Inverse sequential simulation: an inverse
modeling approach for the characterization of non-Gaussian hydraulic conductivities
Teng Xu, J. Jaime Gómez-Hernández, Zi Chen Institute for Water and Environmental Engineering
Universitat Politècnica de València, Spain
Figure 1: Work flow.
Figure 2: Reference lnK and location of wells.
Figure 3: Ensemble mean and ensemble variance of lnK for the initial realizations (top row) and updated realizations at the 50th time steps (bottom row)
Figure 5: Breakthrough curves (BTC) at the two control planes for the initial lnK realizations and the lnK realizations updated after the 50th time step. The red square line corresponds to BTCs in the reference. The black lines correspond to the 5 and 95 percentiles of all realization BTCs, and the green delta line
corresponds to the median.
In this work, an inverse modeling approach named inverse sequential simulation (iSS) for the characterization of
hydraulic conductivities with non-Gaussian distribution is presented (Figure 1). The approach generates realizations using the multivariate Gaussian sequential simulation
based on the experimental non-stationary cross covariance between the conductivities and piezometric heads
calculated from an ensemble of realizations of state variables. The approach is a blend between sequential
simulation and ensemble Kalman filtering. We demonstrate that the iSS can retrieve the main patterns of the reference field after conditioning on enough piezometric heads.
Figure 4: Evolution in time of the piezometric head at the two calibration wells for the initial lnK realizations and the lnK realizations updated after the 50th time step. The red square line corresponds to the piezometric head in the reference, the gray lines correspond to the realizations and the vertical dashed lines marks the end of the conditioning period, the green delta line corresponds to the average of the gray lines.
Figure 1: Work flow
The appproach is demostrated in a synthetic bimodal confined aquifer composed of 35% high permeability sand and 65% low permeability shale. The aquifer is constructed on a 50 m by 50 m square with the
thickness of 5 m and discretized into a grid of 50 by 50 by 1 cells (Figure 2).
From the figure 3 to figure 5, we can see the effect of conditioning on piezometric heads is patent. The updated realizations can retrive the main patters of the reference, and variance gets a great reduction, as well as the spread of the piezometric head
curves in all realizations also gets a significant reduction and cureves are close to the refernce one, besides, the uncertainty about the BTC predictions is significantly reduced after conditioning to the piezometric head data as well.
Initial Initial
Initial Initial t_50 t_50
t_50 t_50
