Mathematical models have been widely used to simulate all aspects of bioenergy production systems including the growth kinetics of energy crops, conversion processes, production economics, supply logistics and environmental impacts. There is limited commercial experience to produce and process energy crops at a large scale around the world. Those models can provide powerful tools to design a bioenergy system and evaluate its technical feasibility, economics and environmental impacts. A crop growth model can be used to estimate the yields of energy crops in a region under different growth conditions. A geographical information system (GIS) model can be used to maximize the energy production of energy crops by indentifying suitable land to grow them based on their specific characteristics and the current use of the land. A combination of process models and reaction kinetics provides advanced computational tools for the design

A regression model was developed to determine the growth rate of C.vulgaris that is affected by the environmental factors of temperature, light intensity and pH value. The optimum environmental condition for growing C.vulgaris was experimentally determined at light intensity of 240 µEm −2 s −1 , 24 • C and pH of 7.4. At the optimum environmental condition, the growth rate of C.vulgaris in swine wastewater with 102 mg N/l and 76 mg P/l was 0.160 g/l/day, compared to 0.191 g/l/day for its growth on a modified Bold's medium with 100 mg N/l and 53 mg P/l. The regression model was further integrated with a light and heat transfer model to estimate the biomass productivity of C.vulgaris grown on the swine wastewater in an open raceway pond

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A spectral radiation-transport model was integrated with a three dimensional computational fluid dynamics model to simulate the hydrodynamics and light transfer in open raceway ponds (ORPs). The predicted threedimensional velocity and light intensity agreed well with measured values collected on a lab-scale ORP. However, there was a slight difference in the predicted velocity profiles using two different types of boundaries for the paddlewheel, i.e., the moving zone boundary and inlet velocity boundary, with R 2 values between the predicted and measured velocities of 0.

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