24-Pet-A6 Well Logging and Formation Evaluation · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
98-Pet-A6 — Reservoir Mechanics · National Exams, May 2015 · 3 hours, closed book, Casio/Sharp approved calculator only · eight problems set (candidates answer Problems 1 and 2 plus any three of the remaining six per the exam's own instructions; all eight are solved in full below as a complete study resource), all questions equal value.
Reference texts: Craft, B.C. & Hawkins, M.F., Applied Petroleum Reservoir Engineering, 3rd ed. (material balance, decline curves, transient well testing, permeability averaging); Ahmed, T., Reservoir Engineering Handbook, 5th ed. (material balance, decline-curve analysis, pressure buildup, PVT correlations); Golan, M. & Whitson, C.H., Well Performance, 2nd ed. (reserves methods, water/gas influx); Lyons, W.C. (ed.), Standard Handbook of Petroleum and Natural Gas Engineering, 3rd ed.
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.
The most broadly used method for estimating gas initially in place (GIIP), and the one this exam's own formula sheet supports directly, is the $p/z$ material-balance method for a volumetric (no water drive), closed dry-gas reservoir.
Derivation. A dry-gas reservoir obeys the real-gas law $pV=nzRT$ at both initial and any later condition. Since the reservoir is closed and volumetric, the total moles of gas originally present equals the moles remaining plus the moles produced, and the reservoir pore volume occupied by gas does not change (no water influx, no compaction assumed). Writing the gas volume at reservoir conditions via $B_g=\dfrac{zTp_{sc}}{pT_{sc}}$ (reservoir barrels or cubic feet per standard cubic foot), a volumetric balance on gas in place gives $G B_{gi}=(G-G_p)B_g$ at any later state, i.e. all the original gas $G$ (initially at $B_{gi}$) either remains in the same pore space (now at the expanded $B_g$) or has been produced. Rearranging, and substituting $B_g\propto z/p$ at fixed reservoir temperature, this reduces to the linear form $$\frac{p}{z}=\frac{p_i}{z_i}\left(1-\frac{G_p}{G}\right).$$ Plotting $p/z$ (using measured shut-in reservoir pressures and gas deviation factors $z$ from the gas's own composition/correlation) against cumulative gas produced $G_p$ gives a straight line: the $p/z$-axis intercept ($G_p=0$) recovers $p_i/z_i$ as a check, and extrapolating the line to $p/z=0$ gives the original gas in place, $G$. The same line, extrapolated instead to the field's economic abandonment $p/z$, gives ultimate recoverable reserves directly.
Assumptions. The method assumes: (i) the reservoir is volumetric — no aquifer/water influx and no significant pore-volume compaction, so that the produced-gas voidage is replaced only by the expansion of the remaining gas (if there is water influx, the $p/z$ trend curves upward, no longer plotting as a straight line, and a $p/z$ extrapolation without an influx correction term will understate $G$); (ii) reservoir pressure is uniform (or a valid volumetric average) at each survey, requiring either a fully-built-up shut-in or a reliable average-pressure correction (Dietz/Matthews-Brons-Hazebroek) if wells are not fully built up; (iii) the produced-gas stream composition (hence $z$) is reasonably constant, or $z$ is tracked with the actual produced-gas gravity through time; and (iv) enough pressure decline has already occurred (typically several percent of $p_i$) for the trend to be well-defined — very early in life, with only one or two data points, the extrapolation is highly uncertain.
Errors and limitations. The two dominant sources of error are: unrecognized water influx (silently curving the plot and biasing $G$ high if force-fitted with a straight line, or requiring a full Havlena–Odeh $F$ vs. $E_g+E_{w,f}$ treatment instead of the simple $p/z$ form); and poor or infrequent shut-in pressure surveys (incompletely built-up wells read low, pulling early points off the true trend and biasing the fitted line, hence $G$). Retrograde-condensate reservoirs violate the "dry gas" assumption outright once pressure falls below the dew point (liquid dropping out changes the effective produced-gas composition and the simple $p/z$ line bends), requiring a compositional or modified two-phase material balance instead. Volumetric methods (net pay $\times$ area $\times$ porosity $\times$ $(1-S_w)$/$B_{gi}$, from log/core/seismic data) provide an independent, geology-based cross-check that does not depend on having any production history at all, and the two methods are best used together — volumetric for an early, pre-production estimate and $p/z$ material balance once enough pressure/production history exists to define a reliable trend.
