Lewis acid has the advantage of reducing equipment corrosion, particularly heterogeneous catalysts, solid Lewis acid, and immobilized catalysts, which not only ensure the catalyst’s recycling in the reaction but also help maintain its long-term activity of the catalyst[
38,
45]. Common solid Lewis acid catalysts such as metal oxides, molecular sieves, ion exchange resins, etc. Vinicius et al. [
46] effects of several metal oxide catalysts on esterification yield under different reaction conditions was studied. Metal oxides, especially alumina and tin oxide, have great potential for producing biodiesel with conversion rates of 80-90%.
Sulfated metal oxide is an effective acid heterogeneous catalyst. Rodrigo Zunta Raia et al.[
47] prepared biodiesel from jatropha curcas oil through simultaneous esterification and transesterification with sulphated zirconia. The sample with the highest acidity had the highest catalytic activity, resulting in an ester yield of 59.4%. Du et al.[
48] is doped with tin oxide through hydrothermal synthesis of sulfated silica. SiO
2 can be highly dispersed in sulfated tin oxides, which contributes to the formation of strong acidic sites in sulfated tin oxides. The catalytic experiments show that tin oxide doped with sulfated silica has higher activity than traditional tin sulfate in the transesterification of triglyceride with methanol. However, the issues of poor stability and low catalytic efficiency of sulfur metal oxides have not been fully resolved. Zn / Sn catalysts supported by modified metal oxides with catalytic activity have potential prospects. Li et al. [
49] studied the interaction between Zn and ZrO on a zirconia-supported zinc catalyst. The introduction of Zn species can significantly improve the acidity of the catalyst. Compared to the catalytic activity of different Zn supported ZrO
2, it was found that 7% Zn / ZrO
+2 catalyst had the best catalytic activity for biodiesel and had good selectivity. The Lewis acid catalyst is immobilized to form a heterogeneous catalyst, effectively eliminating or significantly reducing the use of harmful substances and their production in the chemical reaction process [
50]. Polyoxometalates (POMs) are anionic clusters composed of various metal oxides, which have significant functions in the catalytic field. By introducing Lewis acid sites on the backbone of POMs, these compounds can play a catalytic role in esterification reactions. To improve catalytic efficiency, POMs are often dispersed on various solid supports, including silica, zirconia, carbon materials, titania, alumina, and porous silica. This dispersion method can effectively expand the surface area of POMs, thereby increasing the number of catalytically active sites thereby improving catalytic performance [
51]. Mirit et al. [
45] successfully immobilized Lewis acids into a sol-gel matrix and immobilized Lewis acids (BF
3 and AlCl
3) in a silica matrix as catalysts , allowing their reuse and reuse in continuous biodiesel production. M.A.A. Aziz et al. [
52] prepared WO
3 supported on silica mesoporous-macroparticles catalyst and studied the effect of WO
3 loading on FAME catalytic activity. Under optimal reaction conditions determined by the response surface methodology (RSM), the biodiesel conversion rate was 96%. The catalyst exhibits excellent catalytic performance is attributed to the high Lewis acid site content and pores within and between the catalyst particles. This structure provides efficient transport for reactants and products and significantly improves the efficiency of the entire catalytic reaction. Carbon nanotubes (CNTs) with their high thermal conductivity, accessibility to the active phase, have good chemical stability, and have a high specific surface area in corrosive media hold great promise as catalyst carrier. The wall defect structure of multi-walled carbon nanotubes (MWCNT) contributes to forming more Lewis acid active sites [
53,
54,
55]. The preparation of sodium oxide impregnated on CNTs by Mohd et al.[
56] and as a heterogeneous catalyst for transesterification of waste edible oil, with the positive metal ion Na (cation) having Lewis acidity, enhances the electronegativity of oxygen O
+2-(anion) adjacent oxides, improving the alkaline strength of the catalyst. Shu et al. [
55] prepared the solid Lewis acid catalyst, Al
3+-SO
42-/ MWCNTs. The acid sites are primarily made up of Lewis acids. During the reaction process, the catalytic temperature is reduced, and the quality of the catalyst and reactants is relatively low. The conversion rate of FAME can reach 95%. Metal organic frameworks (MOFs) are a particular type of coordination polymers composed of metal ions and organic ligands [
37]. MOFs have large porosity, uniform pore size, controllable functional groups, and structural durability, making them an ideal choice for synthetic transesterification/esterification catalysts. Hasan et al. [
57] used sulfonic acid functional ligands to hydrothermally synthesize highly porous and acidic MOFs, namely MIL-101 (Cr)-SO
3H. Under microwave irradiation, it only took 20 min for MIL-101 (Cr)-SO
3H to achieve a 93% yield of methyl oleate. The catalyst can also be used under heating, but it takes 10 h to achieve the same yield. After thermal filtration, the catalyst’s yield slightly decreases before the third operation, demonstrating its reusability.