Estimation of the mass transport parameters of aquifers according to data from field tests with a pulse or a continuous source and an arbitrary location of the observation well

An identification method for determining the aquifer’s mass transport parameters is proposed, based on data from field tracer tests with a pulse or a continuous source and an arbitrary position of the observation well in respect to the tracer entry point. The method is also applicable in the presence of a representative set of data on changes in the concentration of pollutants at different points in the aquifer around a short-term (instantaneous) or a continuous surface or underground source. The identification procedure is based on the automated comparison of the observations data with a series of theoretical curves by varying the required parameters in order to achieve maximum compliance. The tracer transport is represented by analytical solutions of the partial differential equation for mass transfer in a homogeneous and isotropic two-dimensional porous media. The developed computer programs include numerical optimization using the Levenberg-Marquardt algorithm. Results from tests performed in order to assess reliability and errors of detection and identification are presented. Using the programs, the mass transport parameters: active porosity n0, effective (sorption) porosity nS, longitudinal dispersivity αL, transverse dispersivity αT and rate constant γ can be determined.

Experimental and numerical study of bed roughness effect on longitudinal dispersion

The effects of bed roughness on the longitudinal dispersion coefficient (DL) were experimentally and numerically investigated in the present study. The tracer experiments were first carried out in a circular flume with a diameter of 1.6 m over both smooth and rough beds (coarse sand) with four sizes (ks = d65) of 1.04, 2.09, 3.01, and 4.24 mm. In addition, the one-dimensional advection-dispersion equation was numerically solved. The longitudinal dispersion coefficient was calculated by comparing the numerical and experimental breakthrough curves. The results showed that by increasing the bed roughness height (from zero to 4.24 mm), the longitudinal dispersion coefficient increased by 34%. In addition, the longitudinal dispersivity (λ = DL/V) increased with increasing relative roughness (ks/h), so that the range of longitudinal dispersivities in smooth bed experiments were 0.037–0.049 m and for rough bed (ks = 4.24 mm) were 0.07–0.084 m. In other words, with increasing the bed roughness height from zero (smooth bed) to 4.24 mm, the longitudinal dispersivities increased from 0.037 to 0.077 m, indicating an increase of about 108%. Furthermore, a relationship was developed using non-dimensional longitudinal dispersion (DL/(Vh)) as a function of relative roughness (ks/h). It can be concluded that taking into consideration bed roughness as the driving force of shear dispersion would improve predictive equations of the longitudinal dispersion in the rivers. Since the bottom of all natural rivers has roughness elements with different sizes, the results of this study will definitely be useful in estimating the longitudinal dispersion coefficient in natural rivers and quantifying the effect of roughness in the longitudinal dispersion coefficient equations.

Aquifer-wide estimation of longitudinal dispersivity by the combination of empirical equations, inverse solution, and aquifer zoning methods

Longitudinal dispersivity is a key parameter for numerical simulation of groundwater quality and this parameter is highly variable in nature. The use of empirical equations and the inverse solution are two main methods of estimating longitudinal dispersivity. In this study, the estimation of values and aquifer-wide spatial distribution of longitudinal dispersivity parameter using a combined approach i.e. a combination of empirical equation method (Pickens and Grisak, Arya, Neuman, and Xu & Eckstein equations), the inverse solution method (using the MT3DMS model with non-automatic calibration) and the aquifer zoning technique is investigated. The combined approach applied to Bandar-e-Gaz aquifer in northern Iran, and Willmott’s index of agreement was used to assess the precision of simulation of total dissolved solids in this aquifer. The values of this criterion were 0.9985 to 0.9999 and 0.9756 to 0.9992 in calibration and validation periods that show the developed combined approach resulted in obtaining high precision for both calibration and validation periods and the simulation show remarkable consistency. Also, the one-way sensitivity analysis indicates that the longitudinal dispersivity is more sensitive than the effective porosity in this simulation. The investigation of the spatial distribution of the estimated longitudinal dispersivity by the combined approach indicates that the value of the parameter has a decreasing trend from the south to the north (50 to 8 m) in the aquifer environment which is consistent with the changes in the characteristics of porous media in this study area, and therefore it concludes that the combined approach provides a reliable and appropriate estimation of the spatial distribution of longitudinal dispersivity.

Truncation Effect on Estimation of Transport Parameters for Slug-injection Tracer Tests

For slug-injection tracer tests, tracer concentrations below the detection limit of the measurement instrument can cause truncation of the observed data. This study investigated the truncation effect on the estimation error of parameters based on analytical solutions and the results of a laboratory-scale experiment. Spatial moment analysis was performed to estimate the measured total mass and transport parameters, including the pore velocity and the longitudinal and transverse dispersivities. Increasing the travel distance and detection limit caused the measured mass and dispersivities to be underestimated regardless of the dimensionality because hydrodynamic dispersion occurs with increasing travel distance, which smoothens the concentration front. The one- and two-dimensional cases showed that the truncation effect on the measured mass and longitudinal dispersivity depended on dimensionality. In contrast, the pore velocity showed no such dependence; the center of mass did not change as the unmeasured portion due to truncation was increased because the plume, which exhibited a Gaussian distribution, was truncated symmetrically. In the experiment, the measured mass and dispersivities likewise depended on the travel distance and detection limit, but there were large differences in the detection limit at which the dimensionless parameter reached a value of zero between the experimental results and analytical solution. This is because the initial plume in the experiment was of a finite size. Thus, experimental design factors such as the scale, device, and dimensionality should be considered to minimize the estimation error of transport parameters, excluding the pore velocity.

Scale-dependent dispersion for solute transport in bounded formations

<p>We present a new method to estimate the displacement covariance and macrodispersivity for solute transport in bounded formations. Here we use circulant embedding, which is based on the fast Fourier transform and is much more efficient than eigen-decomposition for the factorization of random spatial fields. We compute the displacement covariances using the analysis of variance approach and introduce an interpolation process to significantly reduce the number of forward simulations. Once the effect of each eigenvector on the displacement covariance is obtained, it is unnecessary to rerun the simulator for different spatial covariance functions or anisotropy ratios, which saves a large amount of computational effort. The proposed method is validated in various tests in two-dimensional and three-dimensional examples and accurately matches the results from the Monte Carlo simulation. It is found that the longitudinal dispersivity is not sensitive to the boundaries, while the transverse and vertical dispersivities are greatly affected. The method is applied to the Borden site and provides a better explanation of the observed data after considering the effect of vertical boundaries. These results show that our method could serve as a promising tool for studying and predicting the characteristics of solute transport in heterogeneous media.</p>

Three-Dimensional Modelling of Heterogeneous Coastal Aquifer: Upscaling from Local Scale

The aquifer heterogeneity is often simplified while conceptualizing numerical model due to lack of field data. Conducting field measurements to estimate all the parameters at the aquifer scale may not be feasible. Therefore, it is essential to determine the most significant parameters which require field characterization. For this purpose, the sensitivity analysis is performed on aquifer parameters, viz., anisotropic hydraulic conductivity, effective porosity and longitudinal dispersivity. The results of the sensitivity index and root mean square deviation indicated, that the longitudinal dispersivity and anisotropic hydraulic conductivity are the sensitive aquifer parameters to evaluate seawater intrusion in the study area. The sensitive parameters are further characterized at discrete points or at local scale by using regression analysis. The longitudinal dispersivity is estimated at discrete well points based on Xu and Eckstein regression formula. The anisotropic hydraulic conductivity is estimated based on established regression relationship between hydraulic conductivity and electrical resistivity with R2 of 0.924. The estimated hydraulic conductivity in x and y-direction are upscaled by considering the heterogeneous medium as statistically homogeneous at each layer. The upscaled model output is compared with the transversely isotropic model output. The bias error and root mean square error indicated that the upscaled model performed better than the transversely isotropic model. Thus, this investigation demonstrates the necessity of considering spatial heterogeneous parameters for effective modelling of the seawater intrusion in a layered coastal aquifer.

A comparative study in aquifer parameter estimation using MFree point collocation method with evolutionary algorithms

In this study, we present a comparative assessment of simulation-optimization (S-O) models to estimate aquifer parameters such as transmissivity, longitudinal dispersivity, and transverse dispersivity. The groundwater flow and contaminant transport processes are simulated using the mesh-free radial basis point collocation method (RPCM). Four different S-O models are developed by combining the RPCM model separately with genetic algorithm (GA), differential evolution (DE), cat swarm optimization (CSO), and particle swarm optimization (PSO). The objective of the S-O model is to minimize a composite objective function with transmissivity, longitudinal dispersivity, and transverse dispersivity as decision variables. Hydraulic head and contaminant concentration at observation points are the state variables. The S-O models are used to estimate aquifer parameters of a confined aquifer with nine zones. It is found that RPCM-based DE, CSO, and PSO models are more accurate in estimating aquifer parameters than RPCM-GA. However, for noisy observed data, the RPCM-CSO model outperforms other models. The efficiency of the RPCM-CSO model over other models is further established by performing reliability analysis to the noisy observed data set. The comparative study reflects the efficacy of CSO over GA, DE, and PSO.