Mathematical Modeling of a Trickle Bed Bio-desulfurizer of Hydrotreated Diesel for the Production of ULSD (Ultra-low Sulfur Diesel)

M. Mukhopadhyay, R. Chowdhury* and P. Bhattacharya

Chemical Engineering Department, Jadavpur University

Kolkata-700032

India

*Author to whom correspondence may be addressed.

Abstract

Biodesulfurization has been chosen as a complementary second stage desulfurization of hydrodesulfurized diesel to produce near zero sulfur (NZS) diesel (15 ppm sulfur). For such desulfurization, batch studies have been conducted in Erlenmeyer flasks maintaining the concentration of diesel in the range of 0-100% in a diesel supplemented sulfur free aqueous medium. Hydrodesulfurized diesel samples (purchased from Indian Oil Corporation, Kolkata) have the specifications represented in the table1.

Table1:Characteristics of diesel samples used:

Compound	I.B.P.	F.B.P.	Sp. Gravity (Basis:density of water=1000 kg/m3)	Sulfur	Aromatic
Diesel	140 oC	370 oC	0.8216	200 to 540 ppm	27.16 %(w/w)

The concentration of biomass with time has been monitored using dry cell weight method. The concentration of sulfur has been determined by “Trace Sulfur in petroleum distillate by Nickel reduction” (UOP 357-80) method and X-ray fluorescence (XRF) (ASTM-D4294-03) method. From the growth curve it is observed that the system follows uninhibited Monod type model within the range of substrate concentration studied. The intrinsic kinetic parameters, namely, maximum specific growth rate, saturation constant Ks and yield coefficient Y_A/B have been determined by a systematic and programmed investigation and are represented in the following table.

Table2: Value of the intrinsic kinetic parameters:

Saturation constant, Ks (mg/dm3)	Maximum specific growth Rate, (hr -1)	Yield coefficient, YA/B
71	0.0961	0.2

Based on the knowledge gained from the batch fermentative process, experiments have been conducted in a trickle bed reactor, using the same microbial strain immobilized on a solid matrix to understand the reaction engineering behavior of sulfur removal from diesel oil in continuous mode of operation. Biodesulfurization of diesel oil has been conducted in a trickle bed reactor having a diameter of 0.066 m and a height of 0.6 m. Initial substrate concentration, liquid hourly space velocity (LHSV) and recycle ratio have been chosen as process parameters. Hydrotreated diesel fraction having different sulfur concentration, namely, 200, 330, 430, 540ppm has been taken as feed stock for degradation of residual organo-sulfur compounds present in deeply hydrodesulfurized diesel using Rhodococcus sp.(no. 2891 NCIM, Pune).The microorganisms have been immobilized on the packing material, namely pith balls (dia0.012m) prior to desulfurization within the trickle bed reactor (TBR). Bacterial medium containing Rhodococcus sp. having the biomass concentration of 20g/dm³ has been circulated through the packed bed until the bio-film thickness on the sphere becomes 0.1mm. Initial bed porosity has been determined to be 0.6. LHSV has been varied in the range of 1.838 and 3.676 hr^-1.Since, the biodegradation has been carried out with the aid of aerobic bacterial strain, the reactor is continuously sparged with air at 480dm³/hr in the upward direction. The reactor is run under atmospheric pressure. The substrate loading in the reactor has been determined to be initially 1.46X10^-4 kg/m³/hr for initial substrate concentration of 200 ppm at lowest inlet flow rate of  25 dm³/hr and is varied up to 7.84X10^-3 kg/m³/hr for 540 ppm of initial substrate concentration in diesel at 0.5 dm³/hr inlet diesel flow rate. Within the range of process parameter variation, substrate degradation profile with the change in LHSV and recycle ratio have been observed. Under the present process condition, sulfur reduction within the range of 84-98% has been achieved.  It has been found that with the decrease in initial substrate concentration, better substrate degradation efficiency is achieved. Moreover, the substrate concentration decreases with the axial length of the trickle bed reactor. Better removal efficiency results with the increase in recycle ratio and lowering of LHSV. The value of sulfur concentration in the reactor exit stream increases i.e. the ultimate sulfur conversion decreases with the increase in the LHSV. At the lowest LHSV of 1.838hr^-1, the sulfur removal efficiency of 95 % has been achieved. Similarly, the value of sulfur removal efficiency corresponding to the LHSV of 3.767 hr^-1 is 77.8 %. This is, however, expected as the increase in LHSV implies the decrease in reactor residence time causing drop in the ultimate conversion of the reactant.  The reduction in sulfur concentration increases as the recycle ratio increases. At recycle ratio of 0.25 with lowest LHSV of 1.838 hr^-1 sulfur removal efficiency is 95%. Again at recycle ratio of 2 with the same LHSV the result shows 96.4% sulfur removal efficiency. This can be easily realized because the higher the recycle ratio the more is the scope for the substrate to come in contact with the immobilized microorganisms. Therefore, the chance of substrate degradation reaction is more. A deterministic mathematical model for the TBR has been developed using judicious assumptions to predict its performance characteristics. The system equations based on differential mass balance for organo-sulfur compounds of diesel & biomass used in the mathematical model are as follows,

     (1)

Where A_L= 2∏(d/2+L_f).L_f                                                                                                                    (2) The equation for the variation of biofilm thickness due to bacterial growth on the

surface of the packing material is,

                                               (3)

The variation of bed porosity within the reactor is represented by,

                             (4)

The boundary conditions are as follows,

For t, Z=0,

 C_A= C_A0, C_B  = C_B0, L_f = L_f0

For t>0, Z = 0,

C_A= C_A0,  C_B  =

Where,

A           Cross-sectional area of the reactor (m);

A_L          Bio-film area loss per unit packing sphere in contact (m);

C_A0        Initial biomass concentration (mg/dm³);

C_A         Biomass concentration at a particular time (mg/dm³);

C_Af             Final biomass concentration at the reactor outlet (mg/dm³);

C_B0             Initial substrate concentration (mg/dm³);

C_B             Substrate concentration at a particular time (mg/dm³);

C_Bnew      New inlet substrate concentration at a particular time during recycle (mg/dm³);

C_Bout       Final substrate concentration at the reactor outlet (mg/dm³);

F_A          Volumetric flow rate of the liquid stream (dm³/hr);

Ks          Saturation constant;

L            Length of the reactor (m);

L_f            Bio-film thickness over each packing material (m);

N          Number of Pressure drop;

D           Diameter of each packing sphere (pith ball) (m);

R           Recycle ratio;

V           Volume of the TBR (m³);

V_L          Bio-film volume loss per unit packing sphere in contact (m³);

Y_A/_B       Yield coefficient = Mass of biomass produced /mass of substrate consumed;

Z            Axial position within the reactor;

Greek letters:

         Maximum specific growth rate of biomass;

 ₀            Initial bed porosity;

 _f                 Porosity in bed with bio-film; Abbreviations:

I.B.P.       Initial Boiling Point;

F.B.P.      Final Boiling Point;

LHSV      Liquid hourly space velocity = volumetric feed flow rate / catalyst bed volume; The equations have been solved by 4^th order Runge-Kutta technique using a suitable C-program. The simulated data obtained were represented graphically and the corresponding experimental values have been superimposed on the same plot. From the comparison of the simulated and experimental data it is evident that the mathematical model can explain the reality satisfactorily. Key words: Bio-desulfurization, diesel, uninhibited Monod model, intrinsic kinetic parameters, immobilized, trickle bed reactor.