Forecasting long-term migration
Capturing the long-term migration of CO2 within a large-scale saline aquifer may require the simulation of thousands or even millions of years. At such long time horizons, full numerical simulations based on the physical flow equations become practically impossible due to the computational cost. Rather than simulating for a finite number of years, we have implemented a forecasting algorithm that uses spill-point dynamics to predict the long-term migration of CO2, specifically how much will become trapped within the formation and how much is bound to leak out of the aquifer's open boundaries. Reducing the time it takes to perform a single simulation is particularly helpful when many simulations are required for the mathematical optimization of well injection rates. More details of the following example can be found in [1].

Trapping structure of a conceptual grid

Vertically segregated CO2 is found as a thin layer under the formation's top surface (or caprock). Some time after the end of injection, CO2 becomes driven by buoyancy forces rather than by pressure. As such, the shape of the top surface greatly impacts long-term migration.

Here, we show a conceptual grid (left) and associated top surface (right). The local maxima of the undulating top surface create structural traps. Each trap has an associated catchment region, and are connected to other traps by "rivers". More details on the trapping structure can be found here.


Forecasting structural trapping

The middle figure shows a simulated volume of CO2 after it has been injected into the formation. By continuing to simulate for 2000 years post-injection, we create an inventory that shows how much CO2 becomes structurally trapped, leaks from the formation boundary, or remains as a free (mobile) plume over time.

From this trapping inventory (right), we see that about 60% of the injected CO2 becomes structurally trapped, while the remaining 40% has either exited the formation or remains as a free moving plume. (Residual trapping was not considered in this example.) If we were to simulate a longer time horizon, we will find the free plume wedge gets reduced to nothing as it ultimately spills out of the formation.

We also perform a forecast at each simulation time step, to predict the amount that will be structurally trapped, and this forecast converges to the simulated solution after about 500 years. This means the forecast is able to predict the eventual fate of CO2, and we don't need to simulate such a long time horizon to be able to capture the permantely stored volumes. 



Using forecast for optimizing the injection rate

In order to maximize the amount of CO2 trapped within a formation, while penalizing the amount of leakage, we use a nonlinear optimization algorithm. The initial injection rate is computed based on the capacity of the traps that are upsteam from the well. In general, the optimized injection rate is higher than the initial rate because we end up exploiting more structural trapping (and/or other forms of trapping mechanisms) than initially estimated.

We obtain three different optimal solutions for Well 1's injection rate, which were found by simulating for three different time horizons: 500 years, 3000 years, and infinite time via forecasting. With a 500 year time horizon, the optimization algorithm correctly suggests the injection rate can be higher than the initial, however 500 years is not long enough to capture the long-term migration towards the formation boundary. A 3000 year time horizon suggests a lower rate, since more long-term leakage is captured and thus appropriately minimized. However, the infinite time horizon suggests a slightly lower rate, which implies that more than 3000 years is required to simulate the full extent of long-term leakage as part of the optimal solution.



  1. R. Allen, H. M. Nilsen, O. Andersen, and K.-A. Lie. On obtaining optimal well rates and placement for CO2 storage. ECMOR XV - 15th European Conference on the Mathematics of Oil Recovery, Amsterdam, Netherlands, 29 Aug-1 Sept, 2016. DOI: 10.3997/2214-4609.201601823

Published December 9, 2016