J.C. Kantor ([email protected])

_{2} emissions go by solving a mass balance.

In [1]:

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

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?

_{2} in the atmosphere. We'll perform the using a 10 step approach outlined in the textbook.

<img src="https://raw.github.com/jckantor/CBE20255/master/images/Global_CO2.png" width=400px>

_{2}. The stream variables are the mass flowrates of CO

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)
```

_{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.

_{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)
```

_{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)
```

In [ ]:

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