Author//DRA type Test fluid Correlation Remarks
[86]
Polyacrylamide
\(\frac{f_{c}}{f_{c,o}}=0.2+\frac{0.8}{1+N_{De^{\prime}}^{0.8}}\)
\(N_{De^{\prime}}=\frac{w}{w_{0.6}}\) Where \(w_{0.6}\) are the values of \(w\) at \(\frac{f_{c}}{f_{c,o}}=0.6\)
[114]
Polyacrylamide Polyethylene oxide Carboxymethyl cellulose
\(f_{\text{CL}}=\left(9.069-9.438n+4.37n^{2}\right)\left(\frac{a}{R}\right)^{0.5}N_{\text{Dn}}^{\left(-0.768+0.122n\right)}\)
\(70<N_{\text{Dn}}<400\) \(0.01<\frac{a}{R}<0.135\) Theoretical
[107]
Sodium Carboxymethyl cellulose
\(\frac{f_{c}}{f_{s}}=\aleph\left(n\right)N_{Dn^{\prime}}^{\beth\left(n\right)}\) or \(f_{c}=\frac{16}{N_{Re^{\prime}}}\aleph\left(n\right)\left(N_{Re^{\prime}}\sqrt[\frac{a}{R}]{}\right)^{\frac{\beth\left(n\right)}{2}}\) or \(f_{c}=\frac{16}{N_{{Re^{\prime}}_{c}}}\left(\frac{a}{R}\right)^{\frac{\beth\left(n\right)}{2}}\) \(\aleph\left(n\right)=47.969-153\left(n\right)+166.22\left(n\right)^{2}-60.132\left(n\right)^{3}\) \(\beth\left(n\right)=0.875\left(n\right)-0.515\) \(N_{{Re^{\prime}}_{c}}=\frac{\left(N_{Re^{\prime}}\right)^{1-\beth\left(n\right)}}{\aleph\left(n\right)}\) \(10<N_{Dn^{\prime}}<10^{3}\)
[115]
Carboxymethyl cellulose
\(f_{\text{CT}}\left(\frac{R}{a}\right)^{\frac{1}{2}}=0.0075+f_{\text{STD}}\left(\frac{R}{a}\right)^{\frac{1}{2}}\)
\(\frac{1}{f_{\text{STD}}^{\frac{1}{2}}}=4.0\log\log\ \left(N_{\text{Red}}f_{\text{STD}}^{\frac{1}{2}}\right)-0.4\ \) \(N_{\text{Re}_{\text{crit}}}<N_{\text{Re}}<10^{5}\) \(0.003<\frac{a}{R}<0.15\) \(0<\frac{H}{2R}<25.4\)
[115] – Carboxymethyl cellulose \(f_{\text{CL}}=f_{\text{SL}}\left[1-0.033\left(\log\log\ N_{\text{Dn}_{2}}\ \right)^{4.0}\right]\text{\ \ }\) \(f_{\text{SL}}=\frac{16}{N_{\text{Re}_{2}}}\)
[87] Carbopol 934 \(n^{0.4}\left\{0.079\left(N_{Re^{\prime}}\right)^{\frac{1}{4}}+\left[\frac{\left(\frac{a}{R}\right)^{1.5}}{14}\right]\right\}\) \(n^{0.4}\left\{0.079\left(N_{Re^{\prime}}\right)^{\frac{1}{4}}+\left[\frac{\left(\frac{a}{R}\right)^{1.5}}{14}\right]\right\}\)
[116]
Dodecyl trimethylammonium chloride
\(\frac{f_{C}}{f_{\text{SL}}}=0.105\left(\frac{a}{R}\right)^{0.006}\varnothing^{0.146}{Dn^{\prime}}^{0.5}\)
\(\frac{20<R}{a}<50\) \(\frac{\pi}{2}<\varnothing<\pi\) \(C>1000\ ppm\)
[117]
Guar gum, Hydroxyethylcellulose, Xanthan gum, Partially Hydrolysed Polyacrylamide
\(f_{\text{CL}}=\epsilon\left(2\right)^{\frac{n}{n+1}}N_{\text{Dno}}^{\frac{-1}{\left(n+1\right)}}\left(\frac{a}{R}\right)^{\frac{1}{2}}Y^{-\frac{3n}{n+1}}\)
\(Y=c_{0}+\frac{c_{1}}{N_{\text{Dno}}}+c_{2}n+\frac{c_{3}}{N_{\text{Dno}}^{2}}+c_{4}n^{2}+c_{5}\frac{n}{N_{\text{Dno}}}\) \(\epsilon=\left[a^{{}^{\prime}}+b^{\prime}\ln\ln\ \left(n\right)\ \right]^{2}\), \(N_{\text{Dno}}=\frac{\left(2a\right)^{n}U^{2-n}\rho}{K}\), \(c_{0}-c_{5},\ a^{{}^{\prime}}and\ b^{\prime}\) are correlation constant
[111]
Guar gum, Hydroxyethylcellulose, Xanthan gum, Partially Hydrolysed Polyacrylamide
\(f_{\text{CT}}=\frac{\left[c_{1}+c_{2}\ln\ln\ n\ +c_{3}\left(\frac{a}{R}\right)\right]\left[c_{4}+c_{5}\left(\frac{a}{R}\right)^{1.5}\right]}{N_{Dn\_g}^{\beta}}\)
\(N_{Re\_g}=\frac{\rho U^{2-n}d^{n}}{K_{p}8^{n-1}}\) \(N_{Dn\_g}=N_{Re\_g}\left(\frac{a}{R}\right)^{0.5}\)
[73] ODEAO Surfactant
Oleyldihydro-xyethylamineoxide 90% and cetyldimethylamino-aciticacidbetaine 10%
\(\frac{f_{C}}{f_{\text{SL}}}=0.17{N_{\text{Dn}}^{{}^{\prime}}}^{0.42}C_{c}^{0.11}T_{c}^{1.5}\)
\(2\times 10^{2}<N_{Dn^{\prime}}<1.5\times 10^{3}\)
[118] Polymer solution
Bentonite and line solution
\(f_{\text{CT}}=\frac{1.06a^{\prime}}{N_{\text{Re}_{\text{gen}}}^{0.8b^{\prime}}}\left(\frac{a}{R}\right)^{0.1}\)
\(a^{{}^{\prime}}=\frac{\left(n\right)\ +3.93}{50}\) \(b^{{}^{\prime}}=\frac{1.75-\left(n\right)\ }{7}\)
[23] ODEAO Surfactant
Oleyldihydro-xyethylamineoxide 90% and cetyldimethylamino-aciticacidbetaine 10%
\(f_{C}=\frac{1376\left(\frac{a}{R}\right)^{0.62}\left(1+0.94\text{Cc}^{-0.34}\text{Tc}^{-1.57}\right)}{\left(1.56+logN_{De^{\prime}}\right)^{5.73}}\)
\(4<Cc<14\) \(1<T_{c}<1.065\) \(100<N_{\text{Dn}}<N_{\text{Dn}_{\text{crit}}},\frac{r}{a}=0.018-0.045\),
[89]
Partially Hydrolised Polyacrylamide (PHPA)
\(N_{\text{De}}=\frac{1.6675\times 10^{-3}\left(f_{s}N_{\text{Re}_{s}}\right)^{1.4084}\left(\frac{4UT}{a}\right)}{\left[1+{1.0974\times 10^{-3}\left(f_{s}N_{\text{Re}_{s}}\frac{4UT}{a}\right)}^{1.42305}\right]^{0.7511}}\left(\frac{\rho_{p}\mu_{s}}{\rho_{s}\mu_{0}}\right)^{0.1129}\)
\(\mu_{0}\) and \(\mu_{s}\) are zero shear and solvents viscosities respectively. \(22,000\leq N_{\text{Re}_{s}}\leq 430,000\) \(0.754\leq n\leq 1.0\)