## 1 Introduction  
Soil contamination constitutes a severe environmental problem. It is estimated to affect around 2.8 million sites in Europe [1], where mineral oils account for 22-24% of all the soil contamination incidents reported, and comprise 45% when considered together with BTEX and polyaromatic hydrocarbons [2]. The pollution of soils by petroleum hydrocarbons leads to ecological and health risks, due to their relatively low mobility and their toxic, mutagenic and carcinogenic effects [3, 4]. The fate of petroleum hydrocarbons in soil is influenced by the physical and chemical properties of these compounds (e.g., solubility in water and affinity for the organic carbon in soil) as well as by the characteristics of the soil, such as particle size, porosity, organic matter content, permeability and surface area ([PERSON] and [PERSON], 2016; [PERSON] and [PERSON], 2016). In general, soil acts as a sink for pollutants; thus, active cleaning operations must be performed to enable the recovery of contaminated soils within an acceptable timeframe ([PERSON] and [PERSON], 2016). To date, several physical and chemical remediation technologies are available (e.g., physical removal, soil washing and oxidation/reduction via chemical agents) ([PERSON] and [PERSON], 2016; however, there is an increasing willingness for the use of less aggressive and more eco-friendly techniques, such as bioremediation ([PERSON] and [PERSON], 2016; [PERSON] and [PERSON], 2016). Critical factors in bioremediation are the availability of nutrients and electron acceptors (oxygen, nitrate, iron (III), sulfate) as well as the existence of microbial catabolic activity towards hydrocarbons ([PERSON] and [PERSON], 2016; [PERSON] and [PERSON], 2016). Bioavailability of the contaminants also influences microbial activity, since the access of the microorganisms or their enzymes to the compounds can be hampered due to hydrocarbon interactions with the organic carbon content of the soil ([PERSON] and [PERSON], 2016). These aspects are particularly important when hydrocarbon contamination occurs in depth; for example, due to leaking underground storage tanks or pipelines. In permeable soils, the plume can penetrate to a significant depth, hindering the contamination removal and site decontamination ([PERSON] and [PERSON], 2016). Current knowledge of hydrocarbon biodegradation in soils is limited and requires further research. In addition, the selection and implementation of bioremediation approaches, as well as the prediction of the process outcomes, is highly complex. In this framework, mathematical modelling emerges as a promising tool, providing support for decision makers to effectively deal with the complexity of cleaning and restoring contaminated sites ([PERSON] and [PERSON], 2016; [PERSON] and [PERSON], 2016). Over the years, mathematical modelling of hydrocarbon bioremediation has been performed, focused mainly on contaminated aquifers considering that relatively soluble hydrocarbon fractions will be transported from the contaminated soils to the water level, where further transport and biodegradation will occur ([PERSON] and [PERSON], 2016; [PERSON] and [PERSON], 2016). Straight chain alkanes are less water soluble than other aliphatic and aromatic hydrocarbons and present a higher affinity for the organic carbon content of the soil. Moreover, saturated hydrocarbons account for 50-90% of the hydrocarbon fraction in several petroleum products (e.g., aviation gasoline, jet fuel, diesel fuel) ([PERSON] and [PERSON], 2016). As such, sequestration of this less soluble fraction of oil may occur in soils; its environmental fate is still not sufficiently studied. In soils, the majority of the developed models are designed for ex situ bioremediation ([PERSON] and [PERSON], 2016; [PERSON] and [PERSON], 2016; [PERSON] and [PERSON], 2016).