Huge Pressure and Trapped Oil: The Answer in Darcy's Law

Lesson Summary

Why doesn't a well produce despite high reservoir pressure? Because permeability in Darcy's Law might be low.

This lesson is part of the Production & Processing track and lasts 2:26 minutes. Watch the video first, then review the key points and test your understanding with the questions below.

Key Points

1. 1Flow rate is proportional to permeability and pressure differential
2. 2Flow rate is inversely proportional to viscosity

Written Lesson

Lesson Question

We may find a reservoir with very high pressure, yet the well produces at a low rate. The reason is that pressure alone is not enough: fluids need a path to pass between rock grains. This path is measured by Permeability, and the relationship between pressure, permeability, and flow rate is described by Darcy's Law, established by French engineer Henry Darcy in the 19th century from experiments on water flow through sand filters.

The Linear Equation

In linear flow through a rock sample, the rate is directly proportional to permeability, cross-sectional area, and pressure differential, and inversely proportional to fluid viscosity and path length. In field units:

q (bbl/d) = 0.001127 × k (md) × A (ft²) × ΔP (psi) ÷ (μ (cp) × L (ft))

The simple meaning: double the permeability and the rate doubles; double the viscosity and the rate is halved.

The Radial Equation: What Happens Around the Well

In the reservoir, fluid flows from all directions toward the well, so the flow is radial (Radial Flow). Assuming steady-state flow of a single fluid:

q (STB/d) = 0.00708 × k × h × (Pe − Pwf) ÷ (μ × B × (ln(re/rw) + S))

Where h is the producing thickness, Pe is the external boundary pressure, Pwf is the flowing bottomhole pressure, B is the formation volume factor, re is the drainage radius, rw is the wellbore radius, and S is the Skin factor.

Calculated Example: A zone 30 ft thick with 50 md permeability, 1,000 psi Drawdown, 2 cp oil viscosity, B = 1.2, 1,000 ft drainage radius, 0.354 ft wellbore radius (8-1/2 in hole), and zero skin. ln(1,000 ÷ 0.354) = ln(2,825) ≈ 7.95. The numerator is 0.00708 × 50 × 30 × 1,000 = 10,620, and the denominator is 2 × 1.2 × 7.95 ≈ 19.07, so the rate ≈ 557 STB/d. If permeability were only 0.5 md at the same pressure, the rate would be about 5.6 STB/d. This is the answer to the lesson question: huge pressure and trapped oil because the path is narrow.

Skin Factor

Immediately around the wellbore, permeability can be damaged by mud and fines invasion, cement, or production scale. This damage appears in the equation as a positive Skin factor added to the logarithm. Acidizing or fracturing can make it zero or negative.

Calculated Example: In the previous example, if Skin equals 5, the denominator becomes 2.4 × (7.95 + 5) ≈ 31.1, and the rate ≈ 10,620 ÷ 31.1 ≈ 342 STB/d. This means damage within a few feet around the wellbore caused a loss of about 39% of production.

What is the Practical Use?

• Permeability and zone thickness together (k × h) determine the reservoir's capacity and are estimated from well testing.
• Reducing viscosity, for example by heating heavy oils, increases the flow rate.
• Removing damage is often the cheapest way to increase production.
• In very low permeability zones, pressure is not enough; therefore, we use hydraulic fracturing and horizontal wells to increase contact area.

Equation Limits

Darcy's Law in its simple form assumes slow Laminar flow, a single fluid filling the pores, homogeneous rock, and steady-state conditions. In high-rate gas wells, Non-Darcy flow occurs near the wellbore due to high velocities, and with multiple fluids, Relative Permeability for each fluid is used. However, it remains the starting point for understanding any producing well.

The figures and examples in this lesson are for educational purposes. On the job, always follow your company procedures and accredited training center instructions.

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