TUTORIAL FST 359 CHAPTER 3: FILTRATION QUESTION 1 The following data ware obtained from a laboratory model of plate and frame filter press with an area of 2.5 m2 (A) working at a constant pressure of 1200 kPa. Table 2: Data of filtrate volume collected through time Time, t (min) Filtrate volume, V (L) 2.5 15.7 5.0 25.2 7.5 32.3 10.0 39.2 12.5 44.1 15.0 49.2 Based on the information given, calculate the area required for the filtration system if the filter press is to be designed to filter 150 m3 (V) slurry in 30 hours (t). t V B =k 2 + V A A
(10 marks) ANSWER Step 1: State formulas
y=mx +c t k B = 2 V+ V A A where : t y= V k m= 2 A x=V B c= A
Step 2: Design table t, (sec) 150 300 450 600 750 900
B Step 3: Plot the graph and find A
V, (m3) – paksi x 0.0157 0.0252 0.0323 0.0392 0.0441 0.0492
t ( V = x axis, V
Properly labeled and complete graph Step 4: Find B From the graph
B =5400 A B =5400 2. 5 B=5400×2. 5 B=13500
Step 5: Find
k y 2− y1 m= 2 x 2−x1 A by using this formula
y 2− y 1 x 2−x 1 k y 2− y 1 = 2 x 2−x 1 A k 17006 . 80−11904 .76 = A 2 0 . 0441−0 . 0252 k 5102 .04 = A 2 0 . 0189 k =269949 .2063 A2 m=
Step 6: Find k
k =269949 .2063 A2 k =269949 . 2063 2. 52 2 k =269949. 2063 ( 2. 5 ) k =1687182. 539
t/V – paksi y 9554.14 11904.76 13.931.88 15306.12 17006.80 18292.68 = y axis)
Step 7: Find t in sec
t=30 h
60 min 60 sec × 1h 1 min t=108000 sec t=30 h×
Step 8: Find area - A Data calculated
t=108000 sec V =150 m 3 B=13500 k=1687182. 539
Apply all data above in this formula
108000 1687182 .539 ( 150 ) 13500 = 2 + 150 A A 253077380 . 9 13500 720= 2 + A A 13500 A2 720 A 2 =253077380. 9+ A 2 720 A =253077380. 9+13500 A 253077380 .9 13500 A A 2= + 720 720 2 A =351496 .36+18. 75 A 2
Apply in this formula ax +bx + c = 0
ax 2 +bx + c = 0 2 A −18.75 A - 351496.36 = 0 so we know that : a=1 b=−18.75 c=−351496.36
t k B = 2V+ V A A
Step 9: Apply this formula
A=
-b ± √b 2−4 ac 2a
−( -18. 75 ) ±√ ( -18 .75 ) −4 ( 1 ) (−351496 . 36 ) A= 2( 1) (18. 75 )± √( 351 .56 )−(−1405985. 44 ) A= 2 18 . 75± √( 351 .56+1405985.44 ) A= 2 18 . 75± √( 1406337 ) A= 2 18 . 75± 1185. 89 A= 2 2
take +ve answer 1204 .64 A= 2 2 A =602. 32m ignore −ve answer −1167. 14 A= 2 A =−583 .57 m2
QUESTION 2 The following data ware obtained from a laboratory model of plate and frame filter press with an area of 0.1 m2 (A) working at a constant pressure of 700 kPa. Table 2: Data of filtrate volume collected through time Time, t (min) Filtrate volume, V (L) 2.5 17.7 5.0 26.2 7.5 37.3 10.0 45.2 12.5 54.1 15.0 63.2 Based on the information given, calculate the area required for the filtration system if the filter press is to be designed to filter 7 m3 (V) slurry in 1.5 hours (t). t V B =k 2 + V A A
(10 marks) ANSWER Step 1: State formulas y = mx + c t/V = k/A2 V + B/A Where: y = t/V m = k/A2 x=V c = B/A Step 2: Design table t, (sec) 150 300 450 600 750 900
V, (m3) 0.0177 0.0262 0.0373 0.0452 0.0541 0.0632
t/V 8474.57 11450.38 12064.34 13274.33 13863.21 14240.50
Step 3: Plot the graph and find B/A (V = x axis, t/v = y axis) Properly labeled and complete graph t/V = kV/A2 + B/A
Step 4: Find B B = 700 Step 5: Find k/A2 by using this formula m = y2-y1 /x2-x1 k/ A2 = 86482.4372 Step 6: Find k k = 864.8243 Step 7: Find t in sec t = 5400sec Step 8: Find A Data calculated t = 5400 V=7 B= 700 K= 864.8243 Apply all data above in this formula t/V = k/A2 V + B/A A2 = 7.8474 + 0.9074A Apply in this formula ax2 + bx + c = 0 ax2 + bx + c = 0 A2 - 0.9074A – 7.8474 = 0 So we know that a=1 b = -0.9074 c = -7.8474 Step 9: Apply this formula A = (- (b) ± A = 6.583/2 A = 3.2915 m2 Take the +ve answer
A = -4.7682/ 2 A = -2.3841 m2 Ignore the +ve answer
√ b2-4ac) / 2a
QUESTION 3 The following data ware obtained from a laboratory model of plate and frame filter press with an area of 0.1 m2 (A) working at a constant pressure of 50 kPa. Table 2: Data of filtrate volume collected through time Time, t (min) Filtrate volume, V (L) 2.5 7.8 5.0 9.7 7.5 14.5 10.0 17.4 12.5 23.6 15.0 29.4 Based on the information given, calculate the area required for the filtration system if the filter press is to be designed to filter 1 m3 (V) slurry in 1 hours (t). t V B =k 2 + V A A
(10 marks) ANSWER Step 1: State formulas y = mx + c t/V = k/A2 V + B/A Where: y = t/V m = k/A2 x=V c = B/A Step 2: Design table t, (sec) 150 300 450 600 750 900
V, (m3) 0.0078 0.0097 0.0145 0.0174 0.0236 0.0294
t/V 19230.76 30927.83 31034.48 34482.75 31779.66 30612.24
Step 3: Plot the graph and find B/A (V = x axis, t/v = y axis) Properly labeled and complete graph t/V = kV/A2 + B/A
Step 4: Find B B = 2000 Step 5: Find k/A2 by using this formula m = y2-y1 /x2-x1 k/ A2 = 61287.76 Step 6: Find k k = 612.8776 Step 7: Find t in sec t = 3600sec Step 8: Find A Data calculated t = 3600 V=1 B= 2000 K= 612.8776 Apply all data above in this formula t/V = k/A2 V + B/A A2 = +0.0869 + 0.5555A Apply in this formula ax2 + bx + c = 0 ax2 + bx + c = 0 A2 -0.5555A – 0.0869 = 0 So we know that a=1 b = -0.5555 c = -0.0869 Step 9: Apply this formula A = (- (b) ± √ b2-4ac) / 2a A = (-(-0.5555) ± √ (-0.5555)2-4(1)( -0.0869)) / 2(1) A = 1.3655/2 A = 0.6827 m2 Take the +ve answer
A = -0.2545/ 2 A = -0.12725 m2 Ignore the +ve answer
QUESTION 4 The following data ware obtained from a laboratory model of plate and frame filter press with an area of 0.1 m2 (A) working at a constant pressure of 150 kPa. Table 2: Data of filtrate volume collected through time Time, t (min) Filtrate volume, V (L) 2.5 17.8 5.0 19.7 7.5 24.5 10.0 27.4 12.5 33.6 15.0 39.4 Based on the information given, calculate the area required for the filtration system if the filter press is to be designed to filter 12 m3 (V) slurry in 15 hours (t). t V B =k 2 + V A A
(10 marks) ANSWER Step 1: State formulas y = mx + c t/V = k/A2 V + B/A Where: y = t/V m = k/A2 x=V c = B/A Step 2: Design table t, (sec) 150 300 450 600 750 900
V, (m3) 0.0178 0.0197 0.0245 0.0274 0.0336 0.0394
t/V 8426.96 15228.42 18367.34 21897.81 22321.42 22842.63
Step 3: Plot the graph and find B/A (V = x axis, t/v = y axis) Properly labeled and complete graph t/V = kV/A2 + B/A
Step 4: Find B B = 100 Step 5: Find k/A2 by using this formula m = y2-y1 /x2-x1 k/ A2 = 510287.7698 Step 6: Find k k = 5102.8776 Step 7: Find t in sec t = 54000sec Step 8: Find A Data calculated t = 54000 V =12 B= 100 K= 510287.7698 Apply all data above in this formula t/V = k/A2 V + B/A A2 = +1360.7673 + 0.0222A Apply in this formula ax2 + bx + c = 0 ax2 + bx + c = 0 A2 - 0.0222A – 1360.7673 = 0 So we know that a=1 b = -0.0222 c = -1360.7673 Step 9: Apply this formula A = (- (b) ± √ b2-4ac) / 2a A = (-(-0.0222) ± √ (-0.0222)2-4(1)(-1360.7673)) / 2(1) A = 73.7993/2 A = 36.8996 m2 Take the +ve answer
A = -73.7549/ 2 A = -36.8774 m2 Ignore the +ve answer
QUESTION 5 The following data ware obtained from a laboratory model of plate and frame filter press with an area of 0.1 m2 (A) working at a constant pressure of 1550 kPa. Table 2: Data of filtrate volume collected through time Time, t (min) Filtrate volume, V (L) 2.5 116.8 5.0 129.7 7.5 146.5 10.0 173.4 12.5 236.6 15.0 298.4 Based on the information given, calculate the area required for the filtration system if the filter press is to be designed to filter 100 m3 (V) slurry in 120 hours (t). t V B =k 2 + V A A
(10 marks) ANSWER Step 1: State formulas y = mx + c t/V = k/A2 V + B/A Where: y = t/V m = k/A2 x=V c = B/A Step 2: Design table t, (sec) 150 300 450 600 750 900
V, (m3) 0.1168 0.1297 0.1465 0.1734 0.2366 0.2984
t/V 1284.24 2313.03 3071.67 3460.20 3169.90 3016.08
Step 3: Plot the graph and find B/A (V = x axis, t/v = y axis) Properly labeled and complete graph t/V = kV/A2 + B/A
Step 4: Find B B = 130 Step 5: Find k/A2 by using this formula m = y2-y1 /x2-x1 k/ A2 = 8015.6220 Step 6: Find k k = 80.1562 Step 7: Find t in sec t = 432000sec Step 8: Find A Data calculated t = 432000 V =100 B= 130 K= 80.1562 Apply all data above in this formula t/V = k/A2 V + B/A A2 = +1.8554 + 0.03A Apply in this formula ax2 + bx + c = 0 ax2 + bx + c = 0 A2 – 0.03A – 1.8554 = 0 So we know that a=1 b = -0.03 c = -1.8554 Step 9: Apply this formula A = (- (b) ± √ b2-4ac) / 2a A = (-(-0.03) ± √ (-0.03)2-4(1)(-1.8554)) / 2(1) A = 2.7544/2 A = 1.3772 m2 Take the +ve answer
A = -2.6944/ 2 A = -1.3472 m2 Ignore the +ve answer