Analytical solutions for the flow fields near funnel-and-gate reactive barriers with hydraulic losses

摘要

Permeable reactive barriers (PRBs) are a passive in situ technology that is based on the interception and physical, chemical, and/or biological remediation of a contaminant plume through installation of reactive material in an aquifer. The present work is an extension and generalization of a previous paper and derives analytical expressions for flow fields toward PRBs in two dimensions on the basis of the conformal mapping approach. Considered is the classic funnel-and-gate configuration with perpendicular funnel arms (PFGs) as well as PRBs with velocity equalization walls. While the aquifer is assumed to be homogeneous in a uniform far field, the hydraulic conductivity of the reactive material is allowed to take arbitrary values above or below the aquifer conductivity. At the up- and down-gradient interfaces between reactor and aquifer, highly permeable gravel packs are assumed to establish constant head conditions. The flow fields are analyzed regarding the widths and shapes of respective capture zones as functions of PRB type and dimensions, reactor hydraulic resistance (including flow divergence and longevity), and ambient groundwater flow direction. Expressions for discharge fields are developed as needed for particle-tracking algorithms. Charts of relative capture width are given to facilitate PRB design and may be included in more comprehensive PRB design/ optimization approaches. An efficient approach is presented to estimate reactor conductivity and capture flow from monitoring the hydraulic loss at the reactor. Inherent assumptions and results are validated against numerical flow field solutions and water level field data for the PFG PRB at the Moffett Federal Airfield, California.