Numerical Investigation of the Effects of Core Heterogeneities on Waterflood Relative Permeabilities

1970 ◽  
Vol 10 (04) ◽  
pp. 381-392 ◽  
Author(s):  
John D. Huppler
Keyword(s):  
Numerical Simulation ◽  
Porous Medium ◽  
Pressure Drop ◽  
Difference Equation ◽  
Relative Permeability ◽  
Phase Difference ◽  
Two Dimensional ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Relative Permeability Curves

Abstract Numerical simulation techniques were used to investigate the effects of common core heterogeneities upon apparent waterflood relative-permeability results. Effects of parallel and series stratification, distributed high and low permeability lenses, and vugs were considered. permeability lenses, and vugs were considered. Well distributed heterogeneities have little effect on waterflood results, but as the heterogeneities become channel-like, their influence on flooding behavior becomes pronounced. Waterflooding tests at different injection rates are suggested as the best means of assessing whether heterogeneities are important. Techniques for testing stratified or lensed cores are recommended. Introduction Since best results from waterflood tests performed on core plugs are obtained with homogeneous cores, plugs selected for testing are chosen for their plugs selected for testing are chosen for their apparent uniformity. We know, however, that uniform appearance can be misleading. For example, flushing concentrated hydrochloric acid through an apparently homogeneous core plug often produces "wormholes" in higher permeability regions. Also, we sometimes find that all core plugs from a region of interest have obvious heterogeneities, so any flooding tests must be run on nonhomogeneous core plugs. plugs. Nevertheless, relative permeabilities, as obtained routinely from core waterflood data, are calculated using the assumption that the core is a homogeneous porous medium. While it is obvious that porous medium. While it is obvious that heterogeneties mill affect these apparent relative permeabilities, there appear to be no experimental permeabilities, there appear to be no experimental results reported in the literature to indicate just how serious the problem is. Accordingly, a computer simulation study of core waterfloods was conducted to systematically examine the effects of different sizes and types of core heterogeneities on flood results. The study was performed by numerical simulation using two-dimensional, two-phase difference equation approximations to describe the immiscible water-oil displacement. For each simulation the permeability and porosity distribution of the heterogeneous core to be studied was specified; fluid flow characteristics of the system, including a single set of input relative-permeabilities curves, were stipulated The system was set in capillary pressure equilibrium at the reducible water saturation. Then a waterflood simulation was performed. From the resulting fluid production and pressure-drop data a set of production and pressure-drop data a set of relative-permeability curves was calculated using the standard computational procedure applicable to homogeneous cores. In this paper these calculated relative-permeability curves are denoted as "waterflood" curves to distinguish them from the specified input curves. The waterflood relative-permeability curves should closely match the input curves for homogeneous systems. Since the same set of input relative-permeability curves was used for all rock sections, deviations of the waterflood from the input relative-permeability curves gave an indication of the effects of heterogeneities. When the system was heterogeneous and there was good agreement between waterflood and input relative-permeability curves, then the heterogeneities did not strongly influence the flow behavior and the system responded homogeneously. MATHEMATICAL MODEL AND METHOD The waterflood simulations were carried out using two-dimensional, two-phase difference equation approximations to the incompressible-flow differential equations:* .....................(1) ....................(2) SPEJ P. 381

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

Measurement of Three-Phase Relative Permeability with IFT Variation

2005 ◽  
Vol 8 (01) ◽  
pp. 33-43 ◽  
Author(s):  
Yildiray Cinar ◽  
Franklin M. Orr
Keyword(s):  
Experimental Data ◽  
Relative Permeability ◽  
Oil And Gas ◽  
Gas Injection ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Rich Phase ◽  
Injection Process ◽  
Three Phase ◽  
Relative Permeability Curves

Summary In this paper, we present results of an experimental investigation of the effects of variations in interfacial tension (IFT) on three-phase relative permeability. We report results that demonstrate the effect of low IFT between two of three phases on the three-phase relative permeabilities. To create three-phase systems in which IFT can be con-trolled systematically, we used a quaternary liquid system composed of hexadecane(C16), n-butanol (NBA), water (H2O), and isopropanol (IPA). Measured equilibrium phase compositions and IFTs are reported. The reported phase behavior of the quaternary system shows that the H2O-rich phase should represent the "gas" phase, the NBA-rich phase should represent the "oil" phase, and the C16-rich phase should represent the "aqueous" phase. Therefore, we used oil-wet Teflon (PTFE) bead packs to simulate the fluid flow in a water-wet oil reservoir. We determined phase saturations and three-phase relative permeabilities from recovery and pressure-drop data using an extension of the combined Welge/Johnson-Bossler-Naumann (JBN) method to three-phase flow. Measured three-phase relative permeabilities are reported. The experimental results indicate that the wetting-phase relative permeability was not affected by IFT variation, whereas the other two-phase relative permeabilities were clearly affected. As IFT decreases, the oil and gas phases become more mobile at the same phase saturations. For gas/oil IFTs in the range of 0.03 to 2.3 mN/m, we observed an approximately 10-fold increase in the oil and gas relative permeabilities against an approximately 100-fold decrease in the IFT. Introduction Variations in gas and oil relative permeabilities as a function of IFT are of particular importance in the area of compositional processes such as high-pressure gas injection, where oil and gas compositions can vary significantly both spatially and temporally. Because gas-injection processes routinely include three-phase flow (either because the reservoir has been water-flooded previously or because water is injected alternately with gas to improve overall reservoir sweep efficiency), the effect of IFT variations on three-phase relative permeabilities must be delineated if the performance of the gas-injection process is to be predicted accurately. The development of multicontact miscibility in a gas-injection process will create zones of low IFT between gas and oil phases in the presence of water. Although there have been studies of the effect of low IFT on two-phase relative permeability,1–14 there are limited experimental data published so far analyzing the effect of low IFT on three-phase relative permeabilities.15,16 Most authors have focused on the effect of IFT on oil and solvent relative permeabilities.17 Experimental results show that residual oil saturation and relative permeability are strongly affected by IFT, especially when the IFT is lower than approximately 0.1 mN/m (corresponding to a range of capillary number of 10–2 to 10–3). Bardon and Longeron3 observed that oil relative permeability increased linearly as IFT was reduced from approximately 12.5 mN/m to 0.04 mN/m and that for IFT below 0.04, the oil relative permeability curves shifted more rapidly with further reductions in IFT. Later, Asar and Handy6 showed that oil relative permeability curves began to shift as IFT was reduced below 0.18 mN/m for a gas/condensate system near the critical point. Delshad et al.15 presented experimental data for low-IFT three-phase relative permeabilities in Berea sandstone cores. They used a brine/oil/surfactant/alcohol mixture that included a microemulsion and excess oil and brine. The measurements were done at steady-state conditions with a constant capillary number of 10–2 between the microemulsion and other phases. The IFTs of microemulsion/oil and microemulsion/brine were low, whereas the IFT between oil and brine was high. They concluded that low-IFT three-phase relative permeabilities are functions of their own saturations only. Amin and Smith18 recently have published experimental data showing that the IFTs for each binary mixture of brine, oil, and gas phases vary as pressure increases(Fig. 1). Fig. 1 shows that the IFT of a gas/oil pair decreases as the pressure increases, whereas the IFTs of the gas/brine and oil/brine pairs approach each other.

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

Effect of Temperature on Oil/Water Relative Permeabilities of Unconsolidated and Consolidated Sands

1985 ◽  
Vol 25 (06) ◽  
pp. 945-953 ◽  
Author(s):  
Mark A. Miller ◽  
H.J. Ramey
Keyword(s):  
Relative Permeability ◽  
Room Temperature ◽  
Water Saturation ◽  
High Water ◽  
Distilled Water ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Dynamic Displacement ◽  
Irreducible Water Saturation ◽  
Increasing Temperature

Abstract Over the past 20 years, a number of studies have reported temperature effects on two-phase relative permeabilities in porous media. Some of the reported results, however, have been contradictory. Also, observed effects have not been explained in terms of fundamental properties known to govern two-phase flow. The purpose of this study was to attempt to isolate the fundamental properties affecting two-phase relative permeabilities at elevated temperatures. Laboratory dynamic-displacement relative permeability measurements were made on unconsolidated and consolidated sand cores with water and a refined white mineral oil. Experiments were run on 2-in. [5.1-cm] -diameter, 20-in. [52.-cm] -long cores from room temperature to 300F [149C]. Unlike previous researchers, we observed essentially no changes with temperature in either residual saturations or relative permeability relationships. We concluded that previous results may have been affected by viscous previous results may have been affected by viscous instabilities, capillary end effects, and/or difficulties in maintaining material balances. Introduction Interest in measuring relative permeabilities at elevated temperatures began in the 1960's with petroleum industry interest in thermal oil recovery. Early thermal oil recovery field operations (well heaters, steam injection, in-situ combustion) indicated oil flow rate increases far in excess of what was predicted by viscosity reductions resulting from heating. This suggested that temperature affects relative permeabilities. One of the early studies of temperature effects on relative permeabilities was presented by Edmondson, who performed dynamic displacement measurements with crude performed dynamic displacement measurements with crude and white oils and distilled water in Berea sandstone cores. Edmondson reported that residual oil saturations (ROS's) (at the end of 10 PV's of water injected) decreased with increasing temperature. Relative permeability ratios decreased with temperature at high water saturations but increased with temperature at low water saturations. A series of elevated-temperature, dynamic-displacement relative permeability measurements on clean quartz and "natural" unconsolidated sands were reported by Poston et al. Like Edmondson, Poston et al. reported a decrease in the "practical" ROS (at less than 1 % oil cut) as temperature increased. Poston et al. also reported an increase in irreducible water saturation. Although irreducible water saturations decreased with decreasing temperature, they did not revert to the original room temperature values. It was assumed that the cores became increasingly water-wet with an increase in both temperature and time; measured changes of the IFT and the contact angle with temperature increase, however, were not sufficient to explain observed effects. Davidson measured dynamic-displacement relative permeability ratios on a coarse sand and gravel core with permeability ratios on a coarse sand and gravel core with white oil displaced by distilled water, nitrogen, and superheated steam at temperatures up to 540F [282C]. Starting from irreducible water saturation, relative permeability ratio curves were similar to Edmondson's. permeability ratio curves were similar to Edmondson's. Starting from 100% oil saturation, however, the curves changed significantly only at low water saturations. A troublesome aspect of Davidson's work was that he used a hydrocarbon solvent to clean the core between experiments. No mention was made of any consideration of wettability changes, which could explain large increases in irreducible water saturations observed in some runs. Sinnokrot et al. followed Poston et al.'s suggestion of increasing water-wetness and performed water/oil capillary pressure measurements on consolidated sandstone and limestone cores from room temperature up to 325F [163C]. Sinnokrot et al confirmed that, for sandstones, irreducible water saturation appeared to increase with temperature. Capillary pressures increased with temperature, and the hysteresis between drainage and imbibition curves reduced to essentially zero at 300F [149C]. With limestone cores, however, irreducible water saturations remained constant with increase in temperature, as did capillary pressure curves. Weinbrandt et al. performed dynamic displacement experiments on small (0.24 to 0.49 cu in. [4 to 8 cm3] PV) consolidated Boise sandstone cores to 175F [75C] PV) consolidated Boise sandstone cores to 175F [75C] with distilled water and white oil. Oil relative permeabilities shifted toward high water saturations with permeabilities shifted toward high water saturations with increasing temperature, while water relative permeabilities exhibited little change. Weinbrandt et al. confirmed the findings of previous studies that irreducible water saturation increases and ROS decreases with increasing temperature. SPEJ P. 945

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
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