RULES OF THUMB FOR CHEMICAL ENGINEERS
CONTENTS 1 8 14 34 39 44 59 76 79 83 98 150 171 181 216 222 231 234 1 1 PARTICULATE SOLIDS 1 2 PARTICLE SIZE REDUCTION AND ENLARGEMENT 1 3 MOTION OF PARTICLES IN A UID 1 4 FLOW OF UIDS THROUGH GRANULAR BEDS AND PACKED COLUMNS 1 5 SEDIMENTATION 1 6 FLUIDISATION 1 7 LIQUID LTRATION 1 8 MEMBRANE SEPARATION PROCESSES 1 9 CENTRIFUGAL SEPARATIONS 1 10 LEACHING 1 11 DISTILLATION 1 12 ABSORPTION OF GASES 1 13 LIQUID LIQUID EXTRACTION 1 14 EVAPORATION 1 15 CRYSTALLISATION 1 16 DRYING 1 17 ADSORPTION 1 18 ION EXCHANGE 1 19 CHROMATOGRAPHIC SEPARATIONS 235 237 262 265 2 1 REACTOR DESIGN GENERAL PRINCIPLES 2 2 FLOW CHARACTERISTICS OF REACTORS OW MODELLING 2 3 GAS SOLID REACTIONS AND REACTORS 2 4 GAS LIQUID AND GAS LIQUID SOLID REACTORS 271 285 BIOCHEMICAL REACTION ENGINEERING 2 5 SECTION 1 1 PARTICULATE SOLIDS PROBLEM 1 1 THE SIZE ANALYSIS OF A POWDERED MATERIAL ON A MASS BASIS IS REPRESENTED BY A STRAIGHT LINE FROM 0 PER CENT AT 1 M PARTICLE SIZE TO 100 PER CENT BY MASS AT 101 M PARTICLE SIZE CALCULATE THE SURFACE MEAN DIAMETER OF THE PARTICLES CONSTITUTING THE SYSTEM SOLUTION SEE VOLUME 2 EXAMPLE 1 1 PROBLEM 1 2 THE EQUATIONS GIVING THE NUMBER DISTRIBUTION CURVE FOR A POWDERED MATERIAL ARE DN DD D FOR THE SIZE RANGE 0 10 M AND DN DD 100 000 D4 FOR THE SIZE RANGE 10 100 M WHERE D IS IN M SKETCH THE NUMBER SURFACE AND MASS DISTRIBUTION CURVES AND CALCULATE THE SURFACE MEAN DIAMETER FOR THE POWDER EXPLAIN BRIE Y HOW THE DATA FOR THE CONSTRUCTION OF THESE CURVES MAY BE OBTAINED EXPERIMENTALLY SOLUTION SEE VOLUME 2 EXAMPLE 1 2 PROBLEM 1 3 THE NENESS CHARACTERISTIC OF A POWDER ON A CUMULATIVE BASIS IS REPRESENTED BY A STRAIGHT LINE FROM THE ORIGIN TO 100 PER CENT UNDERSIZE AT A PARTICLE SIZE OF 50 M IF THE POWDER IS INITIALLY DISPERSED UNIFORMLY IN A COLUMN OF LIQUID CALCULATE THE PROPORTION BY MASS WHICH REMAINS IN SUSPENSION IN THE TIME FROM COMMENCEMENT OF SETTLING TO THAT AT WHICH A 40 M PARTICLE FALLS THE TOTAL HEIGHT OF THE COLUMN IT MAY BE ASSUMED THAT STOKES LAW IS APPLICABLE TO THE SETTLING OF THE PARTICLES OVER THE WHOLE SIZE RANGE 1 SOLUTION FOR SETTLING IN THE STOKES LAW REGION THE VELOCITY IS PROPORTIONAL TO THE DIAMETER SQUARED AND HENCE THE TIME TAKEN FOR A 40 M PARTICLE TO FALL A HEIGHT H M IS T H 402K WHERE K A CONSTANT DURING THIS TIME A PARTICLE OF DIAMETER D M HAS FALLEN A DISTANCE EQUAL TO KD2H 402K HD2 402 THE PROPORTION OF PARTICLES OF SIZE D WHICH ARE STILL IN SUSPENSION IS 1 D2 402 AND THE FRACTION BY MASS OF PARTICLES WHICH ARE STILL IN SUSPENSION IS 40 0 1 D2 402 DW SINCE DW DD 1 50 THE MASS FRACTION IS 1 50 40 0 1 D2 402 DD 1 50 D D3 4800 40 0 0 533 OR 53 3 PER CENT OF THE PARTICLES REMAIN IN SUSPENSION PROBLEM 1 4 IN A MIXTURE OF QUARTZ OF DENSITY 2650 KG M3 AND GALENA OF DENSITY 7500 KG M3 THE SIZES OF THE PARTICLES RANGE FROM 0 0052 TO 0 025 MM ON SEPARATION IN A HYDRAULIC CLASSI ER UNDER FREE SETTLING CONDITIONS THREE FRACTIONS ARE OBTAINED ONE CONSISTING OF QUARTZ ONLY ONE A MIXTURE OF QUARTZ AND GALENA AND ONE OF GALENA ONLY WHAT ARE THE RANGES OF SIZES OF PARTICLES OF THE TWO SUBSTANCES IN THE ORIGINAL MIXTURE SOLUTION USE IS MADE OF EQUATION 3 24 STOKES LAW WHICH MAY BE WRITTEN AS U0 KD2 S WHERE K G 18 IS A CONSTANT FOR LARGE GALENA U0 K 25 10 6 2 7500 1000 4 06 10 6K M S FOR SMALL GALENA U0 K 5 2 10 6 2 7500 1000 0 176 10 6K M S FOR LARGE QUARTZ U0 K 25 10 6 2 2650 1000 1 03 10 6K M S FOR SMALL QUARTZ U0 K 5 2 10 6 2 2650 1000 0 046 10 6K M S RULES OF THUMB FOR CHEMICAL ENGINEERS 2 IF THE TIME OF SETTLING WAS SUCH THAT PARTICLES WITH A VELOCITY EQUAL TO 1 03 10 6K M S SETTLED THEN THE BOTTOM PRODUCT WOULD CONTAIN QUARTZ THIS IS NOT SO AND HENCE THE MAXIMUM SIZE OF GALENA PARTICLES STILL IN SUSPENSION IS GIVEN BY 1 03 10 6K KD2 7500 1000 OR D 0 0000126 M OR 0 0126 MM SIMILARLY IF THE TIME OF SETTLING WAS SUCH THAT PARTICLES WITH A VELOCITY EQUAL TO 0 176 10 6K M S DID NOT START TO SETTLE THEN THE TOP PRODUCT WOULD CONTAIN GALENA THIS IS NOT THE CASE AND HENCE THE MINIMUM SIZE OF QUARTZ IN SUSPENSION IS GIVEN BY 0 176 10 6K KD2 2650 1000 OR D 0 0000103 M OR 0 0103 MM IT MAY THEREFORE BE CONCLUDED THAT ASSUMING STREAMLINE CONDITIONS THE FRACTION OF MATERIAL IN SUSPENSION THAT IS CONTAINING QUARTZ AND GALENA IS MADE UP OF PARTICLES OF SIZES IN THE RANGE 0 0103 0 0126 MM PROBLEM 1 5 A MIXTURE OF QUARTZ AND GALENA OF A SIZE RANGE FROM 0 015 MM TO 0 065 MM IS TO BE SEPARATED INTO TWO PURE FRACTIONS USING A HINDERED SETTLING PROCESS WHAT IS THE MINIMUM APPARENT DENSITY OF THE UID THAT WILL GIVE THIS SEPARATION HOW WILL THE VISCOSITY OF THE BED AFFECT THE MINIMUM REQUIRED DENSITY THE DENSITY OF GALENA IS 7500 KG M3 AND THE DENSITY OF QUARTZ IS 2650 KG M3 SOLUTION SEE VOLUME 2 EXAMPLE 1 4 PROBLEM 1 6 THE SIZE DISTRIBUTION OF A DUST AS MEASURED BY A MICROSCOPE IS AS FOLLOWS CONVERT THESE DATA TO OBTAIN THE DISTRIBUTION ON A MASS BASIS AND CALCULATE THE SPECI C SURFACE ASSUMING SPHERICAL PARTICLES OF DENSITY 2650 KG M3 SIZE RANGE M NUMBER OF PARTICLES IN RANGE 0 2 2000 2 4 600 4 8 140 8 12 40 12 16 15 16 20 5 20 24 2 RULES OF THUMB FOR CHEMICAL ENGINEERS 3 SOLUTION FROM EQUATION 1 4 THE MASS FRACTION OF PARTICLES OF SIZE D1 IS GIVEN BY X1 N1K1D3 1 S WHERE K1 IS A CONSTANT N1 IS THE NUMBER OF PARTICLES OF SIZE D1 AND S IS THE DENSITY OF THE PARTICLES 2650 KG M3 X1 1 AND HENCE THE MASS FRACTION IS X1 N1K1D3 1 S NKD3 S IN THIS CASE D N KD3N S X 1 200 5 300 000K 0 011 3 600 42 930 000K 0 090 6 140 80 136 000K 0 168 10 40 106 000 000K 0 222 14 15 109 074 000K 0 229 18 5 77 274 000K 0 162 22 2 56 434 400K 0 118 477 148 400K 1 0 THE SURFACE MEAN DIAMETER IS GIVEN BY EQUATION 1 14 DS N1D3 1 N1D2 1 AND HENCE D N ND2 ND3 1 2000 2000 2000 3 600 5400 16 200 6 140 5040 30 240 10 40 4000 40 000 14 15 2940 41 160 18 5 1620 29 160 22 2 968 21 296 21 968 180 056 THUS DS 180 056 21 968 8 20 M THIS IS THE SIZE OF A PARTICLE WITH THE SAME SPECI C SURFACE AS THE MIXTURE THE VOLUME OF A PARTICLE 8 20 M IN DIAMETER 6 8 203 288 7 M3 RULES OF THUMB FOR CHEMICAL ENGINEERS 4