Department of Chemical Engineering, University of Almería, E-04071 Almería, Spain.
Biotechnol Bioeng. 1997 Sep 5;55(5):701-14. doi: 10.1002/(SICI)1097-0290(19970905)55:5<701::AID-BIT1>3.0.CO;2-F.
A mathematical model to estimate the solar irradiance profile and average light intensity inside a tubular photobioreactor under outdoor conditions is proposed, requiring only geographic, geometric, and solar position parameters. First, the length of the path into the culture traveled by any direct or disperse ray of light was calculated as the function of three variables: day of year, solar hour, and geographic latitude. Then, the phenomenon of light attenuation by biomass was studied considering Lambert-Beer's law (only considering absorption) and the monodimensional model of Cornet et al. (1900) (considering absorption and scattering phenomena). Due to the existence of differential wavelength absorption, none of the literature models are useful for explaining light attenuation by the biomass. Therefore, an empirical hyperbolic expression is proposed. The equations to calculate light path length were substituted in the proposed hyperbolic expression, reproducing light intensity data obtained in the center of the loop tubes. The proposed model was also likely to estimate the irradiance accurately at any point inside the culture. Calculation of the local intensity was thus extended to the full culture volume in order to obtain the average irradiance, showing how the higher biomass productivities in a Phaeodactylum tricornutum UTEX 640 outdoor chemostat culture could be maintained by delaying light limitation. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 701-714, 1997.
提出了一种数学模型，用于估算管状光生物反应器在户外条件下的太阳辐照度分布和平均光强，该模型仅需要地理、几何和太阳位置参数。首先，计算任何直射或散射光线进入培养物的路径长度作为三个变量的函数：一年中的天数、太阳小时和地理纬度。然后，考虑 Lambert-Beer 定律（仅考虑吸收）和 Cornet 等人的一维模型（考虑吸收和散射现象）研究了生物质的光衰减现象。由于存在波长吸收的差异，文献中的任何模型都不能用于解释生物质的光衰减。因此，提出了一个经验双曲线表达式。在提出的双曲线表达式中，用计算光程长度的方程代替，再现了在环管中心获得的光强数据。该模型还可以准确估计培养物内部任何点的辐照度。因此，将局部强度的计算扩展到整个培养物体积，以获得平均辐照度，从而表明如何通过延迟光限制来维持三角褐指藻 UTEX 640 户外恒化器培养物中更高的生物量生产力。（c）1997 年 John Wiley & Sons，Inc. 生物技术与生物工程 55：701-714，1997。
