Using hypothesis testing on the mass-transfer effect with sulfate removal as an application

Sulfate and chemical oxygen demand removal by an anaerobic batch reactor treating of acid mine drainage is modelled. Available models are abundant but excessively complex, with large numbers of free parameters. Here, maximum likelihood and chi-squared hypothesis tests are applied to three simple models, with Malthus-Monod and Fick description, in increasing order of complexity: (i) planktonic single population (of sulfate-reducing bacteria); (ii) planktonic double-competing populations (adding fermentative bacteria); (iii) granule bound double-competing populations. The data set consists of 6 time profiles, sampled from 120 days of operation after stabilization of the reactor in pH 4. Single population is refuted by all profiles, in which the sulfate reduction is $$ larger than fermentatives. The planktonic double-competing population description is refuted at 119 days, with inner granule diffusion rate as low as $$ of the previous period. The results showed that, after an operation time, the influence of mass transfer became more evident and the incorporation of Fick's law in the model was fundamental to the description of this trend. All tests and inferences are performed at the $$ confidence interval due to large systematic uncertainties in the data.