Gravel-Pack Completion — Producing Capacity: 24-Pet-A5 Petroleum Production Operations, December 2018, Q4

Question 4: Gravel-Pack Completion — Producing Capacity (25 points)

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. Reservoir/PVT and completion data for an 8-spf gravel-packed well, plus one production test.

Formation permeability, $k_o$	100 md
Skin, $S'$ (no compacted zone)	0
Oil viscosity, $\mu_o$	0.9 cp
Oil FVF, $B_o$	1.20 bbl/STB
Reservoir pressure, $\bar P_R$	2800 psig
Bubble-point pressure, $p_b$	3000 psig
Drainage / wellbore radius, $r_e$, $r_w$	1200 ft, 4.25 in
Net pay, $h$	40 ft
Casing I.D. / screen diameter	6.5 in / 4.5 in
Gravel permeability, $k_g$	40 darcies (40,000 md)
Test: $q_L$, $P_{wf}$	2200 STB/day, 2400 psi

Find. The anticipated producing capacity (AOF) of the completed well at 8 shots per foot.

Check: $p_b$ (3000 psig) is above $\bar P_R$ (2800 psig), so the reservoir is already saturated (two-phase) — the physically correct IPR is Vogel's, applied directly to the test point, and this is used as the primary producing-capacity answer. As a supporting check, the completion's own two resistances in series (formation radial Darcy flow to $r_w$, then radial Darcy flow through the gravel pack between the casing I.D. and the screen O.D.) are computed at the test rate to confirm the 8-spf, no-compacted-zone gravel pack is not the flow-limiting element.

Approach. Use Vogel's equation with the single test point to get the AOF directly (this is the correct IPR shape for a saturated reservoir). Separately, compute the theoretical formation-only and gravel-pack-only pressure drops at the test rate to check that the 8-spf completion is not restricting flow.

Vogel ratio at the test point. $R=P_{wf}/\bar P_R=2400/2800=0.857$. $1-0.2(0.857)-0.8(0.857)^2=1-0.171-0.588=0.241$.
Producing capacity (AOF). $(q_o)_{max}=q_L/0.241=2200/0.241$. $\boxed{\text{AOF}=9136\ \text{STB/day}}$.
Supporting check — formation Darcy drawdown at the test rate. With $r_w=4.25/12=0.354$ ft, $\ln(r_e/r_w)=\ln(1200/0.354)=8.128$: $\Delta P_{formation}=\dfrac{q\,\mu_o B_o(\ln(r_e/r_w)-0.75+S')}{0.00708\,k_o h}=\dfrac{2200\times0.9\times1.20\times(8.128-0.75+0)}{0.00708\times100\times40}$. $\boxed{\Delta P_{formation}\approx619\ \text{psi}}$.
Supporting check — gravel-pack annulus drawdown at the test rate. The gravel occupies the annulus from the casing I.D. ($r=3.25$ in) to the screen O.D. ($r=2.25$ in); $\ln(3.25/2.25)=0.368$. $\Delta P_{gravel}=\dfrac{q\,\mu_o B_o\ln(r_{cas}/r_{scr})}{0.00708\,k_g h}=\dfrac{2200\times0.9\times1.20\times0.368}{0.00708\times40{,}000\times40}$. $\boxed{\Delta P_{gravel}\approx0.08\ \text{psi}}$ — about 0.02% of the observed 400 psi test drawdown, i.e. completely negligible.

The gravel pack itself contributes essentially no additional resistance at 8 shots per foot with no compacted zone (0.08 psi out of 400 psi observed), confirming that the completion is not the bottleneck; the formation's own two-phase (Vogel) behaviour governs the well's producing capacity, which is why the theoretical single-phase Darcy estimate (619 psi at the test rate, exceeding even the full 400 psi observed drawdown) does not reconcile exactly with the field test — the reservoir is saturated and does not follow single-phase Darcy theory at all.

Fig. 4 — Vogel IPR fitted through the single test point (2200 STB/day at 2400 psi), giving AOF = 9136 STB/day.

Quantity	Value
Vogel ratio at test point	0.241
Anticipated producing capacity (AOF)	9136 STB/day
Formation Darcy drawdown at test rate (check)	≈619 psi
Gravel-pack drawdown at test rate (check)	≈0.08 psi (negligible)

Topic: Producing-capacity estimation for a gravel-packed completion in a saturated reservoir.

Key relations: Vogel: $q_o/(q_o)_{max}=1-0.2R-0.8R^2$; radial Darcy pressure drop: $\Delta P=\dfrac{q\mu B(\ln(r_2/r_1)-0.75+S)}{0.00708\,kh}$, applied separately to the formation and to the gravel-filled annulus (McLeod-type series-resistance model for gravel-pack/perforated completions).

Why this works: once $\bar P_R$ falls below $p_b$ the entire drainage area is two-phase, so Vogel's empirically-fitted curve (built to reproduce falling oil relative permeability as gas saturation grows) is the correct IPR shape, not a straight line; the completion's own resistances are then checked independently, in series, to confirm they don't materially change that picture.

Common pitfall: forcing the field test to reconcile with a single-phase Darcy formula when $p_b\gt\bar P_R$ — the mismatch is expected physics, not a data error, and should be explained rather than "corrected away."

Source: Golan & Whitson, Well Performance, 2nd ed., Ch. 2 (Vogel) and Ch. 4 (perforated/gravel-packed completions); McLeod, H.O., "The Effect of Perforating Conditions on Well Performance," JPT, 1983.

Question 4 of 5: Gravel-Pack Completion — Producing Capacity

Question 4: Gravel-Pack Completion — Producing Capacity (25 points)