Carbonate Chemistry Model

The objective of this project is to create a carbonate chemistry model that predicts CO2 losses to the atmosphere and CO2 requirements as function of pH, alkalinity, kLa, temperature and salinity from algae raceway ponds. It is funded by the U.S. Department of Energy and part of the MAGIC (Marine Algae Industrialization Consortium) project headed by Duke University and Professor Zachary Johnson.

Table of Contents

• Revelant Information and Equations
• Technologies
• Usage
• Output of Each File
• Authors

Relevant Information and Equations

In most natural systems, acid buffering capacity is predominately made up by the carbonate system, which consists of four species - dissolved carbon dioxide, carbonic acid, bicarbonate and carbonate. Carbonic acid exists in only very small quantities and to simplify we define it as follows:

CT is defined as the total concentration of carbonate species in solution:

In addition, the carbonate species are related to each other through the following equilibrium relationships:

the molar concentration of each carbonate species is dependent on pH as shown below:

Mass transfer of carbon dioxide is a function of alkalinity and pH, based on the following equation:

Dissolved carbon dioxide concentration can be calculated as follows:

The effect of pH, alkalinity, and algal growth rates on carbon dioxide requirements and losses to the atmosphere were modeled for a raceway pond and operated in batch mode for 4 days. A mass balance on alkalinity and the aqueous concentration of carbon dioxide results in the following equation:

A mass balance on Ct and rearranging results in the following equation for carbon dioxide requirements:

excerpted from Sills' 2013 report

Technologies

This project is created with:

• MATLAB version: R2020a
• Python version: 3.7
• Anaconda package with numpy and matplotlib

Usage

To run this project, you can:

1. To clone with HTTPS, click on:

2. clone using git:

git clone https://github.com/rkd006/Carbonate-Chemistry-Model

Output of Each File

MATLAB:

python code is recently updated

• calc_alpha0: creates a function to calculate alpha0
• calc_alpha1: creates a function to calculate alpha1
• calc_alpha2: creates a function to calculate alpha2
• calc_alphas: calculate CO2 losses to the atmossphere numerically
• calc_density: calculate the density of seawater
• calc_CO2_loss: creates a function to calculate the CO2 losses to the atmosphere with inputs of pH and alkalinity ranges
• calc_CO2_loss_kLa: creates a function to calculate the CO2 losses to the atmosphere with inputs of pH and kLa ranges
• calc_K1: creates a function to calculate K1
• calc_K2: creates a function to calculate K2
• calc_Kh: creates a function to calculate Kh
• calc_CO2_loss_alk: creates a function to calculate the CO2 losses to the atmosphere with inputs of kLa and alk ranges
• calc_CO2_loss_temp: creates a function to calculate the CO2 losses to the atmosphere with inputs of pH and temperature ranges
• calc_CO2_loss_sal: creates a function to calculate the CO2 losses to the atmosphere with inputs of pH and salinity ranges
• calc_inorganiccarbon_pond: calculates inorganic carbon concentration in the pond at four days numerically and figure that plots the inorganic carbon concentration over four days
• calc_algaecarbon: calculates the carbon concentration in algae at four days numerically
• plot_carbonates: figure that plots the distribution of carbonate species (H2CO3*, HCO3, CO3)
• rates: creates a function to calculate the system of ODEs
• rates2: creates a function to calulate the ODE for calc_inorganiccarbon_pond
• pCpHdiagram: creates a open and closed carbonate system based on the model's conditions

with algal growth:

• CO2_loss_algal_growth_alk: plots CO2 requirements and losses over four days at several alkalinites for different kLa values
• CO2_loss_algal_growth_kLa: plots CO2 requirements and losses over four days for several kLa values
• CO2_loss_algal_growth_pH: plots CO2 requirements and losses over four days for several pHs
• CO2_loss_algal_growth_range: plots CO2 requirements and losses over four days for several algal growth rates
• CO2_loss_dynamic: plots CO2 requirements and losses over four days and plots CO2 concentration over four days

without algal growth:

• CO2_loss_kLa_comb: plots CO2 losses to the atmosphere at different alkalinities and pHs for different kLa values
• CO2_loss_kLa_simple: plots CO2 losses to the atmopshere for different alkalinities and figure that plots CO2 losses to the atmosphere for different pHs
• CO2_loss_range_kLa: plots CO2 losses to the atmosphere at different kLa values and pHs
• CO2_loss_script: plots CO2 losses to the atmosphere at different alkalinities and pHs
• CO2_loss_script_temp: plots CO2 losses to the atmosphere at different alkalinities and pHs for different temperatures
• CO2_loss_script_sal: plots CO2 losses to the atmosphere at different alkalinities and pHs for different salinities

Python:

updated recently

see MATLAB files outputs above for replicates if not stated below

• calc_alphas: creates functions to calculate alpha0, alpha1, alpha2
• calc_Ks: creates functions to calculate K1, K2, Kh
• CO2_loss_algal_growth_temp: figure that plots CO2 requirements and losses over four days for several temperatures
• CO2_loss_algal_growth_sal: figure that plots CO2 requirements and losses over four days for several salinities
• temperature_function: plots the saturation concentration of carbon dioxide and the carbonate species as a function of temperature

with algal growth kinetics:

• specific_growth_rate: calculated the specific growth rate as a function of light intensity based on different models
• algae_productiivity: calculate biomass density and productivity as a function of time based on different models
• algae_productivity_monod: plots biomass productivity as a function of time based on Monod for different light intensities
• CO2_loss_dynamic_monod: plots CO2 requirements and losses over four days and plots CO2 concentration over four days at pH = 8, which includes algal growth kinetics based on Monod
• mean_value_theorem: uses the Mean Value Theorem to calculate productivities for the file 'algae_productivity_model'

subplots:

• subplot_algal_growth_pH: creates multiple subplots side by side of the figures from CO2_loss_algal_growth_pH for kLa = 0.5 1/hr and alkalinity = 2.5 eq/m3
• subplot_algal_growth_range: creates multiple subplots side by side of the figures from CO2_loss_algal_growth_range for kLa = 0.5 1/hr, and alkalinity = 3.5 eq/m3 at pH = 6, 7, and 8
• subplot_algal_growth_alk: creates multiple subplots side by side of the figures from CO2_loss_algal_growth_alk for kLa = 0.5 1/hr, kLa = 3 1/hr, alkalinity = 2 and 32 eq/m3 at pH = 6, 7, and 8
• subplot_kLa_comb: creates multiple subplots side by side of the figures of kLa = 0.5 1/hr and kLa = 3 1/hr from CO2_loss_kLa_comb
• subplot_algal_growth_tempsal: creates subplots side by side of the figures from CO2_loss_algal_growth_temp and CO2_loss_algal_growth_sal
• subplot_different_kLa: creates subplots side by side of figures that plot CO2 losses as a function of pH for alkalinity = 2.5 and 7 eq/m3
• subplot_sal: a) creates multiple subplots side by side of the figures from CO2_loss_script_sal b) creates multiple subplots side by side of the figures from CO2_loss_algal_growth_sal
• subplot_temp: a) creates multiple subplots side by side of the figures from CO2_loss_script_temp b) creates multiple subplots side by side of the figures from CO2_loss_algal_growth_temp
• subplot_algae_kinetic_monod: creates multiple subplots side by side plotting CO2 requirements and losses over four days at pHs = 6, 7, and 8, which includes algal growth kinetics based on Monod
• subplot_algae_kinetic_light: creates multiple subplots side by side plotting CO2 requirements and losses over four days at different light intensity, which includes algal growth kinetics based on Monod.
• subplot_algae_kinetics: creates multiple subplots side by side that compare the CO2 requirements and losses over four days from the model without kinetics with the model with kinetics

with CO2 input that is not continuous:

• model_CO2_input: the initial step to model a CO2 input to the pond that is not continuous with a constant algae growth rate
• model_CO2_input_algae_growth: models a CO2 input to the pond that is not continuous with algae growth that follows a monod model

Authors

• Deborah Sills
  • Assistant Professor in the Civil and Environmental Engineering Department at Bucknell University
  • her website
• Riley Doyle
  • Undergraduate Student at Bucknell University, majoring in environmental engineering and graduating in 2022
  • email: rkd006@bucknell.edu
  • LinkedIn