Modelling Simultaneous Transport of Bioreactive Solutes and Microorganisms in Porous Media

Recent years have seen the development of a number of mathematical models for the description of the simultaneous transport of microorganisms and bioreactive solutes in porous media. Most models are based on the advection dispersion equation, with terms added to account for interactions with the surfaces of the solid matrix, transformations and microbial activities. Those models based on the advection dispersion equation have all been shown to represent laboratory experimental data adequately although various assumptions have been made concerning the pore scale distribution of bacteria. This paper provides an overview of the recent work on modelling the transport and fate of microorganisms and bioreactive solutes in porous media and examines the different assumptions regarding the pore scale distribution of microorganisms.

Porous-DeepONet:Learning the Solution Operators of Parametric Reactive Transport Equations in Porous Media

Reactive transport equations in porous media are critical in various scientific and engineering disciplines,but solving these equations can be computationally expensive when exploring different scenarios,such as varying porous structures and initial or boundary conditions.The deep operator network(DeepONet)has emerged as a popular deep learning framework for solving parametric partial differential equations.However,applying the DeepONet to porous media presents significant challenges due to its limited capability to extract representative features from intricate structures.To address this issue,we propose the Porous-DeepONet,a simple yet highly effective extension of the DeepONet framework that leverages convolutional neural networks(CNNs)to learn the solution operators of parametric reactive transport equations in porous media.By incorporating CNNs,we can effectively capture the intricate features of porous media,enabling accurate and efficient learning of the solution operators.We demonstrate the effectiveness of the Porous-DeepONet in accurately and rapidly learning the solution operators of parametric reactive transport equations with various boundary conditions,multiple phases,and multiphysical fields through five examples.This approach offers significant computational savings,potentially reducing the computation time by 50–1000 times compared with the finite-element method.Our work may provide a robust alternative for solving parametric reactive transport equations in porous media,paving the way for exploring complex phenomena in porous media.

Experimental study on the velocity-dependent dispersion of the solute transport in different porous media

The hydrodynamic dispersion is an important factor influencing the reactive solute transport in the porous media, and many previous studies assumed that it linearly varied with the average velocity of the groundwater flow. Actually, such linear relationship has been challenged by more and more experimental observations, even in homogeneous media. In this study, we aim to investigate the relationship between hydrodynamics dispersion and the flow velocity in different types of porous media through a laboratory-controlled experiment. The results indicate that (1) the dispersion coefficient should not be a linear function of the flow velocity when the relationship between the flow velocity and the hydraulic gradient can be described by Darcy's law satisfactorily;(2) Power function works well in describing the dispersion coefficient changing with the flow velocity for different types of porous media, and the power value is between 1.0-2.0 for different particle sizes.

Experimental investigation on rainfall infiltration and solute transport in layered porous and fractured media

Layered structures with upper porous and lower fractured media are widely distributed in the world. An experimen- tal investigation on rainfall infiltration and solute transport in such layered structures can provide the necessary foundation for effectively preventing and forecasting water bursting in mines, controlling contamination of mine water, and accomplishing ecological restoration of mining areas. A typical physical model of the layered structures with porous and fractured media was created in this study. Then rainfall infiltration experiments were conducted after salt solution was sprayed on the surface of the layered structure. The volumetric water content and concentration of chlorine ions at different specified positions along the profile of the experiment system were measured in real-time. The experimental results showed that the lower fractured media, with a considerably higher permeability than that of the upper porous media, had significant effects on preventing water infil- tration. Moreover, although the porous media were homogeneous statistically in the whole domain, spatial variations in the features of effluent concentrations with regards to time, or so called breakthrough curves, at various sampling points located at the horizontal plane in the porous media near the porous-fractured interface were observed, indicating the diversity of solute transport at small scales. Furthermore, the breakthrough curves of the outflow at the bottom, located beneath the underlying fractured rock, were able to capture and integrate features of the breakthrough curves of both the upper porous and fractured media, which exhibited multiple peaks, while the peak values were reduced one by one with time.

Analytical solutions of three-dimensional contaminant transport in uniform flow field in porous media:A library

The purpose of this study is to present a library of analytical solutions for the three-dimensional contaminant transport in uniform flow field in porous media with the first-order decay,linear sorption,and zero-order production.The library is constructed using Green's function method(GFM)in combination with available solutions.The library covers a wide range of solutions for various conditions.The aquifer can be vertically finite,semi-infinitive or infinitive,and laterally semi-infinitive or infinitive.The geometry of the sources can be of point,line,plane or volumetric body;and the source release can be continuous,instantaneous,or by following a given function over time.Dimensionless forms of the solutions are also proposed.A computer code FlowCAS is developed to calculate the solutions.Calculated results demonstrate the correctness of the presented solutions.The library is widely applicable to solve contaminant transport problems of one-or multiple-dimensions in uniform flow fields.

APPLICATION OF SUBPLEX OPTIMIZATION TO SOLUTE-TRANSPORT PROBLEM

Determining parameters,such as interphase exchange rate and dispersivity,in multiphase solute transport problem has always been an interesting issue.These parameters are usually not available because they are too difficult or too expensive to measure although they are necessary as input data or parameters for numerical modeling.To overcome this problem,inverse techniques have been developed.Recently,the subplex optimization approach,which considers reflection,expansion,contraction,and shrinkage as basic components in seeking the minimization point and which uses the subspace concept in search space,has been incorporated into our coupled multiphase fluid－ flow and solute－ transport simulator.In the application of the finite element model to multiphase infiltration and solute transport problem,physical variables,which are easy to observe(such as solute concentrations),are used as constraints in minimizing the differences between computed output and measured data.Therefore,modeling results provide optimized parameter estimates in addition to comparison with field data.Our numerical－ simulation example on interphase－ exchange coefficient as well as water and gas dispersivities shows optimized parameters approaching the same values specified in the forward simulation used to generate the synthetic constrained data.This provides an implication of possible application to the fields of earch sciences,including geotectonics and metallogeny.

Non-invasive image processing method to map the spatiotemporal evolution of solute concentration in two-dimensional porous media

A color visualization-based image processing method is developed in this paper to quantify the concentration evolution of the Brilliant Blue FCF transport through a two-dimensional homogeneous porous medium. A series of images are recorded at known time intervals, then the spatial distribution is estimated using a calibration curve, linking the gray pixel value to the solute concentration. Using a multi-dimensional concentration distribution map extraction technique the longitudinal and transverse concentration distributions could be observed with the physical model. The image-processed concentrations are then compared directly with the measured concentrations sampled at the outlet end. The tracer breakthrough curves sampled at multiple points along the central line of the medium are also compared with the solutions from the standard advection–dispersion equation model. It is shown that the non-invasive image processing method may be used to map the spatiotemporal evolution of a solute＇s concentration without disturbing the flow or the transport dynamics, although the measured solute breakthrough curves feature some non-Fickian dynamics that cannot be efficiently captured by the standard transport model.