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A method is presented for modeling reservoir properties. The method includes an auxiliary time-stepping procedure of the reservoir between an old time and a new time, and calculating a plurality of masses explicitly. A plurality of phase component densities is updated linearly from the plurality of

A method is presented for modeling reservoir properties. The method includes an auxiliary time-stepping procedure of the reservoir between an old time and a new time, and calculating a plurality of masses explicitly. A plurality of phase component densities is updated linearly from the plurality of masses. A plurality of saturation changes is calculated based on the plurality of masses. A plurality of phase flow rates is updated based on the plurality of saturation changes, a plurality of phase flow rates at the old time, and a plurality of saturation derivatives of the phase flow rates at the old time. A plurality of component flow rates may be calculated based on the updated plurality of phase component densities and the plurality of phase flow rates. The method also includes a formulation method based on the auxiliary time stepping procedure.

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1. A method for producing hydrocarbons utilizing a computer system for modeling properties of a reservoir, comprising: providing the computer system comprising one or more processors and further comprising a machine readable medium comprising code configured to direct the processor to perform a simu

1. A method for producing hydrocarbons utilizing a computer system for modeling properties of a reservoir, comprising: providing the computer system comprising one or more processors and further comprising a machine readable medium comprising code configured to direct the processor to perform a simulation based on an IMPSAT formulation method for the reservoir that performs an auxiliary time-stepping procedure to improve the stability of the simulation, wherein the plurality of time steps comprise an old time step and a new time step;performing the simulation comprises: (i) calculating a plurality of phase flow rates at the old time and a plurality of phase flow rate derivatives with respect to a plurality of saturations at the old time;(ii) performing an auxiliary time-stepping procedure between the old time and the new time, wherein the auxiliary time-stepping procedure does not require additional linear solve or black-oil, equation of state property calculations, and wherein the auxiliary time-stepping procedure comprises: calculating a plurality of masses of the reservoir explicitly;updating a plurality of phase component densities of the reservoir linearly from the plurality of masses;calculating a plurality of saturation changes of the reservoir based on the plurality of masses;updating a plurality of phase flow rates of the reservoir based on the plurality of saturation changes, the plurality of phase flow rates at the old time, and the plurality of phase flow rate derivatives with respect to the plurality of saturations at the old time, andcalculating a plurality of component flow rates of the reservoir based on the updated plurality of phase component densities, the plurality of phase flow rates of the reservoir;(iii) performing pressure and saturation linear solve after the performance of the auxiliary time-stepping procedure and between the old time and the new time;outputting a solution from the computer system; andproducing hydrocarbons from the oil and/or gas field based on the solution that is outputted from the computer. 2. The method of claim 1, wherein performing the IMPSAT formulation method for the reservoir comprises: re-calculating, after the auxiliary time-stepping procedure, the plurality of component flow rates based on the plurality of phase component densities at a time level between the old time and the new time and phase flow rates at the old time;calculating a plurality of component flow rates derivatives with respect to a pressure and the plurality of saturations;solving, simultaneously and implicitly, the pressure of the reservoir and the plurality of saturations of the reservoir;updating the plurality of component flow rates of the reservoir based on the solved pressure and the plurality of saturation changes;updating for a simulation time-step the plurality of masses; andupdating for the simulation time-step the plurality of saturations. 3. The method of claim 2, wherein one or more unknown variables of the IMPSAT formulation method are approximated at the time level. 4. The method of claim 1, wherein the IMPSAT formulation method is based on one of: a black-oil model; and a compositional model. 5. The method of claim 1, wherein the time level is a mid-time level or the new time level or a level between old and new time. 6. The method of claim 1, comprising performing a discretization method that is associated with the IMPSAT formulation method. 7. The method of claim 6, wherein the discretization method comprises one of: finite difference; finite volume; finite element; mixed finite element; discontinuous Galerkin, and mimetic finite difference. 8. A system for producing hydrocarbons from a reservoir, comprising: a plurality of processors;a machine readable medium comprising code configured to direct at least one of the plurality of processors to perform a simulation that is based on a sequential implicit (SI) formulation method for the reservoir that performs an auxiliary time-stepping procedure to improve the stability of the simulation, wherein the simulation comprises a plurality of time-steps and wherein the plurality of time-steps comprise an old time step and a new time step, the code is configured to: find a plurality of pressure solutions of a plurality of discretized pressure equations for the reservoir based on the sequential implicit (SI) formulation method;update a plurality of phase flow rates for the reservoir based on the plurality of pressure solutions;calculate a plurality of phase flow rate derivatives for the reservoir with respect to a plurality of saturations for the reservoir;perform an auxiliary time-stepping procedure between the old time and the new time, wherein a total phase flow rate is preserved, wherein the auxiliary time-stepping procedure does not require additional linear solve or black-oil, equation of state property calculations, and wherein the auxiliary time-stepping procedure comprises code configured to: calculate a plurality of masses of the reservoir explicitly;update a plurality of phase component densities of the reservoir in phase linearly from the plurality of masses:calculate a plurality of saturation changes of the reservoir based on the plurality of masses;update the plurality of phase flow rates for the reservoir based on the plurality of saturation changes; andre-calculate a plurality of component flow rates of the reservoir based on the updated plurality of phase component densities and the plurality of phase flow rates;perform saturation linear solve after the performance of the auxiliary time-stepping procedure and between the old time and the new time;output simulation results from the simulation based on the SI formulation method for the reservoir that performs an auxiliary time-stepping procedure; anda well management control system that is triggered to make adjustments in the producing of hydrocarbons from the reservoir based on the output simulation results. 9. The system of claim 8, wherein performing the SI formulation method comprises: re-calculating, after the auxiliary time-stepping procedure, the updated plurality of component flow rates for the reservoir based on the plurality of phase component densities of the reservoir at a time level between the old time and the new time and the updated plurality of phase flow rates after finding the pressure solutions;re-calculating a plurality of component flow rate derivatives for the reservoir with respect to the plurality of saturations based on the plurality of phase component densities at a time level between the old time and the new time and the plurality of phase flow rate derivatives with respect to the plurality of saturations after finding the pressure solutions;solving the plurality of saturation changes of the reservoir implicitly;updating the plurality of component flow rates based on the solved plurality of saturation changes;updating for a simulation time-step the plurality of masses based on the updated plurality of component flow rates; andupdating for the simulation time-step the plurality of saturations. 10. The system of claim 9, wherein the time level is a mid-time level or new time level. 11. The system of claim 8, wherein the SI formulation method is based on one of: a black-oil model; and a compositional model. 12. The system of claim 8, wherein one or more unknown variables of the SI formulation method are approximated at the time level. 13. The system of claim 8, comprising performing a discretization method that is associated with the formulation method. 14. The system of claim 13, wherein the discretization method comprises one of: finite difference; finite volume; finite element; mixed finite element; discontinuous Galerkin, and mimetic finite difference. 15. A method for producing hydrocarbons from an oil and/or gas field using a stabilized formulation method relating to a physical structure, the method for producing hydrocarbons comprising: providing a computer system comprising one or more processors and further comprising a machine readable medium comprising code configured to direct the processor to perform a simulation based on an IMPES formulation method for the oil and/or gas field that performs an auxiliary time-stepping procedure to improve the stability of the simulation, wherein the plurality of time steps comprise an old time step and a new time step;performing the simulation comprises: in the computer system, solving a pressure equation for the oil and/or gas field based on the IMPES formulation method to obtain pressure solutions;in the computer system, updating a plurality of phase flow rates for the oil and/or gas field based on the solved pressure solutions;in the computer system, calculating a plurality of phase flow rate derivatives for the oil and/or gas field with respect to a plurality of saturations for the reservoir;in the computer system, performing an auxiliary time-stepping procedure between the old time and the new time of each of the plurality of time steps, wherein the auxiliary time-stepping procedure does not require additional linear solve or black-oil, equation of state property calculations, and wherein a total phase flow rate is preserved, wherein the auxiliary time-stepping procedure comprises: calculating a plurality of masses for the oil and/or gas field explicitly;updating a plurality of phase component densities for the oil and/or gas field linearly from the plurality of masses;calculating a plurality of saturation changes for the oil and/or gas field based on the plurality of masses;updating the plurality of phase flow rates for the oil and/or gas field based on the plurality of saturation changes; andcalculating a plurality of component flow rates for the oil and/or gas field based on the updated plurality of phase component densities and the plurality of phase flow rates;outputting simulation results from the simulation based on the IMPES formulation method for the oil and/or gas field that performs an auxiliary time-stepping procedure; andproducing hydrocarbons from the oil and/or gas field based at least in part on results of the simulation performed based on the IMPES formulation method for the oil and/or gas field that performs an auxiliary time-stepping procedure. 16. The method of claim 15, comprising: updating for a simulation time-step the plurality of masses based on the plurality of component flow rates;updating for the simulation time-step the plurality of saturations based on the plurality of masses; andextracting hydrocarbons from the oil and/or gas field based on the updated plurality of masses, the updated plurality of saturations, and the plurality of component flow rates. 17. The method of claim 16, wherein one or more unknown variables of the IMPES formulation method are approximated at the time level. 18. The method of claim 17, wherein the time level is the new time level. 19. The method of claim 15, wherein the IMPES formulation method is based on one of: a black-oil model; and a compositional model. 20. The method of claim 15, comprising performing a discretization method that is associated with the formulation method, wherein the discretization method comprises one of: finite difference; finite volume; finite element; mixed finite element; discontinuous Galerkin, and mimetic finite difference.