A continuous process for the production of sodium bicarbonate crystals, comprising: 1) an absorption step of the gaseous carbon dioxide from a gas stream into an aqueous solution comprising a sodium carbonate salt, comprising the steps of: 1a) contacting said gas stream with a first surface of a first porous membrane contactor; and contacting said aqueous solution of sodium carbonate with a second opposite surface of the same first porous membrane contactor, said gaseous carbon dioxide diffusing through the pores of the membrane into said aqueous solution of sodium carbonate where it dissolves; and 1b) reacting the dissolved carbon dioxide with the sodium carbonate salt in the aqueous solution to produce an aqueous solution of sodium bicarbonate; said absorption step being performed in the presence of at least one mass transfer promoter selected from an amino acid or an enzyme; said at least one mass transfer promoter being in suspension in the aqueous solution of sodium carbonate or immobilized on said first porous membrane contactor; then 2) a crystallization step of sodium bicarbonate salt, comprising the steps of: 2a) circulating the aqueous solution containing the sodium bicarbonate at one side of a second porous membrane contactor; 2b) applying a driving force by circulating an extracting fluid at the opposite side of the second porous membrane contactor, so that the water of the aqueous solution evaporates and diffuses through the pores of the second porous membrane contactor towards the extracting fluid at the opposite side of the second porous membrane contactor, where it re-condensates, leading to the progressive concentration of the aqueous solution of sodium bicarbonate, 2c) sending the concentrated aqueous solution of sodium bicarbonate to a crystallization tank at the outlet of the second porous membrane contactor where crystal growth takes place; and 2d) recovering the sodium bicarbonate crystals, wherein said first porous membrane contactor and second porous membrane contactor are in series. 1) an absorption step of the gaseous carbon dioxide from a gas stream into an aqueous solution comprising a sodium carbonate salt, comprising the steps of: 1a) contacting said gas stream with a first surface of a first porous membrane contactor; and contacting said aqueous solution of sodium carbonate with a second opposite surface of the same first porous membrane contactor, said gaseous carbon dioxide diffusing through the pores of the membrane into said aqueous solution of sodium carbonate where it dissolves; and 1b) reacting the dissolved carbon dioxide with the sodium carbonate salt in the aqueous solution to produce an aqueous solution of sodium bicarbonate; said absorption step being performed in the presence of at least one mass transfer promoter selected from an amino acid or an enzyme; said at least one mass transfer promoter being in suspension in the aqueous solution of sodium carbonate or immobilized on said first porous membrane contactor; then 1a) contacting said gas stream with a first surface of a first porous membrane contactor; and contacting said aqueous solution of sodium carbonate with a second opposite surface of the same first porous membrane contactor, said gaseous carbon dioxide diffusing through the pores of the membrane into said aqueous solution of sodium carbonate where it dissolves; and 1b) reacting the dissolved carbon dioxide with the sodium carbonate salt in the aqueous solution to produce an aqueous solution of sodium bicarbonate; said absorption step being performed in the presence of at least one mass transfer promoter selected from an amino acid or an enzyme; said at least one mass transfer promoter being in suspension in the aqueous solution of sodium carbonate or immobilized on said first porous membrane contactor; then 2) a crystallization step of sodium bicarbonate salt, comprising the steps of: 2a) circulating the aqueous solution containing the sodium bicarbonate at one side of a second porous membrane contactor; 2b) applying a driving force by circulating an extracting fluid at the opposite side of the second porous membrane contactor, so that the water of the aqueous solution evaporates and diffuses through the pores of the second porous membrane contactor towards the extracting fluid at the opposite side of the second porous membrane contactor, where it re-condensates, leading to the progressive concentration of the aqueous solution of sodium bicarbonate, 2c) sending the concentrated aqueous solution of sodium bicarbonate to a crystallization tank at the outlet of the second porous membrane contactor where crystal growth takes place; and 2d) recovering the sodium bicarbonate crystals, wherein said first porous membrane contactor and second porous membrane contactor are in series. 2a) circulating the aqueous solution containing the sodium bicarbonate at one side of a second porous membrane contactor; 2b) applying a driving force by circulating an extracting fluid at the opposite side of the second porous membrane contactor, so that the water of the aqueous solution evaporates and diffuses through the pores of the second porous membrane contactor towards the extracting fluid at the opposite side of the second porous membrane contactor, where it re-condensates, leading to the progressive concentration of the aqueous solution of sodium bicarbonate, 2c) sending the concentrated aqueous solution of sodium bicarbonate to a crystallization tank at the outlet of the second porous membrane contactor where crystal growth takes place; and 2d) recovering the sodium bicarbonate crystals,