An Improved Unsteady-State Procedure for Determining the Relative-Permeability Characteristics of Heterogeneous Porous Media (includes associated papers 8028 and 8777 )

1979 ◽  
Vol 19 (01) ◽  
pp. 15-28 ◽  
Author(s):  
P.M. Sigmund ◽  
F.G. McCaffery
Keyword(s):  
Porous Media ◽  
Relative Permeability ◽  
Capillary Rise ◽  
Test Method ◽  
Oil Reservoir ◽  
Sample Length ◽  
Unsteady State ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Core Samples

Abstract With typical heterogeneous carbonate coresamples, large uncertainties of unknown magnitudecan occur in the relative permeabilities derived using different methods. This situation can beimproved by analyzing the recovery and pressureresponse to two-phase laboratory displacement tests by a nonlinear least-squares procedure. Thesuggested technique fits the finite-differencesolution of the Buckley-Leverett two-phase flowequations(which include capillary pressure) to theobserved recovery and pressure data. The procedureis used to determine relative-permeability curves characterized by two parameters and their standarderrors for heterogeneous cores from two Albertacarbonate reservoirs. Introduction Several recent investigations have recognizedpossible problems when obtaining reliable two-phasedisplacement data from heterogeneous carbonate core samples. Huppler stated that waterfloodresults on cores with significant heterogeneitiescan be sensitive to flooding rate, core length, andwettability, and that these effects should beconsidered before applying the laboratory results atfield flooding rates. Brandner and Slotboomsuggested that realistic displacement results maynot be obtainable when vertically flooding aheterogeneous core with a nonwetting phase becauseof the fluid's inability to maintain a properdistribution when the sample length is less than the height of capillary rise. Ehrlich noted thatstandard relative-permeability measurement methodsusing core plugs cannot be applied when the media are heterogeneous. Archer and Wong reported that application of theconventional Johnson- Bossler - Neumann (JBN)methods for determining relative permeabilities froma waterflood test could give erroneous results forheterogeneous carbonate as well as for relativelyhomogeneous porous media having a mixed wettability (see Refs. 1, 6, and 7). The observedstepwise or humped shape of water relativepermeability curves mainly were attributed to theeffect of water breakthrough ahead of the main floodfront entering into the JBN calculation. Archer andWong suggested that such abnormally shapedrelative-permeability curves do not represent theproperties of the bulk of the core sample, and proposed the use of a reservoir simulator forinterpreting laboratory waterflood data. The work referred to above provides the majorbackground for this study involving the developmentof an improved unsteady-state test method tocharacterize the relative-permeability properties ofheterogeneous carbonate core samples. The methodcan be applied to all porous media, regardless ofthe size and distribution of the heterogeneities.However, the presence of large-scaleheterogeneities, especially in the form of vugs, fractures, and stratification, could cause the derivedrelative-permeability relations to be affected by viscosityratio and displacement rate. Remember also that extrapolation of any core test data to a field scaleis associated with many uncertainties, particularlyfor heterogeneous formations. The inclusion ofcapillary pressure effects permits the interpretationof displacement tests at reservoir rates. The proposed calculation procedure extends theapproach suggested by Archer and Wong in thatthe degree of fit between observed laboratory dataand simulator results is quantified. We suggest thatrelative-permeability curves for a variety of rocktypes can be expressed in terms of two adjustable parameters and their standard error estimates.To illustrate the method, the results of displacementtests performed on cores from Swan Hills Beaverhill Lake limestone oil reservoir and Rainbow F KegRiver dolomite oil reservoir are interpreted. SPEJ P. 15^

scholarly journals Steady-State Two-Phase Flow in Porous Media: Laboratory Validation of Flow-Dependent Relative Permeability Scaling

2020 ◽  
Vol 146 ◽  
pp. 03002
Author(s):  
Marios S. Valavanides ◽  
Matthieu Mascle ◽  
Souhail Youssef ◽  
Olga Vizika
Keyword(s):  
Porous Media ◽  
Steady State ◽  
Relative Permeability ◽  
Flow Rate ◽  
Two Phase Flow ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Local Flow

The phenomenology of steady-state two-phase flow in porous media is recorded in SCAL relative permeability diagrams. Conventionally, relative permeabilities are considered to be functions of saturation. Yet, this has been put into challenge by theoretical, numerical and laboratory studies that have revealed a significant dependency on the flow rates. These studies suggest that relative permeability models should include the functional dependence on flow intensities. Just recently a general form of dependence has been inferred, based on extensive simulations with the DeProF model for steady-state two-phase flows in pore networks. The simulations revealed a systematic dependence of the relative permeabilities on the local flow rate intensities that can be described analytically by a universal scaling functional form of the actual independent variables of the process, namely, the capillary number, Ca, and the flow rate ratio, r. In this work, we present the preliminary results of a systematic laboratory study using a high throughput core-flood experimentation setup, whereby SCAL measurements have been taken on a sandstone core across different flow conditions -spanning 6 orders of magnitude on Ca and r. The scope is to provide a preliminary proof-of-concept, to assess the applicability of the model and validate its specificity. The proposed scaling opens new possibilities in improving SCAL protocols and other important applications, e.g. field scale simulators.

scholarly journals Monte Carlo simulation of a two-phase flow in an unsaturated porous media

2012 ◽  
Vol 16 (5) ◽  
pp. 1382-1385 ◽  
Author(s):  
Peng Xu ◽  
Ming-Zhou Yu ◽  
Shu-Xia Qiu ◽  
Bo-Ming Yu
Keyword(s):  
Monte Carlo Simulation ◽  
Porous Media ◽  
Monte Carlo ◽  
Relative Permeability ◽  
Scaling Laws ◽  
Current Model ◽  
Immiscible Fluids ◽  
Unsaturated Porous Media ◽  
Relative Permeabilities ◽  
Two Phase

Relative permeability is a significant transport property which describes the simultaneous flow of immiscible fluids in porous media. A pore-scale physical model is developed for the two-phase immiscible flow in an unsaturated porous media according to the statistically fractal scaling laws of natural porous media, and a predictive calculation of two-phase relative permeability is presented by Monte Carlo simulation. The tortuosity is introduced to characterize the highly irregular and convoluted property of capillary pathways for fluid flow through a porous medium. The computed relative permeabilities are compared with empirical formulas and experimental measurements to validate the current model. The effect of fractal dimensions and saturation on the relative permeabilities is also discussed

Fluid Distributions During Immiscible Displacements in Porous Media

1966 ◽  
Vol 6 (03) ◽  
pp. 261-266 ◽  
Author(s):  
L.L. Handy ◽  
P. Datta
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Steady State ◽  
Relative Permeability ◽  
Capillary Forces ◽  
Unsteady State ◽  
Relative Permeabilities ◽  
Viscous Forces ◽  
Water Imbibition ◽  
Doublet Model

Abstract For a wetting phase displacing a nonwetting phase from a porous medium the distribution of the residual fluid may depend on displacement conditions. Although this subject has been debated in the literature, only a few, experiments have been cited to support the various conclusions. Experimental results presented in this paper show that fluid distributions are dependent on imbibition procedures. Results agree qualitatively with predictions from the pore doublet model. if the rate of water imbibition is restricted, the nonwetting phase is trapped preferentially in the larger pores as expected. But if the rate of water imbibition is unrestricted, trapping occurs somewhat more in the smaller pores. These conclusions were deduced primarily from relative permeability measurements. Introduction Relative permeabilities are known to depend on the saturation history of the porous medium. For either continuously increasing or continuously decreasing wetting phase saturations, however, they have normally been assumed to be single-valued functions of saturation. Several investigators have compared relative permeabilities measured by different method and have reported acceptable agreement. Studies of simple models of the displacement process suggest that the distribution of residual fluids can be influenced by the displacement method. If this is so, relative permeabilities also should depend on the method of displacement. These predictions have not been supported by experimental data. The object of this paper is to investigate experimentally some of the predictions of these model studies. The particular question of importance is whether steady-state and unsteady-state methods should be expected to give the same values of relative permeability. Much of the reported data showing agreement between steady-state and unsteady-state methods have been obtained on unconsolidated sand. Johnson, Bossler and Neumann, however, compared steady-state and unsteady-state results for Weiler sandstone and found no significant difference. Levine made a detailed study of pressure and saturation distributions for a laboratory waterflood in a consolidated system but made no attempt to calculate performance from steady-state relative permeability data. Bail and Marsden in a somewhat similar set of experiments did attempt a comparison of observations with predictions but the results were inconclusive. Excluding gravity, two forces affect the distribution of wetting and nonwetting phases during an unsteady-state, immiscible displacement: viscous and capillary forces. If relative permeabilities are indeed the same when measured by steady- or unsteady-state methods, the fluid distributions at the same fluid saturations must be similar for both methods. Furthermore, the implication is that the relation between capillary and viscous forces is the same for both methods insofar as the effect on microscopic fluid distributions is concerned. Unsteady-state displacements are normally run at high rates to maximize the ratio of the viscous to capillary forces. The objective is to reduce the effect of capillary forces on macroscopic fluid distributions. For floods in which the phase which wets the porous medium displaces the nonwetting phase, capillary forces compete with viscous forces in determining fluid distributions. The residual nonwetting phase is discontinuous. Competitive aspects of viscous and capillary forces and the resulting effect on water-oil distribution in porous media have been illustrated in an elementary way using a pore doublet model. This model and predictions from it have been discussed at considerable length by Rose and Witherspoon, Rose and Cleary and by Moore and Slobod. Rose and Witherspoon show that so long as water invades the model at a rate equal to or greater than the free imbibition rate, the water will move through the larger capillary of a doublet first and trap oil in the smaller capillary. SPEJ P. 261ˆ

Gas-Water Flow Behaviour During Mutual Displacement in Porous Media

2017 ◽  
Vol 10 (1) ◽  
pp. 13-22
Author(s):  
Renyi Cao ◽  
Junjie Xu ◽  
Xiaoping Yang ◽  
Renkai Jiang ◽  
Changchao Chen
Keyword(s):  
Porous Media ◽  
Relative Permeability ◽  
Gas Storage ◽  
Fluid Distribution ◽  
Water Displacement ◽  
Phase Zone ◽  
Two Phase ◽  
Flow Process ◽  
Single Well ◽  
Mutual Displacement

During oilfield development, there exist multi-cycle gas–water mutual displacement processes. This means that a cycling process such as water driving gas–gas driving water–water driving gas is used for the operation of injection and production in a single well (such as foam huff and puff in single well or water-bearing gas storage). In this paper, by using core- and micro-pore scales model, we study the distribution of gas and water and the flow process of gas-water mutual displacement. We find that gas and water are easier to disperse in the porous media and do not flow in continuous gas and water phases. The Jamin effect of the gas or bubble becomes more severe and makes the flow mechanism of multi-cycle gas–water displacement different from the conventional water driving gas or gas driving water processes. Based on experiments of gas–water mutual displacement, the changing mechanism of gas–water displacement is determined. The results indicate that (1) after gas–water mutual displacement, the residual gas saturation of a gas–water coexistence zone becomes larger and the two-phase zone becomes narrower, (2) increasing the number of injection and production cycles causes the relative permeability of gas to increase and relative permeability for water to decrease, (3) it becomes easier for gas to intrude and the invaded water becomes more difficult to drive out and (4) the microcosmic fluid distribution of each stage have a great difference, which caused the two-phase region becomes narrower and effective volume of gas storage becomes narrower.

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 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

Cocurrent Spontaneous Imbibition In Porous Media With the Dynamics of Viscous Coupling and Capillary Backpressure

SPE Journal ◽  
2018 ◽  
Vol 24 (01) ◽  
pp. 158-177 ◽  
Author(s):  
Pål Østebø Andersen ◽  
Yangyang Qiao ◽  
Dag Chun Standnes ◽  
Steinar Evje
Keyword(s):  
Porous Media ◽  
Relative Permeability ◽  
Flow Regimes ◽  
Spontaneous Imbibition ◽  
The Other ◽  
Countercurrent Flow ◽  
Relative Permeabilities ◽  
Viscous Coupling ◽  
Generalized Model ◽  
Matrix Block

Summary This paper presents a numerical study of water displacing oil using combined cocurrent/countercurrent spontaneous imbibition (SI) of water displacing oil from a water-wet matrix block exposed to water on one side and oil on the other. Countercurrent flows can induce a stronger viscous coupling than during cocurrent flows, leading to deceleration of the phases. Even as water displaces oil cocurrently, the saturation gradient in the block induces countercurrent capillary diffusion. The extent of countercurrent flow may dominate the domain of the matrix block near the water-exposed surfaces while cocurrent imbibition may dominate the domain near the oil-exposed surfaces, implying that one unique effective relative permeability curve for each phase does not adequately represent the system. Because relative permeabilities are routinely measured cocurrently, it is an open question whether the imbibition rates in the reservoir (depending on a variety of flow regimes and parameters) will in fact be correctly predicted. We present a generalized model of two-phase flow dependent on momentum equations from mixture theory that can account dynamically for viscous coupling between the phases and the porous media because of fluid/rock interaction (friction) and fluid/fluid interaction (drag). These momentum equations effectively replace and generalize Darcy's law. The model is parameterized using experimental data from the literature. We consider a water-wet matrix block in one dimension that is exposed to oil on one side and water on the other side. This setup favors cocurrent SI. We also account for the fact that oil produced countercurrently into water must overcome the so-called capillary backpressure, which represents a resistance for oil to be produced as droplets. This parameter can thus influence the extent of countercurrent production and hence viscous coupling. This complex mixture of flow regimes implies that it is not straightforward to model the system by a single set of relative permeabilities, but rather relies on a generalized momentum-equation model that couples the two phases. In particular, directly applying cocurrently measured relative permeability curves gives significantly different predictions than the generalized model. It is seen that at high water/oil-mobility ratios, viscous coupling can lower the imbibition rate and shift the production from less countercurrent to more cocurrent compared with conventional modeling. Although the viscous-coupling effects are triggered by countercurrent flow, reducing or eliminating countercurrent production by means of the capillary backpressure does not eliminate the effects of viscous coupling that take place inside the core, which effectively lower the mobility of the system. It was further seen that viscous coupling can increase the remaining oil saturation in standard cocurrent-imbibition setups.

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