Supporting information
Evaluation of the 5 and 8 pH point titration methods for monitoring anaerobic digesters
treating solid waste
T.P.W. Vannecke1,*, D.R.A. Lampens1, G.A. Ekama2 and E.I.P. Volcke1
1
Department of Biosystems Engineering, Ghent University, Ghent, BE
2
Water Research Group, Department of Civil Engineering, University of Cape Town, SA
*
Corresponding author Tel: +32 (0)9 264 61 89; fax: +32 (0)9 264 62 35
E-mail address: Thomas.Vannecke@UGent.be
S.1. Matlab implementation of the 5 pH point titration method
The used procedure for implementing the 5 pH point titration method in the Matlab
environment is summarized in Fig. S1. One text file (txt-file) and seventeen separate scripts,
of which the code can be found in the following chapters, are needed for the calculation. The
results are exported to another text file.
S.1.1. INPUT_TITRA5.txt
5 pH POINT TITRATION INPUT
VARIABLES
UNITS
VALUES
pH0
-
7.36
pH1
-
6.75
pH2
-
5.95
pH3
-
5.18
pH4
-
4.29
Vx1
ml
1.06
1
Vx2
ml
3.50
Vx3
ml
4.84
Vx4
ml
5.40
conc.
mol/l
0.080070189
vsundil
ml
2.5
vsdil
ml
50
temp
°C
18.2
TDS
mg/l
0
SC
mS/m
1200
Nt
mgN/l
650
Pt
mgP/l
67
St
mgS/l
0.41
S.1.2. Titra5.m
% This script calculates H2CO3-alkalinity, short-chain fatty acid
% concentrations, total inorganic carbon concentration and total alkalinity
% in aqueous solutions containing the carbonate, VFA, ammonium, phosphate
% and sulphide weak acid/base subsystems.
% The total species concentrations of the ammonium, phosphate and sulphide
% subsystems need to be entered into the txt-file '5 pH point titration
% input.txt'. The sample has to be titrated from the initial reactor pH to
four
% further pH values measured in the pH region: 6.7, 5.9, 5.2 and 4.3 ± 0.1.
% The script provides an estimate of a possible systematic pH measurement
% error in the event that the carbonate system dominates over the remaining
% weak acid/base subsystems. The results are saved in the txt-file '5 pH
% point titration output.txt'.
clear all
2
clc
global Nt Pt St vsdil vsundil dil temp
%% IMPORT INPUT DATA FROM '5 pH point titration input.txt'
inputfileID= fopen('INPUT_TITRA5.txt');
C = textscan(inputfileID,'%*s %*s %f %*[^\n]','headerlines',3);
fclose(inputfileID);
values = cell2mat(C);
%% ALLOCATE DATA TO VARIABLES
pH0 = values(1); % pH of the reactor
pH1 = values(2); % sample pH (approx. 6.7) after addition of vx1 ml titrant
pH2 = values(3); % sample pH (approx. 5.9) after addition of vx2 ml titrant
pH3 = values(4); % sample pH (approx. 5.2) after addition of vx3 ml titrant
pH4 = values(5); % sample pH (approx. 4.3) after addition of vx4 ml titrant
vx1 = values(6); % volume of titrant added until sample pH approx. 6.7 (ml)
vx2 = values(7); % volume of titrant added until sample pH approx. 5.9 (ml)
vx3 = values(8); % volume of titrant added until sample pH approx. 5.2 (ml)
vx4 = values(9); % volume of titrant added until sample pH approx. 4.3 (ml)
ca = values(10); % normality of titrant (mol/l)
vsundil = values(11);
vsdil = values(12);
% volume of undiluted sample (ml)
% volume of diluted sample (ml)
temp = values(13);
% temperature of sample (°C)
TDS = values(14);
% total dissolved solids in sample (mg/l)
ionstr = values(15);
% specific conductivity (mS/m)
Nt = values(16);
% Inorganic Nitrogen (mgN/l)
Pt = values(17);
% Inorganic Phosphorus (mgP/l)
St = values(18);
% Inorganic Sulphide (mgS/l)
dil = vsdil/vsundil;
% dilution ratio
3
% Calculation of TDS from the specific conductivity if TDS is not measured
if TDS == 0
TDS = ionstr*6.72+20; end
% Calculation of specific conductivity if TDS is not measured
if ionstr == 0
ionstr = 0.1488*(TDS-20); end
%% CALCULATION OF H2CO3-ALK, VFA, CT, TOTAL-ALK AND ESTIMATION OF pH ERROR
atct1
%% EXPORT OUTPUT DATA TO '5 pH point titration output.txt'
title = ('OUTPUT_TITRA5');
outputfileID = fopen('OUTPUT_TITRA5.txt','w');
fprintf(outputfileID,'5 pH POINT TITRATION OUTPUT\r\n');
fprintf(outputfileID,'H2CO3* alkalinity\t%6.1f\tmg
CaCO3/l\r\n',H2CO3alksam);
fprintf(outputfileID,'VFA\t\t\t%6.1f\tmg AcOH/l\r\n',At1);
fprintf(outputfileID,'CT\t\t\t%6.1f\tmg CaCO3/l\r\n',Ct1);
fprintf(outputfileID,'Total alkalinity\t%6.1f\tmg
CaCO3/l\r\n',Totalalksam);
if counter == 20
fprintf(outputfileID,'\n Attention:\n The titration data indicate a
systematic pH error > 0.2!\n Check pH probe calibration!');
elseif x == 'c'
fprintf(outputfileID,'\n Attention:\n Correction for systematic pH error is
not possible for this titration.');
else
fprintf(outputfileID,'Systematic pH error\t%6.2f\r\n',delpH);
end
4
fclose(outputfileID);
OUTPUT=[H2CO3alksam At1 Ct1 delpH];
S.1.3. atct1.m
% This script implements a systematic pH measurement error by making an
% estimation of the error and recalculating the carbonate total species
% concentrations Ct1 and Ct2 until they are approximately equal to each
% other (= until Ctcomp changes sign) to calculate the H2CO3* alkalinity,
% the VFA concentration, the total carbonate total species concentration
% and the total alkalinity
% Calculation apparent pKa values of all the weak acid/base subsystems
pK
% Calculation of Ct1, Ct2 and difference between those two, i.e. Ctcomp
atctcalculation
% Implementation of pH error
delpH = 0;
pHcorr = 0;
counter = 0;
CtAtratio = MAt1/MCt1;
if Ctcomp == 0
x = 'd'; end
if Ctcomp > 0
x = 'a'; end
if Ctcomp < 0
x = 'b'; end
if abs(CtAtratio) > 0.5 % requirement not fulfilled to calculate pH error
x = 'c'; end
5
switch x
case 'a'
pHcorr = -0.01;
while Ctcomp > 0 && counter < 20
delpH = delpH-0.01;
deltapH;
counter = counter+1;
atctcalculation; end
case 'b'
pHcorr = +0.01
while Ctcomp < 0 && counter < 20
delpH = delpH+0.01;
deltapH;
counter=counter+1;
atctcalculation; end
otherwise
end
% Calculation of H2CO3 alkalinity
MH2CO3alksam = MCt1*(perHCO3(pH0)+2*perCO3(pH0));
H2CO3alksam = MH2CO3alksam/vsdil*dil*50000+(10^(pH0-14)-...
10^(-pH0)/10^(logf1))*50000;
Totalalksam = H2CO3alksam+At1/60*50*per(pH0,pKaa);
S.1.4. pK.m
% This script calculates the negative logarithm of the acid dissociation
% constants (pKa values) of the carbonate subsystem (pK1 and pK2), the VFA
% subsystem (pKa), the ammonium subsystem (pKn), the phosphate subsystem
% (pKp), the sulfide subsystem (pKs) and the respective negative logarithm
% of their apparent dissociation constants (respectively pK11, pK22, pKaa,
% pKnn, pKpp and pKss) based on the temperature of the sample in Kelvin and
6
% the ionic strength of the sample.
global logf1 pK11 pK22 pKaa pKnn pKpp pKss
dil = vsdil/vsundil;
ktemp = 273+temp;
% dilution ratio
% temperature in Kelvin
% adjustment of TDS if TDS is too small
if TDS/dil < 20
TDS = 21;
end
logf1 = logf(mue(TDS,dil),ktemp); % monovalent ion activity coefficient fm
logf2 = 4*logf1;
% divalent ion activity coefficient fd
pK1 = -1*(-356.3094-0.06091964*ktemp+21834.37/ktemp+126.8339*...
log10(ktemp)-1684915/(ktemp*ktemp)); % source: Nordstrom et al.(1990)
pK11 = pK1+logf1;
pK2 = -1*(-107.8871-0.03252849*ktemp+5151.79/ktemp+38.92561*log10(ktemp)...
-563713.9/(ktemp*ktemp));
% source: Nordstrom et al.(1990)
pK22 = pK2-logf1+logf2;
pKa = 1170.5/ktemp-3.165+0.0134*ktemp;
% source: Loewenthal et al.(1989)
pKaa = pKa+logf1;
pKn = 2835.8/ktemp-0.6322+0.00123*ktemp; % source: Loewenthal et al.(1989)
pKnn = pKn+logf1;
pKp = 1979.5/ktemp-5.3541+0.01984*ktemp; % source: Loewenthal et al.(1989)
pKpp = pKp-logf1+logf2;
pKs = 7.00+1132.18/ktemp-3.7993;
% source: Loewenthal et al.(1989)
pKss = pKs+logf1;
S.1.5. atctcalculation.m
7
% This script calculates the carbonate total species concentrations Ct1 and
% Ct2 and the VFA concentrations At1 and At2 based on two sets of equations
% as wel as the difference between Ct1 and Ct2 (Ctcomp).
% Set 1
A1 = (vx2-vx1)*ca-MH2O(vx1,vx2,pH1,pH2)-MNH3(pH1,pH2)-MHPO4(pH1,pH2)-...
MHS(pH1,pH2)+dHAcalk(pH1,pH2)/dHAcalk(pH3,pH4)*(MH2O(vx3,vx4,pH3,pH4)+...
MNH3(pH3,pH4)+MHPO4(pH3,pH4)+MHS(pH3,pH4)-(vx4-vx3)*ca);
B1 = dH2CO3alk(pH1,pH2)dHAcalk(pH1,pH2)/dHAcalk(pH3,pH4)*dH2CO3alk(pH3,pH4);
MCt1 = A1/B1;
%mmol CaCO3
Ct1 = MCt1/vsdil*50000*dil; %mg CaCO3/L
MAt1 = 1/dHAcalk(pH3,pH4)*((vx4-vx3)*ca-MCt1*dH2CO3alk(pH3,pH4)-...
MNH3(pH3,pH4)-MHPO4(pH3,pH4)-MHS(pH3,pH4)-MH2O(vx3,vx4,pH3,pH4));%mmol HAc
At1 = MAt1/vsdil*60000*dil;
%mg HAc/L
% Set2
A2 = (vx4-vx1)*ca-MH2O(vx1,vx4,pH1,pH4)-MNH3(pH1,pH4)-MHPO4(pH1,pH4)-...
MHS(pH1,pH4)+dHAcalk(pH1,pH4)/dHAcalk(pH3,pH4)*(MH2O(vx3,vx4,pH3,pH4)+...
MNH3(pH3,pH4)+MHPO4(pH3,pH4)+MHS(pH3,pH4)-(vx4-vx3)*ca);
B2 = dH2CO3alk(pH1,pH4)dHAcalk(pH1,pH4)/dHAcalk(pH3,pH4)*dH2CO3alk(pH3,pH4);
MCt2 = A2/B2;
% mmol CaCO3
Ct2 = MCt2/vsdil*50000*dil; % mg CaCO3/L
MAt2 = 1/dHAcalk(pH1,pH4)*((vx4-vx1)*ca-MCt1*dH2CO3alk(pH1,pH4)-...
MNH3(pH1,pH4)-MHPO4(pH1,pH4)-MHS(pH1,pH4)-MH2O(vx1,vx4,pH1,pH4));%mmol HAc
At2 = MAt2/vsdil*60000*dil;
%mg HAc/L
% pH error present?
Ctcomp = Ct1-Ct2;
8
S.1.6. deltapH.m
% This script corrects the measured pH values with the estimation of the
% systematic pH measurement error.
pH0 = pH0+pHcorr;
pH1 = pH1+pHcorr;
pH2 = pH2+pHcorr;
pH3 = pH3+pHcorr;
pH4 = pH4+pHcorr;
S.1.7. mue.m
% The function mue(TDS,dil) calculates the ionic strength of the diluted
% sample (mue) with an empirical equation based on the Total Dissolved
% Solids concentration of the undiluted sample (TDS) and the dilution ratio
% (dil).
function y = mue(TDS,dil)
y = 0.000025*(TDS/dil-20);
end
S.1.8. logf.m
% The function logf(mue,ktemp) calculates the common logarithm of the
% monovalent ion activity coeffient with the Davies equation based on the
% ionic strength of the sample (mue) and the temperature of the sample in
% Kelvin (ktemp).
function y = logf(mue,ktemp)
y = -1.825*10^6*(78.3*ktemp)^(-1.5)*(sqrt(mue)/(1+sqrt(mue))-0.3*mue);
9
end
S.1.9. MH2O.m
% The function MH2O(vxf,vxs,pHf,pHs) calculates the mass decrease in H2CO3*
% alkalinity due to the water subsystem upon titration of the sample from
% pHf (reached after addition of a titrant volume equal to vxf) to pHs
% (reached after addition of a titrant volume equal to vxs).
function y = MH2O(vxf,vxs,pHf,pHs)
global vsdil logf1
y = (vsdil+vxs)*10^(-pHs)/10^(logf1)-(vsdil+vxf)*10^(-pHf)/10^(logf1)+...
(vsdil+vxf)*10^(pHf-14)-(vsdil+vxs)*10^(pHs-14);
end
S.1.10. MNH3.m
% The function MNH3(pHf,pHs) calculates the mass decrease in H2CO3*
% alkalinity due to the ammonium subsystem upon titration of the sample
% from pHf to pHs.
function y = MNH3(pHf,pHs)
global Nt dil vsdil pKnn
y = Nt/(14000*dil)*vsdil*(per(pHf,pKnn)-per(pHs,pKnn));
end
S.1.11. MHPO4.m
% The function MHPO4(pHf,pHs) calculates the mass decrease in H2CO3*
% alkalinity due to the phosphate subsystem upon titration of the sample
% from pHf to pHs.
10
function y = MHPO4(pHf,pHs)
global Pt dil vsdil pKpp
y = Pt/(31000*dil)*vsdil*(per(pHf,pKpp)-per(pHs,pKpp));
end
S.1.12. MHS.m
% The function MHS(pHf,pHs) calculates the mass decrease in H2CO3*
% alkalinity due to the sulphide subsystem upon titration of the sample
% from pHf to pHs.
function y = MHS(pHf,pHs)
global St dil vsdil pKss
y = St/(32000*dil)*vsdil*(per(pHf,pKss)-per(pHs,pKss));
end
S.1.13. dHAcalk.m
% The function dHAcalk(pHf,pHs) calculates relative contribution of the HA
% subsystem (a weak monoprotic acid/base subsystem) to the mass decrease in
% H2CO3* alkalinity upon titration of the sample from pHf to pHs.
function y = dHAcalk(pHf,pHs)
global pKaa
y = per(pHf,pKaa)-per(pHs,pKaa);
end
S.1.14. dH2CO3.m
% The function dH2CO3alk(pHf,pHs) calculates the relative contribution of
% the carbonate subsystem to the mass decrease in H2CO3* alkalinity upon
% titration of the sample from pHf to pHs.
11
function y = dH2CO3alk(pHf,pHs)
y = perHCO3(pHf)-perHCO3(pHs)+2*(perCO3(pHf)-perCO3(pHs));
end
S.1.15. per.m
% The function per(pH,pKk) calculates the relative contribution of the
% concentration of the dissociated form of the weak acid/base subsystem to
% the sample total species concentration of the weak acid/base subsystem
% concentration (Ct) based on the sample pH and the pK value of the weak
% acid/base subsystem (pKk).
function y = per(pH,pKk)
y = 10^(-pKk)/(10^(-pKk)+10^(-pH));
end
S1.16. perCO3.m
% The function perCO3(pH) calculates the relative contribution of the
% CO3-2 concentration of the sample to the carbonate total species
% concentration (Ct) of the sample based on the sample pH.
function y = perCO3(pH)
global pK11 pK22
y = 1/(10^(-2*pH)/(10^(-pK11)*10^(-pK22))+10^(-pH)/10^(-pK22)+1);
end
S1.17. perHCO3.m
% The function perHCO3(pH) calculates the relative contribution of the
% HCO3- concentration of the sample to the carbonate total species
12
% concentration (Ct) of the sample based on the sample pH.
function y = perHCO3(pH)
global pK11 pK22
y = 1/(10^(-pH)/10^(-pK11)+1+10^(-pK22)/10^(-pH));
end
S 1.18. perH2CO3.m
% The function perH2CO3(pH) calculates the relative contribution of the
% H2CO3* concentration of the sample to the carbonate total species
% concentration (Ct) of the sample based on the sample pH.
function y = perH2CO3(pH)
global pK11 pK22
y = 1/(1+10^(-pK11)/10^(-pH)+10^(-pK11)*10^(-pK22)/10^(-2*pH));
end
13
Figure S1 Implementation of the 5 pH point titration method in Matlab.
14