Imbibition in a cracked porous medium

1969 ◽  
Vol 47 (22) ◽  
pp. 2519-2524 ◽  
Author(s):  
A. P. Verma
Keyword(s):  
Differential Equation ◽  
Porous Medium ◽  
Viscosity Ratio ◽  
Perturbation Technique ◽  
Water Imbibition ◽  
Phase Saturation ◽  
Water Viscosity ◽  
Oil Water ◽  
The Relationship ◽  
Special Case

In this paper, one special case of oil–water imbibition phenomena in a cracked porous medium of a finite length is analytically discussed. The equation for the linear countercurrent imbibition is a nonlinear differential equation whose solution has been obtained by a perturbation technique. For definiteness, specific results have been used for the relationship between relative permeability and phase saturation) impregnation function, oil–water viscosity ratio, and capillary pressure dependence on phase saturation due to Jones, Bokserman et al., Evgen'ev, and Oroveanu, respectively. An expression for the wetting phase saturation has been derived.

A Model for Two-Phase Flow in Consolidated Materials

1969 ◽  
Vol 9 (02) ◽  
pp. 221-231 ◽  
Author(s):  
R. Ehrlich ◽  
F.E. Crane
Keyword(s):  
Porous Medium ◽  
Steady State ◽  
Relative Permeability ◽  
Viscosity Ratio ◽  
Phase Flow ◽  
Unsteady State ◽  
Adequate Description ◽  
Two Phase ◽  
Phase Saturation ◽  
Relative Permeability Curves

Abstract A consolidated porous medium is mathematically modeled by networks of irregularly shaped interconnected pore channels. Mechanisms are described that form residual saturations during immiscible displacement both by entire pore channels being bypassed and by fluids being isolated by the movement of an interface within individual pore channels. This latter mechanism is shown to depend strongly on pore channel irregularity. Together, these mechanisms provide an explanation for the drainage-imbibition-hysteresis effect. The calculation of steady-state relative permeabilities, based on a pore-size distribution permeabilities, based on a pore-size distribution obtained from a Berea sandstone, is described. These relative permeability curves agree qualitatively with curves that are generally accepted to be typical for highly consolidated materials. In situations where interfacial effects predominate over viscous and gravitational effects, the following conclusions are reached.Relative permeability at a given saturation is everywhere independent of flow rate.Relative permeability is independent of viscosity ratio everywhere except at very low values of wetting phase relative permeability.Irreducible wetting-phase saturation following steady-state drainage decreases with increasing ratio of nonwetting- to wetting-phase viscosity.Irreducible wetting-phase saturation following unsteady-state drainage is lower than for steady-state drainage.Irreducible nonwetting-phase saturation following imbibition is independent of viscosity ratio, whether or not the imbibition is carried out under steady- or unsteady-state conditions. Experiments qualitatively verify the conclusions regarding unsteady-state residual wetting-phase saturation. Implications of these conclusions are discussed. Introduction Natural and artificial porous materials are generally composed of matrix substance brought together in a more or less random manner. This leads to the creation of a network of interconnected pore spaces of highly irregular shape. Since the pore spaces of highly irregular shape. Since the geometry of such a network is impossible to describe, we can never obtain a complete description of its flow behavior. We can, however, abstract those properties of the porous medium pertinent to the type of flow under consideration, and thus obtain an adequate description of that flow. Thus, the Kozeny-Carmen equation, by considering a porous medium as a bundle of noninterconnecting capillary tubes, provides an adequate description of single-phase provides an adequate description of single-phase flow. With the addition of a saturation-dependent tortuosity parameter in two-phase flow to account for flow path elongation, the Kozeny-Carmen equation has been used to predict relative permeabilities for the displacement of a wetting permeabilities for the displacement of a wetting liquid by a gas. It has long been recognized that relative permeability depends not only on saturation but permeability depends not only on saturation but also on saturation history as well. Naar and Henderson described a mathematical model in which differences between drainage and imbibition behavior are explained in terms of a bypassing mechanism by which oil is trapped during imbibition. Fatt proposed a model for a porous medium that consisted of regular networks of cylindrical tubes of randomly distributed radii. From this he calculated the drainage relative permeability curves. Moore and Slobod, Rose and Witherspoon, and Rose and Cleary each considered flow in a pore doublet (a parallel arrangement of a small and pore doublet (a parallel arrangement of a small and large diameter cylindrical capillary tube). They concluded that, because of the different rates of flow in each tube, trapping would occur in one of the tubes; the extent of which would depend upon viscosity ratio and capillary pressure. SPEJ p. 221

Calculation of Oil Displacement by Countercurrent Water Imbibition

1964 ◽  
Vol 4 (03) ◽  
pp. 195-202 ◽  
Author(s):  
P.M. Blair
Keyword(s):  
Porous Medium ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Water Saturation ◽  
Pressure Gradients ◽  
Oil Viscosity ◽  
Initial Water ◽  
Water Imbibition ◽  
Pressure Profiles ◽  
Water Viscosity

Abstract This paper presents numerical solutions of the equations describing the imbibition of water and the countercurrent flow of oil in porous rocks. The imbibition process is of practical importance in recovering oil from heterogeneous formations and has been studied principally by experimental means. Calculations were made for imbibition of water into both linear and radial systems. Imbibition in the linear systems was allowed to take place through one open, or permeable, face of the porous medium studied. In the radial system, water was imbibed inward from the outer radius. The effects on rate of imbibition of varying the capillary pressure and relative permeability curves, oil viscosity and the initial water saturation were computed. For each case studied, the rate of water imbibition and the saturation and pressure profiles were calculated as functions of time. The results of these calculations indicate that, for the porous medium studied, the time required to imbibe a fixed volume of water of a certain viscosity is approximately proportional to the square root of the viscosity of the reservoir oil whenever the oil viscosity is greater than the water viscosity. Results are also presented illustrating the effects on rate of imbibition of the other variables studied. Introduction The process of imbibition, or spontaneous flow of fluids in porous media under the influence of capillary pressure gradient s, occurs wherever there exist in permeable rock capillary pressure gradients which are not exactly balanced by opposing pressure gradients (such as those resulting from the influence of gravity). The importance of such capillary movement in the displacement of oil by water or gas was recognized in early investigations and described by Leverett, Lewis and True in 1942. Methods advanced by these authors for studying the process using dynamically scaled models were rendered more general and flexible by the research of later workers. The influence of capillary forces in laboratory water floods has also been discussed by several authors. While imbibition plays a very important role in the recovery of oil from normal reservoirs, Brownscombe and Dyes pointed out that imbibition might be the dominant displacement process in water flooding reservoirs characterized by drastic variations in permeability, such as in fractured- matrix reservoirs. In water-wet, fractured-matrix reservoirs, water will be imbibed from fractures into the matrix with a countercurrent expulsion of oil into the fractures. If the imbibition occurs at a sufficiently rapid rate, a very successful water flood can result; if the imbibition proceeds slowly the project might not be economically attractive. Scaled-model studies have demonstrated the vital importance of imbibition in secondary recovery in fractured reservoirs. It is therefore important in the evaluation of waterflooding prospects to develop a thorough understanding of the quantitative relationships of the factors which control the rapidity of capillary imbibition. The imbibition process serves reservoir engineers in still another important way by providing a technique for studying the wettability of reservoir core samples. Such experiments are usually conducted by observing the rate of expulsion of oil or water from core samples submerged in the appropriate fluid. Several papers have been published on the experimental techniques involved. Although Handy has recently published a method for calculating capillary pressures from experiments with gas-saturated cores, it has not yet been possible to deduce quantitative information regarding water-oil relative permeability and capillary pressure characteristics of the rock from the experimental results. Thus a technique is needed for studying the quantitative dependence of imbibition rate on oil and water viscosity, initial water saturation, relative permeability-saturation, and capillary pressure-saturation relations. The development of such information, including saturation and pressure profiles by laboratory experiments, would be very difficult. SPEJ P. 195ˆ

scholarly journals A further study on Welge equation

2018 ◽  
Vol 36 (5) ◽  
pp. 1103-1113 ◽  
Author(s):  
Jinqing Zhang ◽  
Renfeng Yang
Keyword(s):  
Linear Function ◽  
Relative Permeability ◽  
Fluid Transport ◽  
Viscosity Ratio ◽  
Water Saturation ◽  
Permeability Model ◽  
Simple Method ◽  
Average Water ◽  
Water Viscosity ◽  
Oil Water

Buckley–Leverett theory and Welge equation is one of the most widely used methods for predicting fluid transport in porous media. However, the average water saturation in Welge equation is a function of both water saturation and water cut, which is inconvenient to be used. While the linear relationship (the slope is 2/3) of the average water saturation and outlet water saturation proposed by Зфрос provides a simple method the oil–water viscosity ratio greatly limits the application. In this paper, based on the analytical relative permeability model and Welge equation, a new average water saturation equation with a variable (the outlet water saturation) was derived and applied in some cases under different relative permeability parameters and oil–water viscosity. Moreover, a simplified equation was proposed through certain data regression. Thus, the coefficient calculation method of the linear function was introduced based on the actual production data. Results showed a nonlinear relationship between the average water saturation and outlet water saturation, which is mainly related to water and oil relative permeability, and oil–water viscosity ratio. For the outlet water saturation higher than frontal saturation, the equation can be simplified to a linear function, which is the derivation of Зфрос equation. However, it is a function of both relative permeability and oil–water viscosity ratio instead of a constant slope of 2/3. In view of the fact that oil–water viscosity is mostly bigger than 10 in most reservoirs, the new model is an important supplement to Buckley–Leverett theory and Welge equation.

Statistical behavior of fingering in a displacement process in heterogeneous porous medium with capillary pressure

1969 ◽  
Vol 47 (3) ◽  
pp. 319-324 ◽  
Author(s):  
A. P. Verma
Keyword(s):  
Porous Medium ◽  
Perturbation Method ◽  
Capillary Pressure ◽  
Equation Of Motion ◽  
Perturbation Solution ◽  
Heterogeneous Porous Medium ◽  
Water Displacement ◽  
Statistical Behavior ◽  
Oil Water ◽  
Special Case

The stabilization of fingers in a specific oil–water displacement process with capillary pressure has been statistically discussed for a given heterogeneous porous medium. The equation of motion has been solved by a perturbation method. It is shown that the perturbation solution does produce "stable" fingers in one special case corresponding to the investigated problem.

scholarly journals Phase-Field Simulation of Imbibition for the Matrix-Fracture of Tight Oil Reservoirs Considering Temperature Change

Water ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1004
Author(s):  
Junjie Shi ◽  
Linsong Cheng ◽  
Renyi Cao ◽  
Zhihao Jia ◽  
Gaoling Liu
Keyword(s):  
Viscosity Ratio ◽  
Structure Model ◽  
Water Contact ◽  
Rock Structure ◽  
Matrix Fracture ◽  
The Matrix ◽  
Injection Water ◽  
Water Viscosity ◽  
Oil Water ◽  
The Ideal

Injection water temperature is often different from that of the reservoir during water injection development in the tight reservoir. Temperature change causes different fluid properties and oil-water interface properties, which further affects the imbibition process. In this paper, a matrix-fracture non-isothermal oil-water imbibition flow model in tight reservoirs is established and solved by the finite element method based on the phase-field method. The ideal inhomogeneous rock structure model was used to study the influence of a single factor on the imbibition. The actual rock structure model was used to study the influence of temperature. The mechanism of temperature influence in the process of imbibition is studied from the micro-level. It is found that the imbibition of matrix-fracture is a process in which the water enters the matrix along with the small pores, and the oil is driven into the macropores and then into the fractures. Temperature affects the imbibition process by changing the oil-water contact angle, oil-water interfacial tension, and oil-water viscosity ratio. Reducing oil-water contact angle and oil-water viscosity ratio and increasing oil-water interfacial tension are conducive to the imbibition process. The increase in injection water temperature is usually beneficial to the occurrence of the imbibition. Moreover, the actual core structure imbibition degree is often lower than that of the ideal core structure. The inhomogeneous distribution of rock particles has a significant influence on imbibition. This study provides microscale theoretical support for seeking reasonable injection velocity, pressure gradient, injection temperature, and well-shutting time in the field process. It provides a reference for the formulation of field process parameters.

Analysis of Factors on Nan Pu Oilfield’s Weak Gel Flooding

2011 ◽  
Vol 135-136 ◽  
pp. 268-273
Author(s):  
Jian Wei Gu ◽  
Mei Wu
Keyword(s):  
Conceptual Model ◽  
Viscosity Ratio ◽  
Orthogonal Design ◽  
Model Parameters ◽  
Water Viscosity ◽  
Flooding Time ◽  
Weak Gel ◽  
Oil Water ◽  
Cross Linker

There are lots of factors effect on weak gel flooding.This paper based on the conceptual model by changing the model parameters and using orthogonal design to analyze the effects of different factors on weak gel flooding. The descending order of influence is slug size, flooding time, oil-water viscosity ratio, permeability range, concentration of polymer, slug combination and polymer-cross linker ratio.

Recovery of Heavy Oil From the Monterey Formation in Offshore California by Cyclic Injection of Light-Oil Diluent

2001 ◽  
Vol 4 (01) ◽  
pp. 51-58
Author(s):  
R.L. Garnett
Keyword(s):  
Oil Recovery ◽  
Heavy Oil ◽  
Viscosity Ratio ◽  
Oil Viscosity ◽  
Production Rates ◽  
Monterey Formation ◽  
Light Oil ◽  
Water Viscosity ◽  
Oil Water

Summary This paper describes a single-well pilot in which light-oil diluent was injected through tubing to lower in-situ oil viscosity and increase production from a low-gravity oil well. The pilot well is located on the Heritage platform in the Santa Ynez Unit and produces from the Monterey formation. The pilot validated laboratory data suggesting that large production-rate increases could result from high-rate diluent injection. Introduction The Monterey formation is a complex reservoir with intense structuring, fracturing, and highly variable rock properties. It is a dual-porosity system, with low-permeability matrix rock and extensive fracturing. The fractures provide the flow path to the wells and are well-connected to a very large aquifer. The fluid system is equally complex. The original oil column was 2,000 ft thick, and the oil gravity varied from 5 to 19°API. Gravity/depth relationships vary within the field area. Heavy oil, as defined in this paper, is oil with dead-oil gravities of approximately 11°API or less. Fig. 1 is a geothermal temperature-gradient curve for offshore California. Fig. 2 is an estimation of live-oil viscosities for Monterey crude as a function of temperature and dead-oil gravity. Recovering the heavier oil at economic rates without producing large volumes of water is a challenge owing to a strong aquifer, highly permeable fractures, and a poor oil/water viscosity ratio. Achieving the large drawdown required to produce heavy oil at the high rates needed for economic operations offshore can result in the oil being bypassed by water flowing through the fractures. Even if bypassing can be avoided, the flow rate of heavy oil to the wellbore can be low. Furthermore, cooling of the heavy oil as it reaches the seafloor results in additional producing problems. As seen in Fig. 2, a 10°API oil has an in-situ viscosity of 100 cp at 200°F. As the heavy oil flows to the surface and cools, viscosity can rise above 10,000 cp and cause severe lifting problems. Deep, long throw wells (6,000 to 10,000 ft subsea), an offshore operating environment, a fracture zone with an active aquifer, and low heavy-oil prices rule out most methods of heavy-oil recovery. The challenge is to find a low-cost method to lower the oil viscosity in both the near-well region and the tubing. This paper documents a simple and inexpensive way to lower viscosity by an order of magnitude or more through cyclic injection of light oil. Theory Darcy's Law for radial, steady-state flow describes fluid flow in porous media. This simple equation gives guidance and insight to solve many oil-production problems:Equation 1 This pilot focused on reducing viscosity (µo) as a method to increase production rate (q). While the other components are also important, they were less critical for the following reasons:Fracture permeability in the major producing intervals of the Monterey formation in the Santa Barbara Channel is excellent. Wells have produced at rates in excess of 9,000 STB/D from as little as 40 ft true vertical depth (TVD) of the perforated interval. Average permeabilities are in the multidarcy range.High drawdowns may be harmful in the long run because of an unfavorable oil/water viscosity ratio. High drawdowns can result in water coning and fingering through the fractures, leaving bypassed oil in the formation. In addition, alternative lifting methods to increase drawdown can be costly owing to long throws and deep completions in the offshore environment. Reducing in-situ oil viscosity can improve the oil/water viscosity ratio, reduce water coning and fingering, reduce water cut, reduce lifting problems, and increase production rates and oil recovery from fractured heavy-oil reservoirs. HE-26 Pilot Background. The Heritage platform began producing from the Pescado field in the Santa Ynez Unit in December 1993. Wells produce 10 to 17°API oil from the Monterey and 34°API oil from sandstone formations. The Monterey formation consists of thin beds of porcelanite, chert, calcite, dolomite, and shale. The beds are highly fractured and well-connected both areally and vertically by an extensive fracture network. The fractures provide the primary flow paths in the reservoir and result in well rates as high as 10,000 STB/D. Formation pressure is supported by re-injection of produced gas and by a large, well-connected aquifer. The original oil column was approximately 2,000 ft thick and contained undersaturated oil with gravities grading from 19°API at the crest of the structure to 5°API at the original oil/water contact. Wells either flow naturally or are produced by high-volume gas lift. The sandstone formations lie below the Monterey and contain light oil with an associated gas cap. Sandstone wells flow naturally without the need for artificial lift. HE-26 History. The HE-26 well was drilled and completed in July 1997 in the Monterey formation, with perforations at 6,956 to 6,997 and 7,416 to 7,437 ft subsea. The well was stimulated with a combination of xylene, HCL, and mud acid, using foam and ball sealers for diversion. After stimulation, the well produced approximately 100 STB/D of 10.2°API oil and water. These perforations were isolated with a through-tubing bridge plug, and the well was reworked higher to 6,751 to 6,801 ft subsea. The new perforations were stimulated in a similar fashion. Oil gravity increased slightly, but production rates were unchanged. The interval was isolated with another through-tubing bridge. A final interval was perforated at 6,667 to 6,702 ft subsea. Oil gravity was slightly higher (11.4°API), but oil production rates once again did not change.

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