Modeling of Petroleum Quality with Simple n-Component PVT Fluid Models

Armin I. Kauerauf
IES GmbH – A Schlumberger Company, Aachen, Germany

Petroleum quality is mainly determined by API and viscosity. The GOR is important for live oils. Additionally, the oil formation volume factor, B_o, and the bubblepoint pressure, P_sat, are main characteristics. All of these quantities must be calibrated properly and simultaneously in a comprehensive fluid model, e.g., for predictive usage in unexplored areas.

Because of the complexity of fluid behavior under varying conditions, successful PVT models are exclusively based on a detailed investigation of the fluid, namely its compositional information. This can be obtained by source rock pyrolysis, which yields only crude compositional resolution (di Primio and Horsfield, 2006), or by sophisticated analysis of oil samples (Pedersen and Christensen, 2007). However, a comprehensive fluid model is only possible with several additional assumptions such as tunable component lumping, heavy end expansions with tunable molecular weights, and variable heavy end cut off and tuning of numerous additional parameters such as the binary interaction parameters. Additionally, component parameters, which are derived from large databases with fluid properties, commonly enter the equations of state (EOS) (Zuo et al., 2008).

This approach is not satisfying because high-resolution data and tuning of multiple parameters is necessary for proper fluid models. Consequently, advanced fluid models are difficult to create and to handle. Despite this general approach, they are often only applicable to specific oil types. Additionally, the performance and memory consumption of high-resolution fluid models with binary interaction parameters is very poor in simulation programs.

An alternative approach is proposed. Simple three-parameter EOS are used without heavy end expansion or binary interaction parameters because they cover all important effects of fluid phase behavior. Component parameters are calibrated simultaneously against multiple fluid properties with high accuracy. The number of fluid parameters is reduced drastically, without a reduction in predictive quality. Obviously, a fluid model composed from calibrated components is valid only for a specific oil and not expected to be applicable generally.

This approach is not purely predictive. Basic fluid properties must be known prior to modeling, e.g., from PVT analysis. However, any sophisticated information such as composition is only needed to a crude degree. Only the basic fluid properties such as API density and gas/oil ratio (GOR) are really important.

The following example demonstrates the workflow: A “medium oil” was originally constructed by lumping of a heavy end and a “dry gas” component similar to pure methane. A two-component system based on these two pseudo-components with equal molar amounts does not show a realistic PVT behavior anymore. For example, the coexistence area in the PT diagram is often too small to be realistic (Figure 1). The two-component fluid model is now calibrated against API, GOR, and bubblepoint pressure of a real oil sample by variation of the component parameters of the medium oil. Typical values of API, GOR, and P_sat of real oil samples are found in Stainforth (2004).

After calibration, all properties are well adjusted. The coexistence area also became much bigger and looks more realistic. However, the component parameters are now not in range of a realistic lumped pseudo-component. Instead they are found in a range up to C₃₀ (Table 1). This result should be expected. A correct modeling of a heavy end with only one pseudo-component should yield a variation of the corresponding parameters within a wide range.

This approach to calibration can also be applied to fluid descriptions with a few pseudo- components or even to fluids with highly resolved component information. For a simultaneous calibration of multiple parameters against multiple properties, a Markov Chain Monte Carlo algorithm is used. Unrealistic parameter sets can principally be avoided with additional Bayesian terms. The trade-off is calibrations of less quality.

With such a calibration, it is possible to perform basin modeling simulations with source rock tracking and accurate PVT predictions that are not possible with highly resolved fluid descriptions because of a lack of computer memory and performance.

The procedure also allows a calibration of different oils of the same type with the same compositional formulation against varying properties. For example, a variation of API or GOR with maturity can be calibrated at some reference compositions against one set of pseudo-parameters. Such fluid models are obviously very valuable for basin modeling.

Viscosity can be treated similarly with appropriate models such as the Lohrenz Bray Clark model, if some sample values are known (Lohrenz et al., 1964). Variations of the pseudo-components in the EOS must be taken into account. Calibration and afterwards predictions within a limited range of compositional variations can be made.

References

R. di Primio and B. Horsfield, From petroleum-type organofacies to hydrocarbon phase prediction, AAPG Bulletin, 90: 1031-1058, 2006

K. S. Pedersen and P. L. Christensen. Phase behavior of petroleum reservoir fluids, CRC Taylor & Francis, 2007

J. Y. Zuo, D. Zhang, F. Dubost, C. Dong, O. C. Mullins, M. O’Keefe, S. S. Betancourt, EOS-based downhole fluid characterization, SPE 114702, 2008

J. G. Stainforth. New insights into reservoir filling and mixing processes, in J. M. Cubitt, W. A. England, and S. Larter, editors, Understanding Petroleum Reservoirs: Towards an Integrated Reservoir Engineering, Special Publication, pages 115-132. Geological Society of London, 2004

J. Lohrenz, B. G. Bray, and C. R. Clark. Calculating viscosities of reservoir fluids from their composition, Journal of Petroleum Technology, pages 1171-1176, 1964

Figure 1. Coexistence area of a two-component fluid calculated from a Peng-Robinson EOS, 28 API, Psat of 1,562 psi, and a GOR of 1,732 SCF/STB