Optimized phase stability algorithm in three phase systems with an application to CO$$_2$$ capture and sequestration in subsurface reservoirs

Abstract In optimizing CO $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> capture and sequestration, accurate phase behavior prediction in subsurface reservoirs is critical. This is especially relevant for geologic CO $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> storage in deep saline aquifers and depleted oil/gas reservoirs, and for CO $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> -EOR, where injected CO $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> coexists with brine and resident hydrocarbons across wide pressure–temperature ranges (including near-critical CO $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> ) and with non-negligible mutual solubilities. Our work introduces an efficient algorithm for phase stability testing, combined with multistage equilibrium multiphase negative flash calculations. We explore the stability of a three-phase system (V-L-Aq), using the criterion that the system is stable if the phase fractions of vapor, liquid, and water phases ( $$\beta _V$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>β</mml:mi> <mml:mi>V</mml:mi> </mml:msub> </mml:math> , $$\beta _L$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>β</mml:mi> <mml:mi>L</mml:mi> </mml:msub> </mml:math> , $$\beta _W$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>β</mml:mi> <mml:mi>W</mml:mi> </mml:msub> </mml:math> ) fall between 0 and 1. The stability testing begins with a negative flash calculation using diverse initial K-values to detect multiple phases. The same criterion is applied to two-phase systems (V-L, V-Aq, L-Aq). In case of instability, the algorithm shifts to the most probable two-phase system by systematically using negative flash and tangent plane distance calculations. It determines stable phases based on tangent plane solutions when the negative flash fails to converge, demonstrating adaptability across multiphase systems. The algorithm is validated through simulations of various mixtures, showing reliable convergence near critical points, and is applied to CO $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> storage and EOR scenarios to predict different CO $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> trapping mechanisms in the subsurface.