24-Pet-A3 Fundamental Reservoir Engineering · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
98-Pet-A3 — Fundamental Reservoir Engineering · National Exams, May 2016 · 3 hours, closed book, non-communicating 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, transient well testing and image wells, p/Z and oil material balance, capillary pressure/relative permeability); Craft, B.C. & Hawkins, M.F., Applied Petroleum Reservoir Engineering, 3rd ed. (steady-state radial flow, reservoir drive mechanisms); Lyons, W.C. (ed.), Standard Handbook of Petroleum and Natural Gas Engineering, 3rd ed.; 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) Infinite acting. A well or reservoir is "infinite acting" while the pressure transient created at the wellbore has not yet reached any outer boundary (fault, aquifer edge, or another well); during this period the pressure response depends only on the well/reservoir properties near the well, not on the reservoir's actual size or shape.
b) Threshold (displacement/entry) pressure. The threshold pressure, $P_{ct}$, is the minimum capillary pressure that must be exceeded before the non-wetting phase can first enter and displace the wetting phase from the largest pore throats of a water-saturated rock; on a capillary-pressure curve it is the pressure at which the curve first departs from $S_w=1$ (the near-vertical rise visible in Question 5's chart).
c) Compaction drive. Compaction (rock/pore-volume) drive is a reservoir-energy mechanism in which the pore volume itself shrinks as fluid pressure declines and the rock grains bear a larger share of the overburden load, expelling fluid; it is the mechanism represented by the formation compressibility $c_f$ term in the material balance and is usually a minor contributor except in highly compressible (unconsolidated or overpressured) formations.
d) Well stimulation. Well stimulation is any treatment (matrix acidizing or hydraulic fracturing) applied to the near-wellbore formation to remove damage or create new flow channels, thereby reducing the well's skin factor (making it negative for a successful fracture job) and increasing its productivity index beyond what the undamaged formation alone would give.
e) Productivity index. The productivity index, $J=q/(\bar p-p_{wf})$, is the well's rate of production per unit pressure drawdown between the average reservoir pressure and the flowing bottom-hole pressure; for radial flow at pseudosteady state, $J=\dfrac{7.08kh}{\mu B_o[\ln(r_e/r_w)-3/4+s]}$ (k in Darcy).
f) Drawdown test. A drawdown test puts a well on production at a constant rate (after it has stabilized at $p_i$) and records $p_{wf}$ versus time; a semilog plot of $p_{wf}$ vs. $\log t$ during the infinite-acting period yields permeability and skin from its slope and intercept.
g) Formation volume factor. The formation (oil) volume factor, $B_o$, is the ratio of the volume a unit of oil (plus its dissolved gas) occupies at reservoir pressure and temperature to the volume it occupies as stock-tank oil at surface conditions (bbl reservoir/STB); it captures both the liquid thermal/pressure expansion and the shrinkage on releasing solution gas at the surface.
h) Isothermal compressibility. Isothermal compressibility, $c=-\dfrac{1}{V}\left(\dfrac{\partial V}{\partial p}\right)_T$, is the fractional change in a fluid's (or the pore system's) volume per unit change in pressure at constant temperature; the total system compressibility $c_t=c_o S_o+c_w S_w+c_g S_g+c_f$ that appears in the diffusivity equation sums the oil, water, gas and formation contributions.
i) Oil reserve. An oil reserve is the portion of the discovered oil-in-place, $N$, that is estimated to be technically and commercially recoverable under defined economic and regulatory conditions ($N\times$ recovery factor), as distinct from the total oil-in-place itself, which includes oil that will never be produced.
j) Residual oil saturation. Residual oil saturation, $S_{or}$, is the oil saturation left behind in a swept, water-invaded pore volume after all mobile oil has been displaced by water at the prevailing flood conditions; it is trapped by capillary forces (as isolated, disconnected globules) and is not recoverable by further waterflooding at the same conditions, only by an improved/enhanced-recovery process.
