A new approach for calculating microalgae culture growth based on an inhibitory effect of the surrounding biomass

Ever since the potential of algae in biotechnology was recognized, models describing the growth of algae inside photobioreactors have been proposed. These models are the basis for the optimization of process conditions and reactor designs. Over the last few decades, models became more and more elaborate with the increase of computational capacity. Thus far, these models have been based on light attenuation due to the absorption and scattering effects of the biomass. This manuscript presents a new way of predicting the apparent growth inside photobioreactors using simple models for enzymatic kinetics to describe the reaction between photons and the photosynthetic unit. The proposed model utilizes an inhibition kinetic formula based on the surrounding biomass to describe the average growth rate of a culture, which is determined by the local light intensities inside the reactor. The result is a mixed-inhibition scheme with multiple inhibition sites. The parameters of the new kinetic equation are replaced by empirical regression functions to correlate their dependency on incident light intensity and reactor size. The calibrations of the parameters and the regression functions are based on the numerical solutions of the growth rate computed with a classical Type II model. As a final verification, we apply the new equation in predicting the growth behavior of three phototrophic organisms in reactors of three different sizes.

ANALISIS KESTABILAN DAN KENDALI OPTIMAL PADA MODEL DINAMIKA MODULASI ENERGI CAHAYA DALAM FOTOSINTESIS ALGA

Penelitian tentang alga sebagai sumber energi alternatif masih terus dikembangkan. Model dinamika modulasi energi cahaya dalam fotosintesis alga merupakan salah satu model pertumbuhan alga yang mempertimbangkan pengaruh intensitas cahaya terhadap produktivitas Photosynthetic Unit (PSU). Budidaya alga memerlukan biaya dan perawatan, sehingga diperlukan pengendalian agar diperoleh hasil budidaya yang optimal. Dalam penelitian ini dilakukan pengendalian intensitas cahaya terhadap model. Kemudian dianalisa kestabilan dari titik kesetimbangan model, serta keterkontrolan dan keteramatan model. Prinsip minimum Pontryagin digunakan untuk menyelesaikan masalah kendali optimal pada model. Selanjutnya dilakukan simulasi numerik dengan DOTcvpSB. Hasil analisa menunjukkan bahwa titik kesetimbangan model bersifat stabil bersyarat, dan model bersifat terkontrol serta teramati. Hasil simulasi numerik menunjukkan bahwa model dengan pengendalian intensitas cahaya menghasilkan PSU dalam keadaan tidak aktif yang lebih sedikit dan membutuhkan energi yang lebih rendah daripada model tanpa pengendalian. Kata Kunci: alga, analisis kestabilan, kendali optimal, prinsip minimum Pontryagin, Photosynthetic Unit (PSU).