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Ind. Eng. Chem. Res. 1996, 35, 2438-2443
Effect of Pulping Variables on Enthalpy of Kraft Black Liquors: Empirical Predictive Models Abbas A. Zaman and Arthur L. Fricke* Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611
The effects of pulping variables on enthalpy of slash pine kraft black liquors from a 2k + 2k + 1 (k ) 4) central composite design pulping experiments that were performed in a large pilot scale digester have been studied. The four cooking variables were effective alkali, sulfidity, cooking temperature, and time at temperature. In all cases, the white liquor was adjusted to a causticizing efficiency of 85% and a reduction of 93% with Na2CO3 and Na2SO4. The enthalpy of these liquors was determined over wide ranges of temperature and solids concentrations using a Setaram C-80 calorimeter. In this work, our previous models for enthalpy-concentration relations were used to perform a systematic study on the effects of pulping conditions on enthalpy and to develop statistically based quantitative models for enthalpy as a function of pulping variables. These results are presented, and their utility is discussed. 1. Overview and Background In earlier papers (Stoy and Fricke, 1994; Zaman and Fricke, 1996), the results of the development of enthalpy-concentration relations for kraft black liquors over wide ranges of temperature and solids concentrations have been presented. The enthalpy relations were developed by constructing a base isotherm (at 80 °C) from the heat of dilution data and enthalpy of pure water. By treating black liquor as a binary solution of water and solids, the base isotherm at any solids mass fraction was determined using the following definition (Stoy and Fricke, 1994; Zaman and Fricke, 1996).
H(X,80) ) (1 - X)Hw - XQ∞
(1)
where
H(X,80) ) enthalpy of black liquor solution (at 80 °C) containing X mass fraction of solids (kJ/kg of solution) X ) mass fraction solids
T ) temperature (°C) The enthalpy of water (at 80 °C) was taken from the steam tables in which pure saturated water at 0 °C is used as the reference state. The base isotherms for several of the liquors and the enthalpy-concentration chart for one of the liquors used in this study are shown in Figures 1 and 2, respectively. As can be observed from these figures, the enthalpy is not only a function of temperature and solids concentrations, but it also varies from liquor to liquor due to the differences in the pulping conditions and/or composition of the liquors. The base isotherms for each liquor were correlated to the solids mass fractions using the following empirical equation:
(
Q∞ ) heat of dilution at 80 °C (kJ/kg of solids) Equation 1 was used to develop a relation for enthalpy as a function of solids mass fraction at constant temperature called the “base isotherm”, knowing the heat of dilution at that temperature. As it was shown earlier (Stoy, 1992; Stoy and Fricke, 1994; Zaman and Fricke, 1996), the base isotherm can be used to develop enthalpy-concentration relations at different temperatures, knowing the heat capacity-concentrationtemperature relations for the liquor solution. At any given temperature, enthalpy was determined as
∫80TCp(X,T) dT
Cp(X,T) ) heat capacity of the liquor solution containing X mass fraction of solids at T (kJ/kg °C)
(-Xb))
H(X,80) ) Hw + a -1 + exp
Hw ) enthalpy of pure water at 80 °C (kJ/kg)
H(X,T) ) H(X,80) +
H(X,T) ) enthalpy of black liquor solution containing X mass fraction of solids at T (kJ/kg of solution)
(2)
where * Author to whom correspondence should be addressed. Phone: (352) 392-0884. Fax: (352) 392-9513.
S0888-5885(95)00711-1 CCC: $12.00
(3)
where a and b are constants that vary from liquor to liquor. Differences in a and b for different liquors are the result only of differences in pulping conditions or of differences in the solids composition arising from differences in pulping conditions and type of the wood species. However, in this manner, the variations in liquor enthalpy (at a fixed temperature) due to variations in solids composition arising from differences in pulping conditions can be represented by differences in parameters a and b. The values of a and b along with the cooking conditions for the liquors used in this study are shown in Table 1. The liquors used in this work to determine the effects of pulping conditions on liquor enthalpy quantitatively are from a two-level, four-variable factorially designed experiment with center and star points for kraft pulping of slash pine. The four pulping variables investigated are effective alkali (EA), sulfidity (S), cooking temperature (T), and cooking time (t). The variable ranges for EA, S, T, and t were designed as 11.5-17.5 (% ODW), © 1996 American Chemical Society
Ind. Eng. Chem. Res., Vol. 35, No. 7, 1996 2439
Figure 1. Base isotherms for different slash pine black liquors.
supplies enough information to use surface response methods to study the joint effect of variables on enthalpy of the liquor solution. The objectives of the present paper were to (1) study the effect of pulping inputs on enthalpy by surface response methods and (2) determine appropriate correlations for enthalpy (base isotherm) of slash pine black liquors as a function of the cooking conditions. These correlations will be useful in constructing the base isotherm at operating conditions from the knowledge of pulping conditions which can be used to develop an enthalpy-concentration relation at any desired temperature using eq 2 as described earlier. Mathematical analysis of eq 3 indicates that H(X,80) decreases as the parameter a is increased and increases as the parameter b is increased. The base isotherm decays exponentially as the solids concentration is increased. The values of a and b determined for black liquors of different cooking conditions were used to study the effect of pulping variables on liquor enthalpy and develop different predictive models for a and b by employing different statistical criterion. In this manner, the effects of solids composition on the base isotherm arising from differences in pulping conditions have been partitioned in parameters a and b which have been correlated to the pulping conditions. 2. Response Surface and Models
Figure 2. Enthalpy-concentration diagram for black liquor ABAFX019,20. Table 1. Pulping Conditions and Parameters a and b as in Eq 3 for the Liquors Used in This Studya black liquor
t (min)
T (K)
ABAFX011,12 ABAFX013,14 ABAFX015,16 ABAFX017,18 ABAFX019,20 ABAFX021,22 ABAFX023,24 ABAFX025,26 ABAFX027,28 ABAFX029,30 ABAFX031,32 ABAFX033,34 ABAFX035,36 ABAFX037,38 ABAFX039,40 ABAFX041,42 ABAFX043,44 ABAFX045,46 ABAFX047,48 ABAFX049,50 ABAFX051,52 ABAFX053,54 ABAFX055,56 ABAFX057,58 ABAFX059,60
40 80 80 40 80 40 40 80 80 40 40 80 40 80 80 40 60 20 100 60 60 60 60 60 60
438.76 449.86 438.76 449.86 438.76 449.86 438.76 449.86 438.76 449.86 438.76 449.86 438.76 449.86 438.76 449.86 444.26 444.26 444.26 433.16 455.36 444.26 444.26 444.26 444.26
EA (%) S (%) 13.0 13.0 16.0 16.0 13.0 13.0 16.0 16.0 13.0 13.0 16.0 16.0 13.0 13.0 16.0 16.0 14.5 14.5 14.5 14.5 14.5 11.5 17.5 14.5 14.5
20.0 20.0 20.0 20.0 35.0 35.0 35.0 35.0 20.0 20.0 20.0 20.0 35.0 35.0 35.0 35.0 27.5 27.5 27.5 27.5 27.5 27.5 27.5 12.5 42.5
a
b
83.9 116.54 103.52 107.50 97.06 106.25 103.01 107.31 97.02 98.16 95.16 112.45 92.53 124.08 102.02 109.25 90.02 111.77 120.60
0.243 0.327 0.283 0.305 0.289 0.300 0.294 0.314 0.268 0.271 0.265 0.293 0.272 0.348 0.304 0.334 0.290 0.305 0.358
103.05 0.308 103.88 0.300 105.40 0.282 101.97 0.337
a t ) cooking time; T ) cooking temperature; EA ) effective alkali; S ) sulfidity.
12.5-42.5 (% active alkali), 433.2-455.4 K, and 20100 min, respectively. The range of the independent variables was set so as to include virtually all pulping conditions that could be used commercially within the experimental space. The resulting rotatable composite design with a total of 25 separate pulping conditions
In order to investigate the influence of the cooking conditions on the base isotherm, response surface methodology (Box, 1978) was employed to analyze the response of a and b to the pulping variables and then different statistical approaches were used to develop proper models for a and b as a function of the pulping variables. Since in the design of the pulping experiments, 25 different conditions have been considered, this provides enough information for development of a linear regression model that consists of the main variables; second-, third-, and fourth-order interactions; and quadratic terms for response surface analysis. This model can be described as 4
Y ) a0 +
∑ i)1
4
RiXi +
∑ i
