The two first TechTalks in the series on Fluid Characterization dealt with characterization of single petroleum reservoir fluids. This TechTalk outlines

- How to make a common equation of state (EoS) model applicable for multiple fluids
- How to add a new fluid to an existing EoS model
- How to evaluate whether a series of plus fluid compositions are suited for a common EoS model.

Table 1 shows three plus fluid compositions to C_{10+ }and some key PVT data for each fluid (reservoir temperature, saturation pressure and single stage GOR).

If the standard PVTsim characterization method is used to characterize the three fluid compositions individually and four C_{7+} pseudo-components are selected, the fluids will get the C_{7+ }mole%’s, T_{c}’s and P_{c}’s shown in Table 2. No tuning is applied. For simplicity acentric factors are left out.

As can be seen from Table 3 and the sample plots in Figure 1, a good match is seen of the experimental PVT data using these EoS models.

PVTsim characterizes a plus fluid composition by splitting the plus fraction into carbon number fractions to (typically) C_{80}. Using correlations in molecular weight and density each of the fractions from C_{7}-C_{80} are assigned a T_{c} and a P_{c} as sketched in Figure 2. As also shown in Figure 2, each C_{7+} pseudo-component covers a particular carbon number range. The T_{c} and P_{c} of each pseudo-component are determined by a weight average of the T_{c}’s and P_{c}’s of the carbon number fractions contained in the pseudo-component. The density of a particular carbon number fraction will differ between the fluids and so will the relative weight amounts of the carbon number fractions contained in a particular pseudo-component. For these reasons, the T_{c}‘s and P_{c}‘s of a pseudo-component will differ between fluids, even when covering the same carbon number range.

## COMMON EOS MODEL

A process simulation often handles feed streams from a number of different wells. A mixture of the three fluids in Table 1 characterized as in Table 2 would have a total of 3 x 4 = 12 C_{7+} pseudo-components. With several feed streams, it is advantageous if the properties of the pseudo-components are the same in all feed streams. This is what is called a common EoS model.

Table 4 shows a common EoS model for the heavy ends of the three fluid compositions in Table 1. The mole%’s of each pseudo-component in the individual fluid compositions are the same as in Table 2, but a common set of T_{c}’s and P_{c}’s is assigned to the C_{7+} pseudo-components of three fluid compositions.

Table 5 and Figure 3 show experimental and simulated key PVT data for the three fluid compositions when the common EoS model is used. No tuning has been applied. The match of the experimental data is almost as good as when the fluids are characterized individually. Only the maximum liquid dropout for the rich gas condensate is slightly too high.

The common EoS model was developed by splitting the plus fractions in each of the fluid compositions in Table 1 into carbon fractions to C_{80} and assigning a T_{c} and a P_{c} to each carbon number fraction. This is the same procedure as is used to characterize individual fluids, but when developing a common EoS model, the T_{c}’s and P_{c}’s of each C_{7 }– C_{80} carbon number fraction in each of the (in the case three) fluid compositions are subsequently averaged as shown below:

is the mole fraction of C_{7+} carbon number fraction i in fluid number j.

## SUITABILITY OF COMMON EOS MODEL

Had the T_{c}‘s and P_{c}‘s of each of the pseudo-components in the three individually characterized fluid compositions (Table 2) been identical, the simulation results obtained with the common EoS model would have been the same as for the individually characterized fluids. This raises the question of how much the T_{c}‘s and P_{c}‘s of the individually characterized fluids can vary if one is still to get a good match of the experimental data with a common EoS model.

Such an evaluation can be performed by calculating the standard deviations between the T_{c}’s and the P_{c}’s of the pseudo-components when the liquids are characterized individually and when the common EoS model is used.

where

Ratings of the suitability of a common EoS for a group of plus fluids are shown in Table 6. The *Applicable* category will almost certainly require some parameter tuning of the common EoS model parameters.

For the three fluids in Table 1

- SD_T
_{c}= 14.0 - SD_P
_{c}= 1

This means these fluids compositions are suited for a common EoS, but as seen by comparing the liquid dropout curves of the rich gas condensate in Figure 1 and Figure 3, the common EoS model has caused some deterioration of the match of the experimental data for the rich gas condensate as compared with the results when the rich gas condensate was characterized individually.

## ADDING A NEW PLUS COMPOSION TO A COMMON EOS

A new fluid composition may need to be added to an existing EoS model. Maybe a new sample has been taken from a reservoir with an existing EoS model, or maybe a new feed stream is to be led to a process that uses a previously developed EoS model.

If the gas condensate fluid composition in Table 7 is characterized individually, It will get the T_{c}’s and P_{c}’s in Table 8.

To add the gas condensate in Table 7 to the common EoS model developed for the three fluids in Table 1, the T_{c}’s and P_{c}’s for the gas condensate fluid in Table 8 are to be replaced by the common EoS T_{c}’s and P_{c}’s in Table 4.

Table 9 shows the match of the saturation pressure at the reservoir temperature and the GOR when the common EoS model is used. Figure 4 shows the CVD liquid dropout curves for the gas condensate fluid when characterized individually (T_{c}’s and P_{c}’s in Table 8) and when using the common EoS model in Table 4. Use of the common EoS model rather than the individual model has significantly deteriorated the match the experimental PVT data for the gas condensate.

The deteriorated of the liquid dropout data could have been foreseen by calculating the standard deviations for the T_{c}’s and P_{c}’s of the pseudo-components, which are

- SD_T
_{c}= 42 - SD_P
_{c}= 3.4

As can be seen from Table 6, these standard deviations fall in the category where a common EoS model is less suited.