by Jeffrey Kantor (jeff at nd.edu). The latest version of this notebook is available at https://github.com/jckantor/CBE20255.

This Jupyter notebook provides an analysis of global CO_{2} emissions go by solving a mass balance.

The total global emissons of CO_{2} is estimated by the Netherlands Environmental Assessment Agency to be 34.5 billion metric tons from all sources, including fossil fuels, cement production, and land use changes. As measured by NOAA, in recent years the atmospheric concentration of CO_{2} is increasing at an annual rate of about 2.4 ppmv (parts per million by volume).

<img src = "http://www.esrl.noaa.gov/gmd/webdata/ccgg/trends/co2_trend_gl.png" style="align:center;height:350px;margin-top:0px;margin-bottom:0px">

Assuming these numbers are accurate and that the atmosphere is well mixed, what fraction of global CO_{2} emissions are being retained in the atmosphere?

This problem requires us to perform a material balance for CO_{2} in the atmosphere. We'll perform the using a 10 step approach outlined in the textbook.

The system of interest is the global atmosphere which we assume is well mixed and of uniform composition.

The chemical component to model is CO_{2}. The stream variables are the mass flowrates of CO

This problem could be done on either a molar or mass basis. We'll arbitrarily choose to do this in mass units of kg/year. First we convert global emissions to kg/year.

In [1]:

```
%matplotlib inline
from numpy import *
```

In [2]:

```
mCO2_in = 34.5e9 # inflow, metric tonnes per year
mCO2_in = mCO2_in*1000 # inflow, kg per year
print("Global CO2 emissions = {:8.3g} kg/yr".format(mCO2_in))
```

The rate of accumulation is given as ppm by volume per year. For ideal gases, volume fraction is equivalent to mole fraction. We need to convert the mole fraction, which is the ratio of kg-moles of CO_{2} to kg-moles of air, to mass fraction which has units of kg of CO_{2} to kg of air per year.

In [3]:

```
nCO2_accum = 2.4e-6 # accumulation, kg-mol CO2/kg-mol air/yr
mwAir = 28.97 # kg air/kg-mol air
mwCO2 = 44.01 # kg CO2/kg-mol CO2
wCO2_accum = nCO2_accum*mwCO2/mwAir # kg CO2/kg air/yr
print("Accumulation Rate of CO2 = {:8.3g} kg CO2/kg air".format(wCO2_accum))
```

The basis for the calculation are flows and change in one year. No additional work is required.

The system variable is the rate of accumulation of CO_{2} in kg CO2/year. We need to convert from change in concentration per year to change in total mass per year. The first step is to estimate the total mass of air.

In [4]:

```
# Earth Radius in meters
R = 6371000 # m
# Earth Area in square meters
A = 4*pi*R**2 # m**2
# Mass of the atmosphere in kg
g = 9.81 # N/kg
P = 101325 # N/m**2
mAir = A*P/g # kg
print("Estimated mass of the atmosphere = {:8.3g} kg".format(mAir))
```

To get the rate of change of total CO_{2}, multiply the total mass of by the rate of change of mass fraction of CO_{2}.

In [5]:

```
mCO2_accum = wCO2_accum*mAir # kg CO2/year
print("Change in CO2 = {:8.3g} kg CO2/year".format(mCO2_accum))
```

The inflow and rate of change of CO_{2} are specified, and calculated above.

$$\mbox{Accumulation} = \mbox{Inflow} - \mbox{Outflow} + \underbrace{\mbox{Generation}}_{=0} - \underbrace{\mbox{Consumption}}_{=0}$$

$$\mbox{Outflow} = \mbox{Inflow} - \mbox{Accumulation}$$

In [6]:

```
mCO2_out = mCO2_in - mCO2_accum
print("Global CO2 outflow = {:8.3g} kg CO2/yr".format(mCO2_out))
```

Fraction retained in the atmosphere

In [7]:

```
fCO2 = mCO2_accum/mCO2_in
print("Fraction of CO2 retained in the atmosphere = {:<.2g} ".format(fCO2))
```