions) and write these variable names and their associated units on the chart. Your PFD is an essential part of the problem solution, and will (initially) be assigned marks for completeness. CHEE 221 18
Note on Notation The use of consistent notation is generally advantageous. For the purposes of this course, the notation adopted in Felder and Rousseau will be followed. For example: m mass m V V x i y i mass flow rate volume volumetric flow rate component fractions (mass or mole) in liquid streams (sometimes w i used for wt fractions) component fractions in gas streams CHEE 221 19
Basis of Calculation Basis of calculation is an amount or flow rate of one of the process streams on a mass or mole basis If a stream amount or flow rate is given in the problem statement, use this as the basis of calculation (almost always) If no stream amounts or flow rates are known, you can assume one, preferably a stream of known composition if mass fractions are known, choose a total mass or mass flow rate of that stream (e.g., 100 kg or 100 kg/h) as a basis if mole fractions are known, choose a total number of moles or a molar flow rate CHEE 221 20
Flowchart Scaling Scaling the process of changing the values of all stream amounts or flow rates by a proportional amount while leaving the stream compositions and conditions unchanged. Scaling up final stream quantities are larger than the original quantities Scaling down final stream quantities are smaller than the original quantities 30 mol A/min 70 mol B/min 40 C, 1 atm 100 mol/min 0.30 mol A/mol 0.70 mol B/mol 40 C, 1 atm Scale up process by a factor of 2 60 mol A/min 140 mol B/min 40 C, 1 atm 200 mol/min 0.30 mol A/mol 0.70 mol B/mol 40 C, 1 atm CHEE 221 21
Method for Solving Material Balance Problems 1. Choose a basis of calculation (input, output, mass, moles) 2. Draw and fully label a flowchart with all the known and unknown process variables (flows, compositions) as well as the basis of calculation. Be sure to include units. 3. Write any Process Constraint (PC) equations. 4. Determine the number of unknowns and the number of equations that can be written to relate them. That is, does the number of equations equal the number of unknowns? 5. Solve the equations 6. Check your solution does it make sense? Calculate the quantities requested in the problem statement if not already calculated 7. Cleary present your solution with the proper units and the correct number of significant figures CHEE 221 22
Example 1 Four hundred and fifty kg-moles per hour of a mixture of n-butanol and i-butanol containing 30 mole % n-butanol is separated by distillation into two fractions. The flow rate of n-butanol in the overhead stream is 120 kg-moles n-butanol/h and that of i-butanol in the bottom stream is 300 kg-moles i-butanol/h. The operation is at steady-state. Calculate the unknown component flow rates in the output streams. What is the mole fraction of n-butanol in the bottom stream? What is the mass fraction? CHEE 221 23
Example 2 A spent sulfuric acid solution is brought up to strength for a pickling process in a mixer. Spent solution at 3% sulfuric acid (by weight) is mixed with a 50% solution (by weight) to obtain the desired product concentration of 40% acid by weight. All are aqueous solutions. Determine all flowrates on the basis of 100 lb m /h of product. If the actual flow of the spent stream is 300 lb m /h, what must the flowrates of the streams be? CHEE 221 24
Example (Problem 4.3 F&R) A liquid mixture of benzene and toluene contains 55.0% benzene by mass. The mixture is to be partially evaporated to yield a vapour containing 85.0 wt% benzene and a residual liquid containing 10.6% benzene by mass. For a feed rate of 100.0 kg/h of the 55% mixture, determine the flowrates of the vapour and liquid product streams. CHEE 221 25
Example: Quiz 1 2007 Physical Property Data (S.G.=specific gravity): Benzene S.G.=0.879 MW=78.11 g/mol Toluene S.G.=0.866 MW=92.13 g/mol Water density = 1.00 kg/l MW=18.02 g/mol R = 0.08206 L atm/(mol K) A mixture containing 42 wt % benzene (B) and 58 wt% toluene (T) is fed to a distillation column at a flowrate of 100 kg/min. The product stream leaving the top of the column (the overhead product) contains 90 wt% benzene, and 85 wt% of the total benzene fed to the column exits in this overhead product stream. Calculate the mass flowrate and mass composition of the product stream leaving the bottom of the column. Calculate the volumetric flowrate of the overhead product, assuming that it exits the distillation column as a vapour stream at 82 ºC and 1 atm (abs) CHEE 221 26