Complete Equation of State Thermal Formulation for Simulation of CO2 Storage

Summary Storage of carbon dioxide (CO2) in depleted gas reservoirs or large aquifers is one of the available solutions to reduce anthropogenic greenhouse gas emissions. Numerical modeling of these processes requires the use of large geological models with several orders of magnitude of variations in the porous media properties. Moreover, modeling the injection of highly concentrated and cold CO2 in large reservoirs with the correct physics introduces numerical challenges that conventional reservoir simulators cannot handle. We propose a thermal formulation based on a full equation of state (EoS) formalism to model pure CO2 and CO2 mixtures with the residual gas of depleted reservoirs. Most of the reservoir simulators model the phase equilibriums with a pressure-temperature-based formulation. With this usual framework, it is not possible to exhibit two phases with pure CO2 contents. Moreover, in this classical framework, the crossing of the phase envelope is associated with a large discontinuity in the enthalpy computation, which can prevent the convergence of the energy conservation equation. In this work, accurate and continuous phase properties are obtained, basing our formulation on enthalpy as a primary variable. We first implement a new phase-split algorithm with input variables as pressure and enthalpy instead of the usual pressure and temperature, and we validate it on several test cases. This algorithm can model situations in which the mixture can change rapidly from one phase to the other at constant pressure and temperature. Then, treating enthalpy instead of temperature as a primary variable in both the reservoir and the well modeling algorithms, our reservoir simulator can model situations with pure or near pure components, as well as crossing of the phase envelope that usual formulations implemented in reservoir simulators cannot handle. We first validate our new formulation against the usual formulation on a problem in which both formulations can correctly represent the physics. Then, we show situations in which the usual formulations fail to represent the correct physics and that are simulated well with our new formulation. Finally, we apply our new model for the simulation of pure and cold CO2 injection in a real depleted gas reservoir from the Netherlands.

Complete EOS Thermal Formulation for Simulation of CO2 Storage

Storage of CO2 in depleted gas reservoirs or large aquifers is one of the available solutions to reduce anthropogenic greenhouse gas emissions. Numerical modeling of these processes requires the use of large geological models with several orders of magnitude of variations in the porous media properties. Moreover, modeling the injection of highly concentrated and cold CO2 in large reservoirs with the correct physics is introducing numerical challenges that conventional reservoir simulators cannot handle. We propose a thermal formulation based on a full equation of state formalism to model pure CO2 and CO2 mixtures with the residual gas of depleted reservoirs. Most of the reservoir simulators model the phase-equilibriums with a pressure-temperature based formulation. With this usual framework, it is not possible to exhibit two phases with pure CO2 contents. Moreover, in this classical framework, the crossing of the phase envelope is associated with a large discontinuity in the enthalpy computation which can prevent the convergence of the energy conservation equation. In this work, accurate and continuous phase properties are obtained basing our formulation on enthalpy as a primary variable. We first implement a new phase-split algorithm with input variables as pressure and enthalpy instead of the usual pressure and temperature and we validate it on several test cases. This algorithm can model situations where the mixture can change rapidly from one phase to the other at constant pressure and temperature. Then treating enthalpy instead of temperature as a primary variable in both the reservoir and the well modeling algorithms, our reservoir simulator can model situations with pure or near pure components as well as crossing of the phase envelope that usual formulations implemented in reservoir simulators cannot handle. We first validate our new formulation against the usual formulation on a problem where both formulations can correctly represent the physics. Then we show situations where the usual formulations fail to represent the correct physics and that are simulated well with our new formulation. Finally, we apply our new model for the simulation of pure and cold CO2 injection in a real depleted gas reservoir from the Netherlands.

Saturation Point and Phase Envelope Calculation for Reactive Systems Based on the RAND Formulation

Analysis of multicomponent reactive systems requires reliable and accurate equilibrium calculation. There are many stoichiometric or non-stoichiometric methods to solve the flash-type calculations of a mixture in chemical and phase equilibrium. In contrast, there is a lack of robust and efficient methods for another important type of equilibrium calculation, the saturation point calculation or the calculation under the phase fraction specification (β-specification), for a reactive mixture. In this work, we developed RAND-based algorithms for calculating the saturation points and phase envelope of a reactive mixture. The RAND formulation is a non-stoichiometric approach recently extended to non-ideal mixtures for different flash specifications. We showed here how to modify the RAND-based flash formulation to solve the β-specification problems. We distinguished between two types of phase fractions, the one based on components and the one based on elements. They led to different constraint equations in the formulation. Furthermore, we introduced element-based partition coefficients, similar to the equilibrium ratios or K-factors used for non-reactive mixtures. Use of these new variables is essential to cross the critical point of a reactive mixture in the phase envelope construction. Since the formulation developed for reactive mixtures is general, it can also be reduced and used for the simpler non-reactive mixtures. We showed how the reduction could be made and how the reduced algorithm served as an alternative approach to the prevailing phase envelope algorithm of Michelsen. We illustrated the robustness and efficiency of the proposed algorithm using four examples: Pxy diagrams for CO2-NaCl brine, a solid-liquid T xy diagram for MgCl2-water, a PT phase envelope for a reactive mixture with the alkene hydration reaction, and a PT phase envelope for a non-reactive hydrocarbon mixture.

PHASE ENVELOPE CONSTRUCTION FOR MIXTURES USING HIGHLY ACCURATE HELMHOLTZ ENERGY EQUATION OF STATE

Phase envelope construction for mixtures is very important in the oil and gas industry. The most widely used model for phase envelope construction is Peng — Robinson equation of state (PR-EOS) due to its simplicity. In order to construct phase envelopes of natural gas, a highly accurate Helmholtz energy equation of state GERG-2008 was proposed. In this work, the accuracy of phase envelopes calculated by a highly accurate equation of state GERG-2008, simplified GERG-2008 and traditional cubic PR-EOS was analyzed. The pressure-based algorithm is used to calculate phase envelopes. Phase envelopes of the methane—ethane mixtures were constructed and compared with reference data. The results show that phase envelopes can be constructed with GERG-2008 in high accuracy. PR-EOS has good accuracy in phase envelope construction under low pressure. The simplified GERG-2008 also works well under low pressure; however, as pressure increases, it performs worse than the simpler PR-EOS, especially in the vicinity of critical point. Besides, a modified density solver for the complicated GERG-EOS was proposed. Calculations show that the proposed density solver can provide reliable results.