Question 7 of 7: Real-Gas Formation Volume Factor and Density via the Standing–Katz Chart
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
17-Pet-A2 — Petroleum Reservoir Fluids · National Exams, May 2018 · 3 hours, closed book, Casio/Sharp approved calculators only · a formula sheet is provided; FIVE (5) questions constitute a complete exam paper (the first five as submitted are marked); all questions equal value, all parts of a multipart question equal weight; oilfield-unit questions must be answered in field units.
Reference texts: Craft, B.C. & Hawkins, M.F., Applied Petroleum Reservoir Engineering, 3rd ed. (Ch. 1–2, PVT properties, reservoir/well-stream classification); Lyons, W.C. (ed.), Standard Handbook of Petroleum and Natural Gas Engineering, 3rd ed. (Standing–Katz Z-factor correlation, gas properties); McCain, W.D., The Properties of Petroleum Fluids, 3rd ed. (phase behaviour, black-oil PVT laboratory data, gas hydrates/waxes/asphaltenes); Ahmed, T., Reservoir Engineering Handbook, 5th ed. (material balance, well-stream gravity, pseudo-critical property correlations); Danesh, A., PVT and Phase Behaviour of Petroleum Reservoir Fluids (equilibrium K-value flash calculations, Gibbs' phase rule).
Question 7: Real-Gas Formation Volume Factor and Density via the Standing–Katz Chart (20 marks)
Check: this question reuses the same 7-component separator-gas composition and molecular weights given in Question 6's table (Methane 71%, Ethane 10%, Propane 9%, i-Butane 3%, n-Butane 4%, i-Pentane 2%, n-Pentane 1%) — the source paper prints the identical table a second time on this page rather than cross-referencing it.
Given. Gas-phase composition (as in Question 6); $p=4000$ psia; $T=180\,{}^{\circ}\text{F}$; $MW_{air}=28.97\ \text{lb}_{mass}/\text{lb-mole}$; formula sheet: $T_{pc}=168+325\gamma_g-12.5\gamma_g^2$ (°R), $p_{pc}=677+15.0\gamma_g-37.5\gamma_g^2$ (psia), $B_g=0.02827\dfrac{ZT}{p}$ (ft$^3$/SCF), $\rho=\dfrac{pMW}{ZRT}$ with $R=10.732\ \text{psi-ft}^3/(\text{lb-mole-}{}^{\circ}\text{R})$.
Find. $B_g$ (ft$^3$/SCF) and gas density $\rho$ (lb$_{mass}$/ft$^3$) at the stated conditions.
Approach. Compute the gas's average molecular weight and specific gravity from its composition, use the formula-sheet correlations to get pseudo-critical properties (and hence $T_r$, $p_r$), read the compressibility factor $Z$ off the Standing–Katz chart at that $(T_r,p_r)$, then substitute into the $B_g$ and $\rho$ formulas.
Average molecular weight and gas gravity. $MW_{avg}=\sum y_iMW_i=24.60\ \text{lb}_{mass}/\text{lb-mole}$ (same composition and calculation as Question 6's gas phase). $\gamma_g=\dfrac{MW_{avg}}{MW_{air}}=\dfrac{24.60}{28.97}$, so $\boxed{\gamma_g\approx0.849}$.
Pseudo-critical properties. $T_{pc}=168+325(0.849)-12.5(0.849)^2=168+276.1-9.01$, so $\boxed{T_{pc}\approx434.96\,{}^{\circ}\text{R}}$. $p_{pc}=677+15.0(0.849)-37.5(0.849)^2=677+12.73-27.03$, so $\boxed{p_{pc}\approx662.70\ \text{psia}}$.
Reduced temperature and pressure. $T=180\,{}^{\circ}\text{F}=180+459.67=639.67\,{}^{\circ}\text{R}$. $T_r=\dfrac{T}{T_{pc}}=\dfrac{639.67}{434.96}$, so $\boxed{T_r\approx1.47}$. $p_r=\dfrac{p}{p_{pc}}=\dfrac{4000}{662.70}$, so $\boxed{p_r\approx6.04}$.
Compressibility factor from the Standing–Katz chart. Locating $(p_r,T_r)=(6.04,1.47)$ on the chart (Question 1's formula-sheet page reproduces this same chart) lands on the $T_r\approx1.45$–$1.5$ curve family in its high-pressure, low-$Z$ trough: $\boxed{Z\approx0.85}$.
Gas formation volume factor. $B_g=0.02827\dfrac{ZT}{p}=0.02827\times\dfrac{0.854\times639.67}{4000}$, so $\boxed{B_g\approx0.00386\ \text{ft}^3/\text{SCF}}$.
Gas density. $\rho=\dfrac{pMW_{avg}}{ZRT}=\dfrac{4000\times24.60}{0.854\times10.732\times639.67}$, so $\boxed{\rho\approx16.8\ \text{lb}_{mass}/\text{ft}^3}$ — roughly 22 times denser than the same gas at standard conditions ($\rho_{sc}=MW_{avg}/379.4\approx0.065\ \text{lb}_{mass}/\text{ft}^3$), reflecting the very high reservoir pressure.
Schematic Standing–Katz $Z$-factor chart (see the formula-sheet page for the full chart): the query point at $p_r=6.04$, $T_r=1.47$ falls in the low-$Z$ trough characteristic of moderately reduced temperatures at high reduced pressure, reading $Z\approx0.85$.
