Module 9001 Mass Balance Paul Ashall, 2008
The accounting of all mass in a chemical/pharmaceutical process is referred to as a mass (or material) balance. Paul Ashall, 2008
Uses • ‘day to day’ operation of process for monitoring operating efficiency • Making calculations for design and development of a process i. e. quantities required, sizing equipment, number of items of equipment Paul Ashall, 2008
Simple example – batch mixing process 200 kg of a 40% w/w methanol/water solution is mixed with 100 kg of a 70% w/w methanol/water solution in a batch mixer unit. What is the final quantity and composition? Paul Ashall, 2008
continued Total initial mass = total final mass = 300 kg Initial methanol mass = final methanol mass 80 + 70 = final methanol mass = 150 kg Therefore final composition of batch is (150/300) x 100 = 50 % by wt. Paul Ashall, 2008
Exercise 1000 kg of 8% by wt. sodium hydroxide (Na. OH) solution is required. 20% sodium hydroxide solution in water and pure water are available. How much of each is required? Paul Ashall, 2008
Batch processes operate to a batch cycle and are non-steady state. Materials are added to a vessel in one operation and then process is carried out and batch cycle repeated. Integral balances are carried out on batch processes where balances are carried out on the initial and final states of the system. Paul Ashall, 2008
Batch cycle • Sequence of operations/steps repeated according to a cycle • Batch cycle time • Batch size Paul Ashall, 2008
Simple batch reaction cycle 3 steps Add reactants etc reaction Empty reactor Next cycle Start cycle t=0 t, finish cycle Paul Ashall, 2008
Continuous processes These processes are continuous in nature and operate in steady state and balances are carried out over a fixed period of time. Materials enter and leave process continuously. Paul Ashall, 2008
Law of conservation of mass When there is no net accumulation or depletion of mass in a system (steady state) then: Total mass entering system = total mass leaving system or total mass at start = total final mass Paul Ashall, 2008
General mass balance equation Input + generation – output – consumption = accumulation Notes: 1. generation and consumption terms refer only to generation of products and consumption of reactants as a result of chemical reaction. If there is no chemical reaction these terms are zero. 2. Apply to a system 3. Apply to total mass and component mass Paul Ashall, 2008
Definitions • • System – arbritary part or whole of a system Steady state/non-steady state Accumulation/depletion of mass in system Basis for calculation of mass balance (unit of time, batch etc) • Component or substance Paul Ashall, 2008
Exercise 1000 kg of a 10 % by wt. sodium chloride solution is concentrated to 50 % in a batch evaporator. Calculate the product mass and the mass of water evaporated from the evaporator. Paul Ashall, 2008
Mixing of streams F 2 F 1 F 4 F 3 Paul Ashall, 2008
Example Calculate E and x evaporator feed E, composition x% Fresh feed 1000 kg, 15% by wt sodium hydrogen carbonate Recycle stream 300 kg, 10% satd. soln. Paul Ashall, 2008
Flowsheets • Streams • Operations/equipment sequence • Standard symbols Paul Ashall, 2008
Flowsheets • Process flow diagram • PID Paul Ashall, 2008
Typical simple flowsheet arrangement Recycle of unreacted material reactor Fresh feed (reactants, solvents, reagents, catalysts etc) Separation & purification waste Paul Ashall, 2008 product Byproducts/coproducts
Exercise A 1000 kg batch of a pharmaceutical powder containing 5 % by wt water is dried in a double cone drier. After drying 90 % of the water has been removed. Calculate the final batch composition and the weight of water removed. Paul Ashall, 2008
Exercise – batch distillation 1000 kg of a 20% by wt mixture of acetone in water is separated by multistage batch distillation. The top product (distillate) contains 95% by wt. acetone and the still contains 2% acetone. Calculate the amount of distillate. Paul Ashall, 2008
Use of molar quantities It is often useful to calculate a mass balance using molar quantities of materials and to express composition as mole fractions or mole %. Distillation is an example, where equilibrium data is often expressed in mole fractions. Paul Ashall, 2008
Molar units • A mole is the molecular weight of a substance expressed in grams • To get the molecular weight of a substance you need its molecular formula and you can then add up the atomic weights of all the atoms in the molecule • To convert from moles of a substance to grams multiply by the molecular weight • To convert from grams to moles divide by the molecular weight. • Mole fraction is moles divided by total moles Paul Ashall, 2008 • Mole % is mole fraction multiplied by 100
Molar units Benzene is C 6 H 6. The molecular weight is (6 x 12) + (6 x 1) = 78 So 1 mole of benzene is 78 grams 1 kmol is 78 kg Paul Ashall, 2008
Exercise – batch distillation 1000 kmol of an equimolar mixture of benzene and toluene is distilled in a multistage batch distillation unit. 90 % of the benzene is in the top product (distillate). The top product has a benzene mole fraction of 0. 95. Calculate the quantities of top and bottom products and the composition of the bottom product. Paul Ashall, 2008
Mass balance - crystalliser A crystalliser contains 1000 kg of a saturated solution of potassium chloride at 80 deg cent. It is required to crystallise 100 kg KCl from this solution. To what temperature must the solution be cooled? Paul Ashall, 2008
T deg cent Solubility g. KCl/100 g water 80 51. 1 70 48. 3 60 45. 5 50 42. 6 40 40 30 37 20 34 10 31 0 Paul Ashall, 2008 27. 6
At 80 deg cent satd soln contains (51. 1/151. 1)x 100 % KCl i. e. 33. 8% by wt So in 1000 kg there is 338 kg KCl & 662 kg water. Crystallising 100 kg out of soln leaves a satd soln containing 238 kg KCl and 662 kg water i. e. 238/6. 62 g KCl/100 g water which is 36 g KCl/100 g. So temperature required is approx 27 deg cent from table. Paul Ashall, 2008
Mass balance filtration/centrifuge wash water/solvent solid feed suspension waste water filtrate Paul Ashall, 2008
Filtration 5000 kg DM water F 1 Impurity 55 kg Water 2600 kg API 450 kg Water 7300 kg Impurity 50 kg API 2 kg Paul Ashall, 2008 Water 300 kg API 448 kg Impurity 5 kg
Mass balance - drier water/evaporated solvent product feed Paul Ashall, 2008
Mass balance – extraction/phase split A+B S S+B A – feed solvent; B – solute; S – extracting solvent Paul Ashall, 2008
Example (single stage extraction; immiscible solvents) feed raffinate E 1 solvent extract Paul Ashall, 2008
F = 195 kg; xf = 0. 11 kg API/kgwater S = 596 kg chloroform y = 1. 72 x, where y is kg. API/kg chloroform in extract and x is kg API/kg water in raffinate. Total balance 195 + 596 = E + R API balance 19. 5 = 175. 5 x 1 + 596 y 1 19. 5 = 175. 5 x 1 + 596. 1. 72 x 1 = 0. 0162 and y 1 = 0. 029 R is 175. 5 kg water + 2. 84 kg API and E is 596 kg chloroform + 17. 28 kg API Note: chloroform and water are essentially immiscible Paul Ashall, 2008
Mass balance – absorption unit exit gas stream feed solvent feed gas stream waste solvent stream Paul Ashall, 2008
Mass balances – multiple units • Overall balance • Unit balances • Component balances Paul Ashall, 2008
Multiple units W 2 F 1 E C F P 3 R 4 E – evaporator; C – crystalliser; F – filter unit F 1 – fresh feed; W 2 – evaporated water; 2008 – solid product; R 4 – recycle Paul Ashall, P 3 of saturated solution from filter unit
Mass balance procedures • • Process description Flowsheet Label Assign algebraic symbols to unknowns (compositions, concentrations, quantities) • Select basis • Write mass balance equations (overall, total, component, unit) • Solve equations for unknowns Paul Ashall, 2008
Exercise A mass balance and tracking of usage of a solvent used in an API production process is required for a Pollution Emission Register (PER). Discuss and outline in general terms how you would do this. Ref. www. epa. ie Paul Ashall, 2008
Definitions • • Stoichiometric quantities Limiting reactant Excess reactant Conversion Yield Selectivity Extent of reaction Paul Ashall, 2008
Stoichiometry • Refers to quantities of reactants and products in a balanced chemical reaction. a. A + b. B c. C + d. D i. e. a moles of A react with b moles of B to give c moles of C and d moles of D. a, b, c, d are stoichiometric quantities Paul Ashall, 2008
Reactor mass balances Paul Ashall, 2008
Example – aspirin synthesis reaction Paul Ashall, 2008
Limiting reactant/excess reactant • In practice a reactant may be used in excess of the stoichiometric quantity for various reasons. In this case the other reactant is limiting i. e. it will limit the yield of product(s) Paul Ashall, 2008
continued A reactant is in excess if it is present in a quantity greater than its stoichiometric proportion. % excess = [(moles supplied – stoichiometric moles)/stoichiometric moles] x 100 Paul Ashall, 2008
Example – aspirin synthesis Paul Ashall, 2008
Conversion • Fractional conversion = amount reactant consumed/amount reactant supplied • % conversion = fractional conversion x 100 Note: conversion may apply to single pass reactor conversion or overall process conversion Paul Ashall, 2008
Yield = (moles product/moles limiting reactant supplied) x s. f. x 100 Where s. f. is the stoichiometric factor = stoichiometric moles reactant required per mole product Paul Ashall, 2008
Example – aspirin synthesis Paul Ashall, 2008
Selectivity = (moles product/moles reactant converted) x s. f. x 100 OR Selectivity = moles desired product/moles byproduct Paul Ashall, 2008
Extent of reaction = (moles of component leaving reactor – moles of component entering reactor)/stoichiometric coefficient of component Note: the stoichiometric coefficient of a component in a chemical reaction is the no. of moles in the balanced chemical equation ( -ve for reactants and +ve for products) Paul Ashall, 2008
Examples A B i. e. stoichiometric coefficients a = 1; b = 1 100 kmol fresh feed A; 90 % single pass conversion in reactor; unreacted A is separated and recycled and therefore overall process conversion is 100% R F reactor separation Paul Ashall, 2008 P
Discussion - Synthesis of 3, 3 dimethylindoline Paul Ashall, 2008
Discussion - Aspirin synthesis Paul Ashall, 2008
References • Elementary Principles of Chemical Processes, R. M. Felder and R. W. Rousseau, 3 rd edition, John Wiley, 2000 Paul Ashall, 2008
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