Data Space Inversion for Efficient Predictions and Uncertainty Quantification for Geothermal Models

This repository contains code written as part of the paper "Data Space Inversion for Efficient Predictions and Uncertainty Quantification for Geothermal Models", by Alex de Beer, Andrew Power, Daniel Wong, Ken Dekkers, Michael Gravatt, Elvar K. Bjarkason, John P. O'Sullivan, Michael J. O'Sullivan, Oliver J. Maclaren, and Ruanui Nicholson.

@misc{deBeer2024,
    title={Data Space Inversion for Efficient Predictions and Uncertainty Quantification for Geothermal Models}, 
    author={Alex de Beer and Andrew Power and Daniel Wong and Ken Dekkers and Michael Gravatt and Elvar K. Bjarkason and John P. O'Sullivan and Michael J. O'Sullivan and Oliver J. Maclaren and Ruanui Nicholson},
    year={2024},
    eprint={2407.15401},
    archivePrefix={arXiv},
    url={https://arxiv.org/abs/2407.15401}, 
}

Running Experiments

Simplified Two-Dimensional Reservoir Model

Code to run the experiments for the simplified two-dimensional reservoir model is contained in the Model2D folder. The model is written in Julia 1.9. After installing Julia and cloning this repository, open this folder and run

using Pkg
Pkg.activate(".")
Pkg.instantiate()

to install the project dependencies. You will then be able to run any of the scripts at the top level of the folder.

To compute a full characterisation of the posterior using MCMC, run run_pcn.jl (this will take several days on a desktop computer). To compute a local linearisation about the MAP estimate, run run_lmap.jl, to run the DSI algorithm, run run_dsi.jl, and to sample from the prior, run run_pri.jl. To carry out a comparison of the performance of DSI with varying sample sizes, run run_dsi_comparison.jl.

Three-Dimensional Reservoir Model

Code to run the experiments for the three-dimensional reservoir model is contained in the Model3D folder. The scripts in this folder require Python >= 3.8 to run. After installing Python and cloning this repository, open this folder and run

python3.8 -m pip install -r requirements.txt

to install the project dependencies. You will also need to install the Waiwera geothermal simulator if you would like to run any simulations; for further information, consult the Waiwera website.

• To generate the ensemble of reservoir models used to estimate the covariance matrices required as part of the DSI algorithm, run generate_ensemble.py. The resulting simulation input files can then be run locally using Docker (though this is likely to take a while), or on a high-performance computing cluster which contains a Waiwera build. We have included the jobfile we used to run the simulations on the Maui cluster operated by NeSI (New Zealand eScience Infrastructure).
• To gather the statistics of the quantities of interest, run process_output.py. This will ignore the results associated with failed simulations.
• To run the DSI algorithm to approximate the posterior predictive distribution of the quantities of interest, run run_dsi.py or run_dsi_trans.py (which will run the DSI algorithm with a transformation applied to the pressure predictions).

The models folder contains the meshes for the fine and coarse models used in the paper, and the input and output files for the true system. Files related to the true system are also located in data/truth.

Note: when the code is first run, the covariance matrices (and their Cholesky factors) of the GRFs used as part of the prior parametrisation will be computed. This is likely to take several minutes. You may also need to create folders for these files (data/grf_2d and data/grf_3d).

Note: we have provided files containing the predictive quantites of interest associated with the simulations from the prior produced using process_output.py (these are located in the data folder), so if you are only looking to reproduce the DSI analysis from the paper, you do not need to run the full set of simulations.

Generating Figures

Each model folder contains a script called plotting.py, which can be run to reproduce the figures from the paper associated with the model. Running these script requires Python >= 3.8, and a subset of the dependencies required to run the experiments for the three-dimensional reservoir model. The figures are saved to the figures directory, and have the same numbering as in the manuscript. Some figures are composed of multiple parts; in these instances, the parts that make up the figure as saved as fig1a.pdf, fig1b.pdf, etc.

Issues

If you have any questions about the code or the paper, please open an issue.