Ergun‘s equation was applied to predict pressure drop across the bed by means of the following momentum balance equation [7]:
(1)
International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 825
ISSN 2229-5518
N.S.Yousef (a)
(a)Petrochemical Department, Faculty of Engineering, Pharos University, tel: (+203)3877200, (+203)3877400, (+203)3877212, (+203)3877214; Canal El Mahmoudeya St. Semouha, Alexandria, Egypt.
Abstract:
Natural gas is an important source of primary energy that, under normal production conditions, is saturated with water vapor. Water vapor in a natural gas stream can result in line plugging due to hydrate formation, reduction of line capacity due to collection of free water in the line, and increased risk of damage to the pipeline due to the corrosive effects of water. Therefore, water vapor must be removed from natural gas to prevent hydrate formation and corrosion from condensed water. Gas dehydration is the process of removing water vapor from a gas stream to lower the temperature at which water will condense from the stream; this temperature is called the ‘‘dew point’’ of the gas. There are several methods of dehydrating natural gas. The most common of these are liquid desiccant (glycol) dehydration, solid desiccant dehydration, and refrigeration. Molecular sieves are considered as one of the most important materials that are used as solid desiccant materials in industrial natural gas dehydration. In the present study, a steady state mathematical model was developed to simulate an adsorption process for dehydration of a gas stream in a fixed bed reactor using molecular sieves. Pressure drop inside the bed was calculated by Ergun equation. Heat transfer outside the solid particles was assumed to be convective and inside the particle was assumed to be diffusive. The results obtained from the mathematical model were verified against the ones obtained from a Liquefied Natural Gas Company in Egypt. The model predictions agreed well with the industrial data and the percentage error was very small. The percentage error in case of applying momentum balance equations was -6.7% and -2.9% in case of applying heat balance equations. The error in case of applying heat balance equation was less than that applied by momentum balance equation. Different parameters such as bed voidage, particle diameter, superficial gas velocity, gas density, and gas viscosity were studied to determine their effects on the pressure drop inside the reactor. It was found that pressure drop increases linearly with increasing superficial gas velocity, gas density, and gas viscosity and decreases linearly with increasing bed voidage, and particle diameter. The most effective parameter on the pressure drop is the bed voidage.
∗ Corresponding author: tel: (+203) 01006741024; Email address: nohaysf@yahoo.com
IJSER © 2014 http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 826
ISSN 2229-5518
Natural gas is one of the most important fuels in our life and one of the principle sources of energy for many of our day to day needs and activities [1]. Natural gas is used primarily as a fuel and as a raw material in manufacturing. It is used in home furnaces, water heaters, and cooking stoves. As an industrial fuel, it is used in manufacturing brick, cement, and ceramic-tile kilns; in glass making; aviation; hydrogen production; for generating steam in water boilers; and as a clean heat source for sterilizing instruments and processing foods. As a raw material in petrochemical manufacturing, natural gas is used in a range of fertilizers and as a secondary feed stock for manufacturing other chemicals, including nitric acid and urea. Ethylene, an important petrochemical, is also produced from natural gas [2]. Natural gas is considered as an environmentally friendly clean fuel, offering important environmental benefits when compared to other fossil fuels. The superior environmental quantities over coal or crude oil are that emissions of sulfur dioxide are negligible or that the levels of nitrous oxide and carbon dioxide emissions are lower. This helps to reduce problems of acid rain, ozone layer, or green house gases. Natural gas is also a very safe source of energy when transported, stored, and used [2]. Natural, associated, or non-associated gas usually contains water, in liquid and/or vapor form, at source and/or as a result of sweetening with an aqueous solution, which condense and form solid gas hydrates to block pipeline flow and especially control systems. Natural gas in transit to market should be dehydrated to a controlled water content to avoid hydrate as well as to minimize the corrosion problems [2].There are several methods of dehydrating natural gas. The most common of these are liquid desiccant (absorption) dehydration, solid desiccant (adsorption) dehydration, and refrigeration (i.e., cooling the gas) [3]. Adsorption (or solid bed) dehydration is the process where a solid desiccant is used for the removal of water vapor from a gas stream. The solid desiccants commonly used for gas dehydration are those that can be regenerated and, consequently, used over several adsorption-desorption cycles [1]. The two types of adsorption are physical adsorption and chemical adsorption (chemisorption). Adsorption process has many advantages such as: ability to provide extremely low dew points, less susceptible to corrosion or foaming, simplicity of operation and design of units, less affected by small changes in gas pressure, temperature, or flow rate, and adaptability to dehydration of very small quantities of gas at low cost [4]. The adsorbents most commonly used for dehydration are: Activated carbon, Activated alumina, Silica gel, and Molecular sieves (Zeolites) [5]. In this study, a mathematical model based on the linear driving force model was developed to simulate an adsorption process for dehydration of natural gas stream. The model evaluates the temperature distribution and pressure drop inside the fixed bed reactor. The effects of different parameters on pressure drop inside the reactor were studied. These parameters are: the density of gas mixture, the superficial gas velocity, bed porosity, particle diameter, and gas mixture viscosity. The results obtained from the mathematical model were verified against the ones obtained from a Liquefied Natural Gas Company in Egypt.
In this study, a mathematical model based on the linear driving force model was developed to simulate an adsorption process for dehydration of natural gas stream. The model evaluates the temperature distribution and pressure drop inside the fixed bed reactor. The effects of different parameters on pressure drop inside the reactor were studied. These parameters are: the density of gas
IJSER © 2014 http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 827
ISSN 2229-5518
mixture, the superficial gas velocity, bed porosity, particle diameter, and gas mixture viscosity. The results obtained from the mathematical model were verified against the ones obtained from a Liquefied Natural Gas Company in Egypt.
In driving the model, the following assumptions were made [6]:
1- The temperature and concentration variation are absent in the redial direction.
2- The temperature and concentration varies in the axial direction (one dimensional flow).
3- Profiles of temperature and concentrations are assumed flat.
4- The flow of gas among the cylinder bed length is assumed to follow the plug flow pattern.
5- The bed wall is fully insulated.
6- The heat capacity of the bed wall is neglected.
7- Heat transfer in the bed is result of the generated heat due to conduction through the solid
particles and the heat transferred from the solid surface to the gas phase by convection.
8- Steady state conditions are assumed.
9- Ergun's equation is applied to predict pressure drop across the bed.
Ergun‘s equation was applied to predict pressure drop across the bed by means of the following momentum balance equation [7]:
(1)
Adsorption is an exothermic process, so heat is generated. The generated heat is conducted to the surface of particles and then transferred to the gas phase by convection: the following equations [6] were obtained:
IJSER © 2014 http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 828
ISSN 2229-5518
The above equations were used to find the distribution of temperature both inside the particles and along the bed.
(4)2.2.3.2. Density for ideal gas mixture:
(5)
2.2.3.3. Density of gas mixture:
(6)
IJSER © 2014 http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 829
ISSN 2229-5518
2.2.3.4. Heat capacity of gas mixture [9]:
2.2.3.5. Viscosity of gas mixture [10]:
2.2.3.6. Reynolds number:
2.2.3.7. Thermal conductivity of gas mixture [11]:
2.2.3.8. Convective heat transfer coefficient [6]:
(11,12)
IJSER © 2014 http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 830
ISSN 2229-5518
2.2.3.9. Effective thermal conductivity [12]:
(13)
2.2.3.10. Superficial velocity:
The model developed for dehydration of natural gas was checked against a liquefied natural gas plant in Egypt. The measured and calculated values of pressure drop and temperature were
in good agreement. Different parameters were studied to determine their effects on pressure drop and heat transfer inside the reactor. This analysis was applied using momentum and heat balance equations. MATLAB software which is a tool for solving numerical mathematics both
linear equations and differential equations was used for solving the heat balance equation.
The calculated values of pressure drop obtained by this model were compared with the actual values and a deviation of -6.71% was obtained as shown in table (1).
The results indicated that a very good agreement between the model predictions and industrial values have been reported for evaluating temperature inside the reactor. A deviation of -2.9% was found to be for temperature values inside the reactor as shown in table (2).
IJSER © 2014 http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 831
ISSN 2229-5518
As shown in figure (1), when the particle diameter increases the pressure drop decreases. The particle diameter affects the friction factor which has a direct effect on the pressure drop. Increasing the particle diameter decreases the friction factor and according to that the pressure drop decreases.
1
0.9
0.8
0.7
0.6
∆P (bar) 0.5
0.4
0.3
0.2
0.1
0
0 0.0005 0.001 0.0015 0.002 0.0025 0.003
Particle diameter (dp) (m)
Fig 1. Effect of particle diameter on pressure drop
IJSER © 2014 http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 832
ISSN 2229-5518
Increasing gas density increases the pressure drop as shown in figure (2). High densities are responsible for high frictional shear stress forces which increases the pressure drop inside the bed.
0.8
0.7
0.6
0.5
∆P (bar) 0.4
0.3
0.2
0.1
0
0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007
Gas Density (ρ) ( kg/m3)
Fig 2. Effect of gas density on pressure drop
As shown in figure (3), increasing superficial velocity increases the pressure drop. Superficial velocity is directly proportional to friction factor and according to that when it increases, the pressure drop increases.
0.7
0.6
0.5
∆P (bar)
0.4
0.3
0.2
0.1
0
0 5 10 15 20 25 30
Superficial velocity (m/s)
Fig 3. Effect of gas superficial velocity on pressure drop
IJSER © 2014 http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 833
ISSN 2229-5518
Increasing the bed voidge decreases the pressure drop inside the reactor very highly compared to
the other parameters as shown in figure (4). Because of the large dependence of pressure drop on the bed voidge (as shown in Ergun‘s equation), it is considered to be the most effective
parameter on pressure drop.
5
4.5
4
3.5
3
∆P (bar) 2.5
2
1.5
1
0.5
0
0 0.05 0.1 0.15 0.2 0.25 0.3
Bed voidge (m)
Fig 4. Effect of bed voidge on pressure drop
The viscosity inside the fixed bed is affected by increasing the pressure drop. The viscosity is
directly proportional to friction factor and according to that when increases the pressure drop also increases as shown in figure (5).
1.2
1
0.8
∆ P (bar) 0.6
0.4
0.2
0
0 0.000005 0.00001 0.000015 0.00002 0.000025 0.00003 0.000035
Viscosity (kg/m.s)
Fig 5. Effect of gas viscosity on pressure drop
IJSER © 2014 http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 834
ISSN 2229-5518
From the present work the following conclusions have been arrived at:
• The model predictions agree very well with the actual data from a liquefied natural gas company in Egypt. The model deviation in case of applying momentum balance equations is only -6.7% and -2.9% in case of applying heat balance equations.
• The deviation in case of applying heat balance equation is less than that obtained by
applying the momentum balance equation.
• The calculated pressure drop across the bed is close to that obtained from the industrial
data. As discussed previously the pressure drop calculated from Eurgn‘s equation is
0.4664 bar which is nearly equal to the actual data that is 0.5 bar.
• The calculated temperature inside the bed is relatively the same that taken from the
petrochemical company. The temperature calculated from the model by heat balance
equations is 17 °C which is very close to the actual data that is 17.5 °C.
• The particle diameter increases, as a result of this the pressure drop decreases.
• When the gas density increases, this follows an increase in pressure drop.
• Increasing in superficial velocity causes an increase in pressure drop.
• The increase in bed voidage causes a very high decrease in pressure drop.
• When the viscosity increases, the pressure drop increases also.
• The most effective parameter on the fixed bed reactor is the bed voidage in case of
applying momentum balance equation.
IJSER © 2014 http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 835
ISSN 2229-5518
[1] Saeid Mokhatab, William A. Poe, James G. Speight," Handbook of Natural gas Transmission and Processing ” , p.1, Gulf Professional Publishing, Elsevier, 2006.
[2] Arthur L Kohl, Richard Nielsen, “Gas Purification”, Gulf Professional Publishing, 1997.
[3] Hassan A.A. Farag, Mustafa Mohamed Ezzat, Hoda Amer, Adel William Nashed, “Natural gas dehydration by desiccant materials”, Alexandria Engineering Journal, Chemical Abstracts,
2011.
[4] Marco Tagliabue, David Farrusseng, Susana Valencia, Sonia Aguado, Ugo Ravonb, Caterina Rizzo, Avelino Corma, Claude Mirodatos, “Natural gas treating by selective adsorption: Material science and chemical engineering interplay ”, Chemical Engineering Journal, , vol. 155, pp. 553-
566, 2009.
[5] C.L. (Joe) Chou, “ Dynamic modeling of water vapor adsorption by activated alumina”, Chemical Engineering Communications, vol. 56, no. 1-6, pp. 211-227, 1987.
[6] M. Gholam, M.R. Talaie, S. Roodpeyma, “ Mathematical modeling of gas dehydration using adsorption process ”, Chemical Engineering Science, vol.65, pp. (1-31), 2010.
[7] Wen-Ching Yang, “ HANDBOOK of FLUIDIZATION and FLUID-PARTICLE SYSTEMS
”, Marcel Dekker, Inc., 2003.
[8] Kunii D. and Levenspiel, O, “Fluidization Engineering”, 2nd Ed. Reed Publishing (USA) Inc.,
1991.
[9] Felder, R.M. and Rousseau, R.W., “Elementary principles of chemical processes”, 3rd Ed, John Wiley and Sons, 2005.
[10] Reid, R.C, Promsuitz, J.M, Poling, B.E., “The properties of gases and liquids”, Mc Graw- Hill, New York, 1987.
[11] Green, D.W and Perry, R.H, “Perry’s chemical engineers handbook”, 8th Ed, Mc Graw-Hill,
2008.
[12] K. Wang; J.Y. Wu, R.Z. Wang; L.W. Wang, “Effective thermal conductivity of expanded graphite–CaCl2 composite adsorbent for chemical adsorption chillers”, Energy Conversion and Management, vol.47 , pp. 1902-1912, 2006.
IJSER © 2014 http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 836
ISSN 2229-5518
Symbol | Description | Unit |
A | Cross sectional area of fixed bed | m2 |
Cpg | Molar heat capacity of gas | J/mol .°C |
Cpi | Molar heat capacity of component i | J/mol .°C |
Cp gmix | Molar heat capacity of gas mixture | J/mol .°C |
dp | Particle diameter | m |
D | Bed diameter | m |
g | Acceleration gravity | m2/s |
hb ∆Hi | Gas particle heat transfer coefficient Heat of reaction of component i | W/m2 °C k J/mol |
k keff | Thermal conductivity of gas Effective thermal conductivity | W/m. °C W/m. °C |
kr | Chemical reaction rate constant | s-1 |
kg mix | Thermal conductivity of gas mixture | W/m. °C |
ki | Thermal conductivity of gas i | W/m. °C |
ks L | Particle thermal conductivity Total bed Height | W/m. °C m |
M | Molecular Weight | kg/kmol |
Mi Molecular Weight of component i kg/kmol
Nu Nusselt Number -
IJSER © 2014 http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 837
ISSN 2229-5518
Nu D Nusselt Number for solid particles -
P Total pressure in reactor N/m2
Pr Prandtl Number -
∆P qci | Pressure drop in reactor Concentration of component i in particle crystal | m | N/m2 ol/s |
Q r | Total volumetric flow rate of gas in feed Particle Radius | m3/s m | |
R Re t | Gas constant Reynolds Number Time | - | kJ/kmol.K s |
T | Temperature in Reactor | K | |
Tb | Temperature of the bed reactor | K | |
Tp u | Particle temperature Gas velocity | K m/s | |
U | Superficial gas velocity | m/s | |
xi | Mole fraction of component i | ||
yi z | Mole fraction of component i Bed Height | m | |
Z | Compressibility factor |
IJSER © 2014 http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 838
ISSN 2229-5518
ε εb | Void fraction of packed bed Bed porosity | - | |
ρ | gas density | kg/m3 | |
ρmix ρi | gas mixture density Density of component i | kg/m3 kg/m3 | |
μ | Viscosity | kg/m.s | |
μg | Gas Viscosity | kg/m.s |
μi Viscosity of component i kg/m.s
IJSER © 2014 http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 839
ISSN 2229-5518
Pore diameter | Particle size range |
4ºA | 10 mesh~2mm |
IJSER © 2014 http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 840
ISSN 2229-5518
IJSER © 2014 http://www.ijser.org
International Journal of Scientific & Engineering Research, Volume 5, Issue 2, February-2014 841
ISSN 2229-5518
IJSER © 2014 http://www.ijser.org