Comparison of Calculated with Experimental Imbibition Relative Permeability

1971 ◽  
Vol 11 (04) ◽  
pp. 419-425 ◽  
Author(s):  
Carlon S. Land
Keyword(s):  
Relative Permeability ◽  
Reservoir Rock ◽  
Laboratory Measurements ◽  
Two Phase ◽  
Relative Permeability Curve ◽  
Gas Saturation ◽  
Phase Saturation ◽  
The Difference ◽  
Relative Permeability Curves ◽  
The Relationship

Abstract Two-phase imbibition relative permeability was measured in an attempt to validate a method of calculating imbibition relative permeability. The stationary-liquid-phase method was used to measure several hysteresis loops for alundum and Berea sandstone samples. The method of calculating imbibition relative permeability is described, and calculated relative permeability curves are compared with measured curves. The calculated relative Permeability is shown to be a reasonably good Permeability is shown to be a reasonably good approximation of measured values if an adjustment is made to some necessary data. Due to the compressibility of gas, which is used as the nonwetting phase, a correction to the measured trapped gas saturation is necessary to make it agree with the critical gas saturation of the imbibition relative permeability curve. Introduction The existence of hysteresis in the relationship of relative permeability to saturation has been recognized for many yews. Geden et al. and Osoba et al. called attention to the occurrence of hysteresis and the importance of the direction of saturation change on the relative permeability-saturation relations. It is generally believed that relative permeability is a function of saturation alone for a permeability is a function of saturation alone for a given direction of saturation change, but that there is a distinct difference in relative permeability curves for saturation changes in different directions. The reservoir engineer should be aware of this hysteresis, and he should select the relative permeability curve which is appropriate for the permeability curve which is appropriate for the recovery process of interest. The directions of saturation change have been designated "drainage" and "imbibition" in reference to changes in the wetting-phase saturation. In a two-phase system, an increase in the wetting-phase saturation is referred to as imbibition, while a decrease in wetting-phase saturation is called drainage. The solution-gas-drive recovery mechanism is controlled by relative permeability to oil and gas in which the saturation of oil, the wetting phase, is decreasing. In waterflooding a water-wet reservoir rock, the saturation of water, the wetting phase, is increasing. These two sets of relative permeability curves, gas-oil and oil-water, do not have the same relationship to the wetting-phase saturation. This difference is not due to the difference in fluid properties, but is a result of the difference in properties, but is a result of the difference in direction of saturation change. The flow properties of the drainage and imbibition systems differ because of the entrapment of the nonwetting phase during imbibition. As drainage occurs, the nonwetting phase occupies the most favorable flow channels. During imbibition, part of the nonwetting phase is bypassed by the increasing wetting phase, leaving a portion of the nonwetting phase in an immobile condition. This trapped part phase in an immobile condition. This trapped part of the nonwetting phase saturation does not contribute to the flow of that phase, and at a given saturation the relative permeability to the nonwetting phase is always less in the imbibition direction phase is always less in the imbibition direction than in the drainage direction. The concept that some of the nonwetting phase is mobile and some is immobile during a saturation change in the imbibition direction previously was used to develop equations for imbibition relative permeability. In this development, it was assumed permeability. In this development, it was assumed that the amount of entrapment at any saturation can be obtained from the relationship between initial nonwetting-phase saturations established in the drainage direction and residual saturations after complete imbibition. The equations for imbibition relative permeability were not verified by laboratory measurements. The purpose of this report is m give the results of a laboratory study of imbibition relative permeability and to present a comparison of calculated relative permeability with relative permeability from laboratory measurements. permeability from laboratory measurements. In two-phase systems, hysteresis is more prominent in the relative permeability to the nonwetting phase than in that to the wetting phase. The hysteresis in the wetting-phase relative permeability is believed to be very small, and thus difficult to distinguish tom normal experimental error. SPEJ P. 419

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

A New Two Phase Extension of Modified Brinkman Formulation for Fluid Flow through Porous Media

2005 ◽  
Author(s):  
Hadi Belhaj ◽  
Shabbir Mustafiz ◽  
Fuxi Ma ◽  
M. R. Islam
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Petroleum Reservoirs ◽  
Two Dimensional ◽  
Transient Pressure ◽  
Two Phase ◽  
Phase Saturation ◽  
Brinkman’S Equation ◽  
The Difference ◽  
Relative Permeability Curves

In porous media research, Modified Brinkman’s equation is a very recent development. It is important as it incorporates the concept of viscous effect to inertial effect in a fluid flow system when Darcy’s, Forchheimer’s and Brinkman’s terms are brought all together. So far, researchers have developed the modified equation in its two-dimensional forms; however, limited to only one phase. In reality, petroleum reservoirs experience the multiphase conditions. Therefore, the simulation of a multidimensional, multiphase scenario is mostly desired, the highlight of this paper. The paper presents the formulation of two-dimensional, transient pressure and saturation equations for oil and water phases, one equation for each phase. The difference between phases is noticeable explicitly in their respective saturation, permeability, viscosity and velocity terms. The equations are then solved numerically to generate relative permeability curves. The simultaneous solution of pressure and saturation terms in the governing equations required additional relationships: the phase saturation constraint and capillary pressure as function of saturation. Finally, the numerical results are compared and validated with the experimental results. The implication of this study is manifold. The formulated equations including the solution part for the multiphase conditions are new. The new comprehensive model will describe fluid flow in reservoirs prone to high velocity or fractures more accurately than ever described by Darcy’s or other aforementioned equations.

scholarly journals Fluid and Heat Flow In Gas-Rich Geothermal Reservoirs

1985 ◽  
Vol 25 (02) ◽  
pp. 215-226 ◽  
Author(s):  
M.J. O'Sullivan ◽  
G.S. Bodvarsson ◽  
K. Pruess ◽  
M.R. Blakeley
Keyword(s):  
Pressure Drop ◽  
Relative Permeability ◽  
Field Data ◽  
Lumped Parameter Model ◽  
Natural State ◽  
Two Phase ◽  
Geothermal Reservoirs ◽  
Gas Saturation ◽  
Lumped Parameter ◽  
Relative Permeability Curves

Abstract Numerical simulation techniques are used to study the effects of noncondensable gases (CO2) on geothermal reservoir behavior in the natural state and during exploitation. It is shown that the presence Of CO2 has a large effect on the thermodynamic conditions of a reservoir in the natural state, especially on temperature distributions and phase compositions. The gas will expand two-phase zones phase compositions. The gas will expand two-phase zones and increase gas saturations to enable flow of CO2 through the system. During exploitation, the early pressure drop primarily results from "degassing" of the system. This primarily results from "degassing" of the system. This process can cause a very rapid initial pressure drop, on process can cause a very rapid initial pressure drop, on the order of megapascals, depending on the initial partial pressure of CO2. The flowing gas content from wells can pressure of CO2. The flowing gas content from wells can provide information on in-place gas saturations and provide information on in-place gas saturations and relative permeability curves that apply at a given geothermal resource. Site-specific studies are made for the gas-rich, two-phase reservoir at the Ohaaki geothermal field in New Zealand. A simple lumped-parameter model and a vertical column model are applied to the field data. The results obtained agree well with the natural thermodynamic state of the Ohaaki field (pressure and temperature profiles) and a partial pressure of 1.5 to 2.5 MPa [217 to 363 psi] is calculated in the primary reservoirs. The models also agree reasonably well with field data obtained during exploitation of the field. The treatment of thermophysical properties of H2O/CO2 mixtures for different phase compositions is summarized. Introduction Many geothermal reservoirs contain large amounts of non-condensable gases, particularly CO2. The proportion of noncondensable gas in the produced fluid is an extremely important factor in the design of separators, turbines, heat exchangers, and other surface equipment. In the reservoir itself, the presence of CO2 significantly alters the distribution of temperature and gas saturation (volumetric fraction of gas phase) associated with given heat and mass flows. Therefore, when modeling gas-rich reservoirs it is essential to keep track of the amount of CO2 in each gridblock in addition to the customary fluid and heat content. Several investigators have considered the effects of CO2 on the reservoir dynamics of geothermal systems. A lumped-parameter model using one block for the gas zone and one for the liquid zone was developed by Atkinson et al. for the Bagnore (Italy) reservoir. Preliminary work on the Ohaaki reservoir was carried out by Zyvoloski and O'Sullivan, but these studies were limited because-the thermodynamic package used could only handle two-phase conditions. Generic studies of reservoir depletion and well-test analysis also were made in the previous works. The present study describes the effects of CO2 in geothermal reservoirs in a more complete and detailed way. We emphasize the potential for using the CO2 content in the fluid produced during a well test as a reservoir diagnostic aid, and as a means of gaining information about relative permeability curves. The aim of the present study is to investigate the effects of CO2 on both the natural state of a reservoir and its behavior under exploitation. Several generic simulation studies are described. First, the effect of CO2 on the depletion of a single-block, lumped-parameter reservoir model is briefly examined. Secondly, the relationship between the mass fraction Of CO2 in the produced fluid and the mass fraction in place in the reservoir is studied. It is demonstrated that in some cases the in-place gas saturation can be determined for a given set of relative permeability curves. Finally, the effects of CO2 on the permeability curves. Finally, the effects of CO2 on the vertical distribution of gas saturation, temperature, and pressure of geothermal reservoirs in the natural state are pressure of geothermal reservoirs in the natural state are investigated. The numerical simulator with the H2O/CO2 thermodynamic package is applied to field data from the Ohaaki (formerly Broadlands) geothermal field in New Zealand. Two simple models of the 1966–74 large-scale field exploitation test of the Ohaaki reservoir are presented. The first is a single-block, lumped-parameter model similar to those reported earlier by Zyvoloski and O'Sullivan and Grant. In the former work, a less accurate thermodynamic package for H2O/CO2 mixtures is used; the latter uses approximate methods to integrate the mass-, energy-, and CO2-balance equations. The second model described in the present work is a distributed-parameter model, in the form of a vertical column representing the main upflow zone at Ohaaki. This model produces a good fit to the observed distribution of pressure and temperature with depth in the natural state at Ohaaki and a good match to the observed response of the reservoir during 5 years of experimental production and 3 years of recovery. SPEJ p. 215

scholarly journals Variations in Permeability and Porosity of Synthetic Oil Reservoir Rock-Methods of Control

1965 ◽  
Vol 5 (04) ◽  
pp. 329-332 ◽  
Author(s):  
Larman J. Heath
Keyword(s):  
Porous Media ◽  
Relative Permeability ◽  
Reservoir Rock ◽  
Oil Reservoir ◽  
Natural Reservoir ◽  
Natural Rock ◽  
Unconsolidated Sand ◽  
Synthetic Rock ◽  
Porosity And Permeability ◽  
Relative Permeability Curves

Abstract Synthetic rock with predictable porosity and permeability bas been prepared from mixtures of sand, cement and water. Three series of mixes were investigated primarily for the relation between porosity and permeability for certain grain sizes and proportions. Synthetic rock prepared of 65 per cent large grains, 27 per cent small grains and 8 per cent Portland cement, gave measurable results ranging in porosity from 22.5 to 40 per cent and in permeability from 0.1 darcies to 6 darcies. This variation in porosity and permeability was caused by varying the amount of blending water. Drainage- cycle relative permeability characteristics of the synthetic rock were similar to those of natural reservoir rock. Introduction The fundamental behavior characteristics of fluids flowing through porous media have been described in the literature. Practical application of these flow characteristics to field conditions is too complicated except where assumptions are overly simplified. The use of dimensionally scaled models to simulate oil reservoirs has been described in the literature. These and other papers have presented the theoretical and experimental justification for model design. Others have presented elements of model construction and their operation. In most investigations the porous media have consisted of either unconsolidated sand, glass beads, broken glass or plastic-impregnated granular substances-materials in which the flow behavior is not identical to that in natural reservoir rock. The relative permeability curves for unconsolidated sands differ from those for consolidated sandstone. The effect of saturation history on relative permeability measurements A discussed by Geffen, et al. Wygal has shown quite conclusively that a process of artificial cementation can be used to render unconsolidated packs into synthetic sandstones having properties similar to those of natural rock. Many theoretical and experimental studies have been made in attempts to determine the structure and properties of unconsolidated sand, the most notable being by Naar and Wygal. Others have theorized and experimented with the fundamental characteristics of reservoir rocks. This study was conducted to determine if some general relationship could be established between the size of sand grains and the porosity and permeability in consolidated binary packs. This paper presents the results obtained by changing some of the factors which affect the porosity and permeability of synthetically prepared sandstone. In addition, drainage relative permeability curves are presented. EXPERIMENTAL PROCEDURE Mixtures of Portland cement with water and aggregate generally are designed to have certain characteristics, but essentially all are planned to be impervious to water or other liquids. Synthetic sandstone simulating oil reservoir rock, however, must be designed to have a given permeability (sometimes several darcies), a porosity which is primarily the effective porosity but quantitatively similar to natural rock, and other characteristics comparable to reservoir rock, such as wettability, pore geometry, tortuosity, etc. Unconsolidated ternary mixtures of spheres gave both a theoretically computed and an experimentally observed minimum porosity of about 25 per cent. By using a particle-distribution system, one-size particle packs had reproducible porosities in the reproducible range of 35 to 37 per cent. For model reservoir studies of the prototype system, a synthetic rock having a porosity of 25 per cent or less and a permeability of 2 darcies was required. The rock bad to be uniform and competent enough to handle. Synthetic sandstone cores mere prepared utilizing the technique developed by Wygal. Some tight variations in the procedure were incorporated. The sand was sieved through U.S. Standard sieves. SPEJ P. 329ˆ

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.

An Equation To Predict Two-Phase Relative Permeability Curves in Fractures

2010 ◽  
Author(s):  
Andres Chima ◽  
Efren Antonio Chavez Iriarte ◽  
Zuly Himelda Calderon Carrillo
Keyword(s):  
Relative Permeability ◽  
Two Phase ◽  
Relative Permeability Curves

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.

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