Cubic Equations of State Applied to HT/HP and Highly Aromatic Fluids
- K.S. Pedersen (Calsep A/S) | J. Milter (Statoil) | H. Sørensen (Calsep A/S)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- June 2004
- Document Type
- Journal Paper
- 186 - 192
- 2004. Society of Petroleum Engineers
- 5.2.2 Fluid Modeling, Equations of State, 4.1.5 Processing Equipment, 5.2.1 Phase Behavior and PVT Measurements, 4.4.3 Mutiphase Measurement, 4.1.2 Separation and Treating, 5.2 Reservoir Fluid Dynamics
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Pressure/volume/temperature (PVT) data are presented for 38 reservoir fluids including fluids dominated by paraffins, heavy aromatic fluids with a significant content of C81+, and high-temperature/high-pressure (HT/HP) reservoir fluids. By properly taking into account the compositional differences, these fluid types can all be represented using a classical cubic [Soave-Redlich-Kwong (SRK) or Peng-Robinson (PR)] equation of state (EOS) with volume correction. The plus fraction is split into carbon number fractions and EOS model parameters assigned to each fraction. To keep the number of components at a manageable level, the carbon number fractions are lumped into pseudocomponents, each containing several carbon number fractions. Hydrocarbons as heavy as C200 are considered when splitting up the plus fraction. Neglecting the content of components heavier than C80 will give a false picture of the phase behavior of heavy aromatic fluids. Correlations are presented for Tc, Pc, and ? as a function of molecular weight and density. Problems are experienced representing the thermal expansion of stable oils using a cubic EOS in the classical form. It is shown that this deficiency can be cured by introduction of a temperature-dependent volume correction term.
Cubic EOS such as the SRK1 and the PR2 equations are widely used to simulate the phase behavior of gas and oil mixtures. The liquid densities predicted with these equations in the original form are generally too low, a deficiency that at least to some extent can been overcome by incorporating a volume shift parameter.3 This is an additional EOS parameter affecting volumetric properties without influencing saturation points and phase compositions. To apply a cubic EOS with volume shift parameter, a critical temperature (Tc), a critical pressure (Pc), an acentric factor (?), and a volume shift parameter (c ) must be assigned to each component or pseudocomponent of the actual fluid.
A standard compositional analysis divides the components heavier than nC6 into carbon number fractions. 4 Carbon number fraction CN counts the hydrocarbons with a boiling point from that of nCN-1 +0.5°C to that of nCN+0.5°C. The C7 fraction, for example, consists of the hydrocarbons with a boiling point between 69.3 and 98.9°C (0.5°C above the boiling point of nC6 to 0.5°C above the boiling point of nC7). Each carbon number fraction contains paraffinic (P) and naphthenic (N) as well as aromatic ( A) components, each of which will have different Tc, Pc, and ? values and volume shift parameters. Despite these compositional differences, it is customary to use only one set of EOS parameters to represent a whole carbon number fraction. A compositional analysis usually ends with some plus fraction as with, for example, C10+ . The latter will contain C10 and heavier carbon number fractions. Using high temperature gas chromatography, it is possible to analyze to C80+ 5 or even to C100+, but this type of analysis is not yet standard in the oil industry. There is generally a need for a simulated split-up of the plus fraction.
A generally valid characterization concept must be applicable to reservoir fluids of much varying PNA distribution. While paraffins dominate among the C7+ components of most North Sea fluids, aromatic contents in excess of 50% are often seen in the C7+ fraction of reservoir fluids from the Middle East, China, and Venezuela.
Much exploration activity is currently directed toward deep reservoirs at HT/HP. The ability of the classical cubic EOS to represent the molecular interactions at such conditions has often been questioned. More sophisticated EOS have been proposed, some of which include terms to account for the strong repulsive forces acting at high pressures.6-8
Fluid Compositions and Experimental Data
PVT data have been investigated for a total of 48 fluid compositions. Fluids 1 through 38 are reservoir fluids, an overview of which is given in Table 1 . These fluids can be divided into:
19 "ordinary" reservoir fluids (Fluids 1 through 19) comprising reservoir oils, gas condensates, and fluids that are near critical (NC) at reservoir conditions.
9 aromatic highly dense reservoir fluids (Fluids 20 through 28). The composition of one of these fluids is shown in Table 2.
10 HT/HP reservoir fluids.
The data material further includes thermal expansion data for 10 stable oils. Oil formation volume (or Bo) factors for these oils may be seen from Table 3 . Because the data are for stable oils, the Bo factors are not influenced by gas liberation and thus provide a true picture of the thermal expansion.
Either differential depletion or constant mass expansion (CME) experiments have been conducted for the oil mixtures including the heavy oils in Table 1. The PVT data for the gas condensate mixtures, the NC fluids, and the HT/HP fluids comprise CME and constant volume depletion (CVD) data.
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