Transport in Porous Media 52: 119–122, 2003.

119

Preface

Retrograde Gas–Liquid Behaviour in Porous Media MIKHAIL PANFILOV LAEGO/ENSG, Institute National Polytechnique de Lorraine, Rue du Doyen Marcel Roubault B.P. 40, 545011 Vandoeuvre-les-Nancy, France. e-mail: [email protected] (Accepted: 16 February 2003)

The usual thermodynamic laws of phase equilibrium allow the existence of the so-called retrograde gas–liquid systems. Their properties, however, are very unusual. In such systems, the gas produces liquid with a decrease in pressure. This is an inverse (retrograde) process compared to traditional phase transition. Retrograde systems appear to be very important natural objects as they constitute an enormous class of underground hydrocarbon reservoirs known as gas– condensate fields. The retrograde hydrocarbon liquid of these reservoirs, known as the condensate, may be considered as a very light oil, containing no wax, resins or other impurities. A major part of current world reserves of natural gas exists in the form of gas–condensate fields. Fortunately for science, the thermodynamic and hydrodynamic behaviour of retrograde mixtures is so complex that it will long be the object of scientific research. The thermodynamic problems are basically caused both by the proximity to the critical point (a typical property of retrograde systems) and by the influence of porous media on phase behaviour. Hydrodynamic problems are determined by a strong flow non-linearity which, in turn, is provoked both by contrasted mobilities of gas and liquid and by capillary phenomena in pores. The solid–liquid and liquid–gas surface effects prompt other research problems such as the impact of wettability on the condensate mobility and recovery index. A connection between thermodynamics, hydrodynamics and surface science has given rise to certain new tendencies in scientific research. The historically maiden stage of the analysis of retrograde mixtures came into being thanks to a practical need to enhance condensate recovery. The basic problem was generated by an extremely low phase mobility of retrograde liquid in porous media and, consequently, a low condensate recovery from gas–condensate reservoirs. This gave birth to a theory of multi-component two-phase flow with phase transitions. This first stage represented a formal association of a traditional two-phase hydrodynamic model and an equilibrium, thermodynamic description of phase behaviour examined independently of hydrodynamics. Huge efforts were

120

MIKHAIL PANFILOV

made to create an adequate description of equilibrium for multi-component, twophase systems. The most widely known results derived from this approach refer to the compositional numerical flow model (Nikolaevsky et al., 1968; Coats, 1985) and to the analytical theories of oil/condensate recovery (Barenblatt et al., 1987; Bedrikovetsky, 1993). The second stage in the research apparently came about due to new industrial demand. Since the eighties–nineties, when numerical modelling became a standard tool for the testing of various scenarios of reservoir exploitation, it became obvious to the oil companies that an improvement in numerical models could possibly yield a significant enhancement of oil/condensate recovery. During this second stage, the research in physics and mathematics which was mainly prompted by the need to improve numerical software, was oriented towards a refinement of hydrodynamic flow laws and thermodynamic description. This refinement was occasionally very profound, but the research in thermodynamics remained independent of hydrodynamics. The major results of this period were: a new theory of gas–condensate relative permeabilities dependent on velocity (Henderson et al., 1995) and improved, highly universal thermodynamic equilibrium models (Danesh, 1998; Firoozabadi, 1998). The three-phase hydrocarbon states that may occur and the decomposition of oil into two liquid phases detected in DeSwaan et al. (1992) are very important elements for future research. At the same time, the traditional problem of improving condensate recovery has generated new research in the field of surface physical–chemical phenomena (Morrow, 1998). The third stage will be that of an inter-penetration of thermodynamics, hydrodynamics and surface science. Eight papers presented in this special issue testify to the probable time that this stage begun. Examples of a profound inter-penetration of thermodynamics and surface science are presented in papers by Voronov et al. and Urlic et al. In Voronov et al. the authors study the thermodynamic behaviour of a retrograde fluid confined in a porous medium when the correlation length of molecular dynamics, which is large in a near-critical fluid, becomes comparable to the pore size. It is shown experimentally that a porous medium significantly displaces gas–liquid coexistence curves. In Urlic et al. the Cahn–Hilliard theory of surface phenomena in combination with the Peng–Robinson equation of state was applied to model interfacial tension behaviour in gas–condensate systems. New experimental data is obtained with respect to the thermodynamic behaviour of gas–condensate mixture at high pressure (greater than 24 MPa) and high temperatures (up to 490 K). The interference between hydrodynamics and thermodynamics, resulting in a non-equilibrium behaviour, is clearly presented in papers by Bedrikovetsky, Koldoba and Koldoba, Jamiolahmady et al. and Whitson et al. In Bedrikovetsky, a new gas–condensate flow model is proposed in which the trapped condensate is considered as a third dispersed phase. It is hydrodynamically passive but is very active from a thermodynamic point of view. The model ends with experimental data on kinetics of trapped condensate evaporation. In Koldoba and Koldoba a new

RETROGRADE GAS–LIQUID BEHAVIOUR IN POROUS MEDIA

121

description of the saturation/concentration fronts which appear during condensate displacement by other fluids has been put forward. The authors pay attention to the fact that equations describing gas–condensate flow in porous media have discontinuous solutions (fronts) but are not hyperbolic, whilst the traditional front stability conditions are developed for hyperbolic systems. A new stability condition based on general principles of non-equilibrium thermodynamics is thus introduced. The inter-penetration of fluid dynamics and thermodynamics on the pore scale has determined the research of Jamiolahmady et al. Phase transition within pores leads to a formation of non-stationary, two-phase structures with pore opening/closing by liquid drops. These effects result in non-classical macroscopic relative permeability functions, obtained using a network capillary model. In Whitson et al. the authors prove that the ratio between gas and liquid relative permeability is a purely thermodynamic variable which can replace saturation for a steady-state flow. This yields a generalized model for relative permeabilites which is valid in the vicinity of wells where the flow physics is the most complicated. The inter-penetration of hydrodynamics and surface science is a key element in porous media with heterogeneous or alternated wettability. This is the subject of the papers by Tang and Firoozabadi and Shahizadeh et al. The way in which heterogeneous wettability influences retrograde liquid recovery is the key problem of the paper by Shahizadeh et al. The data obtained experimentally is surprising as it is in contradiction with the widely known results of other authors. In Tang and Firoozabadi, the authors suggest a polymer treatment in order to inverse rock wettability by condensate, from a strong liquid-wetting case to intermediate gaswetting. This effect, which is justified for low and high temperatures, significantly increases condensate mobility and recovery. The field of retrograde fluid behaviour in porous media includes excellent scientific theories based on a high level of physical and mathematical research. At the same time, this area of research is very poorly presented by monographs and thematic collective proceedings. The aim of this special issue was thus twofold: to rectify the bibliographical deficiencies and to illustrate that elegant modern science that is devoted to retrograde mixtures which has now begun the third stage in its evolution. I am sincerely grateful to all the authors who have taken part in the creation of this edition, both those who are recognised as leaders in this field and those whose names can be considered as relatively new. References Barenblatt, G. I., Entov, V. M. and Rizhik, V. M.: 1987, Theory of Fluid Flows through Natural Rocks, Kluwer Academic Publishers, London/Boston/Dordrecht. Bedrikovetsky, P. G.: 1993, Mathematical Theory of Oil and Gas Recovery, Kluwer Academic Publishers, London/Boston/Dordrecht. Coats, K. H.: 1985, Simulation of Gas Condensate reservoir Performance. J. Petrol. Technol., 1870–1886.

122

MIKHAIL PANFILOV

Danesh, A.: 1998, PVT and Phase Behavior of Petroleum Fluids, Elsevier, Amsterdam. Firoozabadi, A.: 1998, Thermodynamics of Hydrocarbon Reservoirs, McGraw-Hill, New York. Gregorowicz, J., de Loos, Th. W. and de Swaan Arons, J.: 1992, Unusual retrograde condensation in thernary hydrocarbon systems, Fluid Phase Equilibria 73, 109–115. Henderson, G. D., Danesh, A., Tehrani, D. and Peden, J. M.: 1995, The effect of velocity and interfacial tension on the relative permeability of gas condensate fluids in the wellbore region, in: 8th European IOR Symposium, May 15–17, Vienna. N. R. Morrow (ed.): 1998, Evaluation of Reservoir Wettability and Its Effect on Oil Recovery. J. Pet. Sci. Eng., 1–301 (Special Issue). Nikolaevski, V. N., Bondarev, E. A., Mirkin, M. I. et al.: 1968, Flow of Hydrocarbon Liquids in Porous Media, Nedra, Moscow (in Russian).