What do you mean by solution exactly? And please mention about the kind of reactor you want to study?

If they are lab scale CSTR, you can measure the gas by using gas collection bags (generally plastic).

If you are interested to find a method to collect biogas for analysis I suggest you to use Supel-Inert sampling bags (from Sigma Aldrich, presently Merck), they are intended for sampling low molecular weight gases because the bag wall is made of 5 layers, including 2 Aluminium layers that impede methane be lost by permeability. Plastic bags like Tedlar are not recommended, you can see the information in the link below. I looked for a solution few months ago and I opted for 5 liters bags but you can select size from 1 to 10 liters, depending on your lab. model. The bags are fitted with valves and gas sampling port. Price is very affordable too.

https://www.sigmaaldrich.com/analytical-chromatography/air-monitoring/gas-sampling-bags.html#foilbags

we use water displacement to measure biogas but I am looking for the solution we should use...I mean what kind of solution, water?acid? or something else

when we use the water we can only measure methane because CO2 dissolves in water but we want to measure the whole biogas and can not use water

I'm sorry, your question was not clear. I would suggest you to use saturated solution of natrium bicarbonate (solubility at 20C is 96 g/l) , the biogas components will not be absorbed (except H2S). Carbon dioxide is very much soluble in water but in a saturated solution it can not be disolved. Methane is very low soluble in water, the absorbed quantity is neglectable. Much better is to do analysis for the biogas sampled directly from the vessel/digestor if possible, otherwise the biogas will catch water.

thank you so much

You can also try biogas 5000, very accurate and online real time measurement of biogas for methane, CO2, H2S etc.

https://www.geotechuk.com/products/biogas-5000/

Dear Singh, Reza is mainly looking for the solution base method for measurement not potable devices like bags or drum type gas meters. Dear Reza, if your purpose to measure through solution is to know the exact composition of biogas (means CO2 %, CH4%, etc.) then I also recommend the method suggested by Dr Carmen. Otherwise you can also use drum type biogas meter and timely analyse the composition through GC by taking samples from bioreactor/digester.