Show me the steps to solve

Problem Set $4$

Do no rounded values.

Doing the calculations manually with a calculator and then enter the value might return your answer as incorrect if your rounding is not the same as the one from the autograding $(1$e$-5).$You should enter formulas in the coding cell instead.

Tasks

For part $1,$ you should answer the multiple choice questions about the differences between the substitution approach and the partitioning approach, and pros and cons of both approaches.

For part $2,$ apply substitution allocation for electricity and heat production respectively, and partitioning based on energy and cost, using equations.

For part $3,$ construct and show the Aff, Abf and Sf matrices for electricity and heat production respectively, and partitioning based on energy and cost. Calculate the different emissions for all four cases.

Please run the cell below before you start the assignment

# Import required Python libraries

import pandas as pd

import numpy as np

import matplotlib.pyplot as plt

import seaborn as sns

# Folder for the files

files$\_$folder $=$ "files$\_$PS$4\_$V$1\_0/"$

### In case formulas are entered in the csv files & correcting the datatypes

def convert$\_$formulas$($matrix$)$:

for row in matrix.index:

for column in matrix.columns:

if type$($matrix$.$loc$[$row$,$ column$])==$ str:

if $""$ in matrix.loc$[$row$,$ column$]$:

matrix.loc$[$row$,$ column$]=$ matrix.loc$[$row$,$ column$].$lstrip$(\text{'}\text{'})$

if $"="$ in matrix.loc$[$row$,$ column$]$:

matrix.loc$[$row$,$ column$]=$ matrix.loc$[$row$,$ column$].$lstrip$(\text{'}=\text{'})$

matrix.loc$[$row$,$ column$]=$ pd$.$eval$($matrix$.$loc$[$row$,$ column$])$

### Get the data types right in the DataFrames

s $=$ matrix.select$\_$dtypes$($include$=$'object'$).$columns

matrix$[$s$]=$ matrix$[$s$].$astype$("$float$64")$

return matrix

Combined heat and power $($CHP$)$ Problem

Consider a combined heat and power $($CHP$)$ plant which uses natural gas as its input. This is a process that produces two joint products that cannot be disaggregated effectively. Thus, allocation is necessary in order to understand the impact due to each unit of its products.

Assume this CHP has an overall efficiency of $87$ per cent. Hence, for every kilowatt$-$hour $($kWh$)$ of natural gas input, it produces $0\mathrm{.}31$ kWh of electricity and $0\mathrm{.}56$ kWh of heat.

The direct CO

emissions per kWh of electricity and heat from a natural gas fired CHP are $230$ g CO

$[1]($i$.$e$.$ per kWh of useful energy output$).$ Assume that there are no other emissions. Your task is to find the GWP allocated to the production of one unit of electricity and one unit of heat from the CHP plant, based on the information given below.

References: $[1]$ Nilsson, M$.$ and Stromberg, P$,2000,$ Evaluation of different methods for allocation in co$-$generation, Final Report

The figure below presents the CHP system $-$ it is without numbers but gives an idea of how the system works:

Part $2.$ Principles and scalar form $-$ without background processes $(40$ points$)$

Use the information given under each sub$-$task $(2$a$.-2$d$.)$ to determine the global warming potential $($GWP$)$ of producing $1$ kWh of electricity and $1$ kWh of heat using formulas from the reader.

You have to write the calculations you are performing directly in the cells. Doing the calculations manually with a calculator and then enter the value might return your answer as incorrect if your rounding is not the same as the one from the autograding.

$2$a$)(10$ points$)$ Substitution of heat $-$ Impact of $1$ kWh of electricity from CHP

Follow the description under and calculate the impact $($in kg CO

$-$eq$)$ of $1$ kWh of electricity from the CHP$.$ Define your answer as answer$\_2$a$.$

a$.$ Apply substitution allocation to find the impacts due to $1$ kWh of electricity production from the CHP$.$ An alternative heat source $$ a light fuel oil furnace with overall efficiency of heat production $85$ per cent $$ is used to calculate the impacts associated with heat production. It has direct CO

emissions of $299$ gCO

$-$eq$/$kWh

$[2]($that is per kWh of useful heat$).$

References: $[2]$ From Eco$-$Invent Database