PD Source Models

Source Models

49 single-phase pressure drop correlations are implemented (1937–2026), all of semi-empirical type. Each model is implemented with its original validity ranges and friction factor formulation.

#	Model	Correlation	Coverage
1	Carman (1937)	$\frac{\Delta P}{L}=\left(\frac{6\phi_s}{Re_m}+0.4\left(\frac{6\phi_s}{Re_m}\right)^{0.1}\right)\frac{S_1\rho U_s^2}{\varepsilon^3}$ $S_1=\frac{6(1-\varepsilon)}{\phi_s D_p}+\frac{4}{D}$ $Re_1=\frac{Re_p\phi_s}{6(1-\varepsilon)}$	$0.01\le Re_1\le10^4$, $D/D_p\ge2$, $\phi_s\ge0.95$, $0.3\le\varepsilon\le0.9$
2	Morcom (1946)1,*	$\frac{\Delta P}{L}=\left(\frac{784.8}{Re_p}+13.73\right)\frac{0.405\rho U_s^2}{\varepsilon^3D_p}$	$Re_p<750$, $\phi_s\ge0.95$, $D/D_p>5$
3	Rose & Rizk (1949)	$\frac{\Delta P}{L}=\left(\frac{1000}{Re_p}+\frac{125}{Re_p^{0.5}}+14\right)\frac{f\rho U_s^2}{D_p}$ $f=36,e^{-0.0915\varepsilon}+0.055$	$100\le Re_p\le10^5$, $D/D_p\ge1$, $\phi_s\ge0.3$, $0.3\le\varepsilon\le0.9$
4	Leva (1949)2,*	$\frac{\Delta P}{L}=2F_m\frac{\rho U_s^2}{D_p}\frac{(1-\varepsilon)^{3-n}}{\varepsilon^3}$ $n = 1$ for $Re_p < 11.5$, $n = f(\log_{10}(Re_p))$ for $Re_p \ge 11.5$ $F_m=10^{f(\log_{10}(Re_p))}$	$Re_p<10^4$, $\phi_s\ge0.95$
5	Ergun (1952)	$\frac{\Delta P}{L}=\left(\frac{150}{Re_m}+1.75\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$	$1.2\le Re_m\le4200$, $D/D_p>10$, $\phi_s\ge0.95$
6	Wentz & Thodos (1963)	$\frac{\Delta P}{L}=\frac{A}{Re_m^{0.05}-1.2}\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$ $A=0.396-0.045,e^{-0.47(L/D_p-5)}$	$2550<Re_m<6.49\times10^4$, $L/D_p\ge5$, $D/D_p\ge11$, $\phi_s\ge0.95$, $0.354<\varepsilon<0.882$
7	Kürten et al. (1966)	$\frac{\Delta P}{L}=\frac{25c_w\rho U_s^2(1-\varepsilon)^2}{4D_p\varepsilon^3}$ $c_w=\frac{21}{Re_p}+\frac{6}{Re_p^{0.5}}+0.28$	$0.1\le Re_p\le4000$, $\phi_s\ge0.95$
8	Handley & Heggs (1968)3,*	$\frac{\Delta P}{L}=\left(\frac{368}{Re_m}+1.24\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$	$200<Re_p<1.3\times10^4$, $\phi_s\ge0.8$
9	Mehta & Hawley (1969)	$\frac{\Delta P}{L}=\left(\frac{150M^2}{Re_m}+1.75M\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$ $M=1+\frac{2D_p}{3D(1-\varepsilon)}$	$Re_m/M\le10$, $D/D_p\ge7$, $\phi_s\ge0.95$
10	Hicks (1970)	$\frac{\Delta P}{L}=6.8,Re_m^{1.2}\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$	$300<Re_m<6\times10^4$, $\phi_s\ge0.95$
11	Tallmadge (1970)	$\frac{\Delta P}{L}=\left(\frac{150}{Re_m}+\frac{4.2}{Re_m^{1/6}}\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$	$0.1<Re_m<10^5$, $\phi_s\ge0.95$, $0.35\le\varepsilon\le0.88$
12	Reichelt (1972)	$\frac{\Delta P}{L}=\left(\frac{150}{Re_w}+B_s\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$ for $\phi_s>0.9$ $\frac{\Delta P}{L}=\left(\frac{200}{Re_w}+B_c\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$ for $0.85\le\phi_s\le0.9$ $Re_w=\frac{Re_mD(1-\varepsilon)}{D(1-\varepsilon)+0.67D_p}$ $B_s=\frac{D^4}{D_p^4(1.5+0.88D^2/D_p^2)^2}$ $B_c=\frac{D^4}{D_p^4(2+0.8D^2/D_p^2)^2}$	$0.2\le Re_w\le3\times10^4$, $D/D_p>1.7$
13	Kuo & Nydegger (1978)4,*	$\frac{\Delta P}{L}=\left(\frac{276.23}{Re_m}+\frac{5.05}{Re_m^{0.13}}\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$	$460\le Re_p\le1.46\times10^4$, $0.376\le\phi_s\le0.39$
14	Macdonald et al. (1979)	$\frac{\Delta P}{L}=\left(\frac{180}{Re_m}+1.8\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$	$Re_m\le10^4$, $0.6\le\phi_s\le1$, $0.36\le\varepsilon\le0.92$
15	KTA (1981)	$\frac{\Delta P}{L}=\left(\frac{160}{Re_m}+\frac{3}{Re_m^{0.1}}\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$	$Re_m\le10^3$ & $D/D_p>34.35-0.06Re_m$ or $Re_m>10^3$ & $D/D_p>5$, $L/D_p>5$, $\phi_s\ge0.95$, $0.36\le\phi_s\le0.42$
16	Jones & Krier (1983)	$\frac{\Delta P}{L}=\left(\frac{150}{Re_m}+\frac{3.89}{Re_m^{0.13}}\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$	$733<Re_m<1.27\times10^5$, $L/D>3.5$, $D/D_p\ge20$, $\phi_s\ge0.95$, $0.372\le\varepsilon\le0.436$
17	Foscolo et al. (1983)	$\frac{\Delta P}{L}=\left(\frac{17.3}{Re_p}+0.336\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^{4.8}}$	$\phi_s\ge0.95$, $\varepsilon\ge0.4$
18	Fahien & Schriver (1983)5,*	$\frac{\Delta P}{L}=\left(\frac{q,f_{1L}}{Re_m}+(1-q)\left(f_2+\frac{f_{1T}}{Re_m}\right)\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$ $q=e^{-\varepsilon^2(1-\varepsilon)Re_m/12.6}$ $f_{1L}=\frac{136}{(1-\varepsilon)^{0.38}}$ $f_{1T}=\frac{29}{(1-\varepsilon)^{1.45}\varepsilon^2}$ $f_2=\frac{1.87\varepsilon^{0.75}}{(1-\varepsilon)^{0.26}}$	$\phi_s\ge0.95$
19	Meyer & Smith (1985)	$\frac{\Delta P}{L}=\frac{\rho U_s^2S_v}{\varepsilon^{4.1}}\frac{2.5\cdot6}{Re_m\phi_s+0.077}$ $S_v=\frac{6(1-\varepsilon)}{\phi_s D_p}$	$0.01\le Re_s\le10^3$, $0.18\le\varepsilon\le0.67$
20	Paterson et al. (1986)6,*	$\frac{\Delta P}{L}=\left(\frac{150A}{Re_m}+1.75B\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$ $A=1+\frac{1.22D_p}{D}$ $B=e^{1.66((1-D_p/D)^2-1)}$	$25<Re_p<900$, $3.5<D/D_p<22$, $\phi_s\ge0.95$
21	Stichlmair et al. (1989)	$\frac{\Delta P}{L}=0.75\left(\frac{24}{Re_p}+\frac{4}{Re_p^{0.5}}+0.4\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^{4.65}}$	$0.01\le Re_p\le10^5$, $\phi_s\ge0.95$, $\mu\le0.006,\text{Pa}\cdot\text{s}$
22	Watanabe (1989)7,*	$\frac{\Delta P}{L}=6.25\left(\frac{21}{Re_p}+\frac{6}{Re_p^{0.5}}+0.28\right)\frac{\rho U_s^2(1-\varepsilon)^2}{D_p\varepsilon^3}$	$0.1<Re_p<4000$, $\phi_s\ge0.95$
23	Comiti & Renaud (1989)	$\frac{\Delta P}{L}=M U_s^2+N U_s$	$2\le Re_p\le150$, $D/D_p\ge10$, $\phi_s\ge0.95$
24	Fand et al. (1990)	$\frac{\Delta P}{L}=\frac{36kM^2}{Re_m}\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$ for $Re_p<3$ $\frac{\Delta P}{L}=\left(\frac{A_\text{eff}M^2}{Re_m}+B_\text{eff}M\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$ for $Re_p\ge3$ $M=1+\frac{2D_p}{3D(1-\varepsilon)}$, $A_\text{eff}$‡, $B_\text{eff}$‡	$3\le Re_m/M\le600$, $D/D_p\ge1.4$, $\phi_s\ge0.95$, $0.4\le\varepsilon\le0.62$
25	Foumeny et al. (1993)	$\frac{\Delta P}{L}=\left(\frac{130}{Re_m}+\frac{D}{D_p(0.336D/D_p+2.28)}\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$	$5<Re_m<8500$, $D/D_p\ge3$, $\phi_s\ge0.95$, $0.386\le\varepsilon\le0.467$
26	Lee & Ogawa (1994)	$\frac{\Delta P}{L}=6.25\left(\frac{29.32}{Re_p}+\frac{1.56}{Re_p^n}+0.1\right)\frac{\rho U_s^2(1-\varepsilon)^2}{D_p\varepsilon^3}$	$1<Re_p<3\times10^5$, $\phi_s\ge0.95$
27	Liu et al. (1994)	$\frac{\Delta P}{L}=\left(85.2A^2+\frac{0.69B,Re_\text{mod}^3}{256+Re_\text{mod}^2}\right)\frac{\mu U_s}{d_s^2}\frac{(1-\varepsilon)^2}{\varepsilon^{11/3}}$ $A=1+\frac{\pi D_p}{6(1-\varepsilon)D}$ $B=1-\frac{\pi^2 D_p}{24(1-0.5D_p/D)D}$ $Re_\text{mod}=\frac{D_p\rho U_s}{\mu}\frac{(1+\sqrt{1-\varepsilon^{0.5}})}{(1-\varepsilon)\varepsilon^{1/6}}$	$Re_\text{mod}\le6000$, $D/D_p\ge1.33$, $\phi_s\ge0.95$, $0.36\le\varepsilon\le0.94$
28	Hayes et al. (1995)	$\frac{\Delta P}{L}=\left(\frac{1-\varepsilon}{T\varepsilon}\sqrt{850+\frac{11.6(3T-1)Re_p}{T(1-\varepsilon)(1-T)}}+0.65\frac{T,Re_p}{3T-1}\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon}$ $T=f(\varepsilon)$	$0.1\le Re_m\le10^5$, $D/D_p\ge2$, $\phi_s\ge0.95$, $0.38\le\varepsilon\le0.43$
29	Avontuur & Geldart (1996)8,*	$\frac{\Delta P}{L}=\left(\frac{141}{Re_m}+1.52\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$	$Re_m\le10^4$, $\phi_s\ge0.95$
30	Critoph & Thorpe (1996)	$\frac{\Delta P}{L}=\left(\frac{317}{Re_m}+3.15\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$	$30\le Re_p\le200$, $L/D\ge2.9$, $D/D_p\ge50$, $0.36\le\varepsilon\le0.4$
31	O'Neill & Benyahia (1997)9,*	$\frac{\Delta P}{L}=\left(\frac{A}{Re_m}+B\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$ $A=521.26-\frac{22581.24}{(D/D_p)^2}$ $B=1.12+\frac{4.2D_p}{D}$	$D/D_p>5$, $\phi_s\ge0.95$
32	Raichura (1999)	$\frac{\Delta P}{L}=\left(\frac{A}{Re_m}+B\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$ $A=103\left(\frac{\varepsilon}{1-\varepsilon}\right)^2\cdot\left(6-6\varepsilon+\frac{80D_p}{D}\right)$ $B=2.8\frac{\varepsilon}{1-\varepsilon}\cdot\left(1-\frac{1.82D_p}{D}\right)^2$	$30\le Re_p\le1700$, $L/D>3$, $D/D_p\ge5$, $\phi_s\ge0.95$, $0.38\le\varepsilon\le0.43$
33	Eisfeld & Schnitzlein (2001)	$\frac{\Delta P}{L}=\left(\frac{K_1A_w^2}{Re_m}+\frac{A_w}{B_w}\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$ $K_1=155$ for $\phi_s<0.95$, $K_1=154$ for $\phi_s\ge0.95$ $k_1=1.42$ for $\phi_s<0.95$, $k_1=1.15$ for $\phi_s\ge0.95$ $k_2=0.83$, $\phi_s<0.95$, $k_2=0.87$ for $\phi_s\ge0.95$ $A_w=1+\frac{2D_p}{3D(1-\varepsilon)}$ $B_w=\left(\frac{k_1}{(D/D_p)^2}+k_2\right)^2$	$0.01\le Re_p\le1.76\times10^4$, $D/D_p\ge1.624$, $\phi_s\ge0.8$, $0.33\le\varepsilon\le0.882$
34	Yu et al. (2002)	$\frac{\Delta P}{L}=\left(\frac{203}{Re_m}+1.95\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$	$750\le Re_p\le2500$, $D/D_p\ge30$, $\phi_s\ge0.95$, $0.36\le\varepsilon\le0.38$
35	Di Felice & Gibilaro (2004)	$\frac{\Delta P}{L}=\left(150\mu\frac{(1-\varepsilon)}{D_p}U_b+1.75\rho(1-\varepsilon)U_b^2\right)\frac{(1-\varepsilon)}{D_p\varepsilon^3}$ $U_b=\frac{U_sD^2}{2.06D^2-1.06(D/D_p-1)^2D_p^2}$	$D/D_p\ge5$, $\phi_s\ge0.95$, $0.4\le\varepsilon\le0.5$
36	Nemec & Levec (2005)	$\frac{\Delta P}{L}=\left(\frac{150}{\phi_s^{1.5}Re_m}+\frac{1.75}{\phi_s^{4/3}}\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$	$1\le Re_m\le10^3$, $D/D_p\ge10$, $\phi_s\ge0.95$, $0.35\le\varepsilon\le0.55$
37	Montillet et al. (2007)	$\frac{\Delta P}{L}=A\cdot B\left(\frac{1000}{Re_p}+\frac{60}{Re_p^{0.5}}+12\right)\frac{\rho U_s^2}{D_p}$ $A=0.061$ for $\varepsilon<0.4$, $A=0.05$ for $\varepsilon\ge0.4$ $B=(D/D_p)^{0.2}$ for $D/D_p<50$, $B=2.2$ for $D/D_p\ge50$	$10\le Re_p\le2500$, $D/D_p\ge3.8$, $\phi_s\ge0.95$, $0.356\le\varepsilon\le0.452$
38	Çarpinlioğlu & Özahi (2008)	$\frac{\Delta P}{L}=70,\rho,U_s^2\left(\frac{Re_m D_p}{L\varepsilon^7}\right)^{-0.4733}$	$675\le Re_m\le7772$, $0.24\le L/D\le1.46$†, $D/D_p\ge5.72$, $\phi_s\ge0.55$, $0.36\le\varepsilon\le0.56$
39	Özahi et al. (2008)	$\frac{\Delta P}{L}=\left(\frac{160}{Re_m}+1.61\phi_s\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$	$708\le Re_m\le7772$, $D/D_p\ge5.72$, $\phi_s\ge0.55$, $0.36\le\varepsilon\le0.56$
40	Cheng (2011)	$\frac{\Delta P}{L}=\left(\frac{A}{Re_m}+B\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$ $A=185+\frac{17\varepsilon}{1-\varepsilon}\left(\frac{D}{D-D_p}\right)^2$ $B=1.3\left(\frac{1-\varepsilon}{\varepsilon}\right)^{1/3}+0.03\left(\frac{D}{D-D_p}\right)^2$	$2\le Re_p\le5550$, $D/D_p\ge1.1$, $\phi_s\ge0.95$, $0.3\le\varepsilon\le0.7$
41	Harrison et al. (2013)	$\frac{\Delta P}{L}=\left(\frac{A}{Re_m}+\frac{B}{Re_m^{1/6}}\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$ $A=119.8\left(1+\frac{\pi D_p}{6(1-\varepsilon)D}\right)^2$ $B=4.63\left(1-\frac{\pi^2 D_p(1-0.5D_p/D)}{24D}\right)$	$0.32<Re_p<7700$, $D/D_p>8.3$, $\phi_s\ge0.95$, $0.33<\varepsilon<0.88$
42	Erdim et al. (2015)	$\frac{\Delta P}{L}=\left(\frac{160}{Re_m}+\frac{2.81}{Re_m^{0.096}}\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$	$2<Re_m<3600$, $D/D_p>4$, $\phi_s\ge0.95$, $0.37<\varepsilon<0.47$
43	Guo et al. (2017)	$\frac{\Delta P}{L}=\left(\frac{A}{Re_m}+\frac{B}{Re_m^C}\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$ $A=\frac{1004}{(D/D_p)^{9.69}}+\frac{57.6D}{D_p}$ $B=\frac{1964D_p}{D}+\frac{502.7D}{D_p}-1984$ $C=-\frac{3.183D_p}{D}-\frac{1.785D}{D_p}+5.241$	$1\le D/D_p\le2$, $\phi_s\ge0.95$, $0.365<\varepsilon<0.682$
44	Seckendorff et al. (2020)	$\frac{\Delta P}{L}=\left(\frac{65.7}{Re_m}+\frac{16.25}{Re_m^{0.343}}\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$	$10\le Re_p\le3000$, $D/D_p\ge4$, $0.86\le\phi_s\le0.89$, $0.32\le\varepsilon\le0.45$
45	Cheng et al. (2021)	$\frac{\Delta P}{L}=k,Re_p^{a_1}\left(\frac{D}{D_p}\right)^{a_2}\frac{\rho U_s^2}{D_p}$ For $U_s<1.15$: $k=395.2$ , $a_1=-0.47$, $a_2=-0.5$ For $U_s\ge1.15$: $k=17.2$, $a_1=-0.19$, $a_2=-0.15$	$200\le Re_p\le6400$, $L/D\ge1.86$, $D/D_p\ge13.8$, $0.69\le\phi_s\le0.89$, $0.52\le\varepsilon\le0.54$
46	Reger et al. (2023)	$\frac{\Delta P}{L}=\left(\frac{160}{Re_m}+\frac{3f(\varepsilon)}{Re_m^{0.1}}\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$	$100\le Re_m\le10^4$, $D/D_p\ge4.4$, $\phi_s\ge0.95$, $0.2\le\varepsilon\le0.9$
47	Dixon (2023)	$\frac{\Delta P}{L}=\left(\frac{A}{Re_m}+\frac{0.922+16/Re_m^{0.46}}{1+52/Re_m}\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\varepsilon^3}$ $A=160\left(1+\frac{2}{3}\frac{0.5459D_p}{(1-\varepsilon)D}\right)^2$	$0.01\le Re_m\le5\times10^5$, $D/D_p\ge5$, $\phi_s\ge0.95$
48	Wu & Hibiki (2025)	$\frac{\Delta P}{L}=F_k\frac{\rho U_s^2}{D_p'}$ $D_p'=\frac{D_p\varepsilon}{6(1-\varepsilon)}$ $F_k=\sqrt[3]{F_{k,\text{lam}}^3+F_{k,\text{turb}}^3}$ $F_{k,\text{lam}}=0.5+\frac{158}{Re_m^{0.8}(L/D_p')^{0.05}}$ $F_{k,\text{turb}}=0.57+\frac{2.07}{Re_m^{0.12}}$	$0.173\le Re_m\le5.02\times10^5$, $63.1\le L/D_p'\le1.7\times10^4$, $0.002\le D_p'/D\le0.029$, $\phi_s\ge0.95$, $0.33\le\varepsilon\le0.651$
49	Xu et al. (2026)	$\frac{\Delta P}{L}=\left(\frac{k_1}{Re_m\phi_s}+k_2\right)\frac{\rho U_s^2(1-\varepsilon)}{D_p\phi_s\varepsilon^3}$ $k_1=902.27-43.33,e^{D_p/22.28}$ $k_2=8.7-0.3,e^{D_p/14.8}$‡	$350\le Re_m\le4980$, $L/D\ge1.8$, $D/D_p\ge13$, $0.578\le\phi_s\le0.846$, $0.57\le\varepsilon\le0.64$

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Footnotes

[*] Unconfirmed models owing to a lack of original papers. Correlations for these models were adopted from review studies, which provide comprehensive reviews, primarily Erdim et al. (2015) and Eisfeld & Schnitzlein (2001), which provide comprehensive reviews.

[†] The restriction was removed from the model.

[‡] Interpolation of table data is required.

[1] Morcom, A. R. (1946). Fluid flow through granular materials. Chem. Eng. Res. Des., 24, 30–43.

[2] Leva, D. W. (1949). Fluid flow through packed beds. Chem. Eng., 56, 115–117.

[3] Handley, D., & Heggs, P. J. (1968). Momentum and heat transfer mechanisms in regular shaped packings. Trans. Inst. Chem. Eng., 46, 251–259.

[4] Kuo, K. K., & Nydegger, C. C. (1978). Flow resistance measurements and correlation in a packed bed of WC 870 ball propellants. J. Ballist., 2(1), 1–25.

[5] Fahien, R. W., & Schriver, C. B. (1983). Fundamentals of transport phenomena. McGraw-Hill. Paper presented at the AIChE Denver Meeting, Denver, CO.

[6] Paterson, W. R., Colledge, R. A., Macnab, J. I., & Maruka, J. A. (1986). Experimental studies of transport processes in packed beds of low tube-to-particle diameter ratio. In Proceedings of the World Congress III of Chemical Engineering (pp. 304–307). Society of Chemical Engineers.

[7] Watanabe, H. (1989). Drag coefficient and voidage function on fluid-flow through granular packed-beds. Int. J. Eng. Fluid Mech., 2(1), 93–108.

[8] Avontuur, P. P. C., & Geldart, D. (1996). A quality assessment of the Ergun equation. Chem. Eng., 51(4), 994–996.

[9] O'Neill, K., & Benyahia, F. (1997). Packed bed systems: An insight into more flexible design. In Proceedings of the IChemE Research Event/The Jubilee Research Event (pp. 1253–1256). Institution of Chemical Engineers.

Packed bed design space coverage by existing semi-empirical correlations with confirmation by the full text of publications

All references are availeble in BibTex format.