Modeling and Simulation of Oil Sludge Pyrolysis in a Rotary Kiln with a

Aug 28, 2014 - ABSTRACT: In this study, a dynamic model of oil sludge pyrolysis in a rotary kiln with a solid heat carrier was developed. In the propo...
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Modeling and Simulation of Oil Sludge Pyrolysis in a Rotary Kiln with a Solid Heat Carrier: Considering the Particle Motion and Reaction Kinetics Zhengzhao Ma, Ningbo Gao, Lei Zhang, and Aimin Li* Key Laboratory of Industrial Ecology and Environmental Engineering (Ministry of Education), School of Environmental Science and Technology, Dalian University of Technology, Dalian, Liaoning 116024, People’s Republic of China S Supporting Information *

ABSTRACT: In this study, a dynamic model of oil sludge pyrolysis in a rotary kiln with a solid heat carrier was developed. In the proposed model, both the particle motion in the rolling mode and oil sludge pyrolysis were taken into consideration. Saeman’s model and a multiple-reaction model were involved to simulate the bed depth profile inside the rotary kiln based on the solid motion and the volatile evolution, respectively. Furthermore, the temperature profiles of three phases (solid carrier, oil sludge, and gaseous phase) in diverse conditions were predicated by combining pyrolysis kinetics, heat transfer, and motion equations. In the proposed model, the yields of CxHy, H2, CO, and CO2 were successfully stimulated and predicted. The validity of the model was verified from both aspects of solid axial velocity and gas yields by comparing numerical values to literature reports and experimental data, respectively. This simulation practice was expected to provide an alternative approach to obtain helpful parameters for the designing of an industry-scale rotary kiln pyrolyzer. by a solid heat carrier in a moving bed had been developed,8 the thermal part of the simulation process in rotary kilns is rarely reported. With respect to chemistry reaction simulation, numerical work is generally represented by the kinetics of the solid thermal decomposition reaction and the dynamics of the secondary decomposition reaction of volatiles in thermal analysis and fixed-bed reactor. The Flynn−Wall−Ozawa (FWO) and Kissinger−Akahira−Sunose (KAS) iso-conversional methods were used to evaluate the dependency of the activation energy upon the degree of conversion in the cocombustion of sewage sludge with straw and coal.9 The evaluation of the oil sludge pyrolysis process in fixed beds were carried out by Liu et al., and a model-free isoconversion approach was employed to investigate CxHy kinetics.10 However, few researchers investigated pyrolysis kinetics together with solid motion based on the heat transfer, which leaves vacancy for this research. In all, in this study, three aspects concerning particle motion, pyrolysis kinetics, and heat transfer are involved in the new developed model, in which the solid motion and product evolution are simulated on the basis of Seaman’s model and a multiple-reaction model, respectively. One breakthrough of this study is that, in the model, the temperature distribution profiles of oil sludge, solid heat carrier, and volatile matters and the yields of CxHy, H2, CO, and CO2 are predicted with crosscoupling and interacting effects being considered under heattransfer theory, which is hardly studied by former researchers. This innovation is successfully testified because the simulated and predicted results were verified by experimental data and literature reports.

1. INTRODUCTION Oil sludge is oily and viscous residues generated in the process of oilfield exploration, transportation, and refining, which is composed of petroleum hydrocarbons, water, solid minerals, etc. Because it is a hazardous material, the inappropriate disposal of oil sludge may cause negative effects on the environment and human health; thus, pyrolysis, an important thermochemical technology, is used in dealing with oil sludge because it has been proven to be a promising method to treat the oil sludge with energy recovery.1 In particular, pyrolysis of oil sludge in a rotary kiln with the solid heat carrier could offer unique advantages compared to other types of reactors. For instance, the slow rotation speed of a rotary kiln enables a better mix of oil sludge, and the residence time of oil sludge in the rotary kiln can be easily controlled to provide optimum heat transfer for the pyrolysis reaction.2 It is more convenient to apply numerical simulation to predict the pyrolysis process compared to doing experiments in terms of the time and expenditure saved. The solid motion in a rotary kiln, including transverse mixing and axial transport, has been widely investigated.3−5 Most of the previous studies were established on the basis of Saemen’s model, whose exact analytical solution of the bed depth profile in the rotary kiln had been found.5,6 However, these studies only focused on the solid-phase motion and solid flow rate inside the rotary kiln. To understand thermochemical phenomena in a rotary kiln better, a dynamic model of pyrolysis should also be considered. Three parts, a solid-phase motion, a thermal part, and a chemistry part,7 composed a global dynamic model. In terms of the solid-phase motion, as mentioned above, Saeman’s model was available. With regard to heat transfer, there were three types of heat transfer, including conductive, convective, and radiant transfer, which generally should be given attention to inside the kiln. Although the numerical model of coal pyrolysis © 2014 American Chemical Society

Received: June 4, 2014 Revised: August 28, 2014 Published: August 28, 2014 6029

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collected gas was analyzed by gas chromatography using a HP model 5890 series II with a thermal conductivity detector, and a packed column was used. The gas yields were calculated by the measured volume and mole mass of mixed gaseous products. All experiments were conducted at least 2 times.

2. EXPERIMENTAL SECTION 2.1. Materials. The oil sludge in this study was obtained from Shengli Oil Field, China. In appearance, the received sample was a black and viscous slurry. The samples were first filtered by an airsuction filter to remove the water and were dried at 105 °C in an oven for 48 h prior to the tests. After drying, the viscosity of the sludge decreased and the sludge became a coal-like sample. The dried sludge was used as the pyrolysis samples to measure the particle size of the samples easily and to be fed to the reactor conveniently. The quartz sand was used as the solid heat carrier, which had a large heat capacity and high heating rate. The physical properties of the oil sludge and quartz sand are given in Table 1. The angle of repose was directly measured inside the kiln in the rolling mode. The results of proximate and ultimate analyses of the oil sludge are listed in Table 2.

3. MODELING 3.1. Assumption. In the oil sludge pyrolysis inside the rotary kiln, the solid heat carrier and the oil sludge will be mixed at the entrance of the rotary kiln instantly. When the mixed materials moved along the axis of the kiln, the oil sludge will be heated and the pyrolysis gas will be evolved. To simulate the model numerically, several assumptions aiming at simplifying the model are made as follows: (1) It is assumed that the axial velocity only affects the material transport along the axis, because the traverse mixing velocity can be considered to be much faster than the axial mixing velocity. (2) It is believed that the rotary kiln is operated in the rolling mode under the steady-state solid flow conditions. The solid motion inside the rotary kiln mainly responses to the depth of solid bed, the rotating rate, and the material properties. The mass flow rate effects the depth of the solid bed. In the Experimental Section, the mass flow rate and rotating rate are adjusted to the suitable value to ensure the solid motion in the rolling mode. (3) The materials are presumed as spherical and homogeneous particles. The internal temperature gradient is negligible. After the oil sludge drying, the form of the sludge changes from slurry to granular materials. Therefore, in the pyrolysis process, both the quartz sand (solid heat carrier) and the dried oil sludge are the granular materials inside the rotary kiln. (4) Another assumption is that the mass of oil sludge decreases during the pyrolysis process because of thermal decomposition, while the volume of the oil sludge is considered to be a constant because of porosity of the pyrolyzed residue. It is considered that the density of the particle decreases with the thermal desorption.8 In addition, the solid heat carrier is assumed to keep steady in the pyrolysis, without any reaction with the volatiles. The parameters for the calculation and simulation of the thermal part are listed in Table 4. The information on the thermal characteristic of the oil sludge has still been very limited thus far. Some parameters in Table 4 are based on the coal and asphaltene.8,11,12 3.2. Granular Material Movement Inside the Rotary Kiln. In this analysis, the movement of the solid is described as a rolling bed in the developing model. The rolling mode is characterized by an active layer where the particles roll down continually, and then they access the passive layer where they are carried up by the rotation of the kiln to the active layer again. The dynamic model of solid transport inside the kiln is based on the geometrical model derived by Saemen6

Table 1. Physical Properties of Materials

oil sludge quartz sand

bulk density (kg/m3)

diameter (m)

dynamic angle of repose (deg)

1300−1500 1600−1800

3 × 10−3 7.6 × 10−3

30 ± 2

2.2. Experimental Apparatus. The experimental apparatus used to perform oil sludge pyrolysis is shown in Figure 1, which consisted of a feed hopper with a screw conveyor, a tubular reactor, an electric heater, an oil condenser and reservoir, a gas sampling device, and a residue receiver. The speed of the rotational kiln was selected as a variable controlling the residence time of the oil sludge in the kiln. The rotary kiln reactor was a stainless-steel cylindrical tubular reactor (1500 mm length and 386 mm inner diameter), which was placed in externalheating electrical furnaces (9 kW, 220 V, and 15 A) to provide heat for the pyrolysis reaction. Four K-type thermocouples with a diameter of 15 mm were mounted through the wall of the reactor to measure the temperatures in the reactor centerline. All experiments were carried out at atmospheric pressure. The geometrical and operational characteristics of the rotary furnace are shown in Table 3. 2.3. Experimental Method. The pyrolysis system and experimental setup are presented in Figures 1 and 2, respectively. The air in the reactor was removed by purging with nitrogen at a certain flow rate. The sand in the rotary kiln was first heated from ambient temperature to a desired temperature before the sludge samples were fed to the kiln. When the sand reached the desired temperature, the screw conveyor would be switched on, making the dried sludge fed into the reactor. The quartz sand with the particles of 7−8 mm was used as the solid heat carriers in the rotary kiln. To examine the effect of the pyrolysis temperature, the pyrolysis temperature varied from 753 to 1123 K in the mixture ratios of 1:1 (oil sludge/quartz sand). The angle of the kiln inclination can be easily adjusted between 0 and 20° by altering the height of the supporter at the kiln inlet end. The pyrolysis tests were carried out in the kiln with a capacity of 0.036 kg/s of oil sludge feeding. The feed rate of materials was adjusted to a certain amount that keeps the depth of the solids in the kiln on a desired value under the constant kiln rotating rate of 5 rpm. This is the depth of the solid bed response to the feed rate. Moreover, in each run, the angle of the kiln was kept to 5° to maintain the inlet solid motion at the rolling mode. The pryolysis products escaped from the reactor at the end of the kiln. The gas products passed through a wet flow meter to measure the volume of the gas, and then the gas were collected in the gas bag. The

3 tan γ m 2 dh tan α = ⌊r − (h − r )2 ⌋−3/2 − dz 4πn ρ cos γ

(1)

Table 2. Proximate and Ultimate Analyses of the Oil Sludge proximate analysis (wt %, wet basis)

a

ultimate analysis (wt %, daf)

ash

volatile matter

fixed carbon

moisture

C

H

N

S

Oa

HHV (MJ/kg)

53.92

29.63

1.14

15.31

23.28

3.54

0.19

1.29

2.47

14.02

By difference. 6030

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Figure 1. Schematic diagram of solid heat carrier rotary kiln system: (1) control panel, (2) nitrogen cylinder, (3) adjustable variable-speed motor, (4) feed hopper, (5) angle modulation screw stem, (6) rotameter, (7) thermocouple wire, (8) electric furnace, (9) motor, (10) residue receiver, (11) water condenser, (12) oil reservoir, (13) filer, (14) exsiccator, (15) volume flowmeter, (16) gas sampling device, and (17) draft fan.

where m is the mass flow (kg/s), ρ is the solid bulk density (kg/m3), n is the rotation speed (revolution/s), r is the internal radius of the kiln (m), α is the inclination angle (deg), and γ is the dynamic angle of repose (deg). It is a nonlinear first-ordinary differential equation, giving the bed height as a function of the axial position. The geometrical description of the material movement inside the kiln is presented in Figure 3. The bed depth at the exit of the kiln is equal to zero because of the dam absence. The average axial velocity of solid was expressed on the basis of the particle trajectory model (PTM)13

Table 3. Parameters of the Rotary Kiln Geometric Internal Structure subset rotary kiln

operating condition

parameter

order of magnitude

internal radius (m) length (m) exit dam (m) rotation speed (rpm) inclination angle (deg) mass flow rate (kg/s)

0.193 1.5 0 5 (0.0833 revolution/s) 2 0.036

⎛ tan γ ⎞ + cot α tan β ⎟ u ̅ = 2πnro cos2 β ⎜ ⎝ sin α ⎠

(2)

where ro is the radius of particle rotation (m), n is the rotation speed (m/s), and α, β, and γ are the inclination angle of the kiln, the bed slope angle, and the dynamic angle of repose (deg), respectively. It is concluded that the bed slope angle is not a constant value along the kiln axis. Through the variation of β, we can deduce the instantaneous velocity along the kiln axis. The cos2 β and tan β are obtained from the geometric analysis. cos2 β approaches 1, and tan β is just the alternative term of −dh/dz. Therefore, eq 2 can be expressed as ⎛ tan α dh ⎞ − cot γ ⎟ u(z) = 2πnro⎜ dz ⎠ ⎝ sin γ

Figure 2. Photograph of the solid heat carrier rotary kiln for oil sludge pyrolysis.

where ro is nearly equal to the kiln radius r for the rolling mode. To ensure the accuracy of ro, the correctional coefficient εt is introduced in this paper, in which the correction to the substitution of r0 by r is considered. The value of εt can be evaluated by the linear least-squares fit of experimental and theoretical data. In the previous studies, Li’s investigation showed that εt is about 1.04 when the rotary kiln was operated in the rolling mode.13 Finally, the instantaneous velocity along the kiln axis can be simplified as

Table 4. Parameters for the Calculation and Simulation of the Thermal Part

solid heat carrier

oil sludge

gas

parameter

order of magnitude

heat capacity (J kg−1 K−1) thermal conductivity (W m−1 K−1) initial temperature (K) bed porosity heat capacity (J kg−1 K−1) thermal conductivity (W m−1 K−1) initial temperature (K) reaction heat (J/kg) emissivity radiation shape factor viscosity heat capacity (J kg−1 K−1) thermal conductivity (W m−1 K−1)

795 1.226 753−1123 0.2 1674.8 0.699 298 −3.5 × 105 0.8 1 3.79 × 10−5 2156 0.2521

(3)

u(z) = 2πn

r ⎛ tan α dh ⎞ − cot γ ⎟ ⎜ 1.04 ⎝ sin γ dz ⎠

(4)

With the initial conditions, the differential equations (eqs 1 and 4) can be solved numerically. 3.3. Pyrolysis of the Oil Sludge. The pyrolysis kinetic model for oil sludge based on the Arrhenius approach of the temperature function of the reaction rate constant is expressed as 6031

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Figure 3. Geometrical description of the material (a) transverse and (b) axial movement inside the kiln.

dw = k 0 exp(E /RTo)f (w) dt

history of each experimental run to construct best fit curves for the yield data. 3.4. Heat Transfer. There are three mechanisms for heat transfer between particles, gas, and solid heat carrier inside the rotary kiln. It is assumed that the oil sludge is surrounded by a solid heat carrier. Contacting heat transfer plays an indispensable role among the solid particles. The mechanisms of the heat transfer might be (1) heat transfer from the solid heat carrier to the oil sludge, (2) heat transfer between the particle and gas, and (3) heat emission with the volatile release from the oil sludge. Besides the above main mechanisms, the heat transfer from the solid heat carrier to the oil sludge can be divided into two different parts. One is the conduction between the solid heat carrier and oil sludge, which is contributed to the temperature gradient of the contact area. Another is the radiation heat transfer between the surfaces of particles with different temperatures. For the gas phase, there are two mechanisms of the heat transfer, that is, the convection heat transfer from the solid heat carrier to the gas and from the gas to the oil sludge. 3.4.1. Heat Transfer to the Oil Sludge Particle. The heat transfers to the oil sludge can be expressed as follows:

(5)

where t is the time, To is the oil sludge temperature, w is the conversion of the reaction at any temperature, dw/dt is the rate of the reaction, f(w) is the representative of the reaction model, k0 and E, the Arrhenius parameters, are the pre-exponential factor and activation energy, respectively. The reaction model may be demonstrated in kinds of forms taking into account the nucleation and nucleus growth, phase boundary reaction, diffusion, and chemical reaction.10 In the present study, multiple independent parallel first-order reactions14 were employed to describe the evolution of volatile products (mainly including CxHy and H2) in oil sludge pyrolysis.8 Thus, the kinetic equation of the volatiles is written as dwj dt

= k 0j exp( −Ej /RTo)(wj∞ − wj)

(6)

where wj is the conversion of the reaction at any temperature for the product j, k0j and Ej, the Arrhenius parameters, are the pre-exponential factor and activation energy for the product j, wj∞ is the value of wj at the end of the reaction. To uniform the equation above, eq 6 could be modified into wj varying with z along the rotary kiln. Therefore, the equation function is obtained as follows: dwj dz

=

k 0j exp( −Ej /RTo)(wj∞ − wj) u(z)

Q oil sludge = Q s → o + Q g → o + Q rad + Q rec

(7) ∞

The parameters k0j, Ej, and wj are obtained from the experiments of oil sludge pyrolysis with a solid heat carrier by the same methods of asphaltene kinetic pyrolysis,15 which is shown in Table 5. The appearance of product j in the oil sludge

where Qoil sludge is the total heat transfer in the oil sludge (J), Qs→o is the conduction heat transfer between the solid heat carrier and the oil sludge (J), Qrad is the radiation heat transfer (J), Qg→o is the convection from the gas to the oil sludge (J) and Qrec is the oil sludge pyrolysis reaction heat (J). Then the oil sludge temperature can be calculated by the following equations during each axial position:

Table 5. Kinetic Parameters of Oil Sludge Pyrolysis in the Rotary Kiln volatile

k0j (s−1)

CH4 C2H4 C2H6 CO CO2 H2

× × × × ×

2.3 9.0 8.3 2.5 2.8 98

5

10 103 104 104 104

Ej (J/mol)

wj∞ (wt %)

120919 130944 106673 114666 104336 77103

6.05 4.12 5.40 5.14 6.18 3.16

(8)

como dTo = dQ oil sludge dz = (dQ s → o + dQ g → o + dQ rad + dQ rec)dz

(9)

where co is the heat capacity of the oil sludge (J kg−1 K−1), mo is the mass of the oil sludge (kg), and To is the temperature of the oil sludge (K). Equation 8 can be inserted in the above equation, and finally, a differential equation can be derived for the heat balance of the oil sludge pyrolysis (more details are given in the Supporting Information).

pyrolysis is modeled as a first-order reaction in the amount of j yet to be produced. Moreover, for the calculation of Ej and k0j values, the evolution of some different gas products is obtained from the previous study.16 Thus, distribution of the activation energy model17 is used with the measured time−temperature 6032

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The equation of heat balance for the solid heat carrier can be expressed as (more details are given in the Supporting Information)

∑ wj)cou(z)dA dTo j

⎧ ⎪ 2k k T − To s o =⎨ + βσχSo(1 − R so) SoR so s ⎪k + k d ps + d po o ⎩ s

θ(1 − ε) csρs u(z)dA dTs θ+1 ⎡ 2k k T − To s o = −⎢ SoR so s + hsg Ss(Ts − Tg) ⎢⎣ ks + ko d ps + d po

(Ts 4 − To 4) + hgoSo(1 − R so)(Tg − To) +

∑j [k 0j exp(−Ej /RTo)(wj* − wj)] ∑j wj*

ρo0

⎫ ⎪ 1−ε ΔH ⎬d ⎪ θ+1 ⎭

A dz

⎤ + βσχSo(1 − R so)(Ts 4 − To 4)⎥dA dz ⎥⎦

(10)

3.4.2. Heat Transfer to the Gas. In the rotary kiln, the heat flow of the gas from the particles is considered to be divided into two actions in parallel. The heat flow contains the different convection heat transfers, including the heat transfer from gas to the oil sludge and from the solid heat carrier to the gas. The heat flow for the gas can be expressed Q gas = Q s → g − Q g → o

4. RESULTS AND DISCUSSION 4.1. Preliminary Simulation and Verification. 4.1.1. Solid Particle Movement Inside the Kiln. To simulate the particle movement in the kiln, the solid motion parameters, such as bed height profile and instantaneous velocity, might be calculated from eqs 1 and 4 with necessary boundary conditions. The first condition was the constant exit height (z = 1.5), where h was 0 because of the absence of a dam, and the second condition defined the velocity at the inlet (z = 0), where u(z) was considered as 0 at initialization. The parameters of the geometric structure and the particle properties used in the model were shown in Tables 1 and 2. When all of these values were substituted in the models, the grouped equations were solved using MATLAB 6.5, and the simulation results of the bed height profile and the axial velocity of particular were presented in Figures 4 and 5, respectively.

(11)

where Qgas is the total heat transfer in the gas (J), Qs→g is the convection from the solid heat carrier to the gas (J), and Qg→o is the convection from the gas to the oil sludge (J). Thus, the balance of the energy for the gas heat transfer can be formulated as follows: cgmg dTg = dQ gas dz = (dQ s → g − dQ g → o)dz

(16)

(12)

where cg is the heat capacity of the gas (J kg−1 K−1), mg is the mass of the gas (kg), and Tg is the temperature of the gas (K). Finally, the heat balance equation of gas is obtained as (more details are given in the Supporting Information) 1−ε ρ ∑ (wj* − wj)cgu(z)dA dTg θ + 1 o0 j = [hsg Ss(Ts − Tg) − hgoSo(1 − R so)(Tg − To)]dA dz (13)

3.4.3. Solid Heat Carrier Heat Transfer. The temperature of the solid heat carrier, which is the main heat source in the pyrolysis process, dropped with the heat transfer along the rotary kiln. For the pyrolysis in the kiln, the heat transfer of conduction and radiation from the solid heat carrier to oil sludge is one of the solid heat carrier heat exports, while the other is the convection heat transfer from the solid heat carrier to the gas. The heat flow and balance for the solid heat carrier can be described by Q solid heat carrier = −Q s → o − Q s → g − Q rad

Figure 4. Solid bed depth profiles along the length of the rotary kiln.

(14)

where Qsoild heat carrier is the total heat transfer in the solid heat carrier (J), Qs→o is the conduction heat transfer between the solid heat carrier and the oil sludge (J), Qs→g is the convection from the solid heat carrier to the gas (J), and Qrad is the radiation heat transfer (J)

The result of the solid bed profile obtained from Saeman’s model agreed well with the data from the previous studies.5,6,18 To verify the accuracy of simulation for the axial velocity of particular inside the rotary kiln model in this paper, the same parameters in the previous study4 was used in the present model. A comparison between the calculated results by the present model to the simulation of the previous study was represented in Figure 6. In general, the two velocities showed a similar increasing trend in Figure 6. The slight difference might be due to the simplification of algorithms in the ref 4, where u(z) = 0.122Rnγ/α. This formula is a semi-empirical model for an industrial rotary kiln. However, in the present model, the

csms dTs = dQ solid heat carrier dz = −(dQ s → o + dQ s → g + dQ rad)dz

(15)

where cs is the heat capacity of the solid heat carrier (J kg−1 K−1), ms is the mass of the solid heat carrier (kg), and Ts is the temperature of the solid heat carrier (K). 6033

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CH4, H2, CO, CO2, C2H4, and C2H6, respectively, which were in the acceptable level. It is indicated that numerical simulation results of volatile yields is in good agreement with experimental values N

APPD (%) =

∑ (wiexp − wipre)/wiexp| × 100/N i=1

(17)

where wiexp and wipre are the volatile yields obtained from experiments and the calculation, respectively, and N is the number of data points. 4.2. Global Model with Solid Motion, Pyrolysis Kinetics, and Heat Transfer. Figure 8 illustrated the axial temperature distributions of gas, oil sludge, and solid heat carrier in the rotary kiln with the initial solid heat carrier temperature at 1123 K. The temperature of the oil sludge was increasing at a high rate in the first 0.5 m along the kiln. At about 0.5 m, the curve of the oil sludge temperature had a peak and then approached a plateau. It is demonstrated that there were the main heat transfer and the major thermal decomposition in the oil sludge at the first 0.5 m along the kiln. The temperature of the gas descended slightly at the head of the kiln. According to the three-dimensional figure (Figure 8), it is obvious that the temperature of gases was affected by the solid axial velocity at the front 0.5 m of the kiln. The higher the speed of the solid movement, the faster the temperature of gases deceased. After 0.5 m of the kiln, the temperature of gases leveled off. It is inferred that convection coefficients of the gas might be changed with the variation of the solid axial velocity, which resulted in a significant heat transfer at the first 0.5 m of the kiln. The temperature of the solid heat carrier decreased sharply at the entrance of the kiln, where a strong heat transfer from the solid heat carrier to the oil sludge occurred. As shown in Figure 8, the solid velocity had negligible influence on the solid heat transfer. The contact areas and temperature were the major factors in the solid heat transfer. In the kiln, because the contact area of solid is a constant, the temperature gradient between the solid heat carrier and oil sludge had critical impact on the solid heat transfer. All in all, the solid velocity and temperature gradient affected the gas heat transfer and solid heat transfer inside the rotary kiln, respectively. Figure 9 showed the yields of gaseous products in the axial direction along the rotary kiln. In general, the fractions of different gases showed an increasing trend along the rotary kiln. On the mass basis, CxHy was the predominant volatile product with the highest conversion rate. The lowest products were H2 and CO2. Most of the hydrocarbon and volatile compounds were released in the first 0.3 m, which is the main reaction zone. However, the evolution of H2 occurred from the entrance of the kiln, where the temperature of the oil sludge was lower. It is revealed that the H2 release was much easier than the other gaseous compounds. Moreover, the evolution of H2 has an obvious increase at the end of the kiln with the solid axial velocity decrease. There might be dehydrogenation reactions in the oil sludge pyrolysis process because of the solid residence time increase inside the kiln. Most of the evolution of CxHy was in the first 1 m of the kiln. After that, CxHy release reached equilibrium. As seen in Figure 9, the evolution of CxHy changed with the variation of solid velocity scarcely. From Figures 8 and 9, it was demonstrated that the evolution profile of CxHy is similar to the oil sludge temperature trend. Thus, the main influence on the CxHy yields was the temperature of the oil sludge because of the decomposition of petroleum hydro-

Figure 5. Profile of the numerical velocity for 5 rpm and 2°.

Figure 6. Comparison of the solid axial velocity simulation in (a) the present model to (b) that in ref 4 under the same parameters.

expression of u(z) is a differential form, derived from the particle trajectory model and the Saemen model. 4.1.2. Process of Pyrolysis and Heat Transfer Inside the Kiln. In this section, the resulting parameters of oil sludge pyrolysis and heat transfer, such as wj, Tg, T0, and Ts, were calculated with eqs 7, 10, 13, and 16. These ordinary differential equations were solved by a four-stage Runge−Kutta scheme with the boundary conditions: z = 0, wj = 0, dTg/dz = 0, T0 = To0, and Ts = Ts0. Figure 7 showed the gaseous products of predictions compared to the experimental value at different temperatures under the initial temperature of the solid heat carrier from 753 to 923 K. The results showed that the simulated values were close to the experimental values. As seen in Figure 7, the experimental and simulation results of different volatile yields increased with the temperature increase, except CO2. The yields of CO2 are low in all temperatures, which might be caused by the low oxygen content in the oil sludge. The differences between experimental and calculated curves were mainly due to the selected parameters, such as physicochemical properties and kinetics parameters, and errors of pyrolysis experiments. The average absolute percentage deviation (AAPD), which was defined by eq 17, was used to quantify the error between the experimental and simulation results. Results show that the AAPD values were 6.27, 5.99, 3.20, 5.37, 7.04, and 5.34% for 6034

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Figure 7. Experimental and prediction of the product yields on different initial temperatures of the solid heat carrier.

Figure 8. Axial temperature distribution of (a) oil sludge, (b) gas, and (c) solid heat carrier with velocity varying under the initial solid heat carrier temperature at 1123 K.

carbons. The behavior of CO and CO2 released with relatively minor intensity. The yields of CO and CO2 also increased in

the slow velocity scope at the end of the kiln, which was the higher temperature zone. This main reason was the 6035

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Figure 9. Different products yield along the rotary kiln with velocity varying under the initial solid heat carrier temperature at 1123 K.

■

decomposition of inorganic carbonate. The lower the solid axial velocity, the longer the residence time. In the high temperature zone, a long residence time of solid inside the kiln can boost the decomposition of inorganic carbonate. However, CxHy released smoothly without an obvious ascent at the end of the kiln in the slow velocity zone. In summary, the evolution of H2 was easier than that of CO and CO2 and the slow velocity helped the gas production in a higher temperature zone, except for CxHy.

ASSOCIATED CONTENT

S Supporting Information *

Details for the development of the heat balance equations for the oil sludge (eqs A1−A14), gas (eqs A15−A21), and solid heat carrier (eqs A22−A26). This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Telephone: 86-411-84707448. Fax: 86-411-84706679. E-mail: [email protected].

5. CONCLUSION In this study, a dynamic model of oil sludge pyrolysis in a rotary kiln with a solid heat carrier was developed. In this numerical model, the bed depth profiles and yields of CxHy, H2, CO, and CO2 were successfully predicted on the basis of Saeman’s model and a multiple-reaction model, respectively. In addition, the temperature profiles of the solid heat carrier, oil sludge, and gas along the kiln were also predicted. The prediction of the temperatures and gas yields along the kiln indicated that H2 released from the head of the kiln and the evolution of CxHy was on a smooth upward curve. CO and CO2 increased monotonically with a sharp ascent at the end of the kiln at a low solid axial velocity. From the prediction, the pyrolysis process along the kiln could be generally known. It could be predicted that the slow solid axial velocity contributed to the gas release at a high temperature zone. The validity of the proposed model was justified from both aspects of solid axial velocity and gas yields by comparing numerical values to literature reports and experimental data, respectively. The data had shown reliable prediction of the oil sludge pyrolysis process inside the rotary kiln. It could be concluded that the model might provide the basic engineering parameters for industrial use. However, continuing studies are still in need to experimentally examine the worked out criteria and enhance the mathematically developed models.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work cited in this paper was supported by the National Natural Science Foundation of China (NSFC) (51476023), the Fundamental Research Funds for the Central Universities (DUT13LAB08), and the Open Foundation of the Key Laboratory of Industrial Ecology and Environmental Engineering (KLIEEE-12-01) (Ministry of Education).

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NOMENCLATURE r = internal radius of the kiln (m) h = bed height (m) n = rotation speed (rpm) z = kiln length (m) m = mass flow (kg/s) ro = radius of particle rotation (m) u = averaged axial velocity (m/s) u(z) = instantaneous velocity (m/s) ug = superficial velocity of gas (m/s) w = conversion of the reaction at any temperature wj = conversion of the reaction at any temperature for product j wj∞ = value of wj at t = ∞ dx.doi.org/10.1021/ef501263m | Energy Fuels 2014, 28, 6029−6037

Energy & Fuels

Article

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Ej = activation energy of the reaction forming product j (J/ mol) koj = pre-exponential factor of the reaction forming product j (s−1) R = ideal gas constant (J mol−1 K−1) co = heat capacity of the oil sludge (J kg−1 K−1) cg = heat capacity of the gas (J kg−1 K−1) cs = heat capacity of the solid heat carrier (J kg−1 K−1) mo = mass of the oil sludge (kg) mg = mass of the gas (kg) ms = mass of the solid heat carrier (kg) ks = thermal conductivity of the solid heat carrier (W m−1 K−1) k0 = thermal conductivity of the oil sludge (W m−1 K−1) dps = diameter of the solid heat carrier (m) dpo = diameter of the oil sludge (m) dp = diameter of the particle (m) To = temperature of the oil sludge (K) Ts = temperature of the solid heat carrier (K) Tg = temperature of the gas (K) hgo = heat-transfer coefficient between the gas and oil sludge (W m−2 K−1) hsg = heat-transfer coefficient between the gas and solid heat carrier (W m−2 K−1) ΔH = reaction heat (J/kg) ao/as = oil sludge/solid heat carrier surface area per unit volume (m2/m3) So/Ss = oil sludge/solid heat carrier contact surface area per unit volume (m2/m3) A = cross-sectional area (m2) Greek Letters

ρ = density of the particle (kg/m3) ρo0 = density of the oil sludge (kg/m3) ρs = density of the solid heat carrier (kg/m3) α = inclination angle of the kiln (deg) β = bed slope angle (deg) γ = dynamic angle of repose (deg) εt = correctional coefficient θ = volume ratio of the solid heat carrier to oil sludge λ = thermal conductivity of gas (W m−2 K−1) β0 = emissivity of oil sludge σ = Stefan−Boltzmann constant (W m−2 K−4) χ = radiation shape factor ε = void ratio ρg = density of gas (kg/m3) μg = viscosity of the gas (kg m−1 s−1) Dimensionless Numbers

Re = Reynolds number Nu = Nusselt number

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dx.doi.org/10.1021/ef501263m | Energy Fuels 2014, 28, 6029−6037