A mathematical model was developed based on data obtained on Fischer-Tropsch (FT) laboratory scale unit operated in steady state, belonging to BIOENERGY 2020+ GmbH, Austria to demonstrate alpha-parameter dependence on carbon number. The lab-scale unit processed the synthesis gas, obtained by the gasification of biomass (woodchips), to produce liquid fuels for transportation applications. The FT reaction took place in a slurry reactor filled with dispersed cobalt-based catalyst. The products were then separated by partial condensation depending on their boiling points. The final output of the FT laboratory scale unit comprised three product streams - wax, diesel and naphtha. The reaction and separation of products were simulated in Aspen Plus software. The mathematical model used kinetic description based on power-law rate equations. The modeled product selectivity was controlled using an alpha-parameter of the Anderson-Schulz-Flory distribution. Because of the significant deviation of products spectrum from typical Anderson-Schulz-Flory distribution, a modified description of reaction selectivity was developed. The description introduces variable alpha-parameter, dependent on number of carbon atoms in the reacting molecule. The mathematical model developed using MATLAB software considered the production of aliphatic paraffins having a number of carbon atoms from C1 to C60. The mathematical model of simulated lab-scale unit comprised an ideally mixed reactor RCSTR and three FLASH2 separators for the separation of desired products. The results from mathematical model were validated by a comparison with experimental results from FT lab-scale unit. The modified polynomial dependency of alpha-parameter on carbon number showed significantly better description of composition and amounts of FT products, especially for wax stream where the description using constant alpha led to enormous deviations. Such better prediction of composition and amounts of acquired products is important for evaluating efficiency of further upgrading the FT products to liquid fuel.