## 1 Introduction  
The increasing demand for energy and the limited resources of fossil fuels [1; 2]. Fischer-Tropsch w humans to look for renewable energy alternatives to fossil fuels [1; 2]. Fischer-Tropsch synthesis (FTS) uses transition metals, such as cobalt (Co), iron (Fe), and nickel (Ni), as catalysts [3; 4; 5; 6] to make non-petroleum raw materials (mostly coal, biomass, and natural gas). Syngas (a mixture of CO and H\({}_{2}\)) is converted into pollution-free fuel and valuable chemicals. It offers a way to convert coal or natural gas into gasoline, diesel fuel, and other useful hydrocarbons such as waves [7; 8; 9; 10]. However, FTS technology has led to the formation of a large amount of Fischer-Tropsch wax residue (FTWR) and has caused serious industrial pollution and public land occupation problems. FTWR is a typical wax-based solid waste mainly from the wax filter unit of FTS. Different wax filter units have various FTWR components, which are mostly composed of 40-80 wt% Fischer-Tropsch wax (FTW), 30-85 wt% Fischer-Tropsch catalyst (FTC), and 0-80 wt% minerals and other impurities [7]. In many countries, FTWR is classified as hazardous waste. If improperly handled, it will produce toxic and hazardous substances [11; 12], causing damage to the ecological environment and posing a threat to human health. Reports have reported that approximately 20,000 tons of slag wax are produced in China each year, 60% of the slag wax is incinerated, and the rest is used for landfill [13]. However, incineration and landfill treatment waste many FTW resources in FTWR, and the organic matter produced by incineration pollutes the atmosphere [14; 15]. Landfill disposal will take up a lot of land resources, cause leachate to seep out, thereby polluting soil and groundwater, and will cause high economic costs and other problems [16]. Recycling the valuable resources in FTWR, avoiding resource waste, and polluting the environment is the correct way to dispose of FTWR. Solvent desorption is a commonly used method to recover lipids from oily waste [17; 18; 19]. It has been widely used to recover aliphatic hydrocarbons from oily sludge and other oily wastes [20; 21]. [PERSON] et al. studied the combination of MEK (polar solvent) and xylene (non-polar solvent) as a mixed solvent for the recovery of hydrocarbons from oil sludge, showing that xylene has a good recovery of hydrocarbons in petroleum efficiency [22]. [PERSON] et al. used isopropanol solvent to extract waste engine oil to obtain regenerated oil [23]. Many studies have investigated solvent desorption to recover oily wastes containing sludge, but few have reported the recycling of FTW resources in FTWR. In fact, the current resource recovery method for wax-based solid waste is mainly pyrolysis, which converts wax into pyrolysis gas and then condenses and recovers it. The presence of the Fischer-Tropsch catalyst in FTWR affect the quality of the finished wax recovered by pyrolysis. As a result, the carbon number of the finished wax and the recovery rate were poor. This will inevitably waste a part of wax resources. The energy requirements of the pyrolysis method were also far greater than that of the solvent method. In this study, wax-based solid waste was compared with oily solid waste, petroleum ether solvent was used to separate recycle Fischer-Tropsch wax (RFTW) from FTWR efficiently to study the influence of several factors, such as solvent/FTWR mass ratio, reaction residence time, and reaction temperature on the product yield. The product recovery rate is obtained by measuring the mass change of FTWR before and after the reaction. Central composite design-response surface methodology (CCD-RSM) was used to screen the best process conditions for FTW desorption. The desorption process of the wax in the three-way environment of Fischer-Tropsch wax, solvent and catalyst was verified and analyzed through isotherm analysis and kinetic fitting, and the desorption mechanism was proposed.