An Imbibition Model - Its Application to Flow Behavior and the Prediction of Oil Recovery

1961 ◽  
Vol 1 (02) ◽  
pp. 61-70 ◽  
Author(s):  
J. Naar ◽  
J.H. Henderson
Keyword(s):  
Porous Medium ◽  
Relative Permeability ◽  
Oil Recovery ◽  
Flow Behavior ◽  
Pore Geometry ◽  
Mathematical Treatment ◽  
Complete Wetting ◽  
Permeability Characteristics ◽  
Relative Permeability Curves ◽  
Wetting Fluid

Introduction The displacement of a wetting fluid from a porous medium by a non-wetting fluid (drainage) is now reasonably well understood. A complete explanation has yet to be found for the analogous case of a wetting fluid being spontaneously imbibed and the non-wetting phase displaced (imbibition). During the displacement of oil or gas by water in a water-wet sand, the porous medium ordinarily imbibes water. The amount of oil recovered, the cost of recovery and the production history seem then to be controlled mainly by pore geometry. The influence of pore geometry is reflected in drainage and imbibition capillary-pressure curves and relative permeability curves. Relative permeability curves for a particular consolidated sand show that at any given saturation the permeability to oil during imbibition is smaller than during drainage. Low imbibition permeabilities suggest that the non-wetting phase, oil or gas, is gradually trapped by the advancing water. This paper describes a mathematical image (model) of consolidated porous rock based on the concept of the trapping of the non-wetting phase during the imbibition process. The following items have been derived from the model.A direct relation between the relative permeability characteristics during imbibition and those observed during drainage.A theoretical limit for the fractional amount of oil or gas recoverable by imbibition.An expression for the resistivity index which can be used in connection with the formula for wetting-phase relative permeability to check the consistency of the model.The limits of flow performance for a given rock dictated by complete wetting by either oil or water.The factors controlling oil recovery by imbibition in the presence of free gas. The complexity of a porous medium is such that drastic simplifications must be introduced to obtain a model amenable to mathematical treatment. Many parameters have been introduced by others in "progressing" from the parallel-capillary model to the randomly interconnected capillary models independently proposed by Wyllie and Gardner and Marshall. To these a further complication must be added since an imbibition model must trap part of the non-wetting phase during imbibition of the wetting phase. Like so many of the previously introduced complications, this fluid-block was introduced to make the model performance fit the observed imbibition flow behavior.

Sandstone and Carbonate Two- and Three-Phase Relative Permeability Characteristics

1970 ◽  
Vol 10 (01) ◽  
pp. 75-84 ◽  
Author(s):  
F.N. Schneider ◽  
W.W. Owens
Keyword(s):  
Relative Permeability ◽  
Oil Recovery ◽  
Flow Behavior ◽  
Water Injection ◽  
Phase System ◽  
Phase Flow ◽  
Two Phase ◽  
Permeability Characteristics ◽  
Three Phase ◽  
Three Phase Flow

Abstract Three-phase relative permeability characteristics applicable to various oil displacement processes in the reservoir such as combustion and alternate gas-water injection were determined on both outcrop and reservoir core samples. Steady-state and nonsteady-state tests were performed on a variety of sandstone and carbonate core samples having different wetting properties. Some of the tests were performed on preserved samples. Some of the three-phase tests were performed on samples that contained two flowing phases and a third nonflowing phase, either gas or oil. These were classed as three-phase flow tests because the third phase played an important role in the flow behavior which was determined. The three-phase relative permeability test results are directly compared with the results of two-phase gas-oil and water-oil test. Wetting-phase relative permeability was found to be primarily dependent on its own saturation, i.e., relative permeability to the wetting phase during three-phase flow was in agreement with and could be predicted from the tow-phase data. Nonwetting-phase relative permeability-saturation relationships were found to be more complex and to depend in some cases on the saturation history of both nonwetting phases and on the saturation ratio of the second nonwetting phase and the wetting phases. Trapping of a given nonwetting phase or mutual flow interference between the two nonwetting phases when both are flowing accounts for most of the low relative permeabilities observed for three-phase flow tests. However, in special cases nonwetting-phase relative permeabilities at a given saturation are higher than those given by two-phase flow data. Despite these complexities some types of three-phase flow behavior can be predicted from two-phase flow data. Through its effect on the spatial distribution of the phases, wettability is shown to be a controlling factor in determining three-phase relative permeability characteristics. however, despite the importance of wettability the present data shown that for both water-wet and oil-wet systems oil recovery can be improved by several different injection processes, but the additional oil recovery is accompanied by lower fluid mobility. Introduction The increasing emphasis on optimizing recovery and the rapid and extensive development and use of mathematical modes for predicting reservoir performance are together creating a widespread need for reliable basic data on rock flow behavior. The two-phase imbibition or drainage flow relationships common to conventional oil recovery processes (depletion, gas or water injection, gravity drainage) are not applicable to some of the newer secondary and tertiary recovery techniques. This is because the reservoir displacement process may differ from that easily simulated in laboratory relative permeability studies. in some situations, data are needed fro a three-phase system where almost any combination of two fluids or even all three fluids may be flowing. In other, however, only two flowing phases are present, but the saturation history of the system is unique. Leverett and Lewis were the first to collect experimental relative permeability data on a three-phase system. Corey et al. were similarly leaders in efforts to define three-phase flow relationships using empirical approaches. Space does not permit a critical review of these earlier works. For those interested, a recent article by Saraf and Fatt provides a brief discussion of the experimental techniques used by earlier investigators. Suffice it to say that both experimental and empirical approaches have been used, but the applicability of both has been limited because in only one case have three-phase relative permeability data been obtained on reservoir rock material. SPEJ P. 75ˆ

scholarly journals In-House Developed Kr Estimator: Implemented to Analyze the Sensitivity of Relative Permeability Data to Variations in Wetting Phase Saturation

2011 ◽  
Vol 29 (6) ◽  
pp. 817-825 ◽  
Author(s):  
Muhammad Khurram Zahoor
Keyword(s):  
Porous Medium ◽  
Pore Size Distribution ◽  
Pore Size ◽  
Relative Permeability ◽  
State Of The Art ◽  
Data Generation ◽  
Phase Saturation ◽  
Complex Models ◽  
Relative Permeability Curves ◽  
Very High

Reservoir surveillance always requires fast, unproblematic access and solution to different relative permeability models which have been developed from time to time. In addition, complex models sometimes require in-depth knowledge of mathematics for solution prior to use them for data generation. For this purpose, in-house software has been designed to generate rigorous relative permeability curves, with a provision to include users own relative permeability models, a part from built-in various relative permeability correlations. The developed software with state-of-the-art algorithms has been used to analyze the effect of variations in residual and maximum wetting phase saturation on relative permeability curves for a porous medium having very high non-uniformity in pore size distribution. To further increase the spectrum of the study, two relative permeability models, i.e., Pirson's correlation and Brooks and Corey model has been used and the obtained results show that the later model is more sensitive to such variations.

scholarly journals Carbon Storage and Enhanced Oil Recovery in Pennsylvanian Morrow Formation Clastic Reservoirs: Controls on Oil–Brine and Oil–CO2 Relative Permeability from Diagenetic Heterogeneity and Evolving Wettability

Energies ◽  
2019 ◽  
Vol 12 (19) ◽  
pp. 3663
Author(s):  
Lindsey Rasmussen ◽  
Tianguang Fan ◽  
Alex Rinehart ◽  
Andrew Luhmann ◽  
William Ampomah ◽  
...  
Keyword(s):  
Carbon Storage ◽  
Enhanced Oil Recovery ◽  
Relative Permeability ◽  
Oil Recovery ◽  
Flow Behavior ◽  
Flow Unit ◽  
Water Production ◽  
Intergranular Porosity ◽  
Diagenetic Processes ◽  
Pore Types

The efficiency of carbon utilization and storage within the Pennsylvanian Morrow B sandstone, Farnsworth Unit, Texas, is dependent on three-phase oil, brine, and CO2 flow behavior, as well as spatial distributions of reservoir properties and wettability. We show that end member two-phase flow properties, with binary pairs of oil–brine and oil–CO2, are directly dependent on heterogeneity derived from diagenetic processes, and evolve progressively with exposure to CO2 and changing wettability. Morrow B sandstone lithofacies exhibit a range of diagenetic processes, which produce variations in pore types and structures, quantified at the core plug scale using X-ray micro computed tomography imaging and optical petrography. Permeability and porosity relationships in the reservoir permit the classification of sedimentologic and diagenetic heterogeneity into five distinct hydraulic flow units, with characteristic pore types including: macroporosity with little to no clay filling intergranular pores; microporous authigenic clay-dominated regions in which intergranular porosity is filled with clay; and carbonate–cement dominated regions with little intergranular porosity. Steady-state oil–brine and oil–CO2 co-injection experiments using reservoir-extracted oil and brine show that differences in relative permeability persist between flow unit core plugs with near-constant porosity, attributable to contrasts in and the spatial arrangement of diagenetic pore types. Core plugs “aged” by exposure to reservoir oil over time exhibit wettability closer to suspected in situ reservoir conditions, compared to “cleaned” core plugs. Together with contact angle measurements, these results suggest that reservoir wettability is transient and modified quickly by oil recovery and carbon storage operations. Reservoir simulation results for enhanced oil recovery, using a five-spot pattern and water-alternating-with-gas injection history at Farnsworth, compare models for cumulative oil and water production using both a single relative permeability determined from history matching, and flow unit-dependent relative permeability determined from experiments herein. Both match cumulative oil production of the field to a satisfactory degree but underestimate historical cumulative water production. Differences in modeled versus observed water production are interpreted in terms of evolving wettability, which we argue is due to the increasing presence of fast paths (flow pathways with connected higher permeability) as the reservoir becomes increasingly water-wet. The control of such fast-paths is thus critical for efficient carbon storage and sweep efficiency for CO2-enhanced oil recovery in heterogeneous reservoirs.

Capillary Impregnation of Viscous Fluids in a Multi-Layered Porous Medium

2019 ◽  
Author(s):  
Shabina Ashraf ◽  
Jyoti Phirani
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Oil Recovery ◽  
Viscous Fluids ◽  
Spontaneous Imbibition ◽  
Lab On Chip ◽  
Capillary Impregnation ◽  
Relative Placement ◽  
Homogeneous Porous Medium ◽  
Wetting Fluid

Abstract Capillary impregnation of viscous fluids in porous media is useful in diagnostics, design of lab-on-chip devices and enhanced oil recovery. The impregnation of a wetting fluid in a homogeneous porous medium follows Washburn’s diffusive law. The diffusive dynamics predicts that, with the increase in permeability, the rate of spontaneous imbibition of a wetting fluid also increases. As most of the naturally occurring porous media are composed of hydrodynamically interacting layers having different properties, the impregnation in a heterogeneous porous medium is significantly different from a homogeneous porous medium. A Washburn like model has been developed in the past to predict the imbibition behavior in the layers for a hydrodynamically interacting three layered porous medium filled with a non-viscous resident phase. It was observed that the relative placement of the layers impacts the imbibition phenomena significantly. In this work, we develop a quasi one-dimensional lubrication approximation to predict the imbibition dynamics in a hydrodynamically interacting multi-layered porous medium. The generalized model shows that the arrangement of layers strongly affects the saturation of wetting phase in the porous medium, which is crucial for oil recovery and in microfluidic applications.

scholarly journals Relative Permeability Characteristics During Carbon Capture and Sequestration Process in Low-Permeable Reservoirs

Materials ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 990
Author(s):  
Mingxing Bai ◽  
Lu Liu ◽  
Chengli Li ◽  
Kaoping Song
Keyword(s):  
Relative Permeability ◽  
Carbon Capture ◽  
Oil And Gas ◽  
Co2 Flooding ◽  
Two Phase ◽  
Permeability Characteristics ◽  
Gas Recovery ◽  
Miscible Flooding ◽  
Relative Permeability Curves ◽  
Carbon Dioxide Co2

The injection of carbon dioxide (CO2) in low-permeable reservoirs can not only mitigate the greenhouse effect on the environment, but also enhance oil and gas recovery (EOR). For numerical simulation work of this process, relative permeability can help predict the capacity for the flow of CO2 throughout the life of the reservoir, and reflect the changes induced by the injected CO2. In this paper, the experimental methods and empirical correlations to determine relative permeability are reviewed and discussed. Specifically, for a low-permeable reservoir in China, a core displacement experiment is performed for both natural and artificial low-permeable cores to study the relative permeability characteristics. The results show that for immiscible CO2 flooding, when considering the threshold pressure and gas slippage, the relative permeability decreases to some extent, and the relative permeability of oil/water does not reduce as much as that of CO2. In miscible flooding, the curves have different shapes for cores with a different permeability. By comparing the relative permeability curves under immiscible and miscible CO2 flooding, it is found that the two-phase span of miscible flooding is wider, and the relative permeability at the gas endpoint becomes larger.

The Characteristics and Impacts Factors of Relative Permeability Curves in High Temperature and Low-Permeability Limestone Reservoirs

2014 ◽  
Vol 1010-1012 ◽  
pp. 1676-1683 ◽  
Author(s):  
Bin Li ◽  
Wan Fen Pu ◽  
Ke Xing Li ◽  
Hu Jia ◽  
Ke Yu Wang ◽  
...  
Keyword(s):  
Relative Permeability ◽  
Oil Recovery ◽  
Water Saturation ◽  
Phase Region ◽  
Two Phase ◽  
Experimental Conditions ◽  
Irreducible Water Saturation ◽  
Productive Water ◽  
Relative Permeability Curves ◽  
Water Cut

To improve the understanding of the influence of effective permeability, reservoir temperature and oil-water viscosity on relative permeability and oil recovery factor, core displacement experiments had been performed under several experimental conditions. Core samples used in every test were natural cores that came from Halfaya oilfield while formation fluids were simulated oil and water prepared based on analyze data of actual oil and productive water. Results from the experiments indicated that the shape of relative permeability curves, irreducible water saturation, residual oil saturation, width of two-phase region and position of isotonic point were all affected by these factors. Besides, oil recovery and water cut were also related closely to permeability, temperature and viscosity ratio.

Foam in Porous Media: Characteristics and Potential Applications

1970 ◽  
Vol 10 (04) ◽  
pp. 328-336 ◽  
Author(s):  
S. H. Raza
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Oil Recovery ◽  
Flow Behavior ◽  
Foaming Agent ◽  
Reservoir Rocks ◽  
Recovery Processes ◽  
Potential Applications ◽  
Foam In Porous Media

Abstract A laboratory study was made of the variables which affect the generation, propagation, quality und nature of foam produced inside a porous medium. It is shown that foam can be generated and propagated in porous media representative of reservoir rocks at pressure levels ranging from atmospheric to 1,000 psig, and under pressure differentials ranging from 1.0 to 50 psi/ft. The quality of foam depends on the type of foaming agent, the concentration of foaming solution, the physical properties of the porous medium, the pressure level, and the composition and saturation of fluids present. The nature of foam depends upon the type of foaming agent and its concentration in the foaming solution. The study shows that the flow behavior of foam in a porous medium is a complex one which cannot he correctly described in terms of the high apparent viscosity of foam. Also, the concept of relative permeability is not applicable to the flow of foam due to the associative nature of its components. On the basis of the discussed characteristics of foam, several applications of foam are suggested in oil recovery processes.

Three-Phase Imbibition Relative Permeability

10.2118/90-pa ◽  
1961 ◽  
Vol 1 (04) ◽  
pp. 254-258 ◽  
Author(s):  
J. Naar ◽  
R.J. Wygal
Keyword(s):  
Oil Recovery ◽  
Oil And Gas ◽  
Water Flooding ◽  
Pressure Curve ◽  
Complete Wetting ◽  
Oil Saturation ◽  
Gas Saturation ◽  
Three Phase ◽  
Oil Gas ◽  
Wetting Fluid

Abstract An equation for three-phase (water, oil, gas) imbibition oil permeability is developed, assuming the water to be the dominant wetting fluid. Oil isoperms are obtained for consolidated sandstones characterized by. The evolution of an oil-gas system imbibing water from is shown to proceed along a line of constant oil saturation with increasing oil permeability and decreasing gas saturations. When the gas saturation cannot be reduced further, the system evolves along a line of constant with decreasing oil saturation and permeability. The initial gas saturation is shown to reduce markedly the effect of complete wetting by either oil or water on flow performance. Introduction Imbibition oil isoperms are required for performance prediction when a well is producing water, oil and gas. This situation occurs in multiphase displacements such as underground combustion, steam injection and the water flooding of highly depleted reservoirs. In a recent paper, a model was presented for the prediction of two-phase imbibition characteristics. This paper extends the imbibition model to the case of three phases by assuming that the water is the dominant wetting fluid. The following results were obtained from the model:an analytical expression of oil isoperms;oil isoperms as functions of reduced water, oil and gas saturations, valid for all sandstones having a capillary pressure curve which can be approximated by; andevaluation of the three-phase flow performance as dictated by complete wetting by either oil or water. The agreement between predicted and observed oil recovery in the presence of a gas phase, reported in Ref. 1, is a partial support for the present development. However, experimental data are not available at this time to check fully the model predictions. Perhaps this paper will stimulate the collection of such data. THEORETICAL The imbibition model of a porous medium has been described previously, and the reader is referred to the paper of Naar and Henderson for details. In brief, the model is formed by the random interconnection of straight capillaries, with a provision for the blocking of the non-wetting phase by the invading wetting fluid.

The Flow of Foam Through Short Porous Media And Apparent Viscosity Measurements

1966 ◽  
Vol 6 (01) ◽  
pp. 17-25 ◽  
Author(s):  
S.S. Marsden ◽  
Suhail A. Khan
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Shear Rate ◽  
Relative Permeability ◽  
Oil Recovery ◽  
Apparent Viscosity ◽  
Viscosity Ratio ◽  
Surfactant Solution ◽  
Liquid Saturation ◽  
Liquid Displacement

Abstract Externally generated foam was injected continuously into short porous media. Both flow rate and pressure drop were measured. Liquid saturation was determined by electrical conductivity. Foam quality G, expressed as the ratio of gas volume to total volume, was varied from 0.70 to 0.96. As measured with a modified Fann VG Meter, apparent viscosity of this foam µa decreases with increasing shear rate but usually falls within the range of 50 to 500 cp. At a given shear rate, µa increases almost linearly with G. When measured with a Bendix Ultraviscoson, kinematic µa is independent of r but absolute µa increases with r from about 3 to 8 cp. The effective permeability-apparent viscosity ratio ke/µa decreases almost linearly with G for porous media of high permeability, but the rate of decrease becomes less for tighter ones. The relative permeability-apparent viscosity ratio kr/µa vs G data does not fall on a single line. The kr/µa ratio increases with liquid saturation in the porous medium and with surfactant concentration. Estimates of µa for foam in porous media vary from 30 to 100 cp. INTRODUCTION Although research on the development of a foam-drive, oil recovery process has been going on for almost a decade, most of the significant publications have appeared within the last several years. This illustrates well the rate at which interest in this process is accelerating. Bond and Holbrook1 were the first to describe the use of foam to improve oil recovery in their patent of 1958. They proposed that an aqueous foaming agent slug be injected into the formation and that this be followed by gas to produce a foam in situ. Fried2 studied the injection of foam into porous media which has already been subjected to conventional gas or water drives and found that gas could be used to drive a foam bank which would, in turn, displace additional oil in the form of an oil bank. He attributed the increased oil recovery to the high effective viscosity of foam flowing in porous media. His microscopic observations showed the importance of foam generation and regeneration within the porous medium. By injecting both air and aqueous surfactant solution, Bernard3 generated foams within the porous medium in which oil displacement was being studied. In a separate empirical test, he also measured the dynamic foaming characteristics of the same surfactants in water and/or oil. With some exceptions and for the seven surfactants studied, there seems to be a qualitative relationship between the efficiency of liquid displacement and the dynamic foaming test used. This relationship was not consistent enough to eliminate the necessity of actual foam flood tests in porous media for surfactant selection. In a study basic to gas storage in aquifers, Bennett4 described the displacement of brine by foam in consolidated porous media. Among other things, he stated that the ability of a surfactant solution to foam is more important than the stability of its foam. The presence of a foam bank between the displacing air and the displaced brine improved both breakthrough and ultimate recovery. In a continuation of this work Kolb5 attributed the great reduction in surfactant solution production rate as displacement by air progressed to a decrease in relative permeability to gas. These several effects reported by both Bennett and Kolb can all be attributed to the high apparent viscosity of foam which was obviously flowing in the porous media.

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