import os
from pathlib import Path

import matplotlib.pyplot as plt
import numpy as np
import ogstools as ot

out_dir = Path(os.environ.get("OGS_TESTRUNNER_OUT_DIR", "_out"))
if not out_dir.exists():
    out_dir.mkdir(parents=True)

H2M process: Liakopoulos benchmark

Problem description


The Liakopoulos experiment was dealing with a sand column which was filled with water first and then drained under gravity. A sketch of the related model set-up including initial and boundary conditions is shown in the above figure. A detailed description of the underlying OGS model is given in Grunwald et al. (2022). Two hydraulic models have been compared; two-phase flow with a mobile and a Richards flow with an immobile gas phase coupled to mechanical processes. Due to the absence of analytical solutions various numerical solutions have been compared in the past (see Grunwald et al., 2022).

The model parameters are given in the below table.

Numerical solution

prj_file = "liakopoulos_TH2M.prj"
model = ot.Project(input_file=prj_file, output_file=prj_file)
model.run_model(logfile=f"{out_dir}/out.txt", args=f"-o {out_dir}")

OGS finished with project file liakopoulos_TH2M.prj.
Execution took 10.838209390640259 s
Project file written to output.

ms = ot.MeshSeries(f"{out_dir}/result_liakopoulos.pvd")

# plausibility checks
max_vals = {"gas_pressure": 1.02e5, "capillary_pressure": 1e4,
            "saturation": 1.0001, "displacement": 0.005}  # fmt:skip


def plot_sample(var: ot.variables.Scalar) -> None:
    fig, ax = plt.subplots(figsize=[6, 3], dpi=150)
    ax.set_xlabel(r"$y$ / m")
    ax.set_ylabel(var.get_label())
    for mesh, t in zip(ms, ms.timevalues()):
        line_mesh = mesh.sample_over_line([0, 0, 0], [0, 1, 0])
        vals = line_mesh.sample(mesh)[var.data_name]
        assert np.all(np.abs(vals) <= max_vals[var.data_name]), max(abs(vals))
        ax.plot(line_mesh.points[:, 1], var.transform(vals), label=f"{t=}", lw=2.5)
    ax.legend()
    ax.grid()
    fig.tight_layout()

Gas Pressure

plot_sample(ot.variables.Scalar("gas_pressure", "Pa", "MPa"))

Capillary Pressure

plot_sample(ot.variables.Scalar("capillary_pressure", "Pa", "kPa"))

Saturation

plot_sample(ot.variables.Scalar("saturation", "", "%"))

Vertical Displacement

plot_sample(ot.variables.displacement["y"])

OGS links

• description: https://www.opengeosys.org/docs/benchmarks/
• project file: https://gitlab.opengeosys.org/ogs/ogs/-/blob/master/Tests/Data/TH2M/H2M/Liakopoulos/liakopoulos_TH2M.prj

Credits

• Norbert Grunwald for set-up the OGS benchmark, https://gitlab.opengeosys.org/ogs/ogs/-/blob/master/Tests/Data/TH2M/H2M/Liakopoulos/liakopoulos_TH2M.prj

References

Grunwald, N., Lehmann, C., Maßmann, J., Naumov, D., Kolditz, O., Nagel, T., (2022): Non-isothermal two-phase flow in deformable porous media: systematic open-source implementation and verification procedure. Geomech. Geophys. Geo-Energy Geo-Resour. 8 (3), art. 107 https://doi.org/10.1007/s40948-022-00394-2

Kolditz, O., Görke, U.-J., Shao, H., Wang, W., (eds., 2012): Thermo-hydro-mechanical-chemical processes in porous media: Benchmarks and examples. Lecture Notes in Computational Science and Engineering 86, Springer, Berlin, Heidelberg, 391 pp https://link.springer.com/book/10.1007/978-3-642-27177-9

Lewis RW, Schrefler BA (1998): The finite element method in the static and dynamic deformation and consolidation of porous media. Wiley, New York https://www.wiley.com/en-us/The+Finite+Element+Method+in+the+Static+and+Dynamic+Deformation+and+Consolidation+of+Porous+Media%2C+2nd+Edition-p-9780471928096

Liakopoulos AC (1964): Transient flow through unsaturated porous media. PhD thesis. University of California, Berkeley, USA. sources: OGS BMB1 (sec. 13.2