24-Pet-A3 Fundamental Reservoir Engineering · December 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
98-Pet-A3 — Fundamental Reservoir Engineering · National Exams, December 2014 · 3 hours, closed book, Casio/Sharp approved calculator only · five (5) questions constitute a complete exam paper (the first five as they appear in the answer book are marked), all questions equal value, all parts of a multipart question equal weight.
Reference texts: Ahmed, T., Reservoir Engineering Handbook, 5th ed. (Darcy's law and fluid potential, transient well testing, p/Z and oil material balance, capillary pressure/relative permeability); Craft, B.C. & Hawkins, M.F., Applied Petroleum Reservoir Engineering, 3rd ed. (reservoir drive mechanisms, material balance fundamentals); Lyons, W.C. (ed.), Standard Handbook of Petroleum and Natural Gas Engineering, 3rd ed. (Standing–Katz Z-factor correlation); McCain, W.D., The Properties of Petroleum Fluids, 3rd ed. (capillary pressure and relative permeability laboratory data).
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.
a) Volumetric reservoir. A volumetric reservoir is bounded by a no-flow (sealing) boundary with no aquifer support, so all production is accounted for solely by expansion of the oil, gas and rock already in place — there is no water influx term in its material balance.
b) Wet gas reservoir. A wet gas reservoir remains single-phase gas throughout the reservoir at all times (temperature above the cricondentherm), but the surface pressure/temperature path taken during production crosses into the two-phase region at the separator, so some liquid (condensate) is recovered at the surface even though none ever existed downhole.
c) Gas-oil gravity drainage. Gas-oil gravity drainage is a recovery mechanism in which oil drains downward and gas rises into an expanding gas cap under the density difference between the phases, rather than being displaced by fluid expansion or an external drive; it is most effective in reservoirs with high vertical permeability and structural relief.
d) Gas cap expansion drive. Under gas cap expansion (gas cap) drive, an existing free-gas cap expands as reservoir pressure declines from oil production, supplying pressure support and displacing oil toward the wells; its relative strength is set by the gas cap size ratio $m=$ (initial gas cap reservoir volume)/(initial oil reservoir volume).
e) Connate water saturation. Connate water saturation, $S_{wc}$, is the water left trapped in the pore space at the time hydrocarbons migrated into and filled the trap; it is immobile at normal producing pressure gradients and is never fully displaced by the invading oil or gas.
f) Formation compressibility. Formation (pore-volume) compressibility, $c_f=-\dfrac{1}{V_p}\dfrac{dV_p}{dp}$, is the fractional shrinkage of pore volume per unit drop in pore pressure as the effective overburden stress increases with depletion; it is one of the (usually small) terms summed into total system compressibility in the material balance.
g) Formation damage. Formation damage is a permeability reduction confined to the near-wellbore region, caused by drilling/completion/production fluids (mud filtrate invasion, fines migration, clay swelling, scale); it is quantified by a positive skin factor $S$ and produces an additional pressure drop beyond that of the undamaged formation.
h) Depletion drive. Depletion (solution-gas) drive is the mechanism by which, once reservoir pressure falls below the bubble point, the expansion of gas evolving out of solution (together with oil, connate-water and rock expansion) supplies essentially the only driving energy, with no water influx or significant gas cap; it typically yields the lowest primary recovery factor of the classical drive mechanisms.
i) Relative permeability. Relative permeability of a phase, $k_{r,\text{phase}}=k_{\text{eff,phase}}/k$, is the ratio of that phase's effective permeability at its current saturation to the rock's absolute (single-phase) permeability; each phase's $k_r$ is a function of its own saturation and governs how the phases partition their flow when moving simultaneously.
j) Wettability. Wettability is the tendency of one fluid phase to preferentially adhere to and spread across the rock's pore surfaces in the presence of another immiscible phase, described by the contact angle $\theta$ measured through the denser (usually water) phase; it controls the shape of both the capillary-pressure and relative-permeability curves (water-wet vs. oil-wet behaviour).
