Upscaling of mass transfer rate coefficient for the numerical simulation of dense nonaqueous phase liquid dissolution in heterogeneous aquifers

Abstract

Mass transfer from entrapped dense nonaqueous phase liquids (DNAPLs) in heterogeneous aquifers takes place in natural, three‐dimensional groundwater flow fields. However, mass transfer processes are characterized in the laboratory in columns or flow cells under conditions of one‐dimensional or two‐dimensional water flow. Dissolution data generated in these test systems are used to determine empirical parameters of correlations that relate a dimensionless form of a mass transfer coefficient (Sherwood number) to other dimensionless groups that capture the basic processes contributing to mass transfer (e.g., Reynolds and Schmidt numbers). These phenomologically based empirical correlations, which are referred to as Gilland‐Sherwood models, are not directly applicable in predicting the dissolution of DNAPLs in the field as they do not capture the effects of aquifer heterogeneity and DNAPL entrapment morphology (referred to as DNAPL entrapment architecture). Numerical simulation of DNAPL dissolution requires the discretization of the problem domain into computational grid blocks and assignment of an effective mass transfer coefficient to each of these blocks containing DNAPL. A methodology for upscaling is needed to determine the grid‐scale effective mass transfer coefficient from the laboratory‐determined empirical correlations. It is our hypothesis that the upscaled effective mass transfer coefficient needs to contain information on the field‐scale heterogeneity and DNAPL entrapment architecture. This hypothesis was tested through a Monte‐Carlo‐based numerical experiment using a laboratory‐validated dissolution model with the goal of developing and testing an upscaling method. The developed upscaling method involves the use of geostatistical parameters that capture the aquifer heterogeneity and the DNAPL entrapment architecture. These parameters were determined to be the variance of log hydraulic conductivity, correlation lengths, and the normalized second moments of DNAPL mass distribution in the entrapment zone. Monte Carlo numerical simulation experiments combined with inverse modeling were used in this theoretical development and to determine parameters of the proposed upscaled Gilland‐Sherwood mass transfer correlation. Through these numerical modeling studies, the upscaled mass transfer correlation was successfully verified. Sensitivity analyses indicate that the normalized second moment, which describes the spreading of DNAPL mass in the vertical directions, was the most sensitive parameter in simulating the mass transfer at large scales.