## 1 Introduction  
Aerobic bioremediation of polluted soils is becoming a common technique to clean up areas contaminated with a variety of biodegradable compounds. Its success is due to some features that must be considered when a soil remediation technique must be chosen: it is cheap, easy to manage, and environmentally compatible, even if it is slow and time consuming. In general, it can be considered a \"green\" technique and a valid alternative to chemical methods. In addition, together with heavy metals and metalloids, biodegradable compounds represent the main group of pollutants in soil, even if at low levels. Their origin is usually anthropogenic, due to industrial activities or events linked to them. Among these anthropogenic-origin pollutants, hydrocarbons represent a significant portion of compounds that can be found in soils that need to be cleaned up. Due to its wide use, diesel oil is an example. This oil is a mixture of several hydrocarbons, with gross composition of 2/3 alkanes and 1/3 aromatic hydrocarbons, all toxic compounds for living organisms. Its removal by biological processes has been the object of many studies [1; 2; 3; 4; 5; 6] and many solutions have been given in terms of operative conditions, kind of microorganisms, and biological strategies. Moreover, soil properties can influence the process, which means that there is no one optimum solution. Biostimulation has proven to be one of the best solutions in terms of easiness and management of application, relative to the achieved results [2; 3; 7; 8]. In this area, previous studies have demonstrated that good removal efficiency can be achieved when indigenous bacteria are stimulated with mineral salt media in order to aerobically biodegrade soil pollutants without any addition of other carbon sources [9; 10]. Given the multitude of findings, it can be useful to know the kinetics of the process for planning in situ remediation activities. Moreover, optimization of the process in terms of the optimal operative parameters for a given system of soil pollution can be of help to maximize the achievable results. Several studies [11; 12; 13; 14; 15] have shown that hydrocarbon removal can be modeled with first- or second-order reaction kinetics. The complexity of the biological process explains the different results produced by these models. The study of kinetics can be used to estimate biodegradation duration, considering the time to obtain acceptable pollutant removal. Process optimization can be based on factorial analysis and response surface methodology (RSM). These statistical tools allow the reciprocal influence of the process parameters to be studied, in order to define those with positive or negative effect and the ones without effect (they can be disregarded). On this base of this statistical analysis, the optimal conditions can be defined. Previous studies [16; 17; 18; 19; 20; 21] have shown that these mathematical techniques, especially used in quality control [22], can also be applied with good success to bioremediation processes. In this study, part of a wider project aimed at monitoring the process by geophysical methods, the kinetics of diesel oil removal from soil was studied, to check which model can best provide reliable evaluation of the results achievable with given operative conditions. This was done by the realization of microcosms, set up considering findings achieved in previous studies of the project (aerobic biostimulation of indigenous bacteria with no carbon source in addition to pollutant). The microcosm set-up also took into account the experimental design properties, namely the properties of factorial design. Moreover, the experimental findings were used to analyze the process variance and optimize the variables by the response surface methodology [22]. We also monitored the microcosms by observing the electrical properties of the systems. Geophysical measurements are widely applied to monitor biological processes at field and laboratory scales [23; 24].