Pedro Henrique Rodrigues Alijó

Classic Examples From Literature

This chapter presents the application of this theory to examples of the literature, from very simple systems (binaries without gravitational field) to more complex ones, like actual reservoirs influenced by thermal diffusion and gravity simultaneously. Examples showing simulations of laboratory experiments splitting the components of simple mixtures by thermal diffusion are also discussed, testing some model parameters. The current practical limitations of such experiments, along with their importance in modeling more complex thermal separation phenomena, open a wide research line. Finally, both thermal diffusion models proposed by the research groups cited in Chapter 4, Irreversible Thermodynamics Applied to Reservoir Engineering, are also tested in case studies for which temperature gradient has contributed for attenuation or enhancement of the compositional grading predicted by isothermal hypothesis.

Irreversible Thermodynamics Applied to Reservoir Engineering

This chapter describes the microscopic equations of fluid transport, which support irreversible thermodynamics. Different contributions for internal entropy generation, such as heat conduction, molecular diffusion, and viscous dissipation are derived. Soret and Duffour effects are discussed and the methods for calculation of thermal diffusion parameters for compositional grading proposed by two main investigation groups in the literature will also be presented. The systems of equations proposed independently by these two groups to eliminate the diffusive fluxes at steady state are compared to those obtained by the constant-temperature hypothesis along reservoir depth. The latter characterizes the gravity-modified thermodynamic equilibrium state. Finally, the equations governing fluid moving by natural convection in 2D systems with lateral temperature gradients are also derived, including a numerical solution sketched specifically for 2D domains.

General Comments and Perspectives

The results presented along this textbook do not lead us to definitive conclusions. But do provide a basis for new discussions and elaboration of new hypothesis, premises, and ideas that would certainly be of help to increase the reliability of the compositional grading predictions. We reinforce that this discipline, although fascinating from the point of view of aggregating value from theory formulation to its final application, must be considered as one more important tool on predicting fluid properties and settling diagnostics of connection/disconnection in oil and gas reservoirs. We strongly recommend the interaction between fluid-modeling engineers with geologists, geochemists, and geophysicists that may bring up more information to corroborate the conclusions generated by grading calculations. In many occasions, the acquired information by these correlate-area professionals serve as inputs for the formulation or reformulation of problems. In this chapter, we enumerate some suggestions for future works that can help improve current predictions; some of them already going on in new joint venturing projects between academy and industry.

Reservoir Fluids and PVT Analysis

One classifies reservoir fluids (liquids or gases) as a function of the relative position of its actual temperature and pressure to the critical point conditions in its phase envelope. Then one proceeds to a description of the experimental procedures for determination of Pressure, Volume and Temperature (PVT) properties of a reservoir fluid. These properties represent the volumetric behavior of this complex hydrocarbon-plus-contaminant mixture as a function of temperature and pressure. Therefore, they can be simulated through thermodynamic equilibrium algorithms using equations of state, once these are duly calibrated to reproduce such experimental data.

Phase Equilibrium Under the Influence of the Gravitational Field

In this chapter, we study the influence of the gravitational field on the conditions necessary for the establishment of the thermodynamic equilibrium in systems with relatively considerable height. The derivation of the maximum-entropy condition (or minimum energy) remains on the specification of total volume and mass, but the total energy now contains a potential-energy term to be added to the internal-energy one. We will see that, although the temperature-equality condition remains the same, the hydrostatic charge generated by the gravitational field leads to equating the so-called piezometric pressure at each height level, introducing also an additional term in the condition of both chemical potential and fugacity equality. After a brief literature review, we discuss the application of this approach in the study of compositional grading in oil reservoirs considered as isothermal, revisiting some classical examples of the literature.

The Influence of Molecular Association

In this chapter, we discuss the influence of molecular association on compositional grading of oil and gas reservoirs. This phenomenon, of which the hydrogen bonding is one of the main examples, is characterized by strong short-range attractive interactions and is intimately related to the polarity of fluid molecules. The angular orientation of the polar sites in a group of molecules and the short distance between them are crucial for the attractive potential around these areas to allow its association, which presents characteristics very similar to a strong (but not permanent) chemical bond.

Chapter 6 – Case Studies

In this chapter, a number of unpublished case studies are presented in reservoirs which show noticeable compositional grading. Based on the theories developed in Chapter 4 and applied in Chapter 5 to examples from the literature, one tries to reproduce the composition profiles observed in some new case-study fields. These fields were carefully selected because of their peculiarities opened up to interpretations, rather to inspire new strategies in fluid modeling and reservoir engineering than to establish definite answers for such problems.

Phase Equilibrium Thermodynamics

In majority of cases, the modeling of vapor–liquid equilibrium involving hydrocarbons (water being treated as an independent component) using cubic equations of state introduced in the 1970s is enough to ensure the robustness of equipments’ project and the development of production systems. More complex mixtures involving macromolecules like asphaltenes, paraffins, and hydrates can lead the system to showing other phases as well as rock–fluid interactions. Such interactions can introduce chemical reactions that change permeability and porosity of the rock and require more elaborated thermodynamic models that are beyond the scope of this book. The asphaltene precipitation, which may be treated as a second ultra-viscous liquid phase that can be modeled using a more complex type equation of state (EoS), which may consider the molecular association effects in their polar-heteroatom sites, The Cubic Plus Association EoS can, for example, be employed for this task and will be discussed in detail in Chapter 7.