Reliable predictions in compositional reservoir simulators require a proper equation of state to describe accurately the phase behavior of fluids both in sub/super-critical regions. In miscible processes such as CO2 and lean gas injections, the injected fluid is usually at it's super-critical temperature, and therefore the current forms of EOS might not be suitable, since their temperature-dependency term (Alpha Function) have been obtained using experimental data of pure components at sub-critical regions. The same problem exists for compositional simulation of gas condensate reservoirs in which the major components are above critical temperature.
A new alpha function was developed using sound velocity data of pure components at their super-critical temperatures, since sound data can be measured accurately at large temperature range. Sound velocity can be thermodynamically related to the EOS parameters. An appropriate form of alpha function has been hence obtained for each component at super-critical temperatures.
In this work, the sound velocity experimental data of pure methane, ethane, propane and carbon dioxide has been used to generate a new form of alpha function at super-critical temperatures using PR EOS. The new function was then tested and validated against different experimental data from binary, ternary and multi-component systems and was found satisfactory in improving the prediction results.
By adapting the new methodology and developing the new alpha function for other components at super-critical region, it diminishes the need for temperature-dependent BIPs and also decreases the task for tuning of a given EOS against experimental data.
Major components of gas condensate fluids are hydrocarbons at/above their super-critical temperature at reservoir conditions. Most of the CO2 and lean gas injection EOR scenarios for oil recovery are done at reservoir temperature which is usually greater than critical temperature of injected gas. Reliable simulation of such complicated process using compositional modeling is vital for the success of the predictions. Therefore it is important to use an appropriate EOS that could predict the phase behavior of super-critical components fairly good.
Generally, The Peng-Robinson (PR) EOS describes accurately the vapor-liquid equilibria of sub-critical mixtures. In other applications, e.g. natural gas mixtures at high temperatures, it poorly represents the supercritical behavior of some substances. This poor behavior may be attributed to the inaccuracy of Soave's a function as it does not fulfill certain basic requirements.
In general, for a substance, an alpha (a)function is a temperature-dependent function which takes into account the attractive forces between molecules. The molecular attraction between the molecules decrease as the temperature increases and a real gas behavior is approached that of ideal gas. Therefore, a function should be a monotonically decreasing function of reduced temperature.
Figure 1 represents a graph of alpha function as proposed by Soave 1. This behavior of Soave alpha function (Eq. A-5) violates the physical meaning of the attractive force and poses some problems on VLE calculations. 4
Twu et al.3 outlined three basic requirements for the temperature-dependent a function:
It should be equal to unity at critical point.
The function must be finite and positive for all temperatures
As temperature tends to infinity, its value tends to zero