# Productivity Analysis

Productivity is one of the most important aspects of a chemical process, that can be expressed in many ways. $/time, $/gram DW, $/reactor volume, instantaneous productivity, Average productivity.....

## Contents

## Definitions of productivity

Productivity is simply the rate of production of something

$$ (mass of X) / basis / time $$

Defining productivity in non-biological systems can be very simple ... moles X/volume reactor /time.
For a biological system, and for a photosynthetic system this becomes much more problematic.
In particular, the chemical analytical methods are often quite indirect, such that significant variations can exist.
For Botryococcus in particular, there are gravimetric methods (extract and weight difference) and direct chemical methods (extract and GC-MS, etc):
Gravimetric will over-estimate, chemical analytics will tyically underestimate unless there is a good internal standard correction.

Let me hit the high-level CONCEPT. Traditional CHE, be very ‘cut and dried’ aA → bB + cC Productivity d[B]/dt The chemical analytics are non ambigious moles, mass … time is usually defined in terms of a rate (if continuous) … so F*[B]/{reactor volume} = mass B produced / reactor volume / time

In biological systems, this can get pretty messy very quickly. We are talking about products that are often not even a ‘single thing’ … like … ‘biological oils’ so that chemical analytics can give very different results. Time becomes ‘confusing’ depending on the bioreactor operational mode … batch, continuous …. And in the case of algae readings, the rate becomes a component of a dynamic property of light throughout the day. My hope was to ‘shake up’ a bit your conception of the simplicity of even the most basic aspects of Chemical Engineering, which really do not change, they can just be hidden.

Above, the expression reactions boils down to stoichiometry; highly defined. The basic stoichiometry of a bioprocess is ‘ambiguous’ ….. CO2 + Nitrogen form → Biomass + H2O + water Note we will talk more later about this, but the water of the reaction is ‘lost’ (not measurable) in the surrounding media. As a result, you have to get used to being very pragmatic in redefining your thinking. I will do this below for the producivity quiz analysis.

BATCH VOLUMETRIC PRODUCTIVITY (g-oil/ L / day) I find that chaninging the UNITS to much more clearly defined information is very helpful. (average g of oil produced during the 10 day interval / volume of media in the reactor / 10 day interval)

Mass balance: (Yf*oilXf*Vf)} - {(Yo,oil*Xo*Vo) = mass of oil produced during the interval of 10 days. Productivity = ((Yf*oilXf*Vf) - (Yo,oil*Xo*Vo)} /(Vreactor)/ 10 days Note that volume is constant and Vo=Vf=Vreactor ; Yo = Yf … composition stays constant This reduces to Y*(Xf - Xo)/10 g-oil/L/day

Instantaneous oil mass production = d/dt{YX} = Y{dX/dt} ; obtained from the slope of the curve at 10 days

Continuous is harder, but remember, WHEN IN DOUBT, START WITH MASS BALANCE. Productivity = stuff coming out of reactor = F*YX / volume reactor ; F/V = dilution rate Cell mass balance accum = in - out +generation // 0= F/V(X) -(mu)X ; F/V = D = dilution rate Productivity = D*Y*Xss ; Y and Xss are given, only need to estimate dilution rate which is based on doublign time. dX/dt = (mu-max)X ; dX/X = (mu-max)dt ; ln(X/Xo) = mu-max * t Mu-max = ln(2) / d.t. Doubling X=2Xo Many got close to this … as note that ln(2) = 0.693 where many simply used units to assume 1/d.t. = 2D

I would like to get feedback from the collective class if these CONCEPTS and my attempt to bring them to actually applied meaning is something you now understand, or requires another iteration.

### Volumetric Productivity

### Specific Productivity

## Papers that have Batch Time Course Data

Rao AR, Dayananda C, Sarada R, Shamala TR, Ravishankar GA. 2007. Effect of salinity on growth of green alga Botryococcus braunii and its constituents. Bioresour. Technol. 98:560–4. https://doi.org/10.1016/j.biortech.2006.02.007 (http://www.ncbi.nlm.nih.gov/pubmed/16782327.)

Analysis is provided at [ THIS LINK ; https://drive.google.com/file/d/0B-MhYeI9HbLGMGZ0b2Qzb0ZTRnc/view?usp=sharing ]

Kojima E, Zhang K. 1999. Growth and hydrocarbon production of microalga Botryococcus braunii in bubble column photobioreactors. J. Biosci. Bioeng. 87:811–5. http://www.ncbi.nlm.nih.gov/pubmed/16232559.