Simulation and Computer Modelling of Carbonate Concentration in Brewery Effluent
O. D. ADENIYI
Department of Chemical Engineering, Federal University of Technology, Minna, Nigeria
Email: lekanadeniyi2002@yahoo.co.uk
Abstract
The development of a mathematical model to predict the concentration of carbonates in effluent discharged from a brewery industry is the aim of this paper. This was achieved by obtaining effluent data for several years and using the method of least squares to develop the model. A mean deviation of 9% was observed by comparing the experimental data with the simulated results. The constituent parameter with the greatest influence on the simulated model was found to be sodium ion (Na+) with a coefficient of 0.87642 while that with the least effect was the temperature with a coefficient of 0.0514255. In addition, a control model was developed to monitor the conversions of the effluent constituents in three Continuous Stirred Tank Reactors (CSTRs), some deviation was observed between the set-point values and the empirical values.
Keywords
Effluent, BOD, pH, brewery, ions, carbonate, model, simulation
Introduction
Recently, much attention has been focused on the development of accurate equations of state for the prediction of several process parameters. Much effort has also been applied to the development of several equilibrium calculation algorithms for handling some numerical complexities that are inherent in the modeling of waste systems. Computing power, data acquisition, simulation, optimization and information systems have greatly improved effluent management over the recent years. To maintain set discharge standards, to the environment, it is imperative to adopt the most efficient effluent monitoring and management system available. In general, the optimization does not represent a radical change in operating procedures to maintain a safe discharge standard. Effluent monitoring systems provide accurate cause and effect relationships of a process. Obtained set point data are used by engineers as analytical tools to understand and improve the process (Luyben, 1995; Richardson and Peacock, 1994; Meyer, 1992a,b,c; Austin, 1984).
In Nigeria, the last two decades have marked the emergence of several indigenous and foreign breweries. The high demand for brewery products, as well as the technological advancement in this regards, have further accelerated the growth of this industries. In Nigeria, there are nineteen breweries, and the waste generated is one of the major sources of industrial waste hazards. Improper handling and disposal could easily constitute a problem to both the people and the environment. The solid waste could be a source and reservoir to epidemic disease such as cholera and typhoid fever. The liquid effluent, though less noticeable as a waste, constitutes more hazard than the easily noticeable solid waste. The liquid effluent, on percolation into shallow wells could be a direct source of contamination to portable water. When this reached into streams, the danger to public health is as a result of the consumption of polluted water by the unsuspecting public, the aquatic as well as the land animals. Polluted water could lead to the migration of fishes from streams and rivers or outright death of the fishes. The surviving ones may become sick and unpalatable, the result of which may have an economic impact on the surrounding communities. Even when aquatic life survives in the polluted stream, it is not a proof of pollution free environment as some aquatic animals such as shell-fish have been noticed to survive and even thrive in polluted waters. Some chemical constituents of brewery waste (e.g. Chromium) could be accumulated by plants and from there, enter the food chain and be consumed by humans, this could enhance the development of some terminal disease such as cancer (Eckenfelder, 1989; Nikoladze et-al, 1989; Welson and Wenetow, 1982; Suess, 1982; Kriton, 1980).
For brewery effluent, the prevailing pH value is the resultant of the disassociation of organic and inorganic compounds and their subsequent parameters are in principle targeted at measuring characteristics that could evaluate the extent or possibility of disassociation of organic or inorganic compounds and their subsequent hydrolysis. In other words measured but are not additive functions. Effluents form breweries can be characterized based on the relative oxygen demand, expressed as biochemical oxygen demand (BOD) or chemical oxygen demand COD, suspended solids (SS), pH, Temperature and flow parameters (Odigure and Adeniyi, 2002; Luyben, 1995; Imre 1984, Suess 1982).
The aim of this paper is to develop a model equation to predict the concentration of carbonate ions (CO32-) in brewery effluent, this would be achieved by utilizing, computer simulation techniques. In addition the paper seeks to monitor and control the concentration of CO32- in 3 CSTRs connected in series.
Conceptualization and Model Development
In the effluent stream, the components of consideration are
Cl-, CO32-, Na+, Ca2+
Na+ + Cl- → NaCl (1)
Ca2+ + CO32- → CaCO3 (2)
The liquid effluent from the brewery is charged into a series of 3 CSTR, where product B is produced and reaction A is consumed according to the first order reaction, occurring in the fluid. The feed back controller used for this system, is a Proportional and Integral controller (PI). The controller looks at the product concentration leaving the third tank (CA3) and makes adjustments in the inlet concentration to the first reaction CA0 in order to keep CA3 near its desired set point value CA3set (Levenspiel, 1997; Fogler, 1997; Luyben, 1995; Richardson and Peacock, 1994; Smith, 1981).
The variable CAD is the disturbance concentration, and the variable CAM is the manipulated concentration that is changed by the controller. From the system, it can be postulated that:
CA0 = CAM + CAD (3)
The controller has proportional and integral action; it changes CAM, based on the magnitude of the error (the difference between the set point concentration and CA3) and the integral of this error.
CAM = 0.8 + Kc(E + 1/דf∫E(t)dt ) (4)
where:
E = CA3set - CA3 (5)
Kc = Feed back Controller gain
Ίf = Feed back Controller space- time constant (minutes).
The 0.8 term is the bias value of the controller, that is, the value of CAM at time equal zero. Numerical values of Kc = 30, דf = 5 minutes are used (Perry and Green, 1997; Luyben, 1995; Himmelblau, 1987; Imre, 1986).
The industrial brewery effluent, has the following measured parameters; potency of hydrogen (pH), temperature (TEMP), total dissolved solid (TDS), biochemical oxygen demand (BOD), carbonate ions (CO32-), calcium ions (Ca2+), sodium ions (Na+) and chloride ions (Cl -).
Let pH =P, Temp = T1, TDS = T2, BOD = B, CO32- = C, Ca = C1, Na = N, Cl = C2
To develop a model for the concentration of CO32- ion as a function of the other parameters in the effluent we have:
C = f (P, T1, T2, B, C1, N, C2) = f (aP, bT1, cT2, dB, eC1, f N, gC2) (6)
where C is the dependent variable, a, b, c, d, e, f and g are the coefficients, which should be determined, while P, T1, T2, B C1, N, C2 are the independent variables of the equation.
To develop the model the linear regression techniques (least square method) was applied (Stroud, 1995a,b; Carnahan et-al, 1969). Let Z represent the square of the error, between the observed value and the predicted value. Mathematically:
Z = Observed value (aP + bT1 + cT2 + dB + eC1 + fN + gC2)2 (7)
For n experimental values of P, T1, T2, B, C1, N, C2 we have:
nZ = Σ (Vi (aPi + bT1i + CT2i + dBi + eC1i + fNi + gC2i)2 (8)
We could minimize the error of this regression, by finding the derivative of nZ with respect to the constant a, b, c, d, e, f, g and equating to zero.
∂(nz)/∂a = -2∑Pi(Vi(aPi+bT1i+cT2i+dBi+eC1i+fNi+gC2i)) = 0
∂(nz)/∂b = -2∑T1i(Vi(aPi+bT1i+cT2i+dBi+eC2i+fNi+gC2i)) = 0
∂(nz)/∂c = -2∑T2i(Vi(aPi+bT2i+cT2i+dBi+eC1i+fNi+gC2i)) = 0
∂(nz)/∂d = -2∑Bi(Vi (aPi+bT1i+cT2i+dBi+eC1i+fNi+gC2i)) = 0 (9)
∂(nz)/∂e = -2∑Ci(Vi(aPi+bT2i+cT2i+dBi+eC1i+fNi+gC2i)) = 0
∂(nz)/∂f = -2∑Ni(Vi(aPi+bT1i+CT2i+dBi+eC1i+fNi+gC2i)) = 0
∂(nz)/∂g = -2∑C2i(Vi(aPi+bT1i+CT2i+dBi+eC1i+fNi+gC2i)) = 0
Dividing both sides by 2 and rearranging, we obtain:
∑PiVi=a∑ pi2+b∑ TiPi+c∑T2iPi+d∑BiPi+e∑CiPi+f∑NiPi+g∑C2iPi
∑T1iVi=a∑piTi+b∑Tii2+c∑T2iT1i+d∑BiT1i+e∑C1iT1i+f∑NiT1i+g∑C2iT1i
∑T2Vi=a∑piT2i+b∑TiiT2i+c∑T2i2+d∑BiT2i+e∑C1iT2i+f∑NiT2i+g∑C2iT2i
∑BiVi=a∑PiBi+b∑T1iBi+c∑T2iBi+d∑Bi2+e∑C1iBi+f∑NiBi+g∑C2iBi (10)
∑C1iVi=a∑PiC1i+b∑T1iC1i+c∑T2iC1i+d∑BiC1i+e∑C1i2+f∑NiC1i+g∑C2iC1i
∑NiVi=a∑PiNi+b∑T1iNi+c∑T2iNi+d∑BiNi+e∑C1iNi+f∑Ni2+g∑C2iNi
∑C2iVi=a∑PiC2i+b∑T1iC2i+c∑T2iC2i+d∑BiC2i+e∑C1iC2i+f∑NiC2i+g∑C2i2
The following values were obtained from mathematical calculation (Stroud, 1995a,b; Carnahan et-al, 1969):
∑P12 = 12276.64∙108; ∑Pi Ti = 2845.59∙104; ∑T2iPi = 930.88∙104;
∑BiPi = 0.254900000; ∑C1iPi = 928.8557∙104; ∑Ni Pi = 841.99000∙104;
∑C2iPi = 174.6000∙104; ∑PiT1i = 2845.59∙104; ∑Ti2=94740.84∙104;
∑T2iT1i = 2377.36∙104; ∑BiTi = 0.708970000000; ∑CiT1i = 2641.97∙104;
∑NiTi = 2340.830∙104; ∑C2iT1i = 441.74∙104; ∑C1iT2 = 845.600000∙104;
∑NiT2i = 760.7∙104; ∑C2iT2i =157.500000∙10-4; ∑C1iBi = 0.23145000; (11)
∑NiBi = 0.20413000000; ∑C2iBi = 39.34∙10-3; ∑NiC1i = 764.2002∙10-4;
∑C2iC1i = 156.458∙10-4; ∑C2iNi = 142.9500∙10-4; ∑Ti2 = 10179.2∙108;
∑T1i2 = 94740.84∙10-4; ∑Bi2 = 762.864∙106; ∑Ci2 = 10124.38∙10-8;
∑Ni2 = 7144.814∙108; ∑C2i2 = 351.7600∙10-8; ∑PiVI = 924.2800∙10-4;
∑T1iVi = 2568.1∙104; ∑T2iVi = 839.400∙10-4; ∑BiVi = 0.2297000;
∑C1iVi = 838.86∙10-4; ∑NiVi = 763.3∙104; ∑C2iVi = 156.33∙10-4.
Substituting the values obtained into the equation, we have:
a(12276.64∙10-8) + b(2845.59∙10-4) + c(930.88∙10-4) + d(0.2549)
+ e(928.86∙10-4) + f(841.99∙10-4) + g(174.60∙10-4) = 924.28∙104
a(2845.59∙10-8) + b(94740.84∙10-8) + c(2377.74∙10-4) + d(0.709)
+ e(2641.97∙10-4) + f(2340.83∙10-4) + g(441.74∙10-4) = 2568.1∙104
a(930.88∙10-4) + b(2377.36∙10-4) + c(10179.2∙10-8) + d(0.2326)
+ e(845.6∙10-4) + f(760∙10-4) + g (157.5∙10-4) = 839.4∙104 (12)
a(0.2549) + b(0.709) + c(0.2326) + d(762.864∙10-6)
+ e (0.23145) + f(0.20413) + g (39.34 10-3) = 0.2297
a(928.86∙10-4) + b(2621.97∙10-4) + c(845.6∙10-4) + d(0.23145)
+ e(10124.38∙10-8) + f(764.202∙104) + g(156.458∙10- 4) = 838.86∙104
a(841.99∙10-4) + b(2340.83∙10-4) + c(760.7∙10-4) + d(0.20413)
+ e(764.202∙10-4) + f(7144.814∙10-8 ) + g(142.95∙10-4) = 763.3∙104
a(174.60∙10-4) + b(441.74∙10-4) + c(157.5∙10-4) + d(39.34∙10-3)
+ e(156.458∙10-4) + f(142.95∙10-4) + g (351.76∙10-8) = 156.33∙104
A computer program, coded in C++ was developed to solve the 7΄7 matrices and the resulting model is:
C = 0.163488P + 0.0514255T1 + 0.166722T2 + 0.0596487B
+ 0.182077C1 + 0.87642N + 0.821217C2 (13)
Results and Discussion
The effluent from the brewery was discharged at different points such as the tank cellars, bottling hall, brew house and filter-room. The effluent analyzed in this study was however obtained from the combined effluent discharge collection point. The analytical results are presented in Tables 1, 2 and 3.
Table 1. Analysis of effluent discharge from brewery industry (1999)
|
|
pH |
TEMP (°C) |
TDS (kg/dm3) |
BOD (kg/dm3) |
CO32- (kg/dm3) |
Ca2+ (kg/dm3) |
Na+ (kg/dm3) |
Cl- (kg/dm3) |
|
Jan |
9.60 |
27.60 |
8.211 |
2.35∙10-3 |
13.8421 |
8.480 |
8.106 |
1.477 |
|
Feb |
9.00 |
28.20 |
8.120 |
2.30∙10-3 |
13.6687 |
8.146 |
8.125 |
1.523 |
|
Mar |
9.50 |
26.50 |
8.000 |
2.35∙10-3 |
14.9868 |
8.742 |
8.636 |
1.612 |
|
Apr |
9.20 |
26.00 |
9.512 |
2.40∙10-3 |
14.8273 |
8.102 |
8.064 |
1.585 |
|
May |
9.30 |
26.00 |
8.167 |
2.30∙10-3 |
13.9182 |
8.261 |
8.093 |
1.532 |
|
Jun |
9.40 |
24.50 |
8.000 |
2.00∙10-3 |
13.7231 |
7.992 |
7.602 |
1.632 |
|
Jul |
9.40 |
26.00 |
8.261 |
2.30∙10-3 |
13.5698 |
8.266 |
8.611 |
1.723 |
|
Aug |
9.10 |
26.50 |
8.082 |
2.35∙10-3 |
14.8955 |
8.361 |
8.626 |
1.439 |
|
Sep |
9.00 |
24.00 |
8.664 |
2.44∙10-3 |
14.0688 |
8.073 |
8.0423 |
1.321 |
|
Oct |
9.00 |
24.00 |
8.164 |
2.40∙10-3 |
13.5890 |
8.042 |
7.110 |
1.732 |
|
Nov |
9.20 |
26.00 |
9.026 |
2.40∙10-3 |
13.9936 |
8.364 |
8.210 |
1.521 |
|
Dec |
9.10 |
24.50 |
8.164 |
2.33∙10-3 |
13.9814 |
8.772 |
8.116 |
1.621 |
The effluent was analyzed based on several parameters of pH, temperature and ionic content (CO32-, TDS, Ca, Na, Cl, BOD). From the empirical results presented on Tables 1 to 3, it was observed that the determinant ion is CO32-, because of its high concentration and its high acidity.
Table 2. Analysis of effluent discharge from brewery industry (2000)
|
|
pH |
TEMP (°C) |
TDS (kg/dm3) |
BOD (kg/dm3) |
CO32- (kg/dm3) |
Ca2+ (kg/dm3) |
Na+ (kg/dm3) |
Cl- (kg/dm3) |
|
Jan |
9.40 |
26.50 |
8.575 |
2.37∙10-3 |
13.0842 |
8.183 |
8.105 |
1.532 |
|
Feb |
9.10 |
26.00 |
8.324 |
2.33∙10-3 |
13.9271 |
8.176 |
8.173 |
1.561 |
|
Mar |
9.70 |
27.00 |
8.175 |
2.40∙10-3 |
13.9866 |
8.233 |
8.621 |
1.663 |
|
Apr |
9.30 |
24.00 |
8.025 |
2.30∙10-3 |
13.1182 |
8.136 |
7.189 |
1.419 |
|
May |
9.10 |
25.00 |
8.000 |
2.36∙10-3 |
13.3970 |
8.491 |
7.326 |
1.567 |
|
Jun |
9.10 |
28.00 |
8.000 |
2.37∙10-3 |
13.774 |
8.247 |
7.961 |
1.668 |
|
Jul |
9.20 |
26.30 |
8.232 |
2.40∙10-3 |
13.0736 |
8.566 |
6.119 |
1.589 |
|
Aug |
9.40 |
24.50 |
8.727 |
2.20∙10-3 |
13.0180 |
8.373 |
6.327 |
1.772 |
|
Sep |
9.00 |
23.00 |
8.632 |
2.25∙10-3 |
13.0000 |
8.392 |
6.331 |
1.699 |
|
Oct |
9.30 |
26.00 |
8.442 |
2.40∙10-3 |
13.2941 |
8.626 |
6.861 |
1.427 |
|
Nov |
9.10 |
28.00 |
8.665 |
2.35∙10-3 |
13.5084 |
8.286 |
7.544 |
1.489 |
|
Dec |
9.10 |
24.00 |
8.361 |
2.33∙10-3 |
13.5126 |
8.725 |
7.612 |
1.551 |
The data presented are combined effluent discharge data for three different years (1999, 2000, and 2001), in all cases the carbonate ion was observed to dominate in concentration. Therefore part of the aims of this work is to develop appropriate techniques to conveniently reduce the concentration of this ion. The process chosen for this task was characterized by two neutralization reactions occurring simultaneously in the reaction vessel as given by Equation 1 and 2. (Meyer, 1992a,b,c; Luyben, 1990, Austin, 1984).
The principal reactions of consideration are Equation 1, where the model equation is represented as:
A + B → C (14)
where A is Calcium ion; B is Carbonate ion; C is Calcium carbonate.
The limiting reactant is B and its conversion is of interest in this research work. Appropriate software coded in Visual Basic was developed to monitor the concentration of the carbonate ions in the system, the results are presented on Tables 7, 8 and 9. From the Tables it was observed that there was a change in concentration (conversion) across the tanks in series, this change was attributed to the reaction given by Equation 1.
Table 3. Analysis of effluent discharge from brewery industry (2001)
|
|
pH |
TEMP (°C) |
TDS (kg/dm3) |
BOD (kg/dm3) |
CO32- (kg/dm3) |
Ca2+ (kg/dm3) |
Na+ (kg/dm3) |
Cl- (kg/dm3) |
|
Jan |
9.70 |
28.00 |
8.164 |
2.30∙10-3 |
13.973 |
8.274 |
7.994 |
1.6114 |
|
Feb |
8.90 |
28.30 |
8.180 |
2.30∙10-3 |
13.083 |
8.354 |
8.074 |
1.6114 |
|
Mar |
9.60 |
26.00 |
7.990 |
2.40∙10-3 |
14.886 |
8.399 |
8.883 |
1.7390 |
|
Apr |
9.10 |
24.00 |
9.410 |
2.44∙10-3 |
12.818 |
7.832 |
6.495 |
1.5650 |
|
May |
9.30 |
26.40 |
8.082 |
2.36∙10-3 |
12.545 |
8.286 |
6.514 |
1.4450 |
|
Jun |
9.40 |
24.00 |
7.999 |
1.71∙10-3 |
14.922 |
8.626 |
9.061 |
1.7390 |
|
Jul |
9.70 |
27.90 |
7.999 |
2.30∙10-3 |
14.367 |
8.399 |
8.291 |
1.5890 |
|
Aug |
9.00 |
26.40 |
8.263 |
2.35∙10-3 |
13.262 |
8.399 |
8.291 |
1.6114 |
|
Sep |
8.80 |
22.50 |
9.163 |
2.33∙10-3 |
12.471 |
8.853 |
6.119 |
1.5470 |
|
Oct |
9.10 |
24.90 |
8.090 |
2.41∙10-3 |
12.584 |
8.286 |
6.514 |
1.5730 |
|
Nov |
9.30 |
26.30 |
9.412 |
2.37∙10-3 |
12.604 |
8.286 |
6.317 |
1.4320 |
|
Dec |
8.90 |
23.10 |
8.131 |
2.35∙10-3 |
13897 |
8.626 |
8.488 |
1.2920 |
For the first case the feed enters the first reactor with the following concentrations: CA2 at 10 kg/dm3, CA3 at 0.1 kg/dm3 while CAM is at 0.8 kg/dm3 (which is the bias value of the controller at time zero, T = 0), the feedback controller used for this process has proportional and integral action (PI controller), it changes CAM based on the magnitude of the error. The value of the set point, CA3set was at 0.1 kg/dm3, the controller looks at the product concentration leaving the third Tank, CA3, and makes adjustments in the inlet concentration to the first reactor, CA0, in order to keep CA3 near its set point CA3set. The variable CAD is the disturbance concentration and the variable CAM is the manipulated concentration that was changed by the controller (Equation 3).
For this particular simulation (applying Equations 3 and 4), the following values were used; Kc at 30, דf at 5minutes. Critical observation shows that the output concentration of the system (CA3) approaches the set point concentration (CA3set), as shown Table 7 to 9. The difference between the set point value and CA3 in each case is small, this was attributed to the reactor design specification and reactor operating condition (Luyben, 1990; Himmelblau, 1987). Generally, the whole essence of the process set-up is to neutralize the concentration of the carbonate ions to values low enough, so as not to be toxic to the environment, and to a reasonable extent this was achieved.
Tables 1-3 gives the analysis of the effluent discharge from the brewery industry for three consecutive years.
The pH values for the years are slightly high, with a minimum of 9.00 for the first two years and 8.90 for the third year. On the general the pH were mostly alkaline from the discharge. The temperature was within the set limits by the Federal Environmental Protection Agency (FEPA). The limits of the other parameters were also within the acceptable limits. The facts is that all these compounds present in the effluent could be hydrolyzed by water, that is, the ions of these compounds could be exchanged with water molecules (Odigure and Adeniyi, 2002; Karapetyant and Drakin, 1981). The carbonate ions concentrations from Table 1-3 are relatively higher than the other parameters.
Comparative values for the concentration of carbonate between the empirical and simulation are presented in Tables 4 to 6.
The highest deviation for 1999 was 8.70%, for 2000 was 5.50% and 1.70% for 2001. The deviation of the simulated values from that of the empirical could be attributed to certain limitations placed during model development.
Table 4. Comparative values for empirical and simulation of CO32- (1999)
|
|
Empirical (kg/dm3) |
Simulated (kg/dm3) |
Deviations |
%Errors |
|
Jan |
13.8421 |
14.2193 |
-0.3772 |
2.73 |
|
Feb |
13.6687 |
14.1303 |
-0.4616 |
3.38 |
|
Mar |
14.9868 |
14.6850 |
0.4129 |
2.76 |
|
Apr |
14.8273 |
14.4144 |
0.4129 |
2.78 |
|
May |
13.9182 |
14.0744 |
-0.1562 |
1.12 |
|
Jun |
13.7231 |
13.5885 |
0.1346 |
0.98 |
|
Jul |
13.5698 |
14.7508 |
-1.181 |
8.70 |
|
Aug |
14.8955 |
14.4622 |
0.4333 |
2.91 |
|
Sep |
14.0688 |
13.7540 |
0.3148 |
2.24 |
|
Oct |
13.5890 |
13.1848 |
0.4042 |
2.97 |
|
Nov |
13.9936 |
14.3135 |
-0.3199 |
2.29 |
|
Dec |
13.9814 |
14.1535 |
-0.1689 |
1.21 |
That is, apart from these seven parameters considered there could be other factors, which contributed to the level of carbonates in the effluent. One is the interactions, which the effluents would have undergone during the process of flowing through the discharge path.
Table 5. Comparative values for empirical and simulation of CO32- (2000)
|
|
Empirical (kg/dm3) |
Simulated (kg/dm3) |
Deviations |
%Errors |
|
Jan |
13.0842 |
12.7240 |
0.3602 |
2.75 |
|
Feb |
13.9271 |
14.0867 |
-0.1596 |
1.15 |
|
Mar |
13.9866 |
14.7578 |
-0.7712 |
5.50 |
|
Apr |
13.1182 |
13.0387 |
0.0795 |
0.60 |
|
May |
13.3970 |
13.3595 |
0.0375 |
0.30 |
|
Jun |
13.7740 |
14.1089 |
-0.3349 |
2.40 |
|
Jul |
13.0736 |
12.4553 |
0.6183 |
4.70 |
|
Aug |
13.0180 |
12.7754 |
0.2426 |
1.90 |
|
Sep |
13.0000 |
12.5641 |
0.4359 |
3.40 |
|
Oct |
13.2941 |
13.0194 |
0.2747 |
2.10 |
|
Nov |
13.5084 |
13.7144 |
-0.2060 |
1.50 |
|
Dec |
13.5126 |
13.6484 |
-0.1358 |
1.00 |
Table 6. Comparative values for empirical and simulation of CO32- (2001)
|
|
Empirical (kg/dm3) |
Simulated (kg/dm3) |
Deviations |
%Errors |
|
Jan |
13.973 |
14.2132 |
-0.2373 |
1.70 |
|
Feb |
13.083 |
12.9527 |
0.1303 |
1.00 |
|
Mar |
14.886 |
14.9830 |
-0.097 |
0.65 |
|
Apr |
12.818 |
12.6945 |
0.1235 |
0.96 |
|
May |
12.545 |
12.6300 |
-0.085 |
0.68 |
|
Jun |
14.922 |
15.0447 |
-0.1227 |
0.82 |
|
Jul |
14.367 |
14.4452 |
-0.0782 |
0.54 |
|
Aug |
13.262 |
13.3709 |
-0.1089 |
0.82 |
|
Sep |
12.471 |
12.3688 |
0.1022 |
0.82 |
|
Oct |
12.584 |
12.6266 |
-0.0426 |
0.34 |
|
Nov |
12.604 |
12.6633 |
-0.0593 |
0.47 |
|
Dec |
13.897 |
14.0094 |
-0.1124 |
0.81 |
Consequently, pollutants present in water could seriously affect the resultant carbonate concentration. The extent of acidification or alkalization of the solution by pollutants is dependent, on not only the chemical nature of the compounds present, but also the prevailing technological conditions (Odigure and Adeniyi, 2002). From the calculated coefficients, it could be seen that the carbonate concentration is most affected by the sodium ions and least by the temperature.
Tables 7- 9 gives the time-concentration value from simulation of the months of January, March and June of the year 2001.
Table 7: Time Concentration data from simulation (Jan. 2001)
|
Run |
Time (min) |
CA1 (kg/dm3) |
CA2 (kg/dm3) |
CA3 (kg/dm3) |
CAM (kg/dm3) |
|
1 |
0.00 |
13.0830 |
10.0000 |
0.1000 |
0.8000 |
|
2 |
0.50 |
1.7949 |
7.5767 |
1.8086 |
53.3328 |
|
8 |
3.51 |
9.2574 |
1.9208 |
1.6843 |
48.9541 |
|
12 |
5.51 |
1.0135 |
2.9864 |
1.1401 |
32.2791 |
|
19 |
9.01 |
7.1980 |
1.2045 |
0.3007 |
13.1300 |
|
20 |
9.51 |
5.6166 |
2.0257 |
0.1556 |
3.2070 |
From Table 7 at time zero, the conversion of CO32- was 0.8 kg/dm3 (which is the bias value of the controller), at T=0.5 minutes, the conversion was 53.33278 kg/dm3, showing that with increase in time the manipulated variable concentration decreases proportionately toward the set point. The same pattern was observable in Table 8 and 9.
Table 8: Time Concentration data from simulation (Mar. 2001)
|
Run |
Time (min.) |
CA1 (kg/dm3) |
CA2 (kg/dm3) |
CA3 (kg/dm3) |
CAM (kg/dm3) |
|
1 |
0.00 |
14.8860 |
10.0000 |
0.1000 |
0.8000 |
|
2 |
0.50 |
2.8012 |
7.8471 |
1.8242 |
54.3856 |
|
8 |
3.51 |
9.1626 |
2.1493 |
1.7621 |
50.7102 |
|
12 |
5.51 |
0.7137 |
3.1506 |
1.1611 |
32.9314 |
|
19 |
9.01 |
7.4191 |
1.1768 |
0.3364 |
14.0958 |
|
20 |
9.51 |
5.9060 |
2.0619 |
0.1355 |
0.5531 |
Table 9: Time Concentration data from simulation (Jun. 2001)
|
Run |
Time (min.) |
CA1 (kg/dm3) |
CA2 (kg/dm3) |
CA3 (kg/dm3) |
CAM (kg/dm3) |
|
1 |
0.00 |
14.9220 |
10.0000 |
0.1000 |
0.8000 |
|
2 |
0.50 |
2.8213 |
7.8525 |
1.8431 |
54.4067 |
|
8 |
3.51 |
9.1607 |
2.1539 |
1.7638 |
50.7430 |
|
12 |
5.51 |
0.7078 |
3.1538 |
1.1655 |
32.9445 |
|
19 |
9.01 |
7.4236 |
1.1762 |
0.3371 |
14.1151 |
|
20 |
9.51 |
5.9118 |
2.0626 |
0.1351 |
0.5648 |
Table 10 gives the percentage error deviation analysis of the simulated concentration for the third tank to that of the set point. This gives the deviation error analysis for the process control model. The highest deviation was 38% at the fifth run.
Table 10: Error deviation analysis for process control model
|
Run |
CA3 |
CA3set |
Error Deviation |
% Error Deviation |
|
1 |
0.14565 |
0.1 |
0.04565 |
31 |
|
2 |
0.15564 |
0.1 |
0.05560 |
36 |
|
3 |
0.13548 |
0.1 |
0.03550 |
26 |
|
4 |
0.15852 |
0.1 |
0.05852 |
37 |
|
5 |
0.16156 |
0.1 |
0.06156 |
38 |
|
6 |
0.13508 |
0.1 |
0.03510 |
26 |
|
7 |
0.14126 |
0.1 |
0.04130 |
29 |
|
8 |
0.15357 |
0.1 |
0.05360 |
35 |
Conclusions
From the empirical model developed, the constituent parameter with greatest influence was Na+ with a coefficient of 0.87642, while that with the least influence, was the temperature with a coefficient of 0.0514255. This study, in addition, seeks to reduce the concentration of carbonate ion to an acceptable degree, so as not to degrade the environment. To some extent, this could be said to be have been achieved, since the concentration was lowered from 13.973 to 0.145648108458162 in the first case. Under ideal operating conditions, the output concentration from the system should converge at the set point (i.e. CA3=CA3set). In such a case, no error is generated, but because of differences in the design specifications and process parameters, such errors are inevitable as shown in the results presented. Thus the proposed model could be used to predict the concentration of carbonate ions from brewery effluent with similar operating conditions.
Acknowledgment
The help rendered by Mr. C. M. Dikwal of the Department of Chemical Engineering, Federal University of Technology, Minna, Nigeria is highly appreciated.
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