Keep in mind wood ash is quite alkaline, also:
Although the relationship between fire and soil nutrients is complex because of the interactions among many factors, fire intensity is usually the most critical factor affecting post-fire nutrient dynamics, with greater nutrient losses occurring with higher fire intensity. Fire intensity both directly and indirectly impacts many of the mechanisms that affect nutrient pools and cycling. Fire temperature directly determines the amounts and kinds of nutrients that will be volatilized. For instance, N begins volatilizing out of organic matter at only 200º C, whereas Ca must be heated to 1240º C for vaporization to occur (Neary et al. 1999).
Convective transport of ash varies from 1% in low intensity fires to 11% in high intensity fires (Neary et al. 1999).
High intensity fires can also change the physical characteristics of the soil making it more susceptible to nutrient loss through erosion (McColl an Grigal 1977).
The impact of fire on site productivity is also related to intensity. While high intensity fires tend to decrease site productivity, low intensity fires can increase site productivity (Carter and Foster 2003)
https://www2.nau.edu/~gaud/bio300w/frsl.htm
Also:
Because many petroleum hydrocarbons are highly mobile, if they are in soil they can be readily transported to water resources. Several petroleum hydrocarbons like benzene, toluene, ethylbenzene, and xylene can cause cancer. There are regulatory standards for safe levels in drinking water.
Soils contaminated by petroleum hydrocarbons can affect soil health
They can harm soil microorganisms, reducing their number and activity. Soil microbes help make nutrients available to plants (read more here)
https://soilsmatter.wordpress.com/2018/06/01/how-do-soil-microbes-influence-nutrient-availability/
Some petroleum hydrocarbons can be taken up by plants and pose a risk to grazing livestock, wildlife, and plant-eating insects. At high levels of contamination, seeds cannot germinate. In some cases, even mature plants cannot grow anymore
This contamination can occur directly through leaks, car accidents, and spills. This type of contamination can be compounded in areas like parking lots and roads. In these high traffic areas, petroleum hydrocarbons can accumulate and be transported to surrounding soil during rain events. If you have ever seen a shiny puddle in a rainstorm, that shine comes from petroleum products. It can get into the stormwater system or the soil.
In lower concentrations, contamination can still cause discoloration in the soil compared to surrounding areas and poor (or no) vegetative growth
Many petroleum hydrocarbons are naturally-occurring compounds, as they are harvested from the earth. Of course, many are also further refined for use in our modern engines. At low levels, soil microorganisms already present in the soil can consume them. This breaks them down into less harmful substances. Thus, in small-scale contaminations, the best course of action may be to simply leave it alone. To increase the speed of natural degradation you can disturb the contaminated soil by digging up, tilling, or piling it. This exposes more of the petroleum product to air. The presence of more oxygen encourages soil microbes to become more active and feed on the petroleum product. Keeping the contaminated area warm and adding fertilizer (especially nitrogen) can speed up its breakdown.
These concepts also apply at large-scale contaminations, taking the form of landfarming, biopiling, or natural breakdown. Additionally, petroleum hydrocarbon contaminated soils may be treated with chemical amendments to speed up their breakdown
Scientists have researched specific plants that can help clean up contaminated sites. Using plants to clean soil is called phytoremediation. Many common prairie plants, like coneflower, survive large amounts of hydrocarbon contamination. In other locations, trees that have deep roots can help dry out soil, which can help in remediation. Read more here
http://dl.sciencesocieties.org/publications/sh/articles/55/5/sh2014-55-5-f
https://www.soils.org/about-soils/contaminants/petroleum/
HOWEVER before you place fertilizer in the area, keep in mind:
Nutrient pollution is the process where too many nutrients, mainly nitrogen and phosphorus, are added to bodies of water and can act like fertilizer, causing excessive growth of algae.
This process is also known as eutrophication. Excessive amounts of nutrients can lead to more serious problems such as low levels of oxygen dissolved in the water. Severe algal growth blocks light that is needed for plants, such as seagrasses, to grow. When the algae and seagrass die, they decay. In the process of decay, the oxygen in the water is used up and this leads to low levels of dissolved oxygen in the water. This, in turn, can kill fish, crabs, oysters, and other aquatic animals.