**5. Accelerated phase behavior calculations**

When flow simulations are considered, reliability undoubtedly comes first as lack of convergence or obtaining unrealistic results during the calculations at any grid block would lead to a general failure of the reservoir simulation run. However, some tolerance can be shown to the accuracy of the EoS model produced results due to the latter's inherent simplicity, to the nonexhaustive fluid's compositional analysis available and to questionable tuning procedures. In fact, small inaccuracies in the fluid behavior calculations that might be introduced can be partially remediated by the history matching procedure of the field model.

On the other hand, the ever increasing demand for complex flow domain models in terms of both grid and fluid models complexity has rendered nowadays the speed of phase behavior calculations as one of the most critical issues of flow simulation, especially for cases of complex thermodynamic phenomena such as near critical phase behavior and multiphase equilibrium in the presence of solids. As a result, speeding up phase behavior calculations is considered as a major issue, even if this involves some sacrifice in the calculations accuracy.

### **5.1 Rigorous methods**

Reducing the number of components used to describe the fluid composition through a splitting and lumping procedure is the standard way to obtain simpler, hence faster EoS models. Firstly, the heavy end, usually corresponding to a limited carbon number, needs to be replaced with a large number of pseudo-components defined by means of computational methods. This way the flexibility during the EoS model tuning increases. The most pronounced method is the one developed by Whitson that utilizes the Gamma distribution [6]. Subsequently, the extended number of components is reduced (lumped) to a small number of pseudocomponents, usually 3 to 5, by means of algorithms which aim at preserving the EoS model's performance [7]. Finally, pure components are grouped together to minimize the composition vector size. Typical selections are N2 with C1, CO2 with C2, nC4 with iC4 and nC5 with iC5. When two or more components are lumped together, the new group's properties need to be rematched against the available PVT measurements. A very illustrative example is given my Ahmed [7] where a full C7+ composition that includes N2 and CO2, thus summing up to 11 components, reduces gradually the number of components to only 7 according to the lumping procedure shown in **Table 3**.

Other accelerating methods include different treatments of the mathematical form of the problem or of its variables [36, 37] and utilizing solution acceleration techniques such as the GDEM update one [5]. Rasmussen et al. [32] provided criteria to completely skip phase behavior calculations during a simulation run when the prevailing equilibrium conditions fall within specific regions of the fluid's phase diagram. Simply speaking, if the fluid is a single phase one, most probably it will keep so if its distance to the phase boundary is large enough. So is the case with fluids lying well inside the two-phase region. In both cases, the stability test can be skipped whereas in the former one the phase split can be skipped as well.

Finally, efforts have been concentrated on utilizing advanced code optimization [38] and High Performance Computing (HPC) techniques which take advantage of


**Table 3.**

*Components' number reduction by splitting and lumping.*

the parallel computing capabilities of modern computer architectures [39]. Despite the difficulties in distributing the work load and in optimizing memory transfer between clusters, impressive acceleration factors have been reported [40].
