Yes, a challenging modeling project with many inherent uncertainties and unknowns, the most important ones having to do with geology/connectivity of the high permeability pathways for fluid flow, and the possibility of leakage pathways thru caprock (and other rock layers that otherwise have low-permeability); such leakage pathways possibly being pre-existing and/or forming during the pressurization accompanying CO2 injection).

Regarding item 6; depending on the numerical approximation scheme used, make sure that each distinct rock/formation layer, particularly caprock and other very low-permeability layers, are gridded at least several grid layers thick; so that the center grid layers are surrounded entirely very low-permeability and very low connected-porosity model layers. This should guard against numerical dispersion in most finite-element computational algorithm schemes (though you should check this for your particular modeling software), and model results for advection, dispersion, and molecular diffusion thru caprock can be held to small values. It seems to me that with very small total porosity and even smaller connected porosity (and corresponding very low permeability) in caprock layers, net diffusion thru the caprock layer approaches that governed by the diffusion coefficients (of e.g. CO2) in solid rock, which are much smaller than the diffusion coefficients in water.

Of course, significant transport of CO2 thru caprock can still occur thru fractures, or other areas where the integrity of the caprock barrier is or has been compromised (e.g. short-circuiting by improperly abandoned or damaged wells and wellbores).

Deducing the volume of CO2 leakage that escapes through aquifer boundaries involves several steps, integrating both theoretical and empirical methods. Here’s a structured approach:

1. Understanding the System:

• Aquifer Characteristics: Gather data on the aquifer's properties, including porosity, permeability, thickness, and pressure conditions.
• Boundary Conditions: Define the boundaries of the aquifer and the conditions at these boundaries (e.g., open, closed, or semi-permeable).

2. Data Collection:

• CO2 Injection Data: Record the rate, pressure, and volume of CO2 injected.
• Monitoring Data: Use sensors and monitoring wells to gather data on CO2 concentrations, pressures, and flow rates over time.

3. Modeling the Aquifer:

• Numerical Simulation: Use software tools (e.g., TOUGH2, CMG-GEM, or ECLIPSE) to create a numerical model of the aquifer. Input the collected data and simulate CO2 injection and migration.
• Analytical Solutions: Apply analytical models (e.g., Darcy’s Law) for simpler systems where possible, to estimate flow rates and volumes.

4. Leakage Pathways:

• Identify Potential Pathways: Determine possible pathways for CO2 leakage, such as faults, fractures, or porous boundaries.
• Parameter Estimation: Estimate parameters like permeability and porosity for these pathways using geological surveys and field data.

5. Calculating Leakage:

• Flow Equations: Use flow equations like Darcy’s Law to estimate the rate of CO2 leakage through the aquifer boundaries. For Darcy’s Law: Q=kA(P1−P2)μLQ = \frac{kA(P1 - P2)}{\mu L}Q=μLkA(P1−P2)​Where:QQQ = volumetric flow rate kkk = permeability of the medium AAA = cross-sectional area perpendicular to flow P1P1P1 and P2P2P2 = pressures at the two points μ\muμ = fluid viscosity LLL = distance between the points

6. Empirical Methods:

• Tracer Tests: Conduct tracer tests by injecting tracers with CO2 and monitoring their movement to identify leakage rates and pathways.
• Observation Wells: Use observation wells around the aquifer to measure changes in CO2 concentration over time.

7. Validation:

• Comparing Results: Validate the modeled results with observed data from monitoring wells and tracer tests.
• Iterative Calibration: Adjust the model parameters iteratively to better match the observed data.

8. Volume Calculation:

• Integrate Leakage Rates: Integrate the leakage rates over time to calculate the total volume of CO2 that has leaked through the aquifer boundaries. If Q(t)Q(t)Q(t) is the leakage rate at time ttt: Vleakage=∫0TQ(t) dtV_{leakage} = \int_0^T Q(t) \, dtVleakage​=∫0T​Q(t)dtWhere TTT is the total time period considered.

Tools and Techniques:

• Software: Utilize specialized software like TOUGH2, CMG-GEM, or ECLIPSE for simulation and analysis.
• Field Equipment: Use sensors, monitoring wells, and tracer injection systems for empirical data collection.

Conclusion:

The volume of CO2 leakage through aquifer boundaries can be deduced through a combination of numerical modeling, empirical data collection, and integration of flow rates over the specified time frame. This process requires thorough understanding and accurate data on the aquifer properties, boundary conditions, and CO2 injection parameters.