In a subsoil bioremediation intervention air or oxygen is injected in the polluted region and then a model for unsaturated porous media it is required, based on the theory of the dynamics of multiphase fluids in porous media. In order to optmize the costs of the intervention it is useful to consider the gas as compressible and this fact introduces nonlinearity in the mathematical model. The physical problem is described by a system of equations and the unknowns are: pollutant; bacteria concentration; oxygen saturation and oxygen pressure. Then, by algebraic manipulations, the model is reduced a to a nonlinear system of partial differential equations describing: oxygen saturation, oxygen density and bacteria concentration. For the proposed model, the results of some simulation experiments performed using COMSOL Multiphysics will be shown.

Here some issues are studied, related to the numerical solution of Richards' equation in a one dimensional spatial domain by a technique based on the Transversal Method of Lines (TMoL). The core idea of TMoL approach is to semi-discretize the time derivative of Richards' equation: afterward a system of second order differential equations in the space variable is derived as an initial value problem. The computational framework of this method requires both Dirichlet and Neumann boundary conditions at the top of the column. The practical motivation for choosing such a condition is argued. We will show that, with the choice of the aforementioned initial conditions, our TMoL approach brings to solutions comparable with the ones obtained by the classical Methods of Lines (hereafter referred to as MoL) with corresponding standard boundary conditions: in particular, an appropriate norm is introduced for effectively comparing numerical tests obtained by MoL and TMoL approach and a sensitivity analysis between the two methods is performed by means of a mass balance point of view. A further algorithm is introduced for deducing in a self-sustaining way the gradient boundary condition on top in the TMoL context.

In this interdisciplinary paper, we study the formation of iron precipitates - the so-called Liesegang rings - in Lecce stones in contact with iron source. These phenomena are responsible of exterior damages of lapideous artifacts, but also in the weakening of their structure. They originate in presence of water, determining the flow of carbonate compounds mixing with the iron ions and then, after a sequence of reactions and precipitation, leading to the formation of Liesegang rings. In order to model these phenomena observed in situ and in laboratory experiments, we propose a modification of the classical Keller-Rubinow model and show the results obtained with some numerical simulations, in comparison with the experimental tests. Our model is of interest for a better understanding of damage processes in monumental stones.

Bioventing is a technology used to abate the presence of pollutants in the subsoil. Microorganisms biodegrade the pollutant but the biochemical reaction requires oxygen and so an airflow is induced in the subsoil by means of injection and/or extraction wells. Costs, final result and decontamination time are reliant on contaminant type, soil permeability and several other factors, but oxygen subsoil concentration plays a very important role. For this reason a rational choice of well locations and flow rates is required. The mathematical definition of the optimal design problem will be set-up starting from a simplified mathematical model describing the bioventing system. A formal definition of decontaminated subsoil will be given and the set of system control variables will be identified. Optimization strategies such as cost minimization and time optimization will be mathematically described.

Bioventing is a technology used to remove some kinds of pollutants from the subsoil and it is based on the capability of some bacteria species to biodegrade contaminants. The biochemical reaction requires, among other things, oxygen and, therefore, oxygen is inflated into the subsoil by wells. The mathematical model describes the movement of the different fluids which are present in the subsoil - air, water, pollutants, oxygen and so on - and the bacteria population dynamics. The presence of source reactive terms in the continuity equations allows the contaminant biodegradation to be described. The design of a subsoil decontamination intervention concerns bioavailability problems and, in particular, the oxygen concentration. Therefore, in order to enhance the biodegradation phenomenon, the optimization of the subsoil oxygen velocity field in the polluted area is required, by an appropriate choice of the well positions and of the well air inflating rates. In mathematical terms, the goal is to obtain the decontamination of the subsoil with an optimal value of an objective function by acting on some control variables which, in this case, are the well positions and the inflating rates. In this paper several kind of objective function are proposed.

A mathematical model describing the evolution of the spatial distribution of a bacteria population in a marine environment is described. The hypothesis is that a certain amount of water polluted by bacteria is introduced into the environment due to an accidental event. In particular, the evolution of the spatial bacteria distribution will be described considering the bacteria transport due to the marine currents and the bacteria diffusion, reproduction and death dynamics. In this paper only a short presentation of the partial differential equations of the model will be reported. The final goal of the study will be to describe the environmental scenario following the accident in the short and long term in presence of different tide phase and kind of wind. To this end the numerical approximate resolution of the model it is required.

Bioventing is a technology used to abate the presence of pollutants in the subsoil. Microorganisms biodegrade the pollutant but the biochemical reaction requires oxygen and so an airflow is induced in the subsoil by means of injection and/or extraction wells. Costs, final result and decontamination time are reliant on contaminant type, soil permeability and several other factors, but oxygen subsoil concentration plays a very important role. For this reason a rational choice of well locations and flow rates is required. The mathematical definition of the optimal design problem will be set-up starting from a simplified mathematical model describing the bioventing system. A formal definition of decontaminated subsoil will be given and the set of system control variables will be identified. Optimization strategies such as cost minimization and time optimization will be mathematically described.

Bioventing is a technology used to abate the presence of pollutants in the subsoil. Microorganisms biodegrade the pollutant but the biochemical reaction requires oxygen and so an air ow is induced in the subsoil by means of injection and/or extraction wells. Costs, final result and decontamination time are reliant on contaminant type, soil permeability and several other factors, but oxygen subsoil concentration plays a very important role. For this reason a rational choice of well location and ow rate is required. The mathematical definition of the optimal design problem will be setup starting from a simplified mathematical model describing the bioventing system. A formal definition of decontaminated subsoil will be given and the set of system control variables will be identified. Several optimimization strategies such as cost minimization, removal rate maximization and time optimization will be mathematically described.

Bioventing is a clean-up technology essentially used to remove hydrocarboon from polluted subsoil by the action of microorganism. The model is based on the theory of fluid flows in porous media and on the mathematical description of population dynamics. The numerical results of a simplified model will be described.

A mathematical model and the simulation of subsoil decontamination by bioventing will be presented. The bases for the model construction are the following: (1) the pollutant is considered as immobile and confined in the unsaturated zone; (2) only oxygen is injected in the subsoil by wells; (3) the bacteria acting the pollutant removal are immobile and their growth depends on oxygen and pollutant concentration.

This paper presents a simple mathematical model describing the bioventing technology for soil remediation. Bacteria biodegrade the pollutant and oxygen is injected in the soil to favorite the biodegradation process. The model is referred to the unsaturated zone and several simplifying hypothesis are used. In particular it is supposed that pure oxygen is injected in the subsoil and it is the unique gas present in the subsoil. From fluid dynamics theory in porous media a system of partial differential equations is obtained.

A mathematical model describing the bioventing technique for the decontamination of pol- luted subsoil will be presented. Bioventing is a biological technique: bacteria remove the contaminant transforming it and oxygen is consumed in the reaction. The numerical model is based on the fluid flow theory in porous media and bacteria population dynamics and it describes: pollutant degradation, oxygen and bacteria concentration. The mathematical model will be numerically solved and the results of some experiments will be presented.

Bioventing is a subsoil bio-remediation technique which improves the activity of bacteria to transform contaminants into less hazardous compounds by inflating air through wells. The mathematical model describes the bacteria population dynamics and the dynamics of a multiphase, multicomponent fluid in porous media and in this paper a simple version of it will be described. A critical point of the design problem is to choose well positions and air flow rates to optimise the biodegradation process. The numerical simulation and some initial optimisation design results for the simple model proposed will be reported. The decontamination time required for different flow rates and for different well spatial configurations will be compared.

A partire da fenomeni reali viene esposto il percorso che, mediante il linguaggio della matematica, conduce all'astrazione ed alle teorie assiomatiche formali.

Si affronta il problema della ottimizzazione delle risorse in interventi di rimozione di inquinanti dal sottosuolo mediante bioventing The report deals with the problem of resource optimization in the removal of pollutants from the subsoil by bioventing

Il bioventing e' una tecnologia di decontaminazione del sottosuolo. Alcune specie batteriche presenti nel sottosuolo stesso biodegradano l'inquinante - ad esempio un idrocarburo - mediante un processo che richiede ossigeno; quest'ultimo e' fornito per mezzo di iniezione di aria in pozzi praticati nella zona inquinata del sottosuolo. Verra' presentato un modello matematico - basato sulla teoria del moto dei fluidi multifase in mezzi porosi e sulle equazioni della dinamica delle popolazioni - descrivente il fenomeno fisico ed utile per la simulazione numerica. Il problema della progettazione ottimale dell'intervento di bonifica consiste nel determinare numero, posizione e portata dei pozzi di iniezione di aria, al fine di massimizzare la velocita' di biodegradazione.