Dear Sir. Concerning your issue about the low cost method of extraction of alumina from class-f fly ash. To improve aluminum extraction efficiency, a two-step acid leaching process was proposed to dissolve aluminum and aluminum-bearing crystals with sulfuric acid. The first leaching residue (FLR) was obtained through direct leaching of coal ash

with sulfuric acid. After roasting a mixture of the FLR and sodium carbonate, the aluminum-bearing crystals in FLR were completely destroyed while sodium silicate was generated. Then the roasted products were leached with water to dissolve the sodium

carbonate. X-ray diffraction (XRD) analysis indicated that the water leaching residues (WLR) mainly contained the amorphous phase, which allowed easy aluminum extraction in the second leaching step. In the first leaching test with 10 mol/L sulfuric acid at

120 °C in 2 h and a solid to liquid ratio (S/L) of 1:2, aluminum dissolution from raw coal ash reached 81.72%. In the second leaching step with 5 mol/L sulfuric acid, the aluminum dissolutions from WLR were 87.31% at 20 °C and 99.06% at 100 °C. Total aluminum dissolutions were more than 97%. Moreover, the leaching process produced two by-products, sodium silicate solution and amorphous silicon dioxide, which contained nearly all the silicon from the coal ash. Recovering aluminum from coal fly ash (CFA) is a practical option for its value-added utilization. The alkali activation of CFA with Na2CO3 was carried out using  two heating methods: the conventional heating (CH) and microwave heating (MWH). Compared to CH, MWH enhanced the atomic diffusion and mass transportation in the  CFA-Na2CO3 mixture, accelerated the decomposition of mullite and the formation of the soluble Al-containing materials, thus greatly reducing the sintering temperature and dramatically shortening the activation reaction time. Under the moderate activation condition in MWH (700°C and 20 min), the aluminum extraction could reach 95.52% or more. I think the following below links  and the attached file may help you in your analysis:

http://dpi-journals.com/index.php/JRST/article/viewFile/1760/1474

http://www.flyash.info/2013/020-Jow-2013.pdf

http://editorbar.com/upload/ReBooks/2014-2/679ac64d810d9082169997c329933e87.pdf

Thanks

I completely agree with Michael.  There is not enough value to make it worthwhile.  Orbite Technologies (formerly Orbite Aluminae) has a process with they are reportedly developing, along with red mud, which also does not have enough value to make it economical at today's alumina prices.

There are some methods. But the Al2O3 in fly ash should be higher than 40%. The cost for evapration of water is the highest in some acid leaching routes. The total cost for preparation of Al2O3 is about 370$/ton. If you don't prepare Al2O3, but just aluminum salts, the cost will be lower.

I fully agree with the above comments. We tried it some time ago with NaOH pressuee leaching  - See Research gate for paper

Can be converted by number of ways but not economical

I fully agree with Pach and Liu. Well, in order to answer your question, one must know the motive behind such extraction. If it is going to commercially exploited, then one need not attach any importance to such extraction procedure. You might feel demotivated by reading this answer. See, in order to commercialize any process of extraction, you can not calculate the cost in terms of money alone. First of all, you must know the kinetics and more importantly the thermodynamics of the process involved. Check if the results of these studies passes your costing calculation and then only go for further studies. To give you an example where such extraction failed to pass any commercial viability test; is the extraction and purification of germanium from fly ash. The next best example was the recovery of gallium from hot fly ash. Like this there are few more examples which was not commercially viable for scale-up studies.