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24-Pet-A6 Well Logging and Formation Evaluation · May 2015

Question 4 of 8: Pressure Communication Between Two Wells

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

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.

Check: this paper's own title page reads “98-PET-A6: Reservoir Mechanics”, not “Well Logging and Formation Evaluation” — the subject heading it is listed under does not match its content. Every problem below is answered as the paper actually printed it (material balance, decline-curve analysis, pressure-transient testing and permeability averaging — classic Reservoir Mechanics/Fundamental Reservoir Engineering topics), not well-logging.

Problem 4: Pressure Communication Between Two Wells (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. Fluid gradient data above; well 1 and well 2 datum elevations (Kelly-bushing elevation minus depth) and measured pressures per the table.

Find. Whether the two pressure/depth points are consistent with a single continuous oil column connecting the wells (pressure communication), and hence whether they could belong to the same reservoir.

Approach. Convert the given oil density directly to a hydrostatic pressure gradient; reduce each well's pressure to a common datum (height above mean sea level, $=$ KB elevation $-$ depth from KB); compare the pressure difference the two data points actually show to what the oil's own gradient would require over that elevation difference.

Sea level (MSL) Well 1 gauge: elev = 7134−5652 = 1482 ft, P₁=2453 psia Well 2 gauge: elev = 7028−5426 = 1602 ft, P₂=2306 psia apparent gradient over Δz=120 ft: (P₁−P₂)/Δz = 1.225 psi/ft (elevation = height above MSL; both wells plotted on the same vertical scale, dashed guide lines mark each gauge depth) Higher elevation (shallower) ↑
Fig. 2: Schematic of the two wells' gauge elevations (height above MSL) and measured pressures. Well 2's gauge sits 120 ft shallower than well 1's.
  1. Fluid gradient. Using the given in-situ oil density directly, $\text{grad}=\rho_o/144=62.366/144$, so $\boxed{\text{grad}=0.4331\ \text{psi/ft}}$.
  2. Datum elevations. Height above MSL $=$ KB elevation $-$ depth from KB: well 1, $7134-5652=1482$ ft; well 2, $7028-5426=1602$ ft. Well 2's gauge sits $\Delta z=1602-1482=120$ ft shallower than well 1's.
  3. Apparent gradient between the wells. If a single continuous oil column connected the two points, $P_1-P_2=\text{grad}\times\Delta z$. The DATA instead give $\dfrac{P_1-P_2}{\Delta z}=\dfrac{2453-2306}{120}=\dfrac{147}{120}$, so $\boxed{\text{apparent gradient}=1.225\ \text{psi/ft}}$ — nearly $3\times$ the oil's own $0.433$ psi/ft.
  4. Consistency check. Projecting well 1's pressure up to well 2's datum using the OIL gradient: $P_{2,\text{pred}}=P_1-\text{grad}\times\Delta z=2453-0.4331(120)=2453-52.0$, so $P_{2,\text{pred}}=2401.0$ psia, versus the actual $P_2=2306$ psia — a $95$ psi discrepancy over just 120 ft, far outside any reasonable gauge/measurement tolerance.
Check: the exam supplies $\rho_o=62.366$ lbm/ft³ directly as a fluid property and it is used as printed for the gradient. A correlation-based check (stock-tank density from $32^{\circ}$API $=54.0$ lbm/ft³, plus dissolved gas per $R_s=500$ scf/stb and $B_o=1.3$) gives an independently-computed live-oil reservoir density of only $\approx45.3$ lbm/ft³ — noticeably lower than the given value — but this does not change the conclusion, since even the lower correlation-based gradient ($\approx0.315$ psi/ft) is still far short of the $1.225$ psi/ft the data actually require.
QuantityValue
Oil hydrostatic gradient0.433 psi/ft
Apparent gradient from well data1.225 psi/ft
Predicted $P_2$ (same oil column)2401.0 psia (actual: 2306 psia)
ConclusionWells are not in pressure communication via a single oil column; the data are inconsistent with them being the same reservoir compartment (a sealing fault or separate accumulation is implied)