CO2 Lumped Parameter Model Physics Knowledge

This skill provides physics knowledge for the 0-D CO2 lumped-parameter model implemented in the co2lpm package.

When This Skill Applies

• Modifying code that implements concentration evolution equations
• Changing ODE solver logic or state variable handling
• Implementing or modifying emissions partitioning (field, plant, degassing)
• Debugging unexpected simulation behavior
• Planning changes to physics-related code
• Explaining why the model behaves a certain way
• Working with pressure reversal scenarios

Core Physics Reference

The model tracks reservoir CO2 concentration over time during geothermal extraction. Key state variables:

| Variable | Symbol | Meaning | Units | |----------|--------|---------|-------| | Pressure | P(t) | Reservoir pressure (relative to hydrostatic) | Pa | | Concentration | C(t) | CO2 mass fraction in reservoir fluid | kg/kg | | Upflow rate | q_up | Mass rate into reservoir from depth | kg/s | | Outflow rate | q_out | Mass rate leaving reservoir to surface | kg/s |

For detailed equations, see EQUATIONS.md. For symbol definitions and units, see SYMBOLS.md. For derivation logic, see DERIVATIONS.md. For edge cases and sanity checks, see SANITY_CHECKS.md.

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Workflow A: Physics Validation

Use this workflow when reviewing or planning code changes.

Step 1: Identify affected equations

Determine which equations from EQUATIONS.md are affected by the change:

• Pressure evolution: E1 (exponential pressure decline)
• Concentration ODE: E2-E4 (with and without delay)
• Emissions: E5-E8 (degassing, field, plant, total)
• Solubility: E9-E10

Step 2: Check dimensional consistency

Using SYMBOLS.md, verify that:

• All terms in an equation have matching units
• ODE coefficients (alpha, beta, gamma, delta) have correct units
• Source terms have correct rate units (kg/s for mass)

Step 3: Verify mass balance

Changes must preserve:

• CO2 mass conservation in the reservoir
• Correct partitioning between dissolved, degassed, and emitted CO2

Step 4: Check sanity conditions

Verify the change doesn't violate sanity checks S1-S5 in SANITY_CHECKS.md.

Step 5: Report findings

Summarize:

• Which equations are affected
• Any dimensional inconsistencies found
• Any mass balance violations
• Any sanity check concerns
• Recommendations for correction

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Workflow B: Physics Reasoning

Use this workflow when explaining behavior, debugging, or proposing solutions.

For explaining physics concepts:

1. Identify the relevant equations and parameters
2. State the physical interpretation
3. Explain cause-and-effect relationships between variables
4. Use the derivation steps from DERIVATIONS.md to show how equations connect

For debugging simulation issues:

1. Identify which state variables are behaving unexpectedly
2. Check if the issue relates to:
   • Pressure reversal (q_eff > q_0c)
   • Delay effects (tau > 0)
   • Solubility limiting (degas=True)
   • ODE coefficient calculation
3. Trace through the analytical solution (gamma_exact or Cf_dde)
4. Check edge cases against SANITY_CHECKS.md

For proposing physics-consistent changes:

1. Identify which equations are affected
2. Show how new terms integrate into the ODE system
3. Demonstrate that mass balance remains satisfied
4. Identify any new sanity checks needed

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Quick Reference: Module Structure

| Module | Purpose | Key Functions/Classes | |--------|---------|----------------------| | model.py | Core LPM class | LumpedParameterModel, StateArrays | | parameters.py | Dataclasses for inputs | ReservoirParams, OperationParams, ChemistryParams | | solvers.py | ODE/DDE solvers | pressure_exp, integrate_ode, dde_solve | | postproc.py | Emissions calculation | emissions() | | utils.py | CO2 solubility | solubility_linear, solubility_slope_vs_T | | scenarios.py | Preset configurations | high_gas(), low_gas(), delay_demo() |

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Key Physical Constraints

These must always hold:

1. Concentration non-negative: C(t) >= 0
2. Solubility limit: C(t) <= C_s(P) when degas=True
3. Pressure reversal: Occurs when q_eff > q_0c (extraction exceeds critical rate)
4. Steady state exists: C_inf = alpha/beta (no delay) or alpha/(beta-gamma) (with delay)
5. Delay stability: For tau > 0, the characteristic root lambda_1 must have negative real part

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Scenario Classification

| Scenario | Key Parameters | Behavior | |----------|---------------|----------| | High-gas (Ohaaki-like) | degas=True, high C0 | Solubility-limited, significant degassing | | Low-gas (Wairakei-like) | degas=False, low C0 | No degassing, concentration dilutes | | Concentrating | fC < critical | CO2 accumulates in reservoir | | Diluting | fC > critical | CO2 decreases in reservoir | | Reversal | fq*q0 > q0c | Outflow reverses direction | | Delay | tau > 0 | Breakthrough lag, DDE dynamics |