Experimental results are presented that demonstrate the effect on residual oil, under water-wet conditions, of particle size, particle-size distribution, macroscopic particle size, particle-size distribution, macroscopic and microscopic heterogeneities, microscopic dimensions such as ratio of pore-body to pore-throat size, and pore-to-pore coordination number. Experiments were pore-to-pore coordination number. Experiments were performed in random packs of equal spheres, heterogeneous performed in random packs of equal spheres, heterogeneous packs of spheres with microscopic and macroscopic packs of spheres with microscopic and macroscopic heterogeneities, two-dimensional (2D) capillary networks having various pore geometries, and Berea sandstone. Detailed information on residual oil structure is presented, including blob-size distributions of residual presented, including blob-size distributions of residual oil. Major conclusions areresidual saturations are independent of absolute pore size, per se, in systems of similar pore geometry;well-mixed two-component aggregates of spheres gave virtually the same residual saturations as random packings of equal spheres;clusters of large pores accessible through small pores will retain oil;high aspect ratios tend to cause entrapment of oil as a large number of relatively small blobs, each held in single pores; andthe role of pore-to-pore coordination number is generally secondary; pore-to-pore coordination number is generally secondary; hence, correlations that have been proposed between residual oil and coordination number are unreliable. Introduction In recent years, there has been increased interest in the factors that determine the magnitude of residual oil and its microscopic distribution. Residual oil remaining in the swept zone of a waterflood is often taken as the target oil for enhanced recovery processes. Oil saturations remaining in these zones typically can occupy 15 to 35% of the pore space, but values outside this range are often measured. For the reservoir, it can be expected that the pore structure, the initial water content, and the superimposed effects of wettability determine recovery behavior and residual oil distribution under normal waterflood conditions. Salathiel has presented examples of the manner in which pore geometry, wettability, and volume throughput of floodwater can interact to affect oil recovery characteristics and final oil saturation. The likely complexity of trapping phenomena is indicated by the work of Wardlaw and Cassan, who investigated possible correlations between residual oil and 27 petrophysical parameters. Rocks with similar macroscopic properties often differed markedly in their residual oil saturations, and no significant correlation was observed between displacement efficiency and permeability. A tendency for residual nonwetting-phase permeability. A tendency for residual nonwetting-phase saturations to increase as porosity decreased was noted. This was related to a strong relationship between trapping and aspect ratio (ratio of pore-body to pore-throat size). A theory of residual oil trapping has been proposed by Larson et al. that provides an alternative explanation of the relationship between residual oil and porosity. It was reasoned that the trapped nonwetting-phase saturation will correspond reasonably well to the percolation threshold i.e., to the oil saturation at which oil continuity through the pore space is lost. SPEJ p. 311

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Capillary number relationships are presented for displacement of both residual and initially continuous oil from water-wet consolidated sandstones having permeabilities that varied over about two orders of magnitude. It was found that the critical displacement ratio, (APILa)cr, for the onset of mobilization could be correlated with sample permeability. Relationships between nominalized reduced residual oil saturation and capillary number (taken as kwAP/Lo) also were correlated satisfactorily. For sandstones, capillary numbers for displacement of continuous oil were lower than values for mobilization of discontinuous oil for down to 50% of normal waterflood residual. Thereafter, capillary number relationships for the two types of displacement were indistinguishable. Conditions for complete recovery of residual oil correspond to values of (kwAP/Lo) of about 1.5 × 10–3 as compared with about 2x 10 -5 for onset of mobilization. Introduction Capillary forces acting within pore networks are responsible for entrapment of one phase by another during immiscible displacements in porous media. Laboratory studies have shown that residual oil can be recovered if the displacing phase causes viscous forces acting on trapped residual oil blobs to exceed the capillary retaining forces. The magnitude of the capillary forces is set by the oil/water interfacial tension (IFT), wettability conditions, and the pore geometry in which trapped oil blobs exist. The apparent magnitude of the viscous forces acting on a trapped oil blob is set by the fluid dynamics of the displacing phase. The ratio of viscous to capillary forces is often called the "capillary number." More than a dozen expressions have been used in the literature to express this ratio," many of which are equivalent. They include the following expressions, which are used also in this paper. (1) (2) and (3) where v, is the Darcy velocity and u is the viscosity of the displacing phase, a is the IFT, and AP/L is the imposed pressure gradient across the sample of length L. ka and kw are specific permeabilities of the sample to air and to the aqueous phase, respectively. In this paper, the term capillary number" implies generic reference to the ratio of viscous to capillary forces. The experimental data found in the EOR literature are still rather limited as far as capillary number results for the immiscible displacement of continuous oil and the mobilization of residual oil from rock samples having widely different transport properties are concerned. In this paper, results and correlations are presented for water-wet sandstones that have comprehensive ranges of permeability and porosity. Theory of Mobilization Consider a water-wet porous medium that has been flooded to normal waterflood residual (ROS). A modified form of Darcy's equation for flow of aqueous phase in linear core flooding is (4) where kw = absolute permeability, krw = relative permeability, u = viscosity, andAP/L = the overall pressure gradient. An expression for capillary number, vu/o, is obtained from Eq. 4 as (5) The so-called "Jamin effect," discovered more than a century ago, provided the basic concept required for the development of a mechanistic interpretation of mobilization of residual oil blobs from water-wet reservoir rocks. The phenomenon of the high pressures required to force nonwetting phase blobs through a periodically constricted capillary is described well by Gardescu, who investigated the resistance to flow observed when an isolated bubble of gas in a liquid was forced into a capillary construction. SPEJ P. 555^

Phase behavior, interfacial tension (1FT), viscosity, and density data were determined for the system 2% CaCl 2 brine/isopropyl alcohol (IPA)/isooctane. Liquid pairs from this system were used in a test of capillary number as a correlating function for mobilization of residual oil in geometrically similar porous media as provided by bead packs. Close correlation of results was obtained for a more than five-fold variation in permeability and a more than six-fold variation in 1FT. Extensive investigation was also made of the change in trapped oil saturation given by vertical upward flooding; the ratio of gravity to capillary forces varied more than 100-fold. A correlation between trapped oil saturation and Bond number was obtained that was in good agreement with previous results obtained for gas entrapment. However, capillary numbers for entrapment of a given reduced residual oil saturation (ROS) were found to be slightly higher than those for entrapment of gas.Relative permeabilities were independent of whether the trapped phase was oil or gas and were determined mainly by the magnitude of the trapped nonwetting-phase saturation.Capillary numbers for mobilization of residual oil from bead packs were much higher than typical values for sandstones. For bead packs that had been consolidated by sintering, capillary numbers for prevention of entrapment increased and those for mobilization decreased. The net result was that differences in capillary numbers for mobilization and entrapment were greatly reduced and results became more akin to relationships observed for consolidated sandstones.

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The Present investigation is a study of the properties of 2-dimensional (2-D) and 3-D network models of capillary tubes generalized for any pore size distribution. These properties include:the breakthrough condition subject to the step-by-step invasion of a non-wetting phase into an empty (evacuated) 2-D or 3-D "network;the accessibility of pores; andthe "pseudo' dead-end pore fractions, characteristic of the fractional amount of the non-conducting penetrated pore volume. It was found that for infinitely deep networks the breakthrough condition is defined by the coordination number Z and the dimensionality of the network through the relations PrZ =2 and PrZ = 1.5 for 2-D and 3-D networks, respectively. 2-D networks do not allow the existence of bicontinua and, as such, they cannot simulate realistically 2-phase flow phenomena. Generalized saturation plots for the accessibility of pores and the pseudo dead-end pore fractions have been established. It was found that the accessibility of pores and the pseudo dead-end pore fractions are determined by (i) the dimensionality of the network, (ii) the coordination numberof the network and (iii) the topology of pore interconnectedness at the microscopic level. The accessibility of pores found in the network analysis of the penetration process into 2-D and 3-D networks has been criticallytested by using:the experimentally known mercury porosimetry capillary pressure curves of two sandstone samples of known "complete" pore size distribution and the experimentally determined accessibility junctions; andthe saturation at breakthrough observed in mercury penetration experiments. It was established that:the accessibility of pores predicted by the network Analysis of 2-D and 3-D network models of randomly distributed capillary tubes does not agree quantitatively with the quantities obtained experimentally;when the length of a capillary is of the same order of magnitude as its diameter, the saturation predicted at breakthrough is about 30% to 80%;with bulges present in the middle of capillary segments a lower-order relationship between the volume and the entry diameter of the segments could be assumed. Fairly good simulations of the experimental capillary pressure curve and the accessibility of pores have been obtained in the case of 3-D networks by assuming that the volume of a capillary segment is proportional to its entry diameter. Introduction EQUILIBRIUM AND TRANSPORT PHENOMENA in a porous medium are strongly dependent on the pore structure of the medium. As the macroscopic properties of a porous medium depend on the pore structure, a thorough understanding of this is important for the purpose of correlating various processes that involve porous media, The customary pore structure parameters, such as the porosity, the hydraulic diameter and the pore-of-entry size distribution, are insufficient for the interpretation of some important static phenomena (i.e. capillary pressure curves) and flow phenomena (i.e. relative permeabilities) in porous media, Permeable porous media contain 3-D networksconsisting of capillary segments or pores of various sizes.

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Reservoir characterization involves describing different reservoir properties quantitatively using various techniques in spatial variability. Nevertheless, the entire reservoir cannot be examined directly and there still exist uncertainties associated with the nature of geological data. Such uncertainties can lead to errors in the estimation of the ultimate recoverable oil. To cope with uncertainties, intelligent mathematical techniques to predict the spatial distribution of reservoir properties appear as strong tools. The goal here is to construct a reservoir model with lower uncertainties and realistic assumptions. Permeability is a petrophysical property that relates the amount of fluids in place and their potential for displacement. This fundamental property is a key factor in selecting proper enhanced oil recovery schemes and reservoir management. In this paper, a soft sensor on the basis of a feed‐forward artificial neural network was implemented to forecast permeability of a reservoir. Then, optimization of the neural network‐based soft sensor was performed using a hybrid genetic algorithm and particle swarm optimization method. The proposed genetic method was used for initial weighting of the parameters in the neural network. The developed methodology was examined using real field data. Results from the hybrid method‐based soft sensor were compared with the results obtained from the conventional artificial neural network. A good agreement between the results was observed, which demonstrates the usefulness of the developed hybrid genetic algorithm and particle swarm optimization in prediction of reservoir permeability.