% This file is an aid function to the script batch1.m which describes
% a batch system relations of substrate, oxygen and one microbial specie
% over time. 
% Oz Nahum, Anibal Perez, Georgia Kastanioti, Januar 2010.


%function f=batch1_rate(t,c1,ko,ks,Ys,Yo,Kdec,umax,kb)
function f=batch1_rate(c1,t,ko)
%ko=0.1;             % Monod coefficients Oxigen [mg/l]
ks=0.1;             % Monod coefficients Substract [mg/l]

umax=0.125/86400;   % Maximun growth rate [1/d]

Yo=0.125;           % Oxigen Yield [mg X / mg O]
Ys=0.25;            % Substract Yield [mg X / mg S]

Kdec=0.01/86400;    % Decay rate
kb=1;              % Biomass Inhibition constant [mg/L]

co=c1(1); %concentration of Oxygen
cs=c1(2); %concentration of Substrate
X=c1(3); %concentration of bacteria

kgr=umax*(co/(ko+co))*(cs/(ks+cs)); % specific uptake rate [mol/m3/s]
Ib=1+X/kb;  				 		% inhibiton caused by biomass

foxi=((-kgr/Yo/Ib)*X);  %dc/dt of Oxygen
fsub=((-kgr/Ys/Ib)*X);  %dc/dt of Substrate
fbio=((kgr/Ib-Kdec)*X); %inhibition for growth only

f=[foxi;fsub;fbio];
end