Predicting microalgae growth
Ward Blankena,⁎ , P. Richard Postmaa , Lenneke deWintera , René H.Wijffelsa,b , Marcel Janssena,⁎

a Bioprocess Engineering, AlgaePARC, Wageningen University, PO Box 16, 6700 AA, Wageningen, The Netherlands1
bFaculty of Biosciences and Aquaculture, University of Nordland, N-8049 Bodø, Norway
Corresponding authors. E-mail addresses: (W. Blanken), (M. Janssen).

"Please note that this page is a prototype. Its purpose is to demonstrate the concept of an interactive publication.
Henceforth it is incomplete. Only the section "2. Theory" has been partially developed."

Article Info

Algal Research, Elsevier
Journal homepage: Algal Research 14 (2016) 28–38
DOI: doi:10.1016/j.algal.2015.12.020

Article history:
Received 30 August 2015
Received in revised form 22 December 2015
Accepted 31 December 2015
Available online 8 January 2016:


A generally applicable kineticmodel is presented to predict light limited microalgal growth. This model combines a mathematical description for photoautotrophic sugar production with a description for aerobic chemoheterotrophic biomass growth. The model is based on five parameters which are directly measurable but were obtained from literature for the purpose of this study. The model was validated for Chlorella sorokiniana with 52 experiments derived from eight publications and for Chlamydomonas reinhardtii with 32 experiments derived from seven publications. The specific growth rate was initially predicted with a mean absolute percent error (MAPE) of 34–36%. The low accuracy is most likely caused by simplifications in the lightmodel and inaccurate parameter estimations. When optimizing the light model per experimental dataset, a 1–2% MAPE was obtained. When optimizing input parameters separately from the light model, a 2–18% MAPE was realized. After validating this model on batch data, we conclude that this model is a reliable engineering tool to predict growth in photobioreactors provided the light field is accurately measured or calculated.
© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (

Keywords: Photosynthesis, Microalgae, Light limited, Growth model, Productivity prediction

1. Introduction

Please note that this page is a prototype. It's purpose is to demonstrate the concept of an interactive publication.
Henceforth it is incomplete. Only the section "2. Theory" has been partially developed.

2. Theory

All of the sugar that is used for aerobic chemoheterotrophic biomass growth is produced by photoautotrophic sugar production. In our model, the photoautotrophic sugar production is represented by coupling photosynthesis and the . Hereby, it is assumed that all energy generated in the form of and NADPH during photosynthesis is used in the Calvin–Benson cycle to incorporate CO2 into triose sugars.

White Board

Calvin-Benson cycle

ATP = Adenosine Tri-Phosphate

The rate of photoautotrophic sugar production is dependent on light intensity (Eq. (1)). This equation is equivalent to the model of Jassby and Plattwhich is based on a hyperbolic tangent function [7]. The original equation proposed by Jassby and Platt has been rewritten to make sugar as the end product of photosynthesis (Eq. (4)). In Eq. (1), the parameter alpha (α) describes the initial slope of the curve which levels off to the maximal specific sugar production (qs,m). Please note that α can also be expressed as the product of the sugar yield on photons and the specific light absorption coefficient (Eq. (2)) which is in accordance with the approach of Geider [16]. Eq. (3) depicts the relation to calculate the specific photon absorption rate based on the light intensity and the specific light absorption coefficient. By incorporating Eqs. (2) and (3) into Eq. (1), the sugar production rate (Eq. (4)) becomes a function of the maximal specific sugar production (qs,m), the specific photon absorption rate (qph), and the sugar yield on photons (Ys/ph) which are process parameters or measurable characteristics of the microalgae. Variable qph thus replaces Iph in the Jassby & Platt model, and this is practical for the integration of the light model within the growth model, which will be discussed later.

qs= sugar rate in mol (cmol s)−1
qs,m= maximal specific sugar production (cmol s)−1
α(alpha) = initial slope of PI curve / product of the sugar yield on photons / specific light absorption coefficient
Iph= light in mol-photon (m2 s)−1
PI = photosynthetic irradiance




The sugar produced in the light reaction is exploited as a fundament for newbiomass and is oxidized in the mitochondria to obtain extra energy that is necessary to support growth related processes and cell maintenance. This partitioning of sugar between anabolic and catabolic reactions can be described using Pirt's Law (Eq. (5)) [8] which states that a small amount of substrate (sugar) is continuously consumed for maintenance (ms). The remaining sugar is available for growth (μ) resulting in new biomass according to a constant biomass yield on sugar (Yx/s), which indirectly implies that a fixed amount of sugar is respired per carbon mol-x (cmol-x) produced. The validity of adopting Pirt's description for partitioning of photosynthetically derived energy has been established for several microalgae species [17,18]. Please note that the specific sugar production rate (qs) in Eq. (5) is predicted employing Eq. (4). To summarize, a typical photosynthesismodel is combined with the classical aerobic chemoheterotrophic growth model of Pirt to predict the specific growth rate of microalgae (Eq. (5)).

White board

Light attenuation within a microalgae suspension in flat plate photobioreactors is described based on the Lambert–Beer Law which states that the attenuation of light over distance is proportional to the light intensity itself with the proportionality constant being the volumetric absorption coefficient. The latter is the product of the specific light absorption coefficient (ax) and the biomass concentration (Cx).

White Board

3. Computational Method

4. Results and Discussion


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