Compaction & Porosity Calculator: Athy's Law for Burial Diagenesis

simulator beginner ~9 min
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φ(5 km) = 4.6% — tight rock, limited reservoir quality

Muddy sediment with 55% surface porosity and compaction coefficient 0.5/km retains only 4.6% porosity at 5 km burial depth. The original 1-meter layer has been compacted to about 0.53 meters — nearly half its original thickness squeezed out as water.

Formula

φ(z) = φ₀ × exp(-c × z) — Athy's law
P_overburden = ∫₀ᶻ [φρ_f + (1-φ)ρ_s] × g × dz
Thickness ratio = (1 - φ_z) / (1 - φ₀)

From Mud to Mudstone

Freshly deposited sediment at the seafloor is mostly water — muds typically have 55-75% porosity (pore space filled with water). As burial depth increases, the weight of overlying sediment squeezes water out, particles rearrange into tighter packing, and porosity decreases exponentially. This mechanical compaction is the first step in turning loose sediment into solid rock — a process called diagenesis that takes millions of years and kilometers of burial.

Athy's Exponential Law

In 1930, L.F. Athy analyzed porosity-depth data from Oklahoma oil wells and discovered that porosity decreases exponentially with depth: phi(z) = phi_0 * exp(-cz). The compaction coefficient c depends on lithology — shales compact rapidly (c = 0.5-1.5/km), sandstones more slowly (c = 0.2-0.4/km). Despite its simplicity, Athy's law captures the first-order compaction behavior observed in sedimentary basins worldwide and remains widely used in basin modeling.

Consequences for Reservoir Quality

Porosity determines the storage capacity of petroleum reservoirs. A sandstone with 25% porosity at 2 km depth is an excellent reservoir; the same formation at 5 km may have only 8% porosity — marginal for production. Predicting porosity with depth is therefore critical for petroleum exploration economics. Chemical compaction (pressure solution, cementation) at greater depths further reduces porosity beyond what mechanical compaction alone would predict.

Overpressure and Fluid Flow

When sedimentation rate exceeds the rate at which pore water can escape, fluid pressure builds above normal hydrostatic — creating overpressure. Overpressured zones are drilling hazards (blowout risk) but also preserve anomalously high porosity at depth by bearing part of the overburden stress. Understanding the coupling between compaction, fluid flow, and pressure is essential for safe and successful drilling in deep sedimentary basins.

FAQ

What is Athy's law of compaction?

Athy's law (1930) describes the exponential decrease of sediment porosity with burial depth: φ(z) = φ₀ × exp(-c×z), where φ₀ is surface porosity, c is the compaction coefficient, and z is depth. It captures the first-order behavior of mechanical compaction driven by increasing overburden pressure.

Why does porosity matter for petroleum geology?

Porosity determines how much oil or gas a rock can store — higher porosity means more storage capacity. Sandstone reservoirs typically need >10% porosity to be commercially productive. Predicting porosity at drilling depth before drilling is essential for exploration economics.

How does lithology affect compaction?

Shales compact rapidly (c ≈ 0.5-1.5/km, φ₀ ≈ 55-75%) because clay particles rearrange under pressure. Sandstones compact more slowly (c ≈ 0.2-0.4/km, φ₀ ≈ 35-45%) due to rigid grain frameworks. Carbonates have variable compaction depending on cementation. Each lithology has characteristic compaction parameters.

What is overpressure and how is it related to compaction?

Overpressure occurs when pore fluid pressure exceeds normal hydrostatic pressure. It develops when sedimentation is so rapid that water cannot escape fast enough during compaction — the trapped water supports part of the overburden load. Overpressure is a major drilling hazard and also helps preserve porosity at depth.

Sources

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