Zhibing Yang

Effects of single-fracture aperture statistics on entrapment, dissolution and source depletion behavior of dense non-aqueous phase liquids.

Understanding of the entrapment and dissolution behavior of dense non-aqueous phase liquids (DNAPLs) in single fractures is important for modeling contaminant flux generation from fractured sites. Here a systematic numerical study is presented to investigate the effect of fracture aperture statistics on DNAPL migration, entrapment and dissolution within individual, variable-aperture fractures. Both fractures with open and closed bottom boundaries were considered. For the simulation a continuum-based two-phase model was used with a capillary pressure function which calculates the entry pressure based on the local aperture. Prior to application the model was compared against the invasion percolation approach and found more suitable for the present study, in particular as it allows a more versatile presentation of boundary conditions. The results showed that increasing aperture standard deviation and/or decreasing correlation length lead to larger amounts of entrapped DNAPL (due to the fact that larger standard deviation produces more distinct contrast between small and large aperture regions and the fact that longer correlation length provides more possible channels through the fracture) as well as larger maximum and average sizes of DNAPL blobs, and subsequently lead to longer times for complete dissolution. To understand the relationship between the solute flux and the remaining mass, a simplified source depletion function which links the outflow concentration to the DNAPL saturation was found adequate to describe the dissolution process for the case where the bottom boundary is open for DNAPL migration and thus the DNAPL does not accumulate to form a pool. The parameters in this function were not very sensitive to variations in correlation length but were sensitive to aperture standard deviation. The same average entrapped DNAPL saturation produced considerably smaller solute concentrations in cases with larger aperture variability due to the larger average size of DNAPL blobs (i.e., smaller contact area for DNAPL dissolution). Boundary conditions had a significant impact on DNAPL entrapment and dissolution. A closed boundary at the bottom led to DNAPL pooling (i.e., large continuous blobs) which causes significant tailing in the dissolution breakthrough curve due to water bypassing.

Dissolution of dense non-aqueous phase liquids in vertical fractures : Effect of finger residuals and dead-end pools

Understanding the dissolution behavior of dense non-aqueous phase liquids (DNAPLs) in rock fractures under different entrapment conditions is important for remediation activities and any related predictive modeling. This study investigates DNAPL dissolution in variable aperture fractures under two important entrapment configurations, namely, entrapped residual blobs from gravity fingering and pooling in a dead-end fracture. We performed a physical dissolution experiment of residual DNAPL blobs in a vertical analog fracture using light transmission techniques. A high-resolution mechanistic (physically-based) numerical model has been developed which is shown to excellently reproduce the experimentally observed DNAPL dissolution. We subsequently applied the model to simulate dissolution of the residual blobs under different water flushing velocities. The simulated relationship between the Sherwood number Sh and Peclet number Pe could be well fitted with a simple power-law function (Sh=1.43Pe⁰·⁴³). To investigate mass transfer from dead-end pools, another type of trapping in rock fractures, entrapment and dissolution of DNAPL in a vertical dead-end fracture was simulated. As the entrapped pool dissolves, the depth of the interface between the DNAPL and the flowing water increases linearly with decreasing DNAPL saturation. The interfacial area remains more or less constant as DNAPL saturation decreases, unlike in the case of residual DNAPL blobs. The decreasing depth of the contact interface changes the flow field and causes decreasing water flow velocity above the top of the DNAPL pool, suggesting the dependence of the mass transfer rate on the depth of the interface, or alternatively, the remaining mass percentage in the fracture. Simulation results show that the resultant Sherwood number Sh is significantly smaller than in the case of residual blobs for any given Peclet number, indicating slower mass transfer. The results also show that the Sh can be well fitted with a power-law function of Pe and remaining mass percentage. The obtained relationships of dimensionless groups concerning the mass transfer characteristics at the level of individual fractures can be further used in predictive modeling of dissolution at a larger (fracture network) scale.

GEOLOGICAL STORAGE OF CO2 IN DEEP SALINE FORMATIONS

This book offers readers a comprehensive overview, and an in-depth understanding, of suitable methods for quantifying and characterizing saline aquifers for the geological storage of CO2. It begins ...

Gaussian Process Emulators for Quantifying Uncertainty in CO2 Spreading Predictions in Heterogeneous Media

Abstract We explore the use of Gaussian process emulators (GPE) in the numerical simulation of CO 2 injection into a deep heterogeneous aquifer. The model domain is a two-dimensional, log-normally distributed stochastic permeability field. We first estimate the cumulative distribution functions (CDFs) of the CO 2 breakthrough time and the total CO 2 mass using a computationally expensive Monte Carlo (MC) simulation. We then show that we can accurately reproduce these CDF estimates with a GPE, using only a small fraction of the computational cost required by traditional MC simulation. In order to build a GPE that can predict the simulator output from a permeability field consisting of 1000s of values, we use a truncated Karhunen-Loeve (K-L) expansion of the permeability field, which enables the application of the Bayesian functional regression approach. We perform a cross-validation exercise to give an insight of the optimization of the experiment design for selected scenarios: we find that it is sufficient to use 100s values for the size of training set and that it is adequate to use as few as 15 K-L components. Our work demonstrates that GPE with truncated K-L expansion can be effectively applied to uncertainty analysis associated with modelling of multiphase flow and transport processes in heterogeneous media.

Mathematical Modeling: Approaches for Model Solution

The governing equations and mathematical models describing CO2 spreading and trapping in saline aquifers and the related hydro-mechanical and chemical processes were described in Chapt. 3. In this chapter, the focus is on methods for solving the relevant equations. The chapter gives an overview of the different approaches, from high-fidelity full-physics numerical models to more simplified analytical and semi-analytical solutions . Specific issues such as modeling coupled thermo-hydro-mechanical-chemical processes and modeling of small-scale processes , such as convective mixing and viscous fingering , are also addressed. Finally, illustrative examples of modeling real systems, with different types of modeling approaches, are presented.