# Comparison of Field-Scale Effective Properties of Two-Phase Flow in Heterogeneous Porous Media Obtained by Stochastic Analysis and Numerical Experiments

## Abstract

The effects of subsurface heterogeneity on two-phase flow can be observed from the characterization functions of field-scale effective relative permeability and capillary pressure with respect to mean saturation. Numerical experiments were used to evaluate such effective properties of two-phase flow in a heterogeneous medium with properties representing the Borden Aquifer, and compared with the results of stochastic analysis developed using a spectral perturbation technique that employs a stationary, stochastic representation of the spatial variability of soil properties. Arbitrary forms of the relative permeability and capillary pressure characteristic functions with respect to saturation can be used in the theoretical analysis and numerical code. A statistical scaling procedure, which is a generalization of Leverett scaling, was developed for the relationship between intrinsic permeability and two capillary parameters. The procedure for estimating the effective properties of two-phase flow using numerical simulation consists of three-steps. Firstly, a local-scale heterogeneous system with random fields of intrinsic permeability and two capillary parameters was generated. Secondly, numerical simulation of single-phase flow in the system, with different sets of flow boundary conditions for different directions, was performed; the field-scale effective saturated hydraulic conductivity tensor was calculated on the basis of the mean Darcy law. The tensor obtained numericallymore »

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

- Sponsoring Org.:
- USDOE Director, Office of Science (US)

- OSTI Identifier:
- 822832

- Report Number(s):
- LBNL-50504

R&D Project: 465119; TRN: US200414%%301

- DOE Contract Number:
- AC03-76SF00098

- Resource Type:
- Conference

- Resource Relation:
- Conference: International Groundwater Symposium on Bridging the Gap Between Measurements and Modeling in Heterogeneous Media, Berkeley, CA (US), 03/25/2002--03/28/2002; Other Information: PBD: 31 May 2002

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 54 ENVIRONMENTAL SCIENCES; 58 GEOSCIENCES; BOUNDARY CONDITIONS; DARCY LAW; HYDRAULIC CONDUCTIVITY; MULTIPHASE FLOW; PERMEABILITY; SATURATION; SIMULATION; SOILS; TWO-PHASE FLOW

### Citation Formats

```
Zhou, Quanlin, Gelhar, Lynn W, and Jacobs, Bruce.
```*Comparison of Field-Scale Effective Properties of Two-Phase Flow in Heterogeneous Porous Media Obtained by Stochastic Analysis and Numerical Experiments*. United States: N. p., 2002.
Web.

```
Zhou, Quanlin, Gelhar, Lynn W, & Jacobs, Bruce.
```*Comparison of Field-Scale Effective Properties of Two-Phase Flow in Heterogeneous Porous Media Obtained by Stochastic Analysis and Numerical Experiments*. United States.

```
Zhou, Quanlin, Gelhar, Lynn W, and Jacobs, Bruce. Fri .
"Comparison of Field-Scale Effective Properties of Two-Phase Flow in Heterogeneous Porous Media Obtained by Stochastic Analysis and Numerical Experiments". United States. https://www.osti.gov/servlets/purl/822832.
```

```
@article{osti_822832,
```

title = {Comparison of Field-Scale Effective Properties of Two-Phase Flow in Heterogeneous Porous Media Obtained by Stochastic Analysis and Numerical Experiments},

author = {Zhou, Quanlin and Gelhar, Lynn W and Jacobs, Bruce},

abstractNote = {The effects of subsurface heterogeneity on two-phase flow can be observed from the characterization functions of field-scale effective relative permeability and capillary pressure with respect to mean saturation. Numerical experiments were used to evaluate such effective properties of two-phase flow in a heterogeneous medium with properties representing the Borden Aquifer, and compared with the results of stochastic analysis developed using a spectral perturbation technique that employs a stationary, stochastic representation of the spatial variability of soil properties. Arbitrary forms of the relative permeability and capillary pressure characteristic functions with respect to saturation can be used in the theoretical analysis and numerical code. A statistical scaling procedure, which is a generalization of Leverett scaling, was developed for the relationship between intrinsic permeability and two capillary parameters. The procedure for estimating the effective properties of two-phase flow using numerical simulation consists of three-steps. Firstly, a local-scale heterogeneous system with random fields of intrinsic permeability and two capillary parameters was generated. Secondly, numerical simulation of single-phase flow in the system, with different sets of flow boundary conditions for different directions, was performed; the field-scale effective saturated hydraulic conductivity tensor was calculated on the basis of the mean Darcy law. The tensor obtained numerically is very close to that determined using the generalized spectral-perturbation approximation. Finally, a number of numerical experiments on two-phase flow in the system were conducted with different infiltration rates of DNAPL; the field-scale effective relative permeability and capillary pressure functions were obtained. In each experiment, a highly heterogeneous saturation field was obtained, leading to large variations of actual nonwetting phase permeability (combination of intrinsic permeability and its positively correlated relative permeability). Both stochastic and numerical analyses produced very similar results of effective properties of multiphase flow. The vertical effective relative permeability is significantly lower than the homogeneous one found using mean capillary parameters, particularly at low mean DNAPL saturation (low mean capillary pressure). On the other hand, the effective capillary pressure function differs only slightly from the homogeneous case. Various statistical properties of local-scale NAPL saturation, capillary pressure and relative permeability and their relationships with intrinsic permeability and capillary parameters were analyzed in detail.},

doi = {},

url = {https://www.osti.gov/biblio/822832},
journal = {},

number = ,

volume = ,

place = {United States},

year = {2002},

month = {5}

}