## 1 Introduction
This work focuses on the dynamic modeling of a Slurry Bubble Column Reactor for Fischer Tropsch synthesis in pilot plant scale under variable loads of synthesis gas. This transient calculation is performed in once-through conditions under a cobalt-supported catalyst to identify _the effect of load change conditions_ on FT selectivity, CO conversion, the alpha value and temperature distribution of the slurry reactor in the Winddiesel Technology. Winddiesel technology developed by the Technical University of Vienna has already been tested at an FT demonstration plant based on synthesis gas from biomass steam gasification and steam electrolysis in cases of availability of renewable energy [11; 12]. In the modeling of the Fischer-Tropsch Slurry Bubble Column reactor (FT-SBCR) in lab-scale, a set of appropriate hydrodynamic parameters is incorporated into coupled FT kinetics and mass transfer through MATLAB code. This new approach enables us to analyze the behavior of _all species_ through the length of the reactor from start-up to steady state condition. Moreover, in this dynamic modeling, change in the superficial gas velocity due to chemical reaction is coupled to the set of PDEs using _the overall species transport equations_. This approach estimates the reliable calculation of the gradient of gas flow rate for bubbles which proposes a realistic prediction of the reactor performance [13]. However, the majority of slurry reactors models for superficial gas velocity within the reactor linearize the gas velocity with syngas conversion [14; 15; 16]. In dynamic modeling SBCR for FT process, a number of methodologies based on several well-developed hydrodynamic concepts such as the Axial dispersion model (ADM), Single bubble class (SBC), two bubble class (TBC), etc. with different FT kinetics have been proposed. In 2002, [PERSON] and [PERSON] [14] developed a model to predict the steady state and dynamic behavior of a bubble column slurry reactor for Fischer Tropsch synthesis. Their numerical procedure was based on four partial differential equations solved using Method Of Lines (MOL). The results indicated that steady-state is achieved within about seven minutes from start-up and no thermal runways were observed in a reactor of commercial scale. Furthermore, the influence of the back-mixing of the liquid phase on hydrogen conversion for two different reactor diameters (1, 7.5 m) was compared. It was concluded that at 1 m diameter the axial dispersion coefficient decreased, leading to a flatter velocity profile in the liquid phase, which in turn results in higher conversions of hydrogen [14]. In 2005, [PERSON] et al. [13] simulated an FT-SBCR with two chemical reaction systems. They analyzed the hydrodynamic behavior of two bubble class models by assuming linear first-order reaction kinetics. They also considered the influence of the Axial Dispersion Model (ADM) on conversion and reactor diameter and compared this effect in ideal reactors i.e., plug flow (PF) and completely stirred tank (CST) [13]. In 2009, [PERSON] et al. [15] developed a dynamic slurry FT for both single and double bubble class at churn turbulent flow regime. They concluded that there is no discrepancy between single and double class models in terms of concentration, temperature and conversion profile. Thus, they considered the single bubble class as a less complex reliable model to analyze the slurry bubble column reactors [15]. In 2008, [PERSON] [17] et al. developed a computer model for a large-scale FT slurry reactor. The simulator was used to optimize superficial gas velocity and reactor geometry for producing 10,000 (barrels/day) of liquid fuels. Different operating conditions were also used to find the maximum space time yield (STY). However, the condition for maximum productivity was considered as the optimum operating condition because of lower operating and capital cost [17].