1. Abstract
The goal was to design a system to capture atmospheric carbon at a
rate of 10 mg/L-day using green algae at the PAS aquaculture center. A
CSTR was designed and modeled using Microsoft Excel. This design
is theoretically able to capture 10.55 mg /L-day using a hydraulic
retention time of 70 hours.
Introduction
Carbon dioxide is an abundant atmospheric gas that is used by algal
cultures as an inorganic carbon source. Removing this greenhouse gas
from the atmosphere while simultaneously using it as an algal growth
source is a developing biological remediation approach to this ongoing
environmental issue.
Algal culture growth can be summarized by the following reaction:
106 CO2+16 NO3
- +HPO4
-2+122 H2O+18 H+ C106H263N16P +138 O2
A common biological reactor design is a continuous flow stirred tank
reactor (CSTR) which has constant influent and effluent flows. The
hydraulic retention time (τ) is a design parameter that is usually used to
optimize the reactor conditions.
The Monod model is a valuable set of equations that accurately
model microbial growth and decay within a system and are used as a
basis for the model development carried out in this project.
The objective of this project is to design and model a CSTR to be
implemented at the PAS aquaculture center that will fix 10mg/L-day.
Materials and Methods
• The mass balance equations with respect to biomass, substrate
(CO2), and nitrate as a nitrogen source were all developed using
Monod model equations and microbial growth in CSTR
parameters.
• The differential mass balances were modeled in excel using
forward finite difference techniques until they reached steady state
conditions, accounting for decreased algal growth at night.
• The model was used to find an ideal retention time to maximize
the steady state biomass concentration (Xb) and to determine
steady state substrate concentration (S).
• The steady state substrate concentration was used to determine the
steady state specific growth rate (μ).
• The rate of actual carbon fixation was calculated using these
values and the Monod model relationship between the parameters.
• The rate of actual carbon fixation was compared to the design
goal.
Model Simulations
This biomass model began with an initial inoculum whose growth was
limited by the amount of availability of inorganic carbon and light. In
order to achieve the design goal, 10 mg/L-day of carbon that needed to
be captured into 1.12mgXb/L-hr, this value was used in the forward
finite difference equation in place of the term for biomass
accumulation. The substrate model was then based on the biomass
concentration at each time step. This model shows how the algae
would stop growing at night due to lack of light and be washed out by
the effluent and grow exponentially in daylight. The substrate
concentration drops considerably during the transient phase and then
levels off at a low concentration. The line shows how as the algae
concentration increased it used more and more substrate, but then the
substrate availability began to limit the algae growth causing the
system to balance out.
Results
• The best hydraulic retention time was found to be 70 hours
• At this time the average biomass concentration at steady state was
12 mg/L
• The steady state substrate concentration was approximately
S=1mg/L
• The specific growth rate was calculated using
• 𝜇𝜇 = 𝜇𝜇 𝑚𝑚𝑚𝑚𝑚𝑚
𝐼𝐼0
(𝐼𝐼0+𝐾𝐾𝐼𝐼)
×
𝑆𝑆0
(𝑆𝑆0+𝐾𝐾𝑆𝑆)
to get 0.1023 hr-1
• The carbon fixation of 10mg/L-day was converted to 0.416 mg/L-
hr.
• The actual accumulation term at steady state was then determined
using 𝜇𝜇𝜇𝜇𝜇𝜇/𝑌𝑌𝑌𝑌= rate of carbon fixation
• So, at steady state, the rate of carbon fixation would be 10.55 mg/L-
day
Conclusions
From the steady state values found with excel, the rate of carbon
captured by this model was determined to be approximately 10.55
mg/L-day, which means the carbon capture goal of 10 mg/L-day was
reached. In order to achieve this goal, a hydraulic retention time of 70
hours and substrate concentration (S) of approximately 1 mg/L are
needed.
Resources
Drapcho, C. 2017. Lecture 10: Biological Pathways for Lithotrophic
and Phototrophic Growth. Unpublished Lecture Notes, BE 4100,
Clemson University.
Drapcho, C. 2017. Lecture 12: Modeling Microbial Growth with
Monod Model. Unpublished Lecture Notes, BE 4100, Clemson
University.
Drapcho, C. 2017. Lecture 16: Microbial Growth in CSTR.
Unpublished Lecture Notes, BE 4100, Clemson University.
Acknowledgements
We would like to thank Dr. Caye Drapcho for her expertise and
guidance throughout this design.
Utilization of Algal Culture for the Fixation
of Atmospheric Carbon
Amanda Dotseth, Kylie Bednarick, Ali Bostwick, and Dr. Caye Drapcho
BE 4100, Biosystems Engineering, Clemson University, Clemson, South Carolina, 29632
Figure 1: Simulation of biomass
concentration and substrate concentration
as reactor reaches steady state
Figure 2: Simulation of nitrogen
concentration in CSTR
The nitrate concentration in the reactor was also modeled since it
would limit algae growth at low levels. Rather than model it as another
limiting nutrient, the goal was to keep the nitrogen levels above zero,
but not so high as to pollute the water. It was determined that with an
influent of 0.68 mg/L-hr, an additional 0.9 mg/L-day would need to be
added to keep the culture growing.
