Inversion of dissolved plume concentration data under unknown initial and boundary conditions: theoretical analysis and laboratory verification
Abstract
An improved inversion method that is suitable for estimating plume pathway of a conservative solute under unknown transport initial and boundary conditions is proposed. To invert solute transport in a steady heterogeneous groundwater velocity field, a direct inverse theory incorporates a set of polynomial and exponential functions that change with time and space as local approximate solutions (LAS) of transport. A four-step process is employed in inversion. First, at a given time step, continuities of concentration values and total solute mass flux are enforced at a set of spatial collocation points using polynomial and exponential functions as a LAS. Second, the estimated plume concentrations, as embodied by the LAS, are conditioned to observed concentration breakthrough curves (BTC) at a set of monitoring wells. Third, residuals of solute transport equation (implementing the same LAS) are simultaneously enforced to be zero at both selected collocation points and the locations of the monitoring wells. In the fourth step, equations developed in the first third steps are implemented for all time steps. As a result, a single system of inversion equations can be assembled and solved with a parallel iterative solver. Unlike many indirect transport inverse methods, the proposed approach does not require the solution of a forward transport model. The key to the accuracy and stability of this approach, however, is the proper selection of LAS. In this work, the new proposed LAS can lead to accurate transport inversion outcomes given enough monitoring wells and accurate BTC measurements. The method was tested using both synthetic BTC data generated using a forward transport model as well as data from a two-dimensional intermediate-scale laboratory test system simulating brine leakage from a deep saline aquifer. For both cases, well density and location play a key role in the accuracy of plume recovery. Moreover, though both the proposed LAS functions can be used in inversion, pro and con exist in using each function. The polynomial LAS leads to fast convergence of the inversion equations, although negative concentrations at some grid locations can result from inversion. The exponential LAS ensures that all the inverted concentrations >=0, however, it can lead to inversion equations that are slow to converge.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2019
- Bibcode:
- 2019AGUFM.H21H1829Z
- Keywords:
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- 1829 Groundwater hydrology;
- HYDROLOGY;
- 1835 Hydrogeophysics;
- HYDROLOGY;
- 1865 Soils;
- HYDROLOGY;
- 1899 General or miscellaneous;
- HYDROLOGY