Real Gas Density and Gas FVF: 24-Pet-A2 Petroleum Reservoir Fluids, December 2014, Q2

Question 2: Real Gas Density and Gas FVF (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Gas composition table above (sums to 100 mole %); $T = 95\,{}^{\circ}\text{F}$; $p = 1200$ psia. Formula sheet: $M_{av}=\sum y_iM_i$, $T_{pc}=\sum y_iT_{c_i}$, $p_{pc}=\sum y_ip_{c_i}$, $\rho=\dfrac{pM}{ZRT}$ with $R=10.732\ \text{psi-ft}^3/(\text{lb-mol-}{}^{\circ}\text{R})$, $B_g=0.02827\dfrac{ZT}{p}$ (ft$^3$/SCF).

Find. The real gas density $\rho$ (lb$_m$/ft$^3$) and the gas formation volume factor $B_g$ (ft$^3$/SCF) at $95\,{}^{\circ}\text{F}$, 1200 psia.

Approach. Build the apparent molecular weight and Kay's-rule pseudo-critical properties from composition, form the reduced temperature and pressure, read/compute the compressibility factor $Z$ from the Standing–Katz correlation (the same chart reproduced on the formula-sheet page), then evaluate density and $B_g$ from the real-gas relations.

Apparent molecular weight. $M_{av}=\sum y_iM_i = 0.96(16.04)+0.035(30.07)+0.003(44.11)+0.0006(58.123)+0.00015(58.123)+0.00055(86.177)+0.0007(128.00)$. Summing term by term gives $\boxed{M_{av}=16.76\ \text{lb}_m/\text{lb-mol}}$.
Pseudo-critical properties (Kay's rule). $T_{pc}=\sum y_iT_{c_i}=352.7\,{}^{\circ}\text{R}$ and $p_{pc}=\sum y_ip_{c_i}=667.2$ psia, using the same mole-fraction weights as Step 1.
Reduced conditions. $T = 95+459.67 = 554.67\,{}^{\circ}\text{R}$. $T_r=\dfrac{T}{T_{pc}}=\dfrac{554.67}{352.7}=1.573$, $\ p_r=\dfrac{p}{p_{pc}}=\dfrac{1200}{667.2}=1.799$.
Compressibility factor. Entering the Standing–Katz $Z$-chart (formula sheet, Fig. 4-16) at $T_r=1.57$, $p_r=1.80$ reads $Z\approx 0.86$; solving the equivalent Dranchuk–Abou-Kassem correlation numerically at the same $(T_r,p_r)$ gives $\boxed{Z=0.863}$, confirming the chart reading.
Real gas density. Substituting into $\rho=\dfrac{pM}{ZRT}=\dfrac{(1200)(16.76)}{(0.863)(10.732)(554.67)}$. The denominator is $(0.863)(10.732)(554.67)=5136.1$; the numerator is $20112$. So $\boxed{\rho = 3.91\ \text{lb}_m/\text{ft}^3}$.
Gas formation volume factor. $B_g=0.02827\dfrac{ZT}{p}=0.02827\times\dfrac{(0.863)(554.67)}{1200}=0.02827\times 0.3990$. So $\boxed{B_g = 0.01128\ \text{ft}^3/\text{SCF}}$ (equivalently $0.01128/5.615 \approx 2.01\times10^{-3}$ RB/SCF).

Quantity	Value
$M_{av}$	16.76 lb$_m$/lb-mol
$T_{pc}$, $p_{pc}$	352.7 °R, 667.2 psia
$T_r$, $p_r$	1.573, 1.799
$Z$ at 95°F, 1200 psia	0.863
Real gas density $\rho$	3.91 lb$_m$/ft$^3$
Gas FVF $B_g$	0.01128 ft$^3$/SCF

Topic: Real-gas density and formation volume factor via pseudo-critical properties.

Key relations: Kay's mixing rule $T_{pc}=\sum y_iT_{c_i}$, $p_{pc}=\sum y_ip_{c_i}$; real gas law $pV=ZnRT \Rightarrow \rho=pM/(ZRT)$; $B_g=V_{res}/V_{std}=0.02827\,ZT/p$.

Why this works: Kay's rule collapses a multicomponent mixture onto a single corresponding-states pair $(T_r,p_r)$ so one universal $Z$-chart applies to any sweet natural gas of similar heavy-end content; the real-gas law then converts that single $Z$ directly into density and volumetric expansion factor at reservoir conditions.

Common pitfall: Forgetting to convert Fahrenheit to Rankine before forming $T_r$, or averaging $Z$ instead of $M_{av}$/$T_{pc}$/$p_{pc}$ — $Z$ itself must always come from the mixture's own $(T_r,p_r)$, never a mole-fraction average of pure-component $Z$'s.

Source: Lyons (ed.), Standard Handbook of Petroleum and Natural Gas Engineering, 3rd ed., Ch. 1 (Gas properties, Standing-Katz correlation); Craft & Hawkins Ch. 1.

Question 2 of 7: Real Gas Density and Gas FVF

Question 2: Real Gas Density and Gas FVF (20 marks)