Maximum hydrocarbon column height before shale seal breach: 24-Pet-B4 Well Testing, December 2015, Q8

Section 3, Q3-2: Maximum hydrocarbon column height before shale seal breach (4 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.

Quantity	Symbol	Value
Sandstone (reservoir) pore-throat diameter	D_sand	37 μm
Shale (seal) pore-throat diameter	D_shale	3.5 μm
Interfacial tension	γ	28 dynes/cm
Hydrocarbon density	ρ_HC	880 kg/m³
Saltwater density	ρ_w	1070 kg/m³
Wettability	θ	0° (water-wet, cosθ = 1)

Find. The maximum hydrocarbon column height z the shale seal can hold before its capillary entry pressure is exceeded and the seal breaches.

Approach. The seal that governs is whichever rock has the smaller (finer) pore throat – here the shale, not the sandstone reservoir – since a smaller pore throat gives a higher capillary displacement pressure. Compute the shale's displacement pressure from the given interfacial tension and pore-throat radius, then convert that pressure to an equivalent hydrocarbon column height using the buoyancy (density-contrast) relation on the exam's own formula sheet.

Confirm which rock governs. Displacement pressure $P_d = \dfrac{2\gamma\cos\theta}{R}$ is inversely proportional to pore-throat radius, so the shale (R = 3.5/2 = 1.75 μm) has a far higher entry pressure than the sandstone (R = 37/2 = 18.5 μm) – the shale seal governs the trapped column, not the sandstone reservoir rock.
Unit conversion. $\gamma = 28\ \text{dynes/cm} = 28\times10^{-3}\ \text{N/m} = 0.028\ \text{N/m}$; $D_{shale}=3.5\ \mu\text{m}=3.5\times10^{-6}\ \text{m}$.
Column height from the given formula. Using the exam's own column-height form (algebraically identical to $P_d/(\Delta\rho\, g)$, since $4/D = 2/(D/2) = 2/R$): $$z=\frac{4\gamma}{D_{shale}}\cdot\frac{1}{(\rho_w-\rho_{HC})g}=\frac{4(0.028)}{3.5\times10^{-6}}\cdot\frac{1}{(1070-880)(9.81)}$$ $$z=\frac{0.112}{3.5\times10^{-6}}\cdot\frac{1}{1{,}863.9}=32{,}000\ \text{Pa/(kg/m}^3\!\cdot\text{m/s}^2)\times5.365\times10^{-4}$$ $$\boxed{z \approx 17.2\ \text{m}}$$

Quantity	Result
Governing seal	Shale (finer pore throat)
Shale displacement pressure, P_d	≈ 32,000 Pa (0.32 bar)
Maximum trapped hydrocarbon column height, z	≈ 17.2 m

Topic. Capillary sealing and maximum hydrocarbon column height.

Key relations. Displacement (entry) pressure $P_d = \dfrac{2\gamma\cos\theta}{R}$; buoyancy-pressure equivalent column height $z=\dfrac{4\gamma}{D}\cdot\dfrac{1}{(\rho_w-\rho_{HC})g}$; the seal that governs the maximum column is whichever adjacent rock has the smallest (finest) connected pore throat, not necessarily the rock explicitly labelled “seal.”

Why this works. A hydrocarbon column exerts an upward buoyancy pressure at its top, proportional to its height and the water–hydrocarbon density contrast; the seal holds as long as its own capillary entry pressure (set by its finest connected pore throats) exceeds that buoyancy pressure – once the column grows tall enough that buoyancy pressure equals $P_d$, hydrocarbon begins to invade and flow through the seal's pore network, and the trap can hold no more.

Common pitfall. Using the reservoir (sandstone) pore-throat diameter instead of the seal (shale) diameter in the formula – the much coarser reservoir pore throats give a trivially small entry pressure and would grossly overstate the column the trap can actually hold; only the finest-pore-throat rock in the seal column is limiting.

Source. Selley & Sonnenberg, ch.9 (capillary sealing, Schowalter's method); Allen & Allen, ch.4.

Question 8 of 18: Maximum hydrocarbon column height before shale seal breach

Section 3, Q3-2: Maximum hydrocarbon column height before shale seal breach (4 marks)