Pressure/Volume Calculations

A “floating drum” storage offers a good, simple way of measuring gas production. You just record the change in height of the drum and volume of gas = area * height (area of a circle = pi Dsquared/4 or pi Rsquared and there are 1000 litres in a cubic metre). If you want more accuracy use a small diameter drum with greater height to get the necessary capacity. Pressure and volume of any gas are related by p1v1=p2v2, where p is pressure, v is volume and 1 represents the initial conditions and 2 is the final conditions. Mass and volume are related by density, where Density = Mass/Volume and the density of biogas is about 1.18 kg/m3. The easiest way to develop the pressure needed for burners etc is to add weight to the drum (bigger diameter – more weight, since Pressure = kg*9.8/sq.metres) and if you measure “pressure” in mm of water you need to know Pressure (Pa) = 9.8 *Height (mm). I think that should let you calculate anything you need and I hope you understand the “useful” metric units I have used.

I have set up a spreadsheet to do the hard work, which provides the example below for you to practice on.


Calculations for gas volume

C Paul Harris, November 2010 Version 1.0








Volume of gas








Diameter of Container
1.3
m





Height
1.2
m





Volume Contained
1.593
m3 or
1593
litres











Volume change with pressure








mm Water
Pa





Initial Pressure
10
101398





Final Pressure
20
101496
Requires
13.3
extra kg


Final Volume

1.591
m3 or
1591
litres


Volume at Atmospheric Pressure
1.594
m3












Mass of gas








Density (Cmp 60% CH4)
1.1607
kgm-3
(At Atmospheric pressure)


Mass
1.851
kg or
1851
g











Volume change with temperature






(based on Final pressure and volume!)







Fixed Vol.
Fixed Press.





Pressure
Volume






(Pa)
(m3)




Initial Temperature (C)
20.0
101496
1.591




Final Temperature (C)
30.0
104958
1.646













Notes







Enter initial data in yellow cells




Enter Final pressure and temperature in the orange cells


If you know the mass adjust the Final Pressure to get the pressure resulting from that mass.