For water-wet reservoirs, several expressions may be used to correlate capillary pressure, or height above the free water level, with the water saturation. These correlations all feature a vertical asymptote at the residual water saturation where the capillary pressure goes to plus infinity.We have developed a general capillary pressure correlation that covers primary drainage, imbibition, secondary drainage, and hysteresis scanning loops. The graph exhibits an asymptote at the residual saturation of water and of oil where the capillary pressure goes to plus and minus infinity, respectively. The shape of the correlation is simple yet flexible as a sum of two terms, each with two adjustable parameters and is verified by laboratory experiments and well-log data. An associated hysteresis scheme is also verified by experimental data.The correlation can be used to make representative capillary pressure curves for numerical simulation of reservoirs with varying wettability and to model and interpret flooding processes.
Copyrfght 1998, Society of Petroleum Engineers, Inc. 7Ms paw was wepared fw preaentaficm al ffw 1998 SPE India Oil and Gas Ccaference and Exhibition held h New DelhL India, 17-19 Rebmary 1998. This paper was selactad for prasantation by an SPE Program Commmee following review of information contained in an abstract submittad by the author(s), Contents of tha papar, as Presentd, have not b-n reviewed by tha Society of Patroleum Engineers and are subjecl to rnrractfon by the author(s). l%e material, as presented, doss not necessarily reflect any position of the Scciety of Petroleum Engineers, its officers, or mambers. Papers presented at SPE meetings are subject 10 pubkdion rew-ew by Editorial Committees of tha Society of Petroleum Engineers. Efactmnlc reprciducticm, distribution, or storage of any pert of this paper for commercial purposes wifhoul fhe WiNen consent of the Society of Petrolaum Engineers IS prohibited. Permission 10 reproduce in print is restricted fo an abstract of no! more than 300 words; iflusbations may not be copied. 7he abstract must contein conspicuous acknowledgment of Mere and by whom the papar was presantad. Write Librarian, SPE, P.O. Etox 833836, Richardson, TX 75063-3336, USA, fax 01.972-952-9435. AbstractFor waterwet reservoirs, several expressions may be used to correlate capillary pressure, or height above the free water level, with the water saturation. These correlations all feature a vertical asymptote at the residual water saturation where the capillary pressure goes to plus infinity. We k developed a general capillary pressure correlation that covers primary drainage, imbibition, secondary drainage, and hysteresis scanning loops. The graph exhibits an asymptote at the residual saturation of water and of oil where the capillary pressure goes to plus and minus infinity, respectively. The shape of the correlation is simple yet flexible as a sum of two terms, each with two adjustable parameters and is verified by laboratory experiments and well-log data. An associated hysteresis scheme is also verified by experimental data.The correlation can be used to make representative capillary pressure curves for numerical simulation of reservoirs with varying nettability and to model and interpret flooding processes.
Summary It is shown that the main characteristics of mixed-wet capillary pressure curves with hysteretic scanning loops can be reproduced by a bundle-of-triangular-tubes model. Accurate expressions for the entry pressures are employed, truly accounting for the mixed wettability and the diverse fluid configurations that arise from contact angle hysteresis and pore shape. The simulated curves are compared with published correlations that have been suggested by inspection of laboratory data from core plug experiments. Introduction Knowledge of the functional relationship between capillary pressure and saturation is required in numerical models to solve the equations for fluid flow in the reservoir. In practice, this relationship is formulated as a capillary pressure correlation with several parameters that usually are to be determined from experimental data. Generally, it is not evident how these parameters should be adjusted to account for variations in physical properties such as wettability, pore shape, pore-size distribution, and the underlying pore-scale processes. Therefore, a more physically based correlation, accounting for observable properties, would improve the reliability of the correlation and extend its applicability range. Analytical correlations may be derived assuming a bundle-of-tubes representation of the pore network. Following this approach for a model of cylindrical tubes, Huang et al. (1997) derived a capillary pressure correlation for primary drainage and the hysteresis bounding loop, accounting for variations in wettability. Princen (1992) computed numerically the relationship between capillary pressure and saturation for primary drainage and imbibition for a bundle of tubes with curved triangular cross sections of uniform wettability. He made no attempt, however, to develop any correlation.
[1] Recently, a considerable effort has been made to determine the precise displacement criteria for three-fluid configurations in pores of angular cross section. These configurations may contain thick conducting fluid layers, such as oil layers residing between gas in the center and water in the corners of the pore. For pores of uniform, but arbitrary, wettability and in the absence of contact angle hysteresis, a precise thermodynamic criterion for the existence of such layers has been established. In this paper we derive similar criteria for layers in pores of nonuniform wettability, where additional and more complicated layer configurations arise. The criteria for formation and removal of layers are consistent with the capillary entry conditions for the accompanying three-phase bulk displacements, which is essential for accurate pore-scale modeling of three-phase flow. We consider the particular case of three-phase gas invasion in a starshaped pore with a specific choice of interfacial tensions and contact angles. For this case all possible fluid configurations arise, but only if the water-wet surface in the pore corners is small.
Two methods are presented for predicting critical oil rate for bottomwater coning in anisotropic, homogeneous formations with the well completed from the top of the formation. The first method is based on an analytical solution where Muskat's assumption of uniform flux at the wellbore has been replaced by 'that of an infinitely conductive wellbore. The potential distribution in the oil zone, however, is assumed unperturbed by the water cone. The method is derived from a general solution of the time-dependent diffusivity equation for compressible, single-phase flow in the steady-state limit. We show that very little difference exists between our solution and Muskat's. The deviation from simulation results is caused by the cone influence on potential distribution.The second method is based on a large number of simulation runs with a general numerical reservoir model, with more than 50 critical rates determined. The results are combined in an equation for the isotropic case and in a single diagram for the anisotropic case. The correlation is valid for dimensionless radii between 0.5 and 50 and shows a rapid change in critical rate for values below five. Within the accuracy of numerical modeling results, Wheatley's theory is shown to predict the correct critical rates closely for all well penetrations in the dimensionless radius range from 2 to 50.
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