PVT Modelling Fundamentals – Part 3
EQUATION OF STATE (EoS) PVT MODELLING
An EoS PVT model is a multi-component description of the reservoir fluids based on the alkane series. Reservoir fluids are composed of thousands of different hydrocarbon components with varying properties and in different proportions. The overall behavior of the reservoir fluid is determined largely by the combined effects of these components and the percentage/proportion in which each is present.
The fundamental principle behind the EoS has evolved from the simple ideal gas laws to the more sophisticated cubic EoS and popular formulations like the Peng Robinson (PR) and Suave-Redlich-Kwong (SRK) equations. Each formulation was developed to improve on some limitations of previous formulations. There are several other formulations in literature aside the popular ones.
Typically, a PVT study is conducted on the reservoir fluid to define the fluid properties at reservoir and surface separation conditions. The PVT study also includes the compositional analysis of the reservoir fluid in terms of mole percent. Some of the components are simple, easy to identify with well-defined properties like the light-ends (methane to propane). From Butane upwards, the hydrocarbons begin to exhibit multiple structures, isomers, which make it more difficult to uniquely identify them. For example, butane can exist in two isomers and pentane as three isomers. The number of isomers increases exponentially with the number of carbons thus making it impractically to precisely identify the composition of the heavier components. This situation is managed by grouping/lumping the heavier components beyond a particular carbon number as a pseudo-component with averaged properties.
The primary input data to the EoS is the composition of the reservoir fluids in terms of mole percent and their physical properties with those of the pseudo-components. The physical properties normally required are molecular weight and density. Since the properties of the well-defined components are well known, most of the PVT modelling efforts is dedicated to tuning the properties of the pseudo-components. The major tuning parameters in the EoS are the critical temperatures and pressures and the acentric factors. Other parameters include Binary Interaction Components (BIC) and volume shifts. It therefor means if the input data set is incomplete or inaccurate, the subsequent tuning of the EoS will be problematical. Additionally, the final EoS is usually a non-unique solution depending on the paths taken, meaning more than one acceptable solution can be arrived at.
Due of the amount of input data and effort required, EoS PVT models are typically used when necessary. They are often able to better capture the behavior of fluids exhibiting rapid changes in properties compared to using black oil empirical correlation. This is typically the case for fluids close to the critical point like volatile oils and gas (retrograde) condensate systems. EoS are also more reliable for modelling complex processes like miscible gas injection or for studying flow assurance conditions like wax, hydrates etc. It is however impossible to build and EoS model, even if that seems to be the appropriate option, when the required data is not available.
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