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COMPRESSIBLE CAKE CONSTANT PRESSURE PROFILE.XLS

INPUTS ********* ********* ********* ********* ********* *********

Total pressure drop: 100000 Pa *********

Slurry concentration: 0.15 by mass *********

Solid density: 2650 kg/m^3 *********

Liquid density: 1000 kg/m^3 *********Liquid viscosity: 0.001 Pa.s *********

Area of filter cell: 1 m^2 *********

Vessel height or clearance: 0.19 m *********

Pressure exponent in concentration: 0.08 *********

Pressure exponent in alpha equation: 0.5 *********

Constant in concentration equation: 0.15 *********

Constant in alpha equation: 450000000 *********

Medium resistance: 2E+12 1/m *********

Time increment to plot: 3600 s

CALCULATED VALUES: ********* ********* ********* *********Initial concentration of slurry: 0.062435 v/v *********

Average cake concentration: 0.3466403 v/v *********

Dry solids/filtrate volume: 201.79972 kg/m^3 *********

Average alpha: 7.115E+10 m/kg *********

Exponent in height expression: 0.1904762 *********

Filtrate volume increment: 0.02 m^3 *********

a: 71791.508

b: 20000

********* ********* ********* ********* ********* ********* *********

Filtration time (s): 0 3600 7200

FIRST ITERATION:

Filtrate vol (m^3): 0 0.1244264 0.2066741

Filtrate rate (m^3/s): 0.00005 2.641E-05 2.013E-05

Cake pressure (Pa): 0 47181.501 59738.216

Cake conc (v/v): 0 0.3264231 0.3326437

Dry solids/filtrate: 204.58332 203.68247

Average alpha: 4.887E+10 5.499E+10

New a: 49992.934 56005.71

SECOND ITERATION:Filtrate vol (m^3): 0.1346678 0.2219959

Filtrate rate (m^3/s): 2.988E-05 2.229E-05

dt/dV change (%): 13.15 10.72

Cake pressure (Pa): 40235.855 55422.886

Cake conc (v/v): 0.322291 0.3306543

Dry solids/filtrate: 205.20555 203.96602

0

20

40

60

80

100

120

140

160

180

200

0

   H  e   i  g   h   t   f  r  o  m   m

  e   d   i  u  m ,  m  m

 .

 

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Average alpha: 4.513E+10 5.297E+10

New a: 46307.171 54020.041

THIRD ITERATION:

Filtrate vol (m^3): 0.1367203 0.2242147

Filtrate rate (m^3/s): 3.062E-05 2.261E-05

dt/dV change (%): 2.46 1.45Cake pressure (Pa): 38767.251 54775.861

Cake conc (v/v): 0.3213337 0.3303438

Dry solids/filtrate: 205.35254 204.01065

Average alpha: 4.43E+10 5.266E+10

New a: 45486.77 53715.543

FOURTH ITERATION:

Filtrate vol (m^3): 0.1371927 0.2245617

Filtrate rate (m^3/s): 3.079E-05 2.266E-05

dt/dV change (%): 0.56 0.22

Cake pressure (Pa): 38425.37 54674.128Cake conc (v/v): 0.3211061 0.3302947

Dry solids/filtrate: 205.38765 204.01772

Average alpha: 4.411E+10 5.261E+10

New a: 45293.5 53667.498

FIFTH ITERATION:

Filtrate vol (m^3): 0.1373049 0.2246167

Filtrate rate (m^3/s): 3.083E-05 2.267E-05

dt/dV change (%): 0.13 0.04

Cake pressure (Pa): 38343.992 54658.014

Cake conc (v/v): 0.3210516 0.3302869Dry solids/filtrate: 205.39606 204.01884

Average alpha: 4.406E+10 5.26E+10

New a: 45247.365 53659.884

SIXTH ITERATION:

Filtrate vol (m^3): 0.1373317 0.2246254

Filtrate rate (m^3/s): 3.084E-05 2.267E-05

dt/dV change (%): 0.03 0.01

Cake pressure (Pa): 38324.52 54655.458

Cake conc (v/v): 0.3210386 0.3302857

Dry solids/filtrate: 205.39807 204.01902Average alpha: 4.405E+10 5.26E+10

New a: 45236.318 53658.676

Cake height (m): 0.0363228 0.0573472

Dimen'ss Cake Cake Cake Cake Cake Cake Cake

height concn. height concn. height concn. height concn.

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(-) (v.f.) (mm) (v.f.) (mm) (v.f.) (mm) (v.f.)

0 190 0 190 0 190 0

0.062435 190 0.062435 190 0.062435 190 0.062435

0 0.062435 0.062435 36.32 0.062435 57.35 0.062435

0.04 0.1890145 34.87 0.1944588 55.05 0.1966095

0.08 0.2156921 33.42 0.2219048 52.76 0.2243590.12 0.2330104 31.96 0.239722 50.47 0.2423732

0.16 0.2461349 30.51 0.2532245 48.17 0.2560251

0.2 0.256822 29.06 0.2642195 45.88 0.2671416

0.24 0.2658976 27.61 0.2735564 43.58 0.2765819

0.28 0.2738206 26.15 0.2817077 41.29 0.2848233

0.32 0.2808745 24.70 0.2889647 39.00 0.2921605

0.36 0.2872471 23.25 0.2955209 36.70 0.2987892

0.4 0.29307 21.79 0.3015115 34.41 0.3048461

0.44 0.298439 20.34 0.3070352 32.11 0.3104309

0.48 0.3034265 18.89 0.3121663 29.82 0.31561870.52 0.308088 17.43 0.3169621 27.53 0.3204676

0.56 0.3124678 15.98 0.321468 25.23 0.3250233

0.6 0.3166012 14.53 0.3257205 22.94 0.3293228

0.64 0.3205172 13.08 0.3297493 20.64 0.3333962

0.68 0.3242398 11.62 0.3335791 18.35 0.3372684

0.72 0.3277892 10.17 0.3372308 16.06 0.3409604

0.76 0.3311824 8.72 0.3407217 13.76 0.3444899

0.8 0.3344339 7.26 0.3440669 11.47 0.3478721

0.84 0.3375564 5.81 0.3472793 9.18 0.3511201

0.88 0.3405608 4.36 0.3503702 6.88 0.35424520.92 0.3434566 2.91 0.3533494 4.59 0.3572573

0.96 0.3462522 1.45 0.3562255 2.29 0.3601652

1 0.348955 0.00 0.3590062 0.00 0.3629767

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0

3600

7200

10800

Cakeconcn.

(v.f.)

0

0.062435

0.062435

0

0

0

00

0

0

0

0

0

0

0

0

010800 0

0

0.2728218 0

1.69E-05 0

66200.556 0

0.3353884 0

203.29805 0

5.789E+10 0

58845.947 0

00.2909422 0

1.844E-05 0

9.09 0.062435

63127.892 0.062435

0.3341156 0.1890145

203.47535 0.2156921

.1 0.2 0.3 0.4

Solid concentration, v/v.

0 3600 7200 10800

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5.653E+10 0.2330104

57514.184 0.2461349

0.256822

0.2930459 0.2658976

1.862E-05 0.2738206

0.99 0.280874562762.01 0.2872471

0.3339603 0.29307

203.4971 0.298439

5.637E+10 0.3034265

57353.399 0.308088

0.3124678

0.2933034 0.3166012

1.864E-05 0.3205172

0.12 0.3242398

62717.095 0.32778920.3339412 0.3311824

203.49978 0.3344339

5.635E+10 0.3375564

57333.629 0.3405608

0.3434566

0.2933351 0.3462522

1.864E-05 0.348955

0.01 0

62711.562 0.062435

0.3339388 0.062435203.50011 0.1944588

5.635E+10 0.2219048

57331.192 0.239722

0.2532245

0.293339 0.2642195

1.864E-05 0.2735564

0.00 0.2817077

62710.879 0.2889647

0.3339385 0.2955209

203.50015 0.30151155.634E+10 0.3070352

57330.892 0.3121663

0.3169621

0.073881 0.321468

Cake 0.3257205

height 0.3297493

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(mm) 0.3335791

190 0.3372308

190 0.3407217

73.88 0.3440669

70.93 0.3472793

67.97 0.350370265.02 0.3533494

62.06 0.3562255

59.10 0.3590062

56.15 0

53.19 0.062435

50.24 0.062435

47.28 0.1966095

44.33 0.224359

41.37 0.2423732

38.42 0.256025135.46 0.2671416

32.51 0.2765819

29.55 0.2848233

26.60 0.2921605

23.64 0.2987892

20.69 0.3048461

17.73 0.3104309

14.78 0.3156187

11.82 0.3204676

8.87 0.32502335.91 0.3293228

2.96 0.3333962

0.00 0.3372684

0.3409604

0.3444899

0.3478721

0.3511201

0.3542452

0.3572573

0.36016520.3629767

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s

s

s

s

Cake Cake Cake Cakeheight height height height

(mm) (mm) (mm) (mm)

190

190

0

0

0

0

00

0

0

0

0

0

0

0

0

00

0

0

0

0

0

0

0

0

00

190

190

36.322751

34.869841

33.416931

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18.3511

16.057213

13.763325

11.469438

9.17555

6.88166254.587775

2.2938875

-1.39E-14

190

190

73.881028

70.925787

67.970546

65.015305

62.06006459.104823

56.149581

53.19434

50.239099

47.283858

44.328617

41.373376

38.418135

35.462894

32.50765229.552411

26.59717

23.641929

20.686688

17.731447

14.776206

11.820965

8.8657234

5.9104823

2.9552411-1.39E-14