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Compositional reservoir simulation is the most powerful tool available to the reservoir engineer upon which, nowadays, most reservoir development decisions rely on. According to the number of components used to describe the fluids, there is a very high demand for computational power due to the complexity and to the iterative nature of the phase behavior problem solution process. Phase stability and phase split computations often consume more than 50% of the simulation's total CPU time as both problems need to be solved repeatedly for each discretization block at each iteration of the non-linear solver. Therefore, the speeding up of these calculations is a challenge of great interest. In this work, machine learning methods are proposed for the solving of the phase equilibrium problem. It is shown that by using proper transformations, the unknown closed-form solution of the Equation-of-State based formulation can be emulated by proxy models. The phase stability problem is treated by classifiers which label the fluid's state in each block as either stable or unstable. For the phase-split problem, regression models provide the prevailing equilibrium coefficients values given the feed composition, pressure and temperature. The development of both models is performed rapidly and offline in an automated way, by utilizing the fluid's tuned-EoS model, prior to running the reservoir simulator. During the simulation run, the proxy models are called to provide direct answers of the phase equilibrium problem at a very small CPU charge instead of solving iteratively the phase behavior problem. The proposed approach is presented in two-phase equilibria formulation but it can be extended to multi-phase equilibria applications. Examples demonstrate the accuracy of the calculations and the very significant CPU time reduction achieved with respect to currently used methods.

A significant proportion of Greek society has created a firm belief (Gainous et al. 2010) that tax laws are unfair and do not apply to everyone equally. This view largely stems from the inability of the public to discern, at the right time, those who attribute legitimate taxes (Robbins and Kiser 2018) versus those who evade taxes (Slemrod 2007). The main failure of the tax system in Greece is that it reproduces "tax evasion" and overdue debts of established taxes, distorting the real economy. Even continuous tax "reforms" have not stopped the continuous reproduction of tax evasion or the continuous increase of non-taxable income. The failure of the tax system is broadening as new financial accounts are recorded. The continuous growth of overdue debts highlights the failures of the tax system, although, in the last 4 years, these failures have been compounded by the constant changes in the legislative framework. The total collectability (timed payments) of income taxes, valueadded tax, other indirect taxes, the real estate single tax and other real estate taxes amounted to 80.67% at the end of 2017. However, the total overdue debts at the end of 2018 exceed €104.0 billion (AADE 2019), a value that more than tripled during a decade of continuous tax reform while the total number of debtors surpassed four million.

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