NOVELTY - Plant for isothermal production of methane from carbon monoxide- and hydrogen containing reactant gas or from carbon di-oxide- and hydrogen containing reactant gas, comprises a bubble column reactor with a three-phase system, and a temperature control device located outside the reactor, through which the liquid phase is tempered. A liquid phase of the reactor comprises at least one ionic fluid in which the catalyst is suspended in a particulate form as a solid phase. The reactant- and product gases form a gas phase.    USE - The bubble column reactor that is charged with at least one ionic fluid forming the liquid phase, is useful for synthesizing methane from a carbon monoxide- and hydrogen containing gas mixture or from carbon di-oxide- and hydrogen containing gas mixture (claimed).    ADVANTAGE - The method: utilizes a compact, cost-effective, and single-stage system; achieves an effective heat discharge such that, the reaction is carried out in the optimum temperature; makes use of a reaction fluid exhibiting a lower vapor pressure, which is highly stable that avoids degradation and discharging of the fluid through the gas phase and utilizes a highly active catalyst.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for isothermal production of methane, comprising (a) providing the bubble column reactor, (b) charging the reactor with at least one ionic fluid, where the catalyst is suspended in the particulate form, (c) introducing carbon monoxide- and hydrogen containing reactant gas stream or carbon di-oxide- and hydrogen containing reactant gas stream at a bottom of the bubble column reactor in the presence of the catalyst suspension, where the reactant gas stream passes through the catalyst suspension where the reactant gas stream is converted into the product gas, (d) discharging methane- and water vapor containing product gas stream from the suspension at a top of the reactor, where the ionic fluid is continuously fed from the bubble column reactor to the temperature control device that regulates the temperature of the ionic fluid, before the ionic fluid is returned to the reactor.