A dynamic mathematical model is developed to estimate microalgae growth in medium- and large-scale compact tubular photobioreactors (PBRs). Besides cell and other chemical species concentrations, temperature and local solar irradiation are important variables to be assessed. Three different experiments were conducted to adjust and validate the mathematical model for which a methodology based on the coefficient of determination is introduced. The first experiment was performed in a 100L prototype PBR, the second in a column 78.5L air-lift PBR, and the third in a 12,000L compact tubular PBR. Initially, cell growth numerical simulation curves were directly compared with data from the first experiment, which resulted in a coefficient of determination R-2=0.4043, showing that model adjustment was needed. As a result, 3 adjustment parameters were defined: (i) local solar irradiation ((1)); (ii) medium CO2 concentration ((2)); and (iii) nutrient concentration ((3)). Then, the first experiment data set was used to solve an inverse problem of parameter estimation, obtaining (1)=1.05, (2)=0.95, and (3)=0.18, which resulted in R-2=0.98584. Next, cell growth numerical simulation curves were compared with measured data from the second and third experiments, obtaining R-2=0.9862 and R-2=0.82969, respectively. With the experimentally validated model, a 29day (or 696hours) simulation of microalgae cultivation was conducted to calculate the 12,000L PBR microalgae-derived oil production, which allowed for the projection of the microalgae species Acutodesmus obliquus oil productivity as approximately 2300Lha(-1)yr(-1), considering 11.4% microalgae dry biomass lipid content. Such low production demonstrates that achieving an economically viable process for microalgae-derived biofuels will require more technological advances and the development of highly optimized processes.