$($c$)$ For the blend of tertiary butyl alcohol, coker gasoline, and FCC gasoline given in Table B$1$ below:

$($i$)$ Determine the volume fractions of the various components in the blend using four significant figures, i$.$e$.$ Y$.$YYY ${10}^Y.$

$[3$ marks$]$

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Module code: CAPE$5420$M$01$

$($ii$)$ Calculate the Research Octane Number $($RON$)$ of the blend by linear mixing of RON $($use $3$ significant figures, i$.$e$.$ Y$.$YY ${10}^Y).$

$[3$ marks$]$

Table B$1$

$\backslash$table$[[$Component$,\backslash$table$[[$Flow Rate$],[($BPD Barrels per$],[$day$)]],\backslash$table$[[$RON$],[($Research Octane$],[$Number$)]]],[$Tertiary butyl alcohol $(\text{'}$TBA$\text{'}),2500,105],[$Coker gasoline $(\text{'}$CKG$\text{'}),4500,68],[$FCC gasoline $(\text{'}$FCCG$\text{'}),17000,84]]$

$($iii$)$ Determine, RON blending indices for each component $(\text{'}$Bloni$\text{'})$ according to equations $1-3$ below. $($Use $3$ significant figures as in $($ii$))$

$[8$ marks$]$

For $11$RON$76$

Bloni $=36\mathrm{.}01+38\mathrm{.}33(RO\frac{N}{100})-99\mathrm{.}8(RO\frac{N}{100}{)}^2+341\mathrm{.}3(RO\frac{N}{100}{)}^3-507\mathrm{.}02$

$(RO\frac{N}{100}{)}^4+268\mathrm{.}64(RO\frac{N}{100}{)}^5$

$Eq(1)$

For $76$RON$103$

Bloni $=-299\mathrm{.}5+1272(RO\frac{N}{100})-1552\mathrm{.}9(RO\frac{N}{100}{)}^2+651(RO\frac{N}{100}{)}^3,Eq(2)$

For $103$RON$106$

Bloni $=2206\mathrm{.}3-4313\mathrm{.}64(RO\frac{N}{100})+2178\mathrm{.}57(RO\frac{N}{100}{)}^2$