U.S. Department of Energy Office of Biological and Environmental Research

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New Approach to Predict Flow and Transport Processes in Fractured Rock Uses Causal Modeling
Published: February 16, 2017
Posted: July 26, 2018

Application of causality theory to hydrological flow and transport studies could lead to more accurate predictions of numerical models.

The Science
Scientists and engineers simulate the flow of fluids through permeable media to determine how water, oil, gas or heat can be safely extracted from subsurface fractured-porous rock, or how harmful materials like carbon dioxide could be stored deep underground. Now, a scientist from Lawrence Berkeley National Laboratory has identified a causal relationship between gases and liquids flowing through fractured-porous media. They observed oscillating liquid and gas fluxes and pressures as the two transitioned back and forth within a subsurface rock fracture.

The Impact
When both liquid and gas are injected into a rock fracture, the cumulative effect of forward and return pressure waves causes intermittent oscillations of liquid and gas fluxes and pressures within the fracture. The Granger causality test is used to determine whether the measured time series of one of the fluids can be applied to forecast the pressure variations in another fluid.  This method could also be used to better understand the causation of other hydrological processes, such as infiltration and evapotranspiration in heterogeneous subsurface media, and climatic processes, for example, relationships between meteorological parameters—temperature, solar radiation, barometric pressure, etc.

Summary
Identifying dynamic causal inference involved in flow and transport processes in complex fractured-porous media is generally a challenging task, because nonlinear and chaotic variables may be positively coupled or correlated for some periods of time but can then become spontaneously decoupled or non-correlated. The author hypothesized that the observed pressure oscillations at both inlet and outlet edges of the fracture result from a superposition of both forward and return waves of pressure propagation through the fracture. He tested the theory by exploring an application of a combination of methods for detecting nonlinear chaotic dynamics behavior along with the multivariate Granger Causality (G-causality) time series test. Based on the G-causality test, the author inferred that his hypothesis was correct, and presented a causation loop diagram of the spatial-temporal distribution of gas, liquid, and capillary pressures measured at the inlet and outlet of the fracture. The causal modeling approach can be used for the analysis of other hydrological processes such as infiltration and pumping tests in heterogeneous subsurface media, and climatic processes.

BER PM Contact
David Lesmes, SC-23.1, David.Lesmes@science.doe.gov

Contact
Susan Hubbard, Lawrence Berkeley National Laboratory, sshubbard@lbl.gov
Deb Agarwal, Lawrence Berkeley National Laboratory, daagarwal@lbl.gov

Funding
This work was supported by the U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research, and Office of Science, Office of Advanced Scientific Computing under Contract No. DE-AC02-05CH11231.

Publication
Faybishenko, B. “Detecting dynamic causal inference in nonlinear two-phase fracture flow.” Advances in Water Resources 106, 111-120 (2017). [DOI:10.1016/j.advwatres.2017.02.011]

Topic Areas:

  • Research Area: Subsurface Biogeochemical Research
  • Cross-Cutting: Scientific Computing and SciDAC

Division: SC-23.1 Climate and Environmental Sciences Division, BER

 

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