The Temperature Response of Compact Tubular Microalgae Photobioreactors

Abstract

A mathematical and computational modeling of a photobioreactor for the determination of the transient temperature behavior in compact tubular microalgae photobioreactors is presented. The model combines theoretical concepts of thermodynamics with classical theoretical and empirical correlations of Fluid Mechanics and Heat Transfer. The physical domain is discretized with the Volume Element Model (VEM) through which the physical system (reactor pipes) is divided into lumped volumes, such that only one time dependent ordinary differential equation, ODE, results for temperature, based on the first law of thermodynamics. The energetic interactions between the volumes are established through heat transfer empirical correlations for convection, conduction and radiation. Within this context, the main goal of this study is to present a numerical methodology to calculate the mixture (algae + water + nutrients) temperature inside the compact photobioreactor. A pilot plant is under construction, in the Center of Research and Development for Self-Sustainable Energy (NPDEAS), located at UFPR, and the experimental data obtained from this research unit will be used to validate the present numerical solution. Temperature is one of the most important parameters to be controlled in microalgae growth. Microalgae that are cultivated outside their growth temperature range may have a low growth rate or die. For this reason a numerical simulation of the system based on the operating conditions and environmental factors is desirable, in order to predict the transient algae growth temperature distribution along the reactor pipes. The VEM creates an “artificial” spatial dependence in the system or process under analysis by dividing the space (physical domain) into smaller sub domains, namely Volume Elements (VE). Each VE interacts with its neighbors by exchanging energy and/or mass. Thus, each VE is treated as a control volume from classical thermodynamics, i.e., with uniform properties and exchanging mass and energy with its neighbors. The problem is then formulated with the energy equation applied to the fluid VE and to the wall VE. These equations form a system of time dependent ODE’s, which are not dependent on space, therefore eliminating the need for the solution of a system of partial differential equations, PDE’s, depend on time and space, as is the case of traditional numerical methods (e.g., finite element, finite volume and finite differences). The resulting ODE’s were solved using a fourth order Runge-Kutta method with adaptive time step.