Brownstock pulp and associated black liquor is stored in the blowtank after batc

Question

Brownstock pulp and associated black liquor is stored in the blowtank after batch kraft cooking. From the blow tank it is pumpe at 12% consistncy to a diffuser washer(Modified norden equal to 5) followed by a vaccum drum washer(modified norden equal to 3). The dilution factor for the washing operation is 2kg fresh water per kg of dry pulp. The pulp and wash liquor move countercurrently in three washers. after the drum washer the pulp becomes part of the countercurrently flowing wash water.

Calculate the washing efficiency E in % for the total washing operation using the formula below which is valid for 12% pulp consistency throughout the washing system: E=100(1-.(1364(DF))/(1+.1364(DF)N+1-1) N- total number of mixing stages DF- net amount of water added(kg/kg pulp)

Also calculate the overall washing efficiency for the entire system of washers and press.

E0=[TF+(1-TF)DR]100

TF=(Win - Wout )/ Win

W= (100- consistency)/consistency

DR=(Cv-Cs)/(Cv-Cw)

Cv= vat solid solution, Cw= wash solids concentration, Cs= solids concentration in sheet leaving water

Explanation / Answer

We need to calculate washing efficiency

E=100(1-0.1364(DF))/(1+0.1364(DF)N+1-1)

Where N is total number of dilution stages and DF is dilution factor.

DF = 2 kg water/kg dry pulp

N = Modified Norden factor = 5+3 = 8

Putting these values in equation

E = 100(1-0.1364(2))/(1+0.1364(2)8+1-1) = 22.85 %

Let us calculate overall washing efficiency for the entire system of washers and press.

E0=[TF+(1-TF)DR]100

TF=(Win - Wout )/ Win

W= (100- consistency)/consistency

DR=(Cv-Cs)/(Cv-Cw)

Cv= vat solid solution, Cw= wash solids concentration, Cs= solids concentration in sheet leaving water

First we need to calculate W (mass flow rate)

W = (100-12) / 12 = 7.333

Win = 7.333

Wout = 7.333 + 3 (as Pulp and water mix in it) = 10.333

TF = (7.333-10.333) / 7.333 = -0.409

Cs= 12 % + 33% = 3.96 % (we add 2 kg water to 1 kg pulp = 3 kg. therefore 1/3 in % = 33%)

Cv = 12 % (consistency) Cw will be zero.

DR = (12-3.96) / (12-0) = 0.67

E0=[TF+(1-TF)DR]100

     = [-0.409+(1+0.409)0.67]100

   E0 = 53.503 %

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