CO2 Lumped Parameter Model Physics Knowledge

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

co2lpm

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:

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.

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

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

Quick Reference: Module Structure

model.py

LumpedParameterModel

StateArrays

parameters.py

ReservoirParams

OperationParams

ChemistryParams

solvers.py

pressure_exp

integrate_ode

dde_solve

postproc.py

emissions()

utils.py

solubility_linear

solubility_slope_vs_T

scenarios.py

high_gas()

low_gas()

delay_demo()

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

Scenario Classification