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## Chapter 3 Mass Balance

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**Contents**• Process classification • Balances • Material Balance Calculations • Balance on Multiple Unit Processes • Recycle and Bypass • Balances on Reactive Systems • Balances on Reactive Processes • Combustion Reaction**OBJECTIVES**• Students will be able to identify types of processes; batch, semibatch and continuous • Students will be able to perform Degree of Freedom Analysis • Students will be able to perform Material Balance on Single Unit, Nonreactive process under steady state condition**Process Classification**Three type of process • Batch process • Feed is charge to the process and product is removed when the process is completed • No mass is fed or removed from the process during the operation • Used for small scale production • Operate in unsteady state • Continuous process • Input and output is continuously red and remove from the process • Operate in steady state • Used for large scale production • Semibatch process • Neither batch nor continuous • During the process a part of reactant can be fed or a part of product can be removed.**Operation of Continuous Process**• Steady state • All the variables (i.e. temperatures, pressure, volume, flow rate, etc) do not change with time • Minor fluctuation can be acceptable • Unsteady state or transient • Process variable change with time, in particular mass flow rate.**Test Yourself**Define type and operation of process given below • A balloon is filled with air at steady rate of 2 g/min • A bottle of milk is taken from the refrigerator and left on the kitchen • Water is boiled in open flask Answer • Semibatch and unsteady state • Batch and unsteady state • Semibatch and unsteady state**Balances**General Balance • A balance on a conserved quantity (total mass, mass of a particular species, energy, momentum) in a system ( a single process unit, a collection of units, or an entire process) may be written in the following way: INPUT + GENERATION– OUTPUT – CONSUMPTION = ACCUMULATION**Differential vs. Integral Balances**Two types of balances may be written: • Differential balances • balances that indicate what is happening in a system at an instant time. • balance equation is a rate (rate of input, rate of generation, etc.) and has units of the balanced quantity unit divided by a time unit (people/yr, g SO2/s). • usually applied to a CONTINUOUS process. • Integral balances • Balances that describe what happens between two instants of time. • balance equation is an amount of the balanced quantity and has the corresponding unit (people, g SO2). • usually applied to a BATCH process, with the two instants of time being the moment after the input takes place and the moment before the product is withdrawn.**Simplified Rule for Mass Balance**• If the balanced quantity is TOTAL MASS, set generation = 0 and consumption = 0. Mass can neither be created nor destroyed. • If the balanced substances is a NONREACTIVE SPECIES (neither a reactant nor a product), set generation = 0 and consumption = 0. • If a system is at STEADY STATE, set accumulation = 0, regardless of what is being balanced.**Balances on Continuous Steady State Process**• Steady state: accumulation = 0 INPUT + GENERATION– OUTPUT – CONSUMPTION = 0 • If balance on nonreactive species or total mass; balance equation become INPUT = OUTPUT**Integral Balances on Batch Process**• Ammonia is produced from nitrogen and hydrogen in a batch reactor. At time t = 0 there are n0 mol of NH3 in the reactor, and at a later time tf the reaction terminates and the contents of the reactor, which include nf ammonia, are withdrawn. Between t0 and tf no ammonia enters or leaves through the reactor boundaries. From GMBE: (input=0; output=0) Generation – Consumption = Accumulation For batch reactor: Accumulation = Final output – Initial Input Final GMBE for batch process Initial input + Generation = Final output + Consumption**General Procedure for Single Unit Process Material Balance**Calculation • Choose as basis of calculation an amount or flow rate of one of the process streams. • Draw a flowchart and fill in all unknown variables values, including the basis of calculation. Then label unknown stream variables on the chart. • Express what the problem statement asks you to determine in terms of the labeled variables. • If you are given mixed mass and mole units for a stream (such as a total mass flow rate and component mole fractions or vice versa), convert all quantities to one basis. • Do the degree-of-freedom analysis. • If the number of unknowns equals the number of equations relating them (i.e., if the system has zero degree of freedom), write the equations in an efficient order (minimizing simultaneous equations) and circle the variables for which you will solve. • Solve the equations. • Calculate the quantities requested in the problem statement if they have not already been calculated. • If a stream quantity or flow rate ng was given in the problem statement and another value nc was either chosen as a basis or calculated for this stream, scale the balanced process by the ratio ng/nc to obtain the final result.**Flowcharts**• When you are given process information and asked to determine something about the process, ORGANIZE the information in a way that is EASY for subsequent calculations. • The best way draw a flowchart • using boxes or other symbols to represent process units (reactors, mixers, separation units, etc.) • lines with arrows to represent inputs and outputs.**Flowchart Example**An experiment on the growth rate of certain organism requires an environment of humid air enriched in oxygen. Three input streams are fed into an evaporation chamber to produce an output stream with the desired composition. A: Liquid water fed at rate of 20 cm3/min B: Air (21% O2 and 79% N2) C: Pure O2 with a molar flow rate one-fifth of the molar flow rate of stream B The output gas is analyzed and is found to contain 1.5 mole% water. Draw and label the flowchart of the process, and calculate all unknown stream variables.**mol O2/min**Evaporation mol/min 0.015 mol H2O/mol y mol O2 /mol (0.985-y) mol N2/mol mol air/min 0.21 mol O2 /mol 0.79 mol N2 /mol 20 cm3 H2O (l)/min mol H2O/min Flowchart Example**Flowcharts**• The flowchart of a process can help get material balance calculations started and keep them moving. • Flowchart must be fully labeled when it is first drawn, with values of known process variables and symbols for unknown variables being written for each input and output stream. • Flowchart will function as a scoreboard for the problem solution: as each unknown variable is determined its value is filled in, so that the flowchart provides a continuous record of where the solution stands and what must still be done.**400 mol/h**0.21 mol O2/mol 0.79 mol N2/mol T = 320˚C, P = 1.4 atm Flowcharts Labeling • Write the values and units of all known stream variables at the locations of the streams on the flowchart. • For example, a stream containing 21 mole% O2 and 79% N2 at 320˚C and 1.4 atm flowing at a rate of 400 mol/h might be labeled as:**100 kmol/min**0.6 kmol N2/kmol 0.4 kmol O2/kmol 60 kmol N2/min 40 kmol O2/min 10 lbm 0.3 lbm CH4/lbm 0.4 lbm C2H4/lbm 0.3 lbm C2H6/lbm 3.0 lbm CH4 4.0 lbm C2H4 3.0 lbm C2H6 Flowcharts Labeling • Process stream can be given in two ways • As the total amount or flow rate of the stream and the fractions of each component • Or directly as the amount or flow rate of each component.**mol/h**400 mol/h 0.21 mol O2/mol 0.79 mol N2/mol T = 320˚C, P = 1.4 atm y mol O2/mol (1-y) mol N2/mol T = 320˚C, P = 1.4 atm Flowcharts Labeling • Assign algebraic symbols to unknown stream variables [such as m (kg solution/min), x (lbm N2/lbm), and n (kmol C3H8)] and write these variable names and their associated units on the flowchart.**Flowcharts Labeling**• If that the mass of stream 1 is half that of stream 2, label the masses of these streams as m and 2m rather than m1 and m2. • If you know that mass fraction of nitrogen is 3 times than oxygen, label mass fractions as y g O2/g and 3y g N2/g rather than y1 and y2. • When labeling component mass fraction or mole fraction, the last one must be 1 minus the sum of the others • If volumetric flow rate of a stream is given, it is generally useful to label the mass or molar flow rate of this stream or to calculate it directly, since balance are not written on volumetric qualities**Flowchart Scaling & Basis of Calculation**• Flowchart scaling – procedure of changing the values of all stream amounts or flow rates by a proportional amount while leaving the stream compositions unchanged. The process would still be balance. • Scaling-up – if final stream quantities are larger than the original quantities. • Scaling down – if final stream quantities are smaller than the original quantities.**1 kg C6H6**2 kg 0.5 kg C6H6/kg 0.5 kg C7H8/kg 1 kg C7H8 x 300 300 kg C6H6 600 kg 0.5 kg C6H6/kg 0.5 kg C7H8/kg 300 kg C7H8 kg kg/h Replace kg with lbm 300 lbm/h 600 lbm/h 0.5 lbm C6H6/lbm 0.5 lbm C7H8/lbm 300 lbm/h Flowchart Scaling & Basis of Calculation**Flowchart Scaling & Basis of Calculation**• Suppose you have balanced a process and the amount or flow rate of one of the process streams is n1.You can scale the flow chart to make the amount or flow rate of this stream n2 by multiplying all stream amounts or flow rate by the ratio n2/n1. Scaling Factor= Desired amount / Old amount • You cannot, however, scale masses or mass flow rates to molar quantities or vice versa by simple multiplication; conversions of this type must be carried out using the methods as discussed in mass fraction and mol fraction section.**Class Discussion for Example 4.3-2**TEST YOURSELF Page 95**3 kg C6H6/min**m (kg/min) x (kg C6H6/kg) (1-x) (kg C7H8/kg) 1 kg C7H8/min Balancing a Process 3.0 kg/min of benzene and 1.0 kg/min of toluene are mixed • Two unknown quantities – m and x, associated with process, so two equations are needed to calculate them. • For NONREACTIVE STEADY STATE process, input = output. • 3 possible balance can be written – Balance on total mass, benzene, and toluene – any two of which provide the equations needed to determine m and x. For example, Total Mass Balance: 3.0 kg/min + 1.0 kg/min = m kg/min = 4.0 kg/min Benzene Balance: 3.0 kg C6H6/min = 4.0 kg/min (x kg C6H6/kg) x = 0.75 kg C6H6/kg**Balancing a Process**• Which balance to be used when a choice exists and the order in which these balanced should be written? • Rules of thumb for NONREACTIVE process • The maximum number of independent equations that can be derived by writing balances on a nonreactive system equals the number of chemical species in the input and output streams. • Write balances first that involve the fewest unknown variables.**General Procedure for Single Unit Process Material Balance**Calculation • Choose as basis of calculation an amount or flow rate of one of the process streams. • Draw a flowchart and fill in all unknown variables values, including the basis of calculation. Then label unknown stream variables on the chart. • Express what the problem statement asks you to determine in terms of the labeled variables. • If you are given mixed mass and mole units for a stream (such as a total mass flow rate and component mole fractions or vice versa), convert all quantities to one basis. • Do the degree-of-freedom analysis. • If the number of unknowns equals the number of equations relating them (i.e., if the system has zero degree of freedom), write the equations in an efficient order (minimizing simultaneous equations) and circle the variables for which you will solve. • Solve the equations. • Calculate the quantities requested in the problem statement if they have not already been calculated. • If a stream quantity or flow rate ng was given in the problem statement and another value nc was either chosen as a basis or calculated for this stream, scale the balanced process by the ratio ng/nc to obtain the final result.**Basis of Calculation**• Balanced process can always be scaled. Mean that material balance calculation can be performed on the basis of any convenient set of stream amount or flow rate and the results can afterward be scaled to any desired extent. • A basis of calculation is an amount (mass or moles) of flow rate (mass or molar) of one stream or stream component in a process. All unknown variables are determined to be consistent with the basis. • If a stream amount or flow rate is given in problem, choose this quantity as a basis • If no stream amount or flow rate are known, assume one stream with known composition. If mass fraction is known, choose total mass or mass flow rate as basis. If mole fraction is known, choose a total moles or molar flow rate as basis**General Procedure for Single Unit Process Material Balance**Calculation • Choose as basis of calculation an amount or flow rate of one of the process streams. • Draw a flowchart and fill in all unknown variables values, including the basis of calculation. Then label unknown stream variables on the chart. • Express what the problem statement asks you to determine in terms of the labeled variables. • If you are given mixed mass and mole units for a stream (such as a total mass flow rate and component mole fractions or vice versa), convert all quantities to one basis. • Do the degree-of-freedom analysis. • If the number of unknowns equals the number of equations relating them (i.e., if the system has zero degree of freedom), write the equations in an efficient order (minimizing simultaneous equations) and circle the variables for which you will solve. • Solve the equations. • Calculate the quantities requested in the problem statement if they have not already been calculated. • If a stream quantity or flow rate ng was given in the problem statement and another value nc was either chosen as a basis or calculated for this stream, scale the balanced process by the ratio ng/nc to obtain the final result.**Degree-of-Freedom**• Before doing any material balance calculation, use a properly drawn and labeled flowchart to determine whether there is enough information to solve a given problem. • The procedure for doing so is referred to as degree-of-freedom analysis. • Procedure to perform a degree-of-freedom analysis: • draw and completely label a flowchart • count the unknown variables on the chart (n unknowns) • count the independent equations (n indep. eq.) • Find number of degree-of-freedom (ndf) ndf= n unknowns- n indep. eq.**Number of Degree-of-Freedom**• Three possibilities number of degree-of-freedom (n df) 1. If ndf = 0 • the problem can in principle be solved. 2. If ndf > 0 • there are more unknowns than independent equations relating to them • at least ndf additional variable values must be specified before remaining variable values can be determined. • Either relations have been overlooked or the problem is underspecified. 3. If ndf < 0 • there are more independent equations than unknowns. • Either the flowchart is incompletely labeled or the problem is overspecified with redundant and possibly inconsistent relations. • There is little point wasting time trying to solve material balance for n df > 0 or n df <0.**6 Sources of Equation for Balance**• Material balances. • For a nonreactive process, number of independent equation can be written is not more than number of molecules species (n ms) of the process • If benzene and toluene is involve in stream, we can write balance on benzene, toluene, total mass, atomic carbon and etc., but only TWO INDEPENDENT balance equation exist • An energy balance. • If the amount of energy exchanged between the system and its surroundings is specified or if it is one of the unknown process variables, an energy balance provides a relationship between inlet and outlet material flows and temperatures. • Process specifications • The problem statement may specify how several process are related. • i.e: Outlet flow rate is two times than flow rate stream 1 or etc.**6 Sources of Equation for Balance**• Physical properties and laws • Two of the unknown variables may be the mass and volume of a stream material, in which case a tabulated specific gravity for liquids and solids or an equation of state for gases would provide an equation relating the variables. • Physical constraints • For example, if the mole fractions of the three components of a stream labeled xA, xB, and xC, then the relation among these variables is xA + xB + xC = 1. • Instead label as xc, the las fraction should be 1-xA-xB • Stoichiometric relations • If chemical reactions occur in a system, stoichiometric equation provide a relationship between the quantities of reactant and the product**General Procedure for Single Unit Process Material Balance**Calculation • Choose as basis of calculation an amount or flow rate of one of the process streams. • Draw a flowchart and fill in all unknown variables values, including the basis of calculation. Then label unknown stream variables on the chart. • Express what the problem statement asks you to determine in terms of the labeled variables. • If you are given mixed mass and mole units for a stream (such as a total mass flow rate and component mole fractions or vice versa), convert all quantities to one basis. • Do the degree-of-freedom analysis. • If the number of unknowns equals the number of equations relating them (i.e., if the system has zero degree of freedom), write the equations in an efficient order (minimizing simultaneous equations) and circle the variables for which you will solve. • Solve the equations. • Calculate the quantities requested in the problem statement if they have not already been calculated. • If a stream quantity or flow rate ng was given in the problem statement and another value nc was either chosen as a basis or calculated for this stream, scale the balanced process by the ratio ng/nc to obtain the final result.**CLASS DISCUSSION**EXAMPLE 4.3-4 EXAMPLE 4.3-5