50-year-old convention in permeability prediction is upended using machine learning by Heriot-Watt research

Four step diagram showing the rock information gathering and machine learning process

Engineers at the Institute of GeoEnergy Engineering at Heriot-Watt have used machine learning to create the next generation of flow prediction software.

The innovation could lead to a range of improvements including better predictions for the geothermal energy industry. This is where powerplants extract hot water and steam from deep underground and use it to drive turbines and generate electricity.

Miles below the surface of the Earth, water is flowing through the microscopic spaces between the grains inside different types of rocks. Many of these rocks have complex, nested structures that make it difficult to predict flow patterns.

Dr Hannah Menke, Dr Julien Maes, and Professor Sebastian Geiger have extracted key structural features from 3D images of the rock at the micrometre and nanometre scales and then used machine learning to understand how these features impact permeability. They then integrated this learning into a next generation flow model to predict permeability as reported in Nature.

Over the past century, scientists have been using flow models to predict how fluids flow through rocks for a range of purposes. In hydrology these models are used to manage water resources and ensure dangerous heavy metals aren’t contaminating our freshwater reserves. Understanding how CO2 moves inside a reservoir is crucial for storage permanence during Carbon Capture and Storage (CCS). With the recent focus on renewable energy, engineers have been modelling how to optimise hot water extraction from the subsurface for low-cost energy solutions.

Previously, engineers have used a simple formula that relates permeability to the porosity of the rock. It’s called the Kozeny-Carman formulation and it’s based on the premise that the rock is built out of equally sized spherical grains that are evenly distributed. The grain size and porosity then dictate the overall permeability. This has been the underpinning approach used by scientists to model the variation of permeability with porosity for the last fifty years.

However, the scientists have shown that porosity and grain size are poor predictors of permeability in complex rock structures such as carbonates where the grain size and shape vary greatly, and where the grains themselves are made up of even smaller grains (usually called microporosity). Using a machine learning technique called multivariate regression, the team have revealed the significance of this microporous flow in the overall permeability prediction, which is not accounted for in traditional modelling methods.

The importance of this new machine learning-based approach to flow modelling is that engineers around the world will now be able to more accurately model how fluids move in complex rock structures with far less computational expense.

Dr Hannah Menke, lead author on the study and Research Fellow said: “Upscaling permeability to the larger scale in a realistic way has proven to be a major scientific and engineering challenge. The general approach of the last few decades of adding more computing power at finer and finer resolutions will only work up to a point if some of the fundamental physics is lacking. Our new model is able to capture the details of the structures which underpin the flow process.  This will enable engineers to update their modelling techniques with real information about the rock structure, increasing their accuracy.”

To produce the 3D images in the machine learning database, the researchers used state-of-the-art x-ray imaging at the micron and nanoscales at Zeiss Labs.  The images were then correlated in space and the structural features were extracted and overlayed. Numerical flow models were run at three progressively increasing scales (micron, mm and cm) to solve for permeability using the open-source numerical framework OpenFOAM. Finally, a machine learning model was used to regress the permeability results against the features to create an upscaled description of permeability for the largest scale that encapsulated all structural information from the smaller scales. This new upscaled model successfully predicts permeability with improved accuracy at a fraction of the computational cost of traditional approaches.  

However, this technique is limited to predicting permeability for a single-phase system where the structure doesn’t change. The team plan to use this workflow as a steppingstone toward investigating more complex physics - in particular multiphase flow and reactive transport. They are currently using multivariate regression to probe the relationship between rock structure and the flow of acidic water saturated with CO2. The hope is to help engineers understand how changes in structure due to chemical reaction affect the overall permeability of underground reservoirs during CCS.

The research, published in Nature, is jointly funded by The Engineering and Physical Sciences Research Council (EPSRC) and Energi Simulation.


Susan Kerr

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