## System of Equations

In order to describe the model in a mathematical way 3 types of equations are used:

- Mass conservation

e.g. balance equation

sum of inputs = sum of outputs + change in stock

or

e.g. stock equation

stock i = stock i -1+ change in stock i-1

with i…period

i.e. the amount of stock at the beginning of a period can be calculated from the amount of stock in the previous period plus the change in stock during this previous period. - Linear relations

e.g. transfer coefficient equation

output 1 = TC1 * Sum of inputs

output 2 = TC2 * Sum of inputs

with TC1 + TC2 = 1

or

e.g. additional linear relation equation between similar quantities

flow x = factor * flow y -
Concentration equation

mass substance = mass good * concentration substance

or

mass substance = volume good * concentration substance

mass good = volume good * density good