Abstract
The fundamental laws of mass, heat, and momentum transport are briefly presented in this chapter and their relationships with chemical kinetics depicted. The approach presented starts with estimation of basic properties like viscosity, thermal conductivity, and mass diffusivity, all of which are of fundamental importance in describing transport phenomena. Transport phenomena originate gradients in temperature, pressure, and concentration that are the driving forces for transformations occurring in a system. Two scales of transformation can be considered, i.e., molecular and macroscopic. Molecular-transport phenomena are normally much slower than macroscopic ones and this can result in a limitation on chemical reaction rates. In this chapter, detailed examples of basic property calculations are reported as are examples of chemical gas–solid reactions limited by diffusional resistance (like ammonia oxidation). Finally, a great part of the chapter is dedicated to the evaluation of catalyst effectiveness factor. Matlab code associated with the examples in this chapter is available online.
Keywords
- Catalytic Particles
- Boundary layerBoundary Layer
- High Thermal conductivityThermal Conductivity
- Feed Mass Flow Rate
- Reynolds numberReynolds Number
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Aris, R.: On shape factors for irregular particles—I: The steady state problem. Diffusion and reaction. Chem. Eng. Sci. 6(6), 262–268 (1957)
Bird, R.B., Stewart, W.E., Lightfoot., E.N.: Transport Phenomena. John Wiley & Sons (1960)
Bird, R.B., Stewart, W.E., Lightfoot, E.N.: Transport Phenomena Italian Edition Casa Editrice Ambrosiana (1970)
Bradshaw, R.D., Bennet, C.O.: Fluid-particle mass transfer in a packed bed. A.I.Ch.E. J. 7(1), 48–52 (1961)
Bridgman, P.W.: The thermal conductivity of liquids. sProc. Natl. Acad. Sci. USA 9(10), 341–345(1923)
Brush, G.: Kinetic Theory, Vol. 1: The Nature of Gases and of Heat. Oxford (1965)
Carberry, J.J.: A boundary-layer model of fluid-particle mass transfer in fixed beds. A.I.Ch.E. J. 6(3),s1960)
Carberry, J.J.: Physico-chemical aspects of mass and heat transfer in heterogeneous catalysis (Chap. 3). In: Anderson, J.R., Boudart, M. (ed.) Catalysis, vol. 8, pp. 131–171. Springer, Berlin (1987)
Carrà, S., Forni, L.: Aspetti Cinetici della Teoria del Reattore Chimico. Tamburini Ed. (1974)
Carrà, S., Ragaini, V., Zanderighi, L.: Operazioni di Trasferimento di Massa. Manfredi Editore, Milano (1969)
Chapman, S.: The kinetic theory of simple and composite monatomic gases: viscosity, thermal conduction, and diffusion. Proc. Roy. Soc. London A 93, 1–20 (1916)
Chapman S., Cowling T.G.: The Mathematical Theory of Non‐Uniform Gases, 3rd edn. Cambridge University Press (1970)
Chilton, T.C., Colburn, A.P.: Mass transfer (absorption) coefficients prediction from data on heat transfer and fluid friction. Ind. Eng. Chem. 26(11), 1183–1187 (1934)
De Acetis, J., Thodos, G.: Mass and heat transfer in flow of gases through spherical packings. Ind. Eng. Chem. 52(12), 1003–1006 (1960)
Dwydevi, P.N., Upadhay, S.N.: Particle-fluid mass transfer in fixed and fluidized beds. Ind. Eng. Chem. Process Des. Dev. 16, 157 (1977)
Einstein, A.: Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann. J. Physik 17, 549–561 (1905)
Enskog, D.: Kinetische Theorie der Vorgänge in mässig verdiinten Gases (Almqvist and Wiksells, Uppsala, (1917); translation by S.G. Brush in Kinetic Theory Vol. 3, Pergamon, Oxford (1965)
Fairbanks, D.F., Wilke, C.R.: Diffusion coefficients in multicomponent gas mixtures. Ind. Eng. Chem. 42(3), 471–475 (1950)
Fogler, H.S.: Elements of Chemical Reaction Engineering. Prentice Hall Int. Editions (1986)
Forni, L.: Fenomeni di Trasporto. Edizioni Cortina Milano (1979)
Froment, G.F.: Fixed bed catalytic reactors—current design status. Ind. Eng. Chem. 59(2), 18–27 (1967)
Froment, G.F., Bischoff, K.B.: Chemical Reactor Analysis and Design. Wiley, New York (1990)
Frössling, N.: Über die Verdunstung fallender Tropfen. Gerlands Beitr. Geophys. 52, 170–216 (1938)
Gimeno, M.P., Gascon, J., Tellez, C., Herguido, J., Menedez, M.: Selective oxidation of o-xylene to phthalic anhydride over V2O5/TiO2: kinetic study in a fluidized bed reactor. Chem. Eng. Process. 47(9–10), 1844–1852 (2008)
Hirschfelder, J.O., Bird, R.B., Spotz, E.L.: The transport properties of gases and gaseous mixtures. Chem. Revs. 44(1), 205–231 (1949)
Hirschfelder, J.O., Curtiss, C.F., Bird, R.B.: Molecular theory of gases and liquids. Wiley, New York (1954)
Holland, C.D., Anthony, R.G.: Fundamentals of Chemical Reaction Engineering. Prentice-Hall, London (1979)
Horak, J., Pasek, J.: Design of Industrial Chemical Reactors from Laboratory Data. Heyden, London (1978)
Johnson, P.A., Babb, A.L.: Liquid diffusion of non-electrolytes. Chem. Rev. 56, 387–453 (1956)
Lee, H.H.: Heterogeneous Reactor Design. Butterworth Pu. (1984)
Levenspiel, O.: The Chemical Reactor Omnibook. OSU Book Store, Oregon (1984)
Missen, R.W., Mims, C.A., Saville, B.A.: Introduction to Chemical Reaction Engineering and Kinetics. Wiley. New York (1999)
Ranz, W.E., Marshall Jr., W.R.: Evaporation from drops. Chem. Eng. Prog. 48(3), 141–146 (1952a)
Ranz, W.E., Marshall Jr., W.R.: Evaporation from drops part II. Chem. Eng. Prog. 48(4), 173–180 (1952b)
Rase, H.F.: Chemical Reactor Design for Process Plant, Vol. 2: Case Study N. 109, pp. 115–122j. Wiley, New York (1977)
Riggs, J.B.: Introduction to numerical methods in chemical engineering. Texas Tech Univ. Press (1988)
Rowlinson, J.S., Townley, J.R.: The application of the principle of corresponding states to the transport properties of gases. Trans. Faraday Soc. 49, 20–27 (1953)
Santacesaria, E.: Kinetics and transpssort phenomena in heterogeneous gas-solid and gas-liquid-solid systems. Catal. Today 34(3–4), 411–420 (1997)
Satterfield, C.N., Sherwood, T.K.: The Role of Diffusion in Catalysis. Addison Wesley Pu. Co. Inc. (1963)
Satterfield, C.N.: Heterogeneous Catalysis in Practice. Addison-Wesley (1972)
Satterfield, C.N., Cortez, D.H.: mass transfer characteristics of woven-wire screen catalysts. Ind. Eng. Chem. Fundam. 9(4), 613–620 (1970)
Smith J.M.: Chemical Engineering Kinetics. Mc Graw-Hill Book Co., New York (1981)
Stull, D.R., Westrum, E.F., Sinke, G.C.:The Chemical Thermodynamics of Organic Compounds. Wiley, New York (1969)
Thoenes, D., Kramers, H.: Mass transfer from spheres in various regular packings to a flowing fluid. Chem. Eng. Sci. 8(3–4), 271–283 (1958)
Treybal, R.E.: Mass Transfer Operations. Mc Graw-Hill Co., New York (1955)
Weisz, P.B., Hicks, J.S.: The behavior of porous catalyst particles in view of internal mass and heat diffusion effects. Chem. Eng. Sci. 17, 265-275 (1962)
Weisz, P.B., Prater, C.D.: Interpretation of measurements in experimental catalysis. Adv. Catal. 6, 143–196 (1954)
Wilke, C.R., Chang, P.: Correlation of diffusion coefficients in dilute solutions, AICHE J. 1(2), 264-270 (1955)
Winterbottom, J.M., King, M.: Reactor Design for Chemical Engineers. CRC Press, 1ed (1999)
Author information
Authors and Affiliations
Corresponding author
6.1 Electronic Supplementary Material
Below is the link to the electronic supplementary material.
Appendices
Appendix 1: Lennard–Jones Force Constants Calculated from Viscosity Data
Compound | \( \epsilon /k,\;^\circ {\text{K}} \) | σ, A | Compound | \( \epsilon /k,\;^\circ {\text{K}} \) | σ, A |
---|---|---|---|---|---|
Acetylene | 185 | 4.221 | Hydrogen | 33.3 | 2.968 |
Air | 97 | 3.617 | Hydrogen chloride | 360 | 3.305 |
Argon | 124 | 3.418 | Hydrogen iodide | 324 | 4.123 |
Arsine | 281 | 4.06 | Iodine | 550 | 4.982 |
Benzene | 440 | 5.270 | Krypton | 190 | 3.61 |
Bromine | 520 | 4.268 | Methane | 136.5 | 3.822 |
i-Butane | 313 | 5.341 | Methanol | 507 | 3.585 |
n-Butane | 410 | 4.997 | Methylene chloride | 406 | 4.759 |
Carbon dioxide | 190 | 3.996 | Methyl chloride | 855 | 3.375 |
Carbon disulfide | 488 | 4.438 | Mercuric iodide | 691 | 5.625 |
Carbon monoxide | 110 | 3.590 | Mercury | 851 | 2.898 |
Carbon tetra-chloride | 327 | 5.881 | Neon | 35.7 | 2.789 |
Carbonyl sulfide | 335 | 4.13 | Nitric oxide | 119 | 3.470 |
Chlorine | 357 | 4.115 | Nitrogen | 91.5 | 3.681 |
Chloroform | 327 | 5.430 | Nitrous oxide | 220 | 3.879 |
Cyanogen | 339 | 4.38 | n-Nonane | 240 | 8.448 |
Cyclohexane | 324 | 6.093 | n-Octane | 320 | 7.451 |
Ethane | 230 | 4.418 | Oxygen | 113 | 3.433 |
Ethanol | 391 | 4.455 | n-Pentane | 345 | 5.769 |
Ethylene | 205 | 4.232 | Propane | 254 | 5.061 |
Fluorine | 112 | 3.653 | Sulfur dioxide | 252 | 4.290 |
Helium | 10.22 | 2.576 | Water | 356 | 2.649 |
n-Heptane | 282 | 8.88 | Xenon | 229 | 4.055 |
n-Hexane | 413 | 5.909 |
Appendix 2: Collision Integrals Ωµ and ΩD as a Function of T* = KBT/ε for Apolar Molecules: Lennard–Jones Approach
As explained in the text, the following correlation was used for interpolating both of the collision integrals:
The best-fitting coefficients for the polynomials related to ΩD and Ωμ are listed in the following table.
Integral | a | b | c | d | e | f | g |
---|---|---|---|---|---|---|---|
ΩD | −0.0120 | 0.0877 | −0.2146 | 0.1426 | 0.1948 | −0.4848 | 0.1578 |
Ωμ | −0.0165 | 0.1204 | −0.3011 | 0.2360 | 0.1708 | −0.4922 | 0.1997 |
Data to be interpolated are reported in the following table.
T* | ΩD | Ωμ | T* | ΩD | Ωμ | T* | ΩD | Ωμ |
---|---|---|---|---|---|---|---|---|
0.30 | 2.6620 | 2.7850 | 1.65 | 1.1530 | 1.2640 | 4.00 | 0.8836 | 0.9700 |
0.35 | 2.4760 | 2.6280 | 1.70 | 1.1400 | 1.2480 | 4.10 | 0.8788 | 0.9649 |
0.40 | 2.3180 | 2.4920 | 1.75 | 1.1280 | 1.2340 | 4.20 | 0.8740 | 0.9600 |
0.45 | 2.1840 | 2.3680 | 1.80 | 1.1160 | 1.2210 | 4.30 | 0.8694 | 0.9553 |
0.50 | 2.0660 | 2.2570 | 1.85 | 1.1050 | 1.2090 | 4.40 | 0.8652 | 0.9507 |
0.55 | 1.9660 | 2.1560 | 1.90 | 1.0940 | 1.1970 | 4.50 | 0.8610 | 0.9464 |
0.60 | 1.8770 | 2.0650 | 1.95 | 1.0840 | 1.1860 | 4.60 | 0.8568 | 0.9422 |
0.65 | 1.7980 | 1.9820 | 2.00 | 1.0750 | 1.1750 | 4.70 | 0.8530 | 0.9382 |
0.70 | 1.7290 | 1.9080 | 2.10 | 1.0570 | 1.1560 | 4.80 | 0.8492 | 0.9343 |
0.75 | 1.6670 | 1.8410 | 2.20 | 1.0410 | 1.1380 | 4.90 | 0.8456 | 0.9305 |
0.80 | 1.6120 | 1.7800 | 2.30 | 1.0260 | 1.1220 | 5.00 | 0.8422 | 0.9269 |
0.85 | 1.5620 | 1.7250 | 2.40 | 1.0120 | 1.1070 | 6.00 | 0.8124 | 0.8963 |
0.90 | 1.5170 | 1.6750 | 2.50 | 0.9996 | 1.0930 | 7.00 | 0.7896 | 0.8727 |
0.95 | 1.4760 | 1.6290 | 2.60 | 0.9878 | 1.0810 | 8.00 | 0.7712 | 0.8538 |
1.00 | 1.4390 | 1.5870 | 2.70 | 0.9770 | 1.0690 | 9.00 | 0.7556 | 0.8379 |
1.05 | 1.4060 | 1.5490 | 2.80 | 0.9672 | 1.0580 | 10.00 | 0.7424 | 0.8242 |
1.10 | 1.3750 | 1.5140 | 2.90 | 0.9576 | 1.0480 | 20.00 | 0.6640 | 0.7432 |
1.15 | 1.3460 | 1.4820 | 3.00 | 0.9490 | 1.0390 | 30.00 | 0.6232 | 0.7005 |
1.20 | 1.3200 | 1.4520 | 3.10 | 0.9406 | 1.0300 | 40.00 | 0.5960 | 0.6718 |
1.25 | 1.2960 | 1.4240 | 3.20 | 0.9328 | 1.0220 | 50.00 | 0.5756 | 0.6504 |
1.30 | 1.2730 | 1.3990 | 3.30 | 0.9256 | 1.0140 | 60.00 | 0.5596 | 0.6335 |
1.35 | 1.2530 | 1.3750 | 3.40 | 0.9186 | 1.0070 | 70.00 | 0.5464 | 0.6194 |
1.40 | 1.2330 | 1.3530 | 3.50 | 0.9120 | 0.9999 | 80.00 | 0.5352 | 0.6076 |
1.45 | 1.2150 | 1.3330 | 3.60 | 0.9058 | 0.9932 | 90.00 | 0.5256 | 0.5973 |
1.50 | 1.1980 | 1.3140 | 3.70 | 0.8998 | 0.9870 | 100.00 | 0.5130 | 0.5882 |
1.55 | 1.1820 | 1.2960 | 3.80 | 0.8942 | 0.9811 | 200.00 | 0.4644 | 0.5320 |
1.60 | 1.1670 | 1.2790 | 3.90 | 0.8888 | 0.9755 | 300.00 | 0.4360 | 0.5016 |
400.00 | 0.4170 | 0.4811 |
The coefficients were obtained using a MATLAB program importing all data from an Excel file. By applying the correlations found to the collision integrals, average absolute percent errors of 0.1396 and 0.2343% are obtained for, respectively, ΩD and Ωμ. Plots of the fittings obtained with the same program are reported in the following figures.
Figures related to Appendix 2. Fittings obtained by mathematical regression analysis on the data of ΩD and Ωμ available in the literature and plots of the errors.
These results can be obtained using a MATLAB program available as Electronic Supplementary Material.
Appendix 3: Parameters of the Stockmayer Equation for Some Polar Molecules
Substance | Dipol moment \( \mu_{\text{d}} ({\text{D}}) \) | \( \sigma \) \( ({\AA}) \) | \( \epsilon_{\text{o}} {/k}_{\text{B}} (k) \) | \( \delta = \frac{{\mu_{\text{d}}^{2} }}{{2\epsilon_{\text{o}} \sigma^{3} }} \) |
---|---|---|---|---|
H2O | 1.85 | 2.52 | 775 | 1.0 |
NH3 | 1.47 | 3.15 | 358 | 0.7 |
HCl | 1.08 | 3.36 | 328 | 0.34 |
HBr | 0.80 | 3.41 | 417 | 0.14 |
HI | 0.42 | 4.13 | 313 | 0.029 |
SO2 | 1.63 | 4.04 | 347 | 0.42 |
H2S | 0.92 | 3.49 | 343 | 0.21 |
NOCl | 1.83 | 3.53 | 690 | 0.4 |
CHCl3 | 1.013 | 5.31 | 355 | 0.07 |
CH2Cl2 | 1.57 | 4.52 | 483 | 0.2 |
CH3Cl | 1.87 | 3.94 | 414 | 0.5 |
CH3Br | 1.80 | 4.25 | 382 | 0.4 |
C2H5Cl | 2.03 | 4.45 | 423 | 0.4 |
CH3OH | 1.70 | 3.69 | 417 | 0.5 |
C2H5OH | 1.69 | 4.31 | 431 | 0.3 |
n-C3H7OH | 1.69 | 4.71 | 495 | 0.2 |
i-C3H7OH | 1.69 | 4.64 | 518 | 0.2 |
(CH3)2O | 1.30 | 4.21 | 432 | 0.19 |
(C2H5)2O | 1.15 | 5.49 | 362 | 0.08 |
(CH3)2CO | 1.20 | 3.82 | 428 | 1.3 |
CH3COOCH3 | 1.72 | 5.04 | 418 | 0.2 |
CH3COOC2H5 | 1.78 | 5.24 | 499 | 0.16 |
CH3NO2 | 2.15 | 4.16 | 290 | 2.3 |
Appendix 4: Collision Integral Ωμ as a Function of T* = KBT/ε and δ for Polar Molecules
The following correlations were used for determining both the collision integrals:
The best-fitting coefficients for the functions related to ΩD and Ωμ are listed the following table.
Collision integrals | ||
---|---|---|
Parameter | ΩD | Ωμ |
d 1 | 0.066225 | 0.067498 |
d 2 | −0.002888 | −0.002375 |
d 3 | 0.0000707 | 0.0000618 |
d 4 | −0.0000626 | −0.0000865 |
d 5 | −0.0000785 | −0.0001022 |
K | 4.507 | 3.934 |
a 1 | 0.010254 | 0.010948 |
a 2 | −0.033249 | −0.039147 |
a 3 | −0.014026 | −0.005066 |
a 4 | 0.096320 | 0.105559 |
a 5 | 0.068759 | 0.049660 |
a 6 | −0.434055 | −0.425989 |
a 7 | 0.163439 | 0.203885 |
These coefficients were determined by mathematical regression analysis made on the data reported by the literature and summarized in the following two tables.
ΩD | ||||||||
---|---|---|---|---|---|---|---|---|
T* | δ | |||||||
0.00 | 0.25 | 0.50 | 0.75 | 1.00 | 1.50 | 2.00 | 2.50 | |
0.10 | 4.00790 | 4.00200 | 4.65500 | 5.52100 | 6.45400 | 8.21300 | 9.52400 | 11.31000 |
0.20 | 3.13000 | 3.16400 | 3.35500 | 3.72100 | 4.19800 | 5.23000 | 6.22500 | 7.16000 |
0.30 | 2.64940 | 2.65700 | 2.77000 | 3.00200 | 3.31900 | 4.05400 | 4.78500 | 5.48300 |
0.40 | 2.31440 | 2.32000 | 2.40200 | 2.57200 | 2.81200 | 3.38600 | 3.97200 | 4.53900 |
0.50 | 2.06610 | 2.07300 | 2.14000 | 2.27800 | 2.47200 | 2.94600 | 3.43700 | 3.91800 |
0.60 | 1.87670 | 1.88500 | 1.94400 | 2.06000 | 2.22500 | 2.62800 | 3.05400 | 3.47400 |
0.70 | 1.72930 | 1.73800 | 1.79100 | 1.89300 | 2.03600 | 2.38800 | 2.76300 | 3.13700 |
0.80 | 1.62200 | 1.62200 | 1.67000 | 1.76000 | 1.88600 | 2.19800 | 2.53500 | 2.87200 |
0.90 | 1.51750 | 1.52700 | 1.57200 | 1.65300 | 1.76500 | 2.04400 | 2.34900 | 2.65700 |
1.00 | 1.43980 | 1.45000 | 1.49000 | 1.56400 | 1.66500 | 1.91700 | 2.19600 | 2.47800 |
1.20 | 1.32040 | 1.33000 | 1.36400 | 1.42500 | 1.50900 | 1.72000 | 1.95600 | 2.19900 |
1.40 | 1.23360 | 1.24200 | 1.27200 | 1.32400 | 1.39400 | 1.57300 | 1.77700 | 1.99000 |
1.60 | 1.16790 | 1.17600 | 1.20200 | 1.24600 | 1.30600 | 1.46100 | 1.63900 | 1.82700 |
1.80 | 1.11660 | 1.12400 | 1.14600 | 1.18500 | 1.23700 | 1.37200 | 1.53000 | 1.69800 |
2.00 | 1.07530 | 1.08200 | 1.10200 | 1.13500 | 1.18100 | 1.30000 | 1.44100 | 1.59200 |
2.50 | 1.00060 | 1.00500 | 1.02000 | 1.04600 | 1.18000 | 1.17000 | 1.27800 | 1.39700 |
3.00 | 0.95003 | 0.95380 | 0.96560 | 0.98520 | 1.01200 | 1.08200 | 1.16300 | 1.26500 |
3.50 | 0.91311 | 0.91620 | 0.92560 | 0.94130 | 0.96260 | 1.01900 | 1.09000 | 1.17000 |
4.00 | 0.88453 | 0.88710 | 0.89480 | 0.90760 | 0.92520 | 0.97210 | 1.03100 | 1.09800 |
5.00 | 0.84277 | 0.84460 | 0.85010 | 0.85920 | 0.87160 | 0.90530 | 0.94830 | 0.99840 |
6.00 | 0.81827 | 0.81420 | 0.81830 | 0.82510 | 0.83440 | 0.85980 | 0.89270 | 0.93160 |
7.00 | 0.78976 | 0.79080 | 0.79400 | 0.79930 | 0.80660 | 0.82650 | 0.85260 | 0.88360 |
8.00 | 0.77111 | 0.77200 | 0.77450 | 0.77880 | 0.78460 | 0.80070 | 0.82190 | 0.84740 |
9.00 | 0.75553 | 0.75620 | 0.75840 | 0.76190 | 0.76670 | 0.78000 | 0.79760 | 0.81890 |
10.00 | 0.74220 | 0.74280 | 0.74460 | 0.74750 | 0.75150 | 0.76270 | 0.77760 | 0.79570 |
12.00 | 0.72022 | 0.72060 | 0.72200 | 0.72410 | 0.72710 | 0.73540 | 0.74640 | 0.76000 |
14.00 | 0.70254 | 0.70290 | 0.70390 | 0.70550 | 0.70780 | 0.71420 | 0.72280 | 0.73340 |
16.00 | 0.68776 | 0.68800 | 0.68880 | 0.69010 | 0.69190 | 0.69700 | 0.70400 | 0.71250 |
18.00 | 0.67510 | 0.67530 | 0.67600 | 0.67700 | 0.67850 | 0.68270 | 0.68840 | 0.69550 |
20.00 | 0.66405 | 0.66420 | 0.66480 | 0.66570 | 0.66690 | 0.67040 | 0.67520 | 0.68110 |
25.00 | 0.64136 | 0.64150 | 0.64180 | 0.64250 | 0.64330 | 0.64570 | 0.64900 | 0.65310 |
30.00 | 0.62350 | 0.62360 | 0.62390 | 0.62430 | 0.62490 | 0.62670 | 0.62910 | 0.63210 |
35.00 | 0.60882 | 0.60890 | 0.60910 | 0.60940 | 0.60990 | 0.61120 | 0.61310 | 0.61540 |
40.00 | 0.59640 | 0.59640 | 0.59660 | 0.59690 | 0.59720 | 0.59830 | 0.59980 | 0.60170 |
50.00 | 0.57626 | 0.57630 | 0.57640 | 0.57660 | 0.57680 | 0.57750 | 0.57850 | 0.57980 |
75.00 | 0.54146 | 0.54150 | 0.54160 | 0.54160 | 0.54180 | 0.54210 | 0.54240 | 0.54290 |
100.00 | 0.51803 | 0.51810 | 0.51820 | 0.51840 | 0.51840 | 0.51850 | 0.51860 | 0.51870 |
Ωμ | |||||||
---|---|---|---|---|---|---|---|
T* | δ | ||||||
0.00 | 0.25 | 0.50 | 0.75 | 1.00 | 1.50 | 2.00 | |
0.10 | 4.10050 | 4.26600 | 4.83300 | 5.74200 | 6.62900 | 8.62400 | 10.34000 |
0.20 | 3.26260 | 3.30500 | 3.51600 | 3.91400 | 4.43300 | 5.57000 | 6.63700 |
0.30 | 2.83990 | 2.83600 | 2.93600 | 3.16800 | 3.51100 | 4.32900 | 5.12600 |
0.40 | 2.53100 | 2.52200 | 2.58600 | 2.74900 | 3.00400 | 3.64000 | 4.28200 |
0.50 | 2.28370 | 2.27700 | 2.32900 | 2.46000 | 2.66500 | 3.18700 | 3.72700 |
0.60 | 2.08380 | 2.08100 | 2.13000 | 2.24300 | 2.41700 | 2.86200 | 3.32000 |
0.70 | 1.92200 | 1.92400 | 1.97000 | 2.07200 | 2.22500 | 2.61400 | 3.02800 |
0.80 | 1.79020 | 1.79500 | 1.84000 | 1.93400 | 2.07000 | 2.41700 | 2.78800 |
0.90 | 1.68230 | 1.68900 | 1.73300 | 1.82000 | 1.94400 | 2.25800 | 2.59600 |
1.00 | 1.59290 | 1.60100 | 1.64400 | 1.72500 | 1.83800 | 2.12400 | 2.43500 |
1.20 | 1.45510 | 1.46500 | 1.50400 | 1.57400 | 1.67000 | 1.91300 | 2.18100 |
1.40 | 1.35510 | 1.36500 | 1.40000 | 1.46100 | 1.54400 | 1.75400 | 1.98900 |
1.60 | 1.28000 | 1.28900 | 1.32100 | 1.37400 | 1.44700 | 1.63000 | 1.83800 |
1.80 | 1.22190 | 1.23100 | 1.25900 | 1.30600 | 1.37000 | 1.53200 | 1.71800 |
2.00 | 1.17570 | 1.18400 | 1.20900 | 1.25100 | 1.30700 | 1.45100 | 1.61800 |
2.50 | 1.09330 | 1.10000 | 1.11900 | 1.15000 | 1.19300 | 1.30400 | 1.43500 |
3.00 | 1.03880 | 1.04400 | 1.05900 | 1.08300 | 1.11700 | 1.20400 | 1.31000 |
3.50 | 0.99630 | 1.00400 | 1.01600 | 1.03500 | 1.06200 | 1.13300 | 1.22000 |
4.00 | 0.96988 | 0.97320 | 0.98300 | 0.99910 | 1.02100 | 1.07900 | 1.15300 |
5.00 | 0.92676 | 0.92910 | 0.93600 | 0.94730 | 0.96280 | 1.00500 | 1.05800 |
6.00 | 0.89616 | 0.89790 | 0.90300 | 0.91140 | 0.92300 | 0.95450 | 0.99550 |
7.00 | 0.87272 | 0.87410 | 0.87800 | 0.88450 | 0.89350 | 0.91810 | 0.95050 |
8.00 | 0.85379 | 0.85490 | 0.85800 | 0.86320 | 0.87030 | 0.89010 | 0.91640 |
9.00 | 0.83795 | 0.83880 | 0.84140 | 0.84560 | 0.85150 | 0.86780 | 0.88950 |
10.00 | 0.82435 | 0.82510 | 0.82730 | 0.83080 | 0.83560 | 0.84930 | 0.86760 |
12.00 | 0.80184 | 0.80240 | 0.80390 | 0.80650 | 0.81010 | 0.82010 | 0.83370 |
14.00 | 0.78363 | 0.78400 | 0.78520 | 0.78720 | 0.78990 | 0.79760 | 0.80810 |
16.00 | 0.76834 | 0.76870 | 0.76960 | 0.77120 | 0.77330 | 0.77940 | 0.78780 |
18.00 | 0.75518 | 0.75540 | 0.75620 | 0.75750 | 0.75920 | 0.76420 | 0.77110 |
20.00 | 0.74364 | 0.74380 | 0.74450 | 0.74550 | 0.74700 | 0.75120 | 0.75690 |
25.00 | 0.71982 | 0.72000 | 0.72040 | 0.72110 | 0.72210 | 0.72500 | 0.72890 |
30.00 | 0.70097 | 0.70110 | 0.70140 | 0.70190 | 0.70260 | 0.70470 | 0.70760 |
35.00 | 0.68545 | 0.68550 | 0.68580 | 0.68610 | 0.68670 | 0.68830 | 0.69050 |
40.00 | 0.67232 | 0.67240 | 0.67260 | 0.67280 | 0.67330 | 0.67450 | 0.67620 |
50.00 | 0.65099 | 0.65100 | 0.65120 | 0.65130 | 0.65160 | 0.65240 | 0.65340 |
75.00 | 0.61397 | 0.61410 | 0.61430 | 0.61450 | 0.61470 | 0.61480 | 0.61480 |
100.00 | 0.58870 | 0.58890 | 0.58940 | 0.59000 | 0.59030 | 0.59010 | 0.58950 |
A mathematical regression analysis was performed using a MATLAB program available as Electronic Supplementary Material.
By applying the correlations found in the calculation of the collision integrals, average absolute percent errors of 1.62 and 1.85% are obtained for, respectively, ΩD and Ωμ. The obtained fittings can be appreciated in the plots reported in the following figures.
Figures 1 related to Appendix 4. Fittings obtained by mathematical regression analysis on the data of ΩD available in the literature and parity plot .
Figures 2 related to Appendix 4. Fittings obtained by mathematical regression analysis on the data of Ωμ available in the literature and parity plot .
Appendix 5: Additive Volume Increments for the Estimation of the Molar Volume Vb at Normal Boiling Point
Substance | Vb increment, cm3/g mol |
---|---|
Air | 29.9 |
Ammonia | 25 |
Bromine | 27 |
Carbon | 14.8 |
Chlorine, terminal, as R–CI | 21.6 |
Medial, as R–CHC1–R | 24.6 |
Fluorine | 8.7 |
Helium | 1.0 |
Hydrogen (in compound) | 3.7 |
Hydrogen (molecular) | 14.3 |
Mercury | 15.7 |
Nitrogen | 31.2 |
In primary amines | 10.5 |
In secondary amines | 12.0 |
Oxygen, molecular | 14.8 |
Doubly bound | 7.4 |
Methyl esters and ethers | 9.1 |
Ethyl esters and ethers | 9.9 |
Higher esters and ethers | 11.0 |
Acids | 12.0 |
Joined to S, P, or N | 8.3 |
Phosphorus | 27 |
Sulfur | 25.6 |
Rings: 3-membered | −6 |
4-membered | −8.5 |
5-membered | −11.5 |
6-membered | −15 |
Naphthalene | −30 |
Anthracene | −47.5 |
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Santacesaria, E., Tesser, R. (2018). Kinetics of and Transport Phenomena in Gas–Solid Reactors. In: The Chemical Reactor from Laboratory to Industrial Plant. Springer, Cham. https://doi.org/10.1007/978-3-319-97439-2_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-97439-2_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-97438-5
Online ISBN: 978-3-319-97439-2
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)