Youn Sim

One-dimensional virus transport in homogeneous porous media with time-dependent distribution coefficient

Abstract A stochastic model for one-dimensional virus transport in homogeneous, saturated, semi-infinite porous media is developed. The model accounts for first-order inactivation of liquid-phase and adsorbed viruses with different inactivation rate constants, and time-dependent distribution coefficient. It is hypothesized that the virus adsorption process is described by a local equilibrium expression with a stochastic time-dependent distribution coefficient. A closed form analytical solution is obtained by the method of small perturbation or first-order approximation for a semi-infinite porous medium with a flux-type inlet boundary condition. The results from several simulations indicate that a time-dependent distribution coefficient results in an enhanced spreading of the liquid-phase virus concentration.

Analytical Models for One‐Dimensional Virus Transport in Saturated Porous Media

Analytical solutions to two mathematical models for virus transport in one-dimensional homogeneous, saturated porous media are presented, for constant flux as well as constant concentration boundary conditions, accounting for first-order inactivation of suspended and adsorbed (or filtered) viruses with different inactivation constants. Two processes for virus attachment onto the solid matrix are considered. The first process is the nonequilibrium reversible adsorption, which is applicable to viruses behaving as solutes; whereas, the second is the filtration process, which is suitable for viruses behaving as colloids. Since the governing transport equations corresponding to each physical process have identical mathematical forms, only one generalized closed-form analytical solution is developed by Laplace transform techniques. The impact of the model parameters on virus transport is examined. An empirical relation between inactivation rate and subsurface temperature is employed to investigate the effect of temperature on virus transport. It is shown that the differences between the two boundary conditions are minimized at advection-dominated transport conditions.

Virus transport in unsaturated porous media

A numerical model for one-dimensional virus transport in homogeneous, unsaturated porous media was developed. The model accounts for virus sorption onto liquid-solid and air-liquid interfaces as well as inactivation of viruses suspended in the liquid phase and viruses attached at both interfaces. The effects of the moisture content variation on virus transport in unsaturated porous media were investigated. In agreement with previous experimental studies, model simulations indicated that virus sorption is greater at air-liquid than liquid-solid interfaces. Available data from experiments of colloid transport through unsaturated columns were successfully simulated by the virus transport model developed in this study. Most of the common viruses present in the subsurface orig- inate from human and animal sewage through wastewater dis- charges, sanitary landfills, septic tanks, and agricultural prac- tices. Experimental studies revealed that viruses survive a considerable period of time in unsaturated porous media be- fore they reach the water table (Schaub and Sorber, 1977). Therefore it is important to understand fully the mechanisms governing the transport and fate of these microorganisms in unsaturated porous media. Virus transport in unsaturated porous media is distinguished from transport in saturated porous media, because virus sorp- tion and inactivation are considerably influenced by the soil moisture content and subsurface temperature fluctuations (Vilker and Burge, 1980; Vilker, 1981; Thompson and Yates, 1999). Unsaturated porous media consist of liquid, solid, and air phases. For water-wet solid surfaces, both liquid-solid and air-liquid interfaces exist. Virus sorption within unsaturated porous media is significantly affected by the presence of these two interfaces. An illustration of the three phases present in unsaturated porous media together with viruses in the liquid phase and at the associated two interfaces is shown in Figure 1.

Three-Dimensional Analytical Models for Virus Transport in Saturated Porous Media

Analytical models for virus transport in saturated, homogeneous porous media are developed. The models account for three-dimensional dispersion in a uniform flow field, and first-order inactivation of suspended and deposited viruses with different inactivation rate coefficients. Virus deposition onto solid particles is described by two different processes: nonequilibrium adsorption which is applicable to viruses behaving as solutes; and colloid filtration which is applicable to viruses behaving as colloids. The governing virus transport equations are solved analytically by employing Laplace/Fourier transform techniques. Instantaneous and continuous/periodic virus loadings from a point source are examined.

One‐Dimensional Virus Transport in Porous Media With Time‐Dependent Inactivation Rate Coefficients

A model for virus transport in one-dimensional, homogeneous, saturated porous media is developed, accounting for virus sorption and inactivation of liquid phase and adsorbed viruses with different time dependent rate coefficients. The virus inactivation process is represented by a pseudo first-order rate expression. The pseudo first-order approximation is shown to simulate available experimental data from three virus inactivation batch studies better than the frequently employed constant rate inactivation model. Model simulations indicated that the pseudo first-order approximation, compared to the constant inactivation, leads to extended survival of viruses and, consequently, more distant migration. Results from a parameter sensitivity analysis demonstrated that estimation of pseudo first-order inactivation rate coefficients from field observations requires data collection near the source of virus contamination during initial stages of virus transport.

Analytical solutions for solute transport in saturated porous media with semi-infinite or finite thickness

Three-dimensional analytical solutions for solute transport in saturated, homogeneous porous media are developed. The models account for three-dimensional dispersion in a uniform flow field, first-order decay of aqueous phase and sorbed solutes with different decay rates, and nonequilibrium solute sorption onto the solid matrix of the porous formation. The governing solute transport equations are solved analytically by employing Laplace, Fourier and finite Fourier cosine transform techniques. Porous media with either semi-infinite or finite thickness are considered. Furthermore, continuous as well as periodic source loadings from either a point or an elliptic source geometry are examined. The effect of aquifer boundary conditions as well as the source geometry on solute transport in subsurface porous formations is investigated.

Analytical models for virus adsorption and inactivation in unsaturated porous media

Abstract Analytical models for virus adsorption and inactivation in batch systems of homogeneous, isothermal, unsaturated porous media were developed. The models account for virus sorption onto liquid–solid as well as air–liquid interfaces and inactivation of viruses in the liquid phase and at both interfaces. Mathematical expressions appropriate for virus sorption onto liquid–solid and air–liquid interfaces were developed as functions of the soil moisture variation. The models were solved analytically by Laplace transform procedures. The effects of soil moisture variation on virus sorption at the liquid–solid as well as air–liquid interfaces were investigated. Available experimental data from virus adsorption-inactivation batch studies were successfully simulated by one of the models developed in this work.

Enhanced nonlinearity interval mapping scheme for high‐performance simulation‐optimization of watershed‐scale BMP placement

Integrated continuous simulation-optimization models can be effective predictors of a process-based responses for cost-benefit optimization of best management practices (BMPs) selection and placement. However, practical application of simulation-optimization model is computationally prohibitive for large-scale systems. This study proposes an enhanced Nonlinearity Interval Mapping Scheme (NIMS) to solve large-scale watershed simulation-optimization problems several orders of magnitude faster than other commonly used algorithms. An efficient interval response coefficient (IRC) derivation method was incorporated into the NIMS framework to overcome a computational bottleneck. The proposed algorithm was evaluated using a case study watershed in the Los Angeles County Flood Control District. Using a continuous simulation watershed/stream-transport model, Loading Simulation Program in C++ (LSPC), three nested in-stream compliance points (CP)—each with multiple Total Maximum Daily Loads (TMDL) targets—were selected to derive optimal treatment levels for each of the 28 subwatersheds, so that the TMDL targets at all the CP were met with the lowest possible BMP implementation cost. Genetic Algorithm (GA) and NIMS were both applied and compared. The results showed that the NIMS took 11 iterations (about 11 min) to complete with the resulting optimal solution having a total cost of

Economic Consideration in Water Quality Improvement Practices under Extreme Flow Conditions: Water Quality Design Storm

67.2 million, while each of the multiple GA executions took 21–38 days to reach near optimal solutions. The best solution obtained among all the GA executions compared had a minimized cost of

Correction to “Analytical Models for One-Dimensional Virus Transport in Saturated Porous Media”

67.7 million—marginally higher, but approximately equal to that of the NIMS solution. The results highlight the utility for decision making in large-scale watershed simulation-optimization formulations.