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McCabe Thiele with Murphree Efficiency implemented within Python

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# McCabe-Thiele Method with Murphree Efficiency

## McCabe-Thiele Method
The method was first published by Warren L. McCabe and Ernest Thiele in 1925, and is a graphical procedure of determining the number of trays within a distillation collumn. The Murphree tray efficiency modifies the equilibrium curve of the two components in order to better account for non-idealities.

### Current implimentation
The current implementation presented here allows for a Murphree efficiency to be applied to the classical McCabe-Thiele plot. Whilst it is relatively easy online to find McCabe-Thiele 'calculators', there are few that have implementations accounting for the Murphree plate efficiency.

### Limitations
* The molar heats of vaporization of the feed components are equal
* For every mole of liquid vaporized, a mole of vapor is condensed
* Heat effects such as heats of solution are negligible

## Effect of parameters
<img align="center" src="https://github.com/TomRSavage/McCabeThiele/blob/master/q.gif" width="400"> <img align="center" src="https://github.com/TomRSavage/McCabeThiele/blob/master/R.gif" width="400">

Here shown on the left is the effect of changing the feed condition q, and on the right is shown the effect of changing the reflux ratio R.

Here shown on the left is the effect of changing the desired distillate composition xd, and on the right is shown the effect of changing the Murphree efficiency.

## Function Use
```
    DESCRIPTION: 
    Performs the McCabe-Thiele construction in order to calculate
    optimum number of stages, and optimum feed stage. Also taking into 
    account the Murphree Efficiency of the system.

INPUTS: 
    PaVap       :Vapour pressure of component a (more volatile)
    PbVap       :Vapour pressure of component b (less volatile)
    R_factor    :Amount Rmin is scaled by to obtain the actual reflux ratio
    xf          :Feed composition 
    xd          :Distillate composition 
    xb          :Bottoms composition 
    q           :Liquid fraction of feed
    nm          :Murphree Efficiency

OUTPUTS: 
    A McCabe-Thiele plot, displaying optimum number of equilibrium stages, 
    optimum feed stage, actual reflux ratio, actual bottoms composition. 
```
## Example
Runnning the following: 
```
PaVap=179.2     # Vapour pressure of a
PbVap=74.3      # Vapour pressure of b 
xd=0.975        # Distillate composition 
xb=0.025        # Bottoms composition 
xf=0.5          # Feed composition 
q=0.5           # q (liquid fraction of feed)
R_factor=1.8    # Reflux ratio = R_min* R_factor
nm=0.75         #Murphree tray efficiency

McCabeThiele(PaVap,PbVap,R_factor,xf,xd,xb,q,nm)
```
Produces the following output:

**Please note: I wouldn't reccomend actually using this code to design a real distillation collumn,  you should probably get an expert.**

## Author

* **Tom Savage** - *Initial work* - [TomRSavage](https://github.com/TomRSavage)

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