CO2 Plume Simulator — Composite Finite-Core / Barenblatt Model

Analytical MATLAB simulator for CO₂ plume evolution in porous media under time-dependent (stair-like) injection schedules. Fernando Alonso-Marroquin and Christian Tantardini

This repository implements a vertically averaged sharp-interface model based on:

• Nonlinear diffusion (q–Porous Media Equation)
• Barenblatt compact-support similarity solutions
• A transient full-thickness core model
• Piecewise-constant (stair-like) injection schedules

The simulator produces:

• Time evolution of plume thickness profile b(r,t)
• Core radius a(t)
• Plume edge R(t)
• Injection-rate history
• Movie of plume evolution

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Physical Model

Governing Structure

The plume thickness is modeled as:

b(r,t) =

• H for 0 ≤ r ≤ a(t)
• Barenblatt tail for a(t) < r < R(t)
• 0 for r ≥ R(t)

This represents:

• A full-thickness CO₂ core near the well
• A compact-support nonlinear diffusion tail
• A sharp plume edge

The Barenblatt tail is:

b(r,t) = t^{-α_B} [ C(t) - K_b r² t^{-2β_B} ]_+^{1/(1-q)}

with exponents:

β_B = 1 / [ 2(2 - q) ]
α_B = 1 / (2 - q)

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Vertical Segregation Assumption

The model assumes rapid vertical segregation:

• CO₂ forms a uniform upper layer of thickness b(r,t)
• Brine occupies the lower region
• Vertical mixing and capillary transition zones are neglected
• Phase densities are treated as constant

This reduces the 3D problem to a 1D radial thickness evolution.

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Injection Schedule Handling

The simulator supports stair-like injection schedules:

Q(t) = piecewise constant

Examples:

• Constant injection
• Shut-in (Q = 0)
• Variable-rate field operation
• Alternating injection/shut-in

Each injection stage updates:

• Total injected volume
• Core radius a(t)
• Tail amplitude C(t)

This allows realistic operational histories to be approximated analytically.

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Software Structure

The repository contains:

1️⃣ run_plume_simulation.m

Driver script where you define:

• Aquifer thickness H
• Porosity φ
• Residual brine saturation S_br
• Diffusivity D_b
• q exponent
• Injection schedule (time intervals + rates)
• Simulation time

2️⃣ plume_solver.m

Main function that:

• Computes b(r,t), a(t), R(t)
• Evolves plume over time
• Plots injection rate vs time
• Generates movie of plume evolution
• Exports video file

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How to Run

1. Open MATLAB
2. Edit parameters in:

run_plume_simulation.m