Calculation of Relative Permeability from
preparation, characterization, materials
Creation of a dual-porosity micromodel for pore-level visualization of multiphase flowM.Buchgraber,M.Al-Dossary 1,C.M.Ross,A.R.Kovscek ⁎Department of Energy Resources Engineering,Stanford University,Stanford,CA 94305,USAa b s t r a c ta r t i c l e i n f o Article history:Received 22November 2011Accepted 14March 2012Available online 27March 2012Keywords:micromodelflow visualization two-phase flow pore-level carbonateThis paper describes the creation and testing of an etched-silicon micromodel that has the features and char-acteristics of a dual-porosity pore system mimicking those found in certain carbonate reservoir rocks.This micromodel consists of a two-dimensional (2D)pore network etched into a silicon wafer with a bonded glass cover that permits direct visual examination of pore-level displacement mechanisms and pore-network characteristics during fluid flow experiments.The approach began by creating a mosaic of images from a carbonate thin section of a sample with both high porosity and permeability using a scanning electron microscope (SEM)in back-scattered mode (BSE).Connections based on high-pressure mercury injection data were made to ensure that the 2D connectivity in the imaged pore structure was representative of the three dimensional (3D)pore network of the carbonate sample.Microelectronic photolithography techniques were then adapted to create micromodels for subsequent fluid flow experiments.Micromodel surfaces were made oil-or water-wet by various techniques.One of the main advantages of having a representative carbonate dual-porosity micromodel is the ability to observe pore-level mechanisms of multiphase flow and interpret petrophysical properties.Another advantage is that multiple replicates are available with iden-tical conditions for each new experiment.Micromodel utility is demonstrated here through the measurement of porosity,permeability,fluid desaturation patterns,and recovery factors.©2012Elsevier B.V.All rights reserved.1.IntroductionMicroporosity can be a signi ficant porosity type in carbonate reservoirs.Micropores or pores that are 10μm or less in diameter in the Middle Eastern Arab-D reservoir quality rock comprise 25%to as much as 50%of the total porosity (Cantrell and Hagerty,1999).The abundance of microporosity has signi ficant implications for fluid flow properties as well as for the distribution of fluids and sometimes leads to misinterpretation of log response.There is also a strong rela-tionship between pore types,their distribution,and sizes as well as pore throat sizes associated with each given pore type (Ross et al.,1995).Direct pore-level observation of displacement mechanisms improves our understanding of two-phase flow behavior and petrophysical properties that depend strongly on the pore network structure (Oren et al.,1992).This paper reports the creation of a dual-porosity micromodel that simulates typical Arab-D carbonates including microporosity.The task is more dif ficult with carbonate rocks,in comparison to sand-stones.Carbonates tend to show a variety of length scales with some correlation among the pore and throat sizes and pore shapes (Ross et al.,1995).We attempt to understand further the keycomponents of a rock's pore system which impact multiphase flow behavior and,hence,the petrophysical properties.The paper starts with an overview of microporosity types and their signi ficance.Next,the methodology is given for the creation and development of the carbonate micromodel mask and etched-silicon micromodels.A first step is to mosaic and modify SEM BSE micrographs from an epoxy-impregnated thin section.Next,the apparatus and procedures used during the experiment are presented.The petrophysical characterization of the carbonate micromodel follows.A summary completes the paper.2.MicroporosityBefore discussing the geologic features of Arab-D reservoir rocks and our carbonate thin section,a de finition for microporosity is needed as there are multiple de finitions.For example,microporosity in carbonate rocks was de fined by Choquette and Pray (1970)as any pore less than 62.5μm in diameter,whereas Pittman's (1971)de finition has a threshold less than 1μm in size.For the design of our carbonate micromodel,however,we use the de finition of Cantrell and Hagerty (1999)in which micropores are 10μm or less in diameter.The Arab-D Member is part of the Jurassic Arab Formation that consists mainly of skeletal and non-skeletal grainstones and pack-stones sealed with an impermeable anhydrite layer.Producing from the Arab-D interval,Ghawar is the largest oil field in the world atJournal of Petroleum Science and Engineering 86–87(2012)27–38⁎Corresponding author.Tel.:+16507231218;fax:+16507252099.E-mail address:Kovscek@ (A.R.Kovscek).1Currently at SaudiAramco.0920-4105/$–see front matter ©2012Elsevier B.V.All rights reserved.doi:10.1016/j.petrol.2012.03.012Contents lists available at SciVerse ScienceDirectJournal of Petroleum Science and Engineeringj o u r n a l h om e p a g e :ww w.e l s e v i e r.c o m /l o c a t e /p e t r o l1260square miles.It currently produces5million barrels of oil per day(6.25%of global production)and its total estimated reserves are around70billion barrels of oil(US EIA,2011).Microporosity in the Arab-D Member contributes a quarter to half of the total core porosity(Cantrell and Hagerty,1999).This micropo-rosity exists as microporous grains,microporous matrix,microporous fibrous to bladed cements,and microporous equant cements(Cantrell and Hagerty,1999).Microporous grains contribute the“most volumetrically significant microporosity type”in the Arab carbonates (Cantrell and Hagerty,1999).Micropores are observed in most skeletal and non-skeletal grain types.SEM examination reveals that microporosity within grains occurs as pores0.3to3.0μm in diameter and is highly interconnected by uniform-sized straight tubular to laminar pore throats as determined using epoxy pore casts(Cantrell and Hagerty,1999).Given the abundance of intragranular porosity in the Arab-D formation,microporous grains and,to a lesser extent, interparticle micropores are incorporated in the micromodel design.Microporosity has direct and indirect implications onfluidflow properties andfluid distribution.Microporosity is also relevant to wireline log interpretation in that calculations of producible water saturations are sometimes too high.For example,micropores are usuallyfilled with capillary-bound water while macropores arefilled with oil for mixed-wet reservoir rocks.This gives a high water satura-tion response and may lead to a decision of not producing the inter-val,even though most of the water is immobile and only the oil filling the macroporesflows(Petricola and Watfa,1995).According to Chilinger and Yen(1983),80%of carbonate oil reservoirs are oil-wet,while12%are intermediate-wet and8%are water-wet.Furthermore,literature on Arab-D carbonate wettability found that Arab-D rocks exhibit neutral to oil-wet properties(Clerke, 2009).3.MicromodelsA typical micromodel consists of a silicon wafer in which the image of a pore network is etched to a certain depth(say20μm)and bonded to a glass wafer(e.g.,Rangel-German and Kovscek,2006).The concept of developing micromodels has been around for decades,and most early micromodels were etched glass with uniform mesh pore geometry(Mattax and Kyte,1961).Due to the drawbacks of such micromodels including concave shaped pore walls during the etching process,a new technique was developed whereby a photoresist was used to coat the glass,a network pattern was exposed selectively removing the photoresist,and the glass was etched where the photore-sist was removed(Davis and Jones,1968).This technique showed better pore geometry representation(Chambers and Radke,1989).In cross section,however,this technique results in pores that are mainly eye shaped.The pore networks and structures incorporated into a micromodel are typically created in one of two ways:(1)by analyzing thin section images or(2)by process-based analysis.McKellar and Wardlaw (1982)used a photo-imaging technique of thin sections followed by chemical etching of glass to produce micromodels.Thefirst silicon micromodel replicated the pore body and throat sizes of a Berea sand-stone pore network(Hornbrook,et al.,1991).Currently,micromodels are made from silicon wafers and glass plates.The attraction of silicon is that the etching process is more controllable,more precise,and small-scale pore structures can be represented.This results in the ability to etch more complex and multifaceted pore network structures that are more similar to real pore structures found in reservoir rocks.3.1.Mask creationMicromodel fabrication starts by defining a base image that undergoes some digital modification to improve pore network connectivity and allow for seamless overlap of the edges.Once the base image is completed,it is used for mask preparation.The modi-fied base image serves as a unit cell that is repeated or arrayed to fill the pore network portion of the micromodel.The number of repeats used in the array depends upon the size of the base image as well as the desired size of the micromodel.In this case,a three by three matrix was used.The base image for our Arab-D proxy micromodel was collected using a JEOL JSM-5600LV SEM in BSE mode.An epoxy-impregnated thin section was imaged using overlapping views at a magnification of250×(Fig.1).Each SEM image is2048by1600pixels with a pixel size of0.235μm.The resulting composite or mosaicked image has dimensions of10,065by13,407pixels that represent a thin section area of2.4by3.15mm.The resulting image is135megapixels. The pixel size was increased later during the mask preparation due to resolution limitations of the mask makingsystem.Fig.1.Carbonate micromodel base image generated by creating a mosaic of SEM EDS gray scale images,250×.Black represents epoxy-filled pores and white represents rockmatrix.Fig.2.Example views from(a)carbonate micromodel base image and(b)modified bi-nary image.Red circles highlight where areas of incomplete epoxy impregnation were filled and pores isolated in2D were reconnected.Black(or gray)represents epoxy-filled pores and white represents rock matrix.28M.Buchgraber et al./Journal of Petroleum Science and Engineering86–87(2012)27–38Once the mosaic was constructed,it was converted to a binary image.In BSE images,gray-scale values correlate to average atomic number values that provide contrast between mineral and epoxy-filled regions.Thresholding the gray scale values produces a binary image in which black pixels correspond to the epoxy-filled pores whereas the white pixels represent the rock matrix.Further modi fica-tions were performed by hand to correct areas of incomplete epoxy impregnation,reconnect pores isolated in the 2D image,and erase regions obstructed with pore-filling gypsum cements (Fig.2).In regions with incomplete impregnation,the areas are painted black for porosity unless particles intersect the uppermost plane of the thin section.Epoxy-filled pores that are isolated in the 2D base image are reconnected with throat-sizes derived from mercury injection data measured at pressures up to 33,000psi (not shown).The presence of epoxy in the isolated pores indicates that they are connected in 3D.Also,the edges of the base image were modi fied to allow for seamless overlap during the array process and ensure flow conductivity between the arrayed images.After the work of digitizing and modifying the base image was finished and the optimal array pattern had been selected,the mask preparation process continued.The base image was arrayed three times in both vertical and horizontal directions to fill a matrix area of 5by 5.3cm.Channels were added along the entire length of the inlet and production sides of the micromodel.These channels improve flow communication and provide a linear flow boundary condition rather than a point boundary condition.Each channel is connected to two ports that allow fluids to be either injected or pro-duced from the micromodel.The repeated pattern image was then used,essentially,to create a photographic negative picture depicted on a chrome glass mask.Only one mask is needed for producing an endless supply of micromodels.Complications arose due to machine limitations for writing the mask in that the system has a guaranteed minimum write dimension of 1.5μm whereas our smallest size in the base image is 0.235μm.This problem was overcome by converting the pixel size from 0.235μm to 1.5μm thereby retaining the heterogeneity and relativeabcFig.3.(a)Carbonate-based chrome-quartz mask with nine repeated base images,injection and production ports,and communication fractures or channels outlined in red;(b)SEM micrograph of etched silicon wafer at 1000×;(c)Typical flow direction schematic for micromodels.29M.Buchgraber et al./Journal of Petroleum Science and Engineering 86–87(2012)27–38pore size distribution compared to other options such as resampling.The base image will be used in the future when technology allows for the base image to be written such that it preserves its high resolution and matrix size.Fig.3shows the carbonate pore structure mask with the nine repeated base images with four ports (inlet and production)and the two flow-distribution channels as well as a flow direction schematic and an SEM image of the etched-silicon wafer.3.2.Micromodel fabricationMicromodel fabrication occurred at the Stanford Nanofabrication Facility (SNF).It has a clean room equipped with machines and tools used to fabricate micro and nano devices ( ).The fabrication process includes etching,cleaning,and bonding and it is presented schematically in Fig.4.The steps in the fabrication process are the same for each micromodel;only the duration of certain steps is changed depending on the desired etch depth.The imaging process begins by spin coating uniformly the type K-test silicon wafer with a Shipley 3612photoresist layer that is 2μm thick.One quality control action is to make sure that the wafers are dry and no moisture is present before the coating begins.If the wafers are suspected of being wet,they are “cooked ”for 20min at a temperature of 150°C in a singe oven.After the wafers are coated,the mask is placed over the wafer and the assembly is exposed to ultra-violet (UV)light.Then,the excess photoresist is removed and the wafers are ready to be etched.Hydro fluoric acid gasses etch the regions exposed to UV light to the desired depth.The micromo-dels used in this study have etch depths of 5,12,14,18,and 25μm;however,most experiments were completed with a 25μm±2μm depth.A special tool,known as the Zygo White-Light 3D Surface Pro filer,was used to verify the etching depths especially before depth sensitive measurements such as micromodel permeability.The Zygo has the ability to characterize and quantify the surface topographical characteristics.(Fig.5;/Equipment/EquipByName.html )After the wafers are etched,holes for the four ports used for the inlets and outlets are drilled through the wafer.Wafers then undergo an intensive cleaning process to make sure that noremainingabd e fFig.4.Micromodel fabrication process:(a)vapor prime HMDS coating,(b)photoresist coating (1.6μm),(c)contact alignment using themask,(d)developing,(e)etching,and (f)anodic bonding.Fig.5.Zygo pro filometry measurement for quality control:(a)top view and (b)side view.Negative values indicate etched channels.30M.Buchgraber et al./Journal of Petroleum Science and Engineering 86–87(2012)27–38photoresist and precipitated particles are present.To do so,the wafers are cleaned by immersing them in piranha,that is a heated solution consisting of sulphuric acid and hydrogen peroxide(9:1 H2SO4:H2O2),for20min.The last step of the fabrication process is the bonding(Fig.4).At this stage,the silicon wafers are etched and depict a pore network structure,but they are open on the top.A wafer is bonded anodically to a500μm thick,opticallyflat,borosilicate(Pyrex)glass cover plate that has a similar thermal expansion coefficient as the silicon.To achieve this,a silicon wafer is placed on top of a temperature-controlled hot plate at700°F for30min.During heating,the silicon surfaces of the wafer are oxidized.Once heated,the glass plate is placed on the micromodel and a roughly1000V potential is applied to complete the bonding.More details of bonding are discussed else-where(George,1999;George et al.,2005).3.3.Wettability alterationNeinhuis and Barthlott(1997)showed that the hydrophobicity of a solid surface is governed by the chemical composition and micro-structure of the surface.In our attempt to change micromodel wettability from water to oil wet,we tried various techniques.One successful method adapted a process described by Rao et al.(2010) where the micromodel is immersed in a solution that is10%by volume of hexadecyltrimethylammonium bromide(C19H42BrN)in hexane solvent for24h.Heating then occurs at100°C and150°C for1h each.This technique needed somefine tuning to avoid foam formation and accumulation within the micromodel when water is injected and mixes with any residual solution.Foaming tends to plug the smallest pore throats.It was also noticed during testing that the wettability of a micro-model changed as a result of beingflooded with crude oil and aged with no initial water saturation.Presumably crude-oil components, such as asphaltenes and maltenes,adsorb to the solid thereby chang-ing wettability in the absence of an aqueous phase(Kovscek et al., 1993).Wettability alteration persisted from test to test provided that micromodels were not cleaned with toluene or other harsh solvents.In the event of cleaning,retreatment with crude oil reestab-lished oil-wet conditions.For both methods of wettability alteration,the technique used to observe the successfulness of the wettability alteration is visual analysis of the oil and water phase distributions at the pore-level under the microscope.Fig.6shows the micromodel with hydropho-bic surfaces.Water is lightly shaded and is found to be disconnected, trapped,and surrounded by continuous oil phase.These observationsare consistent with a surface that is oil wet(Kovscek et al.,1993). Given the somewhat simpler crude-oil treatment procedure,it was adopted as the method of choice for wettability alteration.4.Experimental apparatus and proceduresThis section provides a general overview of the tools,equipment, and procedures used to conductflow experiments.The experimental set-up typically includes a syringe pump,pressure vessels asfluid containers,and a digital video camera for recording images.A model100D Teledyne ISCO syringe pump was used either for water injection immediately to the micromodel or for pushing water into pressure-transfer vessels to displace thefluids inside the vessels.Only deionized water is ever placed in the pump.Thefluid transfer vessels used are steel piston and cylinders that are attached vertically to a holder for stability.Thefluid supply and production tubes used during the experiments are transparent1/8″Teflon that are attached to the vessels.The microscope is a Nikon Eclipse ME 600.A Sony HDR-CX150camcorder was mounted to the microscope using an adapter.Pictures and video were collected and then ana-lyzed using image analysis tools.4.1.Micromodel holderAll experiments were conducted in a pressure range of0to 130psi.Therefore,a regular low pressure micromodel holder was used.The holder provides a means to inject and producefluids through the ports incorporated in the micromodel.The micromodel holder consists of two aluminum plates.This micromodel holder has fourfluid entry and production ports that align with the ports on the micromodel.To seal properly the micromodel,O-rings are used around thefluid injection and production ports.The two halves of the holder are attached with eight screws.During the experiments,fluids are injected into the micromodel through one of the four ports.Fluidsfirstfill the port volumes as well as the O-ring pool before reaching the micromodel,thereby contributing some dead fluid volume.4.2.ProceduresBefore starting the experiment,both the micromodel and micro-model holder have to be cleaned.If a complete cleaning is needed, the process starts byflushing the micromodel and its holder with abFig.6.Wettability altered micromodel with(a)water bubbles trapped in oil and(b)oil film(circled)that is coating the grains.31M.Buchgraber et al./Journal of Petroleum Science and Engineering86–87(2012)27–38isopropanol (IPA)at a constant pressure drop of 50psi.Then toluene is pumped also at constant pressure drop of 50psi until no signi ficant residual debris are noted.After that,CO 2is injected to get rid of tolu-ene.If after CO 2injection,toluene appears to still occupy some of the micromodel pore space,the micromodel is subjected to vacuum pump and a heat lamp to evaporate any remaining toluene.Water (or crude oil)was injected with a constant pressure drop of 10to 120psi into the micromodel in order to check if liquid completely filled the micromodel pore space.The micromodel is examined under the microscope at multiple locations until it is found to be 100%saturated.One aspect to note is that the water (or oil)injection time is extended for several hours after breakthrough to ensure no CO 2bubbles are present inside the pore space.Back pressure is increased slightly to drive CO 2into solution.Generally,it is found that either fluid (water or oil)is able to saturate fully a micromodel with the above procedure provided that the micromodel is well-etched and the quality control procedures were followed.4.3.Image analysisAll of the pictures collected throughout the experiments were an-alyzed using image analysis to determine the micromodel porosity,saturations,recovery factors,and flow patterns.The image analysis method is required because of dif ficulties associated with performing accurate material balance calculations.For example,the micromodel etched to 25μm with an average porosity of 46%has a pore volume (PV)of about 0.0294mL.Each of the four ports has a volume of about 0.1mL.Most of the volume of the micromodel is occupied by the four ports and the machined O-ring grooves.Any material balance calculation is,accordingly,dif ficult.In the image analysis method,the pore structure is divided into a de fined number of boxes,pictures are taken using the high resolution camera,and analysis is conducted using photostudio software.During our experiments,G.I.M.P.2.6.0,a photo editing software,was used ( )to convert the images to black and white based on a chosen threshold value between 0and 255for the composite color image.A frequency versus intensity plot and a preview image are utilized to de fine the threshold value.After setting the threshold,all pixels having a lower intensity are converted to black pixels and pixels having greater intensity are converted to white pixels.After-wards the histogram of the resulting black and white image is utilized to obtain the phase saturation.The threshold value is adjusted manually and its value is set by means of visual examination.It is important to choose the correct threshold value to get a representative and accurate calculation.Failing to choose a proper threshold value affects the image analysis accuracy.For instance,Fig.7shows a comparison of an original image that was converted to black and white with two different threshold values.The porosity obtained changes correspondingly.The intensity versus frequency graphs show two humps where the left hump represents the high intensity pixels (oil)and the hump on the right side represents the low intensity pixels (water and grains).5.Characterization resultsThe new micromodels were subjected to a variety of petrophysi-cal characterization tests of increasing complexity.Porosity and permeability were examined first.These were followed by tests ex-amining the connectivity and multiphase flow properties of the micromodel.Color IntensityF r e q u e n c yc.)b.)a b cd100 µmFig.7.(a)Black (grains)and white (voids)image in RGB mode;(b)Transformed black and white image with appropriate threshold value of 146and a porosity of 40.5%;(c)Trans-formed black and white image with inappropriate threshold of 153and a porosity of 38%;(d)Color intensity histogram of RGB picture with different threshold values of 146(b)and 153(c).32M.Buchgraber et al./Journal of Petroleum Science and Engineering 86–87(2012)27–385.1.PorosityThe base image and the etched silicon wafer both have essential-ly an equal porosity of 45.5%,where pore structures equal to and smaller than 21μm comprise about 25%of the total pore volume.As part of quality control procedures,micromodel porosities were measured to make sure that they exhibit good correlation with the mask ually,micromodel porosity values determined by image analysis differ from mask porosity values.This discrepancy occurs because of the shadowing effects of the grains (Buchgraber et al.,2011).The shadowing effect tends to increase the number of the black pixels that then changes the porosity obtained.In order to remove the shadow effect,the carbonate micromodel was fully saturated with crude oil,the micromodel was illuminated with UV light,and pictures were taken for nine different positions inside one of the repeated patterns.The crude oil fluoresces under UV light providing excellent illumination and negates the shadowing effects observed under plain light.Eight pictures were taken and analyzed.The corresponding porosities averaged to 46%.As a result of being a dual-porosity carbonate micromodel,some areas exhibit very low porosity of 11%compared to some areas that exhibit high porosity values up to 74%(Fig.8).This is a clear indication of dual porosity.5.2.PermeabilityOne of the most important petrophysical properties to be determined for the carbonate micromodel is permeability.Several experiments were conducted to determine the micromodel perme-ability for different etching depths (4,12,14,18,and 25μm).Thepermeability was interpreted using single-phase Darcy's law for in-compressible (Eq.(1))and compressible (Eq.(2))flows,respectively:k ¼q μL A p 1−p 2ðÞð1Þk ¼2q μLp b A p 21−p 22ÀÁ:ð2ÞThe experiments conducted to determine the permeability were done by one or two of the following approaches:(1)The micromodel was flooded with distilled water at constantpressure and the corresponding flow rates measured;or,steady-state flow rates were imposed and corresponding pressure drop.(2)The micromodel was flooded with CO 2gas at various injectionpressures and the corresponding flow rates measured via a bubble flow meter.(3)The permeability value of each etching depth was averagedand plotted as shown in Fig.9.The standard deviation of each measurement is about 35mD.5.3.Tracer testA tracer test with water and water containing a UV-sensitive dye was performed in order to evaluate the main transport channels and check for complete access of injected fluid to all pore spaces.The model was first 100%saturated with distilled water and after-wards flooded with UV dyed water.As expected in a dual-porosity system,the larger interconnected pores that contribute most to the100 µm10 µm100 µmabFig.8.Carbonate micromodel black (grains)and white (voids)images for two different regions that exhibit a wide range of porosity values,(a)regions of intragranular micropo-rosity exist with 12%porosity,and (b)very porous areas with 74%porosity.33M.Buchgraber et al./Journal of Petroleum Science and Engineering 86–87(2012)27–38。
基于动态数据反演的相渗曲线及应用效果
基于动态数据反演的相渗曲线及应用效果崔传智; 郑文乾; 李立峰; 冯绪波; 吴忠维【期刊名称】《《石油钻采工艺》》【年(卷),期】2019(041)004【总页数】5页(P516-520)【关键词】动态数据反演; 相对渗透率曲线; 数值模拟; 剩余油【作者】崔传智; 郑文乾; 李立峰; 冯绪波; 吴忠维【作者单位】中国石油大学 (华东) 石油工程学院; 中国石化江苏油田分公司采油一厂【正文语种】中文【中图分类】TE3410 引言油藏数值模拟研究中，通常采用基于岩心驱替测得的相对渗透率曲线进行计算，由于岩心所代表的储层物性受局限［1-3］，且油藏物性在高含水期会发生变化，所以基于原始岩心驱替实验获得的相对渗透率不能完全表征实际的油水流动能力［4-7］。
在注水开发过程中，油藏储层物性、开发方式等动态变化都会综合反映在生产数据中，因此基于油藏动态数据反演的相对渗透率曲线能真实反映实际的油水流动能力。
国内学者深入研究了水驱特征曲线和相对渗透率的关系：蒋明等［8］利用乙型水驱特征曲线推导出用于计算不同时刻含水饱和度和油水相对渗透率比值的关系式，再结合相对渗透率的指数关系式求解相渗曲线；阎静华等［9］依据甲型水驱特征曲线直线段出现后的数据计算出系数值，再根据相对渗透率的指数函数计算出相对渗透率曲线；杨宇等［10］采用适用范围很广的张金庆水驱特征曲线对相对渗透率曲线进行了理论推导；王继强等［11］应用二项式函数拟合特高含水期油水相对渗透率的比值与含水饱和度在半对数坐标上的关系，推导出了适用于特高含水期渗透率的计算方法。
以上成果对于研究油水流动能力具有指导意义，但也存在一些不足，先计算不同含水饱和度对应的油水相对渗透率比值，再根据相对渗透率的指数关系式求解相渗曲线，需要进行多次回归，并且在求不同含水饱和度对应的油水相对渗透率比值时需要基于一些经验公式，导致公式的求解结果受人为因素影响，且这些公式未考虑油藏物性的变化。
基于水驱曲线计算相对渗透率曲线的新方法
基于水驱曲线计算相对渗透率曲线的新方法唐林;郭肖;苗彦平;刘玉奎;陈晨【摘要】In order to calculate the reservoir relative permeability curves accurately and simply, according to the water flooding rules of water drive oilfields, based on the previous studies and starting from Yu’s water drive curve, a new calculation method of relative permeability curve is established. By examples, its calculation results are compared with the measured values. The study results show that the oil/water relative permeability is similar to the measured value when the water saturation is medium-low. The oil phase relative permeability is smaller and the aqueous phase relative permeability is larger than the measured value when water saturation is high. It is indicated that the calculation results of the proposed method is accurate and reliable, and can truly reflect the relative reservoir permeability characteristics by comparison of corrected relative permeability curves with the water cut increasing rules of the actual oilfield production.% 为了准确、简便地计算油藏的相对渗透率曲线，根据水驱油田的水驱规律特征，在前人研究的基础上，从俞启泰水驱曲线出发，提出了计算相对渗透率曲线的新方法，并通过实例将该方法的计算结果与实测值作了对比。
渗吸剂体系基本性能对采收率的影响分析
渗吸剂体系基本性能对采收率的影响分析江敏;范洪富;张翼;吴英【摘要】针对渗吸剂体系的基本性能对渗吸采收率影响研究的局限性,通过室内实验,在对渗吸剂体系的油水界面张力、接触角、乳化综合指数、黏度和pH值等测试的基础上,将多因素方差分析和多元线性回归分析方法引入到影响分析中,通过数理统计分析方法,明确影响采收率的关键性能指标及其权重.研究表明,渗吸剂体系降低油水界面张力的能力、对原油乳化的能力和改变岩石润湿性的能力是对采收率影响最重要的因素.该研究可为渗吸剂的筛选和评价提供一定的理论指导.【期刊名称】《特种油气藏》【年(卷),期】2019(026)003【总页数】5页(P138-142)【关键词】渗吸剂;性能;权重;影响因素分析【作者】江敏;范洪富;张翼;吴英【作者单位】大连理工大学北京研究院博士后工作站,北京 100044;中国地质大学(北京),北京 100083;中国石油勘探开发研究院,北京 100083;中海油田服务股份有限公司,天津 300459【正文语种】中文【中图分类】TE357.40 引言低渗透裂缝性油藏利用渗吸机理进行采油的过程中，影响渗吸采收率的因素非常多[1-9]，这些因素互相影响互相制约，形成一种复杂多变的关系。
关于渗吸剂体系的基本性能对采收率的影响，前人已进行了大量的相关研究工作[10-21]，但均局限于对单一影响因素的讨论和分析，对各种影响因素的权重还缺乏定量研究。
目前，在对渗吸剂的筛选和评价中，一般对表征其基本性能的几种指标进行测试，主要包括油水界面张力、油水接触角、渗吸剂体系对目标油藏原油的乳化性能、渗吸剂体系的黏度以及渗吸剂体系的pH值等。
这些指标与渗吸采收率之间的关联性以及在选择渗吸剂时应重点考虑渗吸剂的哪些基本性能，目前还没有统一的筛选和评价标准。
因此，在大量描述渗吸剂基本性能实验数据的基础上，利用SPSS数据分析，将多因素方差分析和多元线性回归分析方法引入到低渗透油藏渗吸剂体系的性能指标对采收率的影响分析中，对各性能参数影响采收率的次序及权重进行了深入讨论和分析。
相对渗透率RelativePermeability-ppt
Corey’s model
Stone I and II models
Stone I • Scaling technique • Input two sets of relative perm data Krow, krw = f(Sw) Krog, krg = f(Sg) • And Sor for three-phase system • Find kro = f(Sw,Sg) Stone II • Probabilistic model • Does not require Sor • Find kro = f(Sw, Sg)
Relative Permeability
Applications of relative permeability data:
• to model a particular process, for example, fractional flow, fluid distributions, recovery and predictions
Relative Permeability
Definitions Absolute permeability – ability of the porous media to transmit fluids Effective permeability – permeability of a given phase when more than one phase is present Relative permeability is the ratio of the effective permeability for a particular fluid to a reference or base permeability of the rock.
气井见水后产能评价研究进展
第25卷第1期断块油气田FAULT-BLOCK OIL &GAS FIELD2018年1月doi: 10.6056/dkyqt201801013气井见水后产能评价研究进展张睿&，孙兵&，秦凌嵩2,杨小松&，顾少华&，王妍妍1(1.中国石化石油勘探开发研究院，北京100083;2.中国石化中原油田分公司勘探开发研究院，河南郑州450000)基金项目：国家科技重大专项课题“超深层复杂生物礁底水气藏高效开发技术”（2016Z X05017-005);中国石油化工股份有限公司科技攻关项目“礁滩相气藏精细建模及控水稳产对策研究"（P15050)摘要气藏开发中后期，气井见水后的气液两相流动降低了近井地带气相相对渗透率，对气井产能影响显著。
通过对国内外见水气井产能评价的相关研究进行调研，总结并分析了几种主要的产水气井产能评价方法的优势及存在的不足，并对未来研究产水气井产能的关键问题及攻关方向提出了建议。
结果表明：采用液相伤害的复合模型和引入气水两相拟压力和水气比的二项式产能方程是目前常用的见水气井产能评价方法。
含水饱和度的变化对气水相渗及近井非达西流影响较大，增加了含水气井产能预测的难度。
井筒积液及气液两相管流对产能影响较大，但考虑井筒气藏耦合的产能模型研究较少。
水侵量计算、气水相渗实验和计算以及井筒气藏耦合模型的研究应成为见水气井产能研究的重点。
关键词气水两相；产能；拟压力；相渗；数值模拟中图分类号：文献标志码：AAdvances in productivity evaluation of water producing gas wellsZ H A N G Rui1, SUN Bing1, Q IN Lingsong2, Y A N G Xiaosong1, G U Shaohua1, W A N G Yanyan1 (l.Petro1eum Exploration and Production Research Institute, SINOPEC, Beijing 100083, China; 2.Research Institute o f Exploration and Development, Zhongyuan Oilfield Company, SINOPEC, Zhengzhou 450000, China) Abstract：In the middle and late stage of gas reservoir development, the gas liquid two-phase flow can reduce the gas relative permeability in the near wellbore, and has a significant effect on gas well productivity. This paper investigates the related research progress of the gas well deliverability evaluation, analyzes the main advantages and disadvantages of various deliverability evaluation methods, and gives suggestions for future research and key issues of water production gas wells. The research results show that the composite liquid damage model, two-phase pseudo pressure and water gas ratio were commonly considered in the binomial deliverability equation. The change of water saturation has a great influence on gas relative permeability and non Darcy flow in the near wellbore. Liquid loading and gas liquid two phase flow have great influences on productivity, but the productivity model coupling wellbore and reservoir is less. The calculation of aquifer influx, gas relative permeability and coupling of wellbore gas reservoir model should be focused on in the future research.Key words：two-phase flow; gas well deliverability; pseudo pressure; relative permeability; numerical simulation0引言对边、底水气藏而言，在气田开发的中后期普遍存 在见水现象。
遗传学名词解释F
FF+ cell -- A bacterial cell having a fertility (F) factor. Acts as a donor in bacterial conjugation.F- cell -- A bacterial cell that does not contain a fertility (F) factor. Acts as a recipient in bacterial conjugation.F factor -- An episome in bacterial cells that confers the ability to act as a donor in conjugation.F' factor -- A fertility (F) factor that contains a portion of the bacterial chromosome.F1 generation -- First filial generation; the progeny resulting from the first cross in a series.F2 generation -- Second filial generation; the progeny resulting from a cross of the F1 generation.F pilus -- See pilus.facultative heterochromatin -- A chromosome or chromosome region that becomes heterochromatic only under certain conditions, e.g., the mammalian X chromosome.familial trait -- A trait transmitted through and expressed by members of a family.fate map -- A diagram or "map" of an embryo showing the location of cells whose development fate is known.fertility (F) factor -- See F factor.filial generations -- See F1 and F2 generations.fingerprint -- The pattern of ridges and whorls on the tip of a finger. The pattern obtained by enzymatically cleaving a protein or nucleic acid and subjecting the digest to two-dimensional chromatography or electrophoresis.FISH -- See fluorescence in situ hybridization.Back to topfitness -- A measure of the relative survival and reproductive success of a given individual or genotype.fixation -- In population genetics, a condition in which all members of a population are homozygous for a given allele.fluctuation test -- A statistical test developed by Salvadore Luria and Max Delbrück to determine whether bacterial mutations arise spontaneously or are produced inresponse to selective agents.fluorescence in situ hybridization (FISH) -- A method of in situ hybridization thatutilizes probes labeled with a fluorescent tag, causing the site of hybridization tofluoresce when viewed in ultraviolet light under a microscope.flush-crash cycle -- A period of rapid population growth followed by a drasticreduction in population size.fmet -- See formylmethionine.folded-fiber model -- A model of eukaryotic chromosome organization in whicheach sister chromatid consists of a single fiber, composed of double-stranded DNAand protein, which is wound up like a tightly coiled skein of yarn.footprinting -- A technique for identifying a DNA sequence that binds to a particular protein, based on the idea that the phosphodiester bonds in the region covered by the protein are protected from digestion by deoxyribonucleases.formylmethionine (fmet) -- A molecule derived from the amino acid methionine byattachment of a formyl group to its terminal amino group. This is the first amino acidinserted in all bacterial polypeptides. Also known as N - formyl methionine.founder effect -- A form of genetic drift. The establishment of a population by asmall number of individuals whose genotypes carry only a fraction of the differentkinds of alleles in the parental population.fragile site -- A heritable gap or nonstaining region of a chromosome that can beinduced to generate chromosome breaks.fragile X syndrome -- A genetic disorder caused by the expansion of a CGGtrinucleotide repeat and a fragile site at Xq27.3, within the FMR-1 gene.frameshift mutation -- A mutational event leading to the insertion of one or morebase pairs in a gene, shifting the codon reading frame in all codons following themutational site.fraternal twins -- See dizygotic twins.F—cell F—细胞：E．coli K菌株中无F因子的细胞。
地热与渗流
(Li and Horne, 2006)
Brooks-Corey Model to calculate krnw:
2 * * krnw (1 S w ) 2[1 (S w ) ]
Calculation of Capillary Pressure
Core Core
Cold Trap Water Scale Dry Ice Vacuum
Pcsw and Pcaw at 98oC
25 20 Air-Water Steam-Water
Pc (cm H2o)
15 10 5 0 0 20 40 60 80 100
Water Saturation (%)
Li (2007) derived the relationship:
k rw 1 S I
* w
where:
* Sw
S w S wr 1 S wr
Rt I S w n R0
Calculation of Relative Permeability
Purcell Model to calculate krw:
Conclusions
Gas slippage affects N2 and steam krg significantly; neglecting the gas slip effect in gas-liquid flow will overestimate krg. The gas slip factor increases with Sw but is almost constant at Sw below about 18%. Gas slip effect is not only an experimental consideration but may also be of consequence in reservoir engineering in many cases.
利用相渗曲线研究低渗气藏水锁效应的新方法_吕渐江
4 贺承祖 , 华明琪 .水锁 效应 研究 [ J] .钻井 液与 完井液 , 1996, 13(6):16 -15.
5 朱国华等 .砂岩气藏 水锁 效应实 验研 究 [ J] .天然气 勘 探与开发 , 2003, 26(1):29 -36.
· 49·
开 发 试 采 天 然 气 勘 探 与 开 发 2008年 9月出版
ΔWi— 驱替压水增量 , cm3 ; Δt— 驱替压时间增量 , s;
A— 驱替压岩心截面积 , cm2;
Kt— 驱替压干岩心 在相 同围 压 、驱 替压 差下 的 气测 绝 对渗透率值 , mD。
=WW32
-W1 -W1
×100%
Krg =AKtΔ2PμΔgLt(PP2 Δ1 G+iP2 ) Krw =AμKwtLΔΔPWΔit
式中 :
Sw— 岩心含 水饱和度 , %; W , W — 岩心饱和 地层水前 、后的重量 , g;
12
W3 — 相渗实验中某一时刻 的岩心重量 , g; Krg— 气相相对渗透率 , 小数 ; Krw— 水相相对渗透率 , 小数 ; μg— 氮气粘度 , mPa· s; μw — 地层水粘度 , mPa· s; L— 岩心长度 , cm;
本文利用低渗气藏的真实岩心 , 通过开展气水 两相渗流实验 , 模拟了气井生产时含水饱和度下降 至束缚水饱和度的 过程 , 总结出一 些规律性 的认 识 , 以期能对低渗气藏的有效开发有所启示 。
1 气水两相渗流实验
1.1 实验装置及实验步骤 本次气水相对渗透率测试实验采用如图 1 所
示的装置 , 实验步骤如下 : ①岩心抽真空饱和模拟地层水 , 并在饱和液中
磁导率的英文
磁导率的英文一、“磁导率”的英文“磁导率”：permeability或magnetic permeability。
二、英语释义1. The measure of the ability of a material to support the formation of a magnetic field within itself.（一种材料支持其内部磁场形成能力的度量。
）三、短语1. relative permeability（相对磁导率）2. magnetic permeability of free space（真空磁导率）3.plex permeability（复磁导率）四、单词1. permeate（动词，渗透；弥漫；扩散。
与磁导率相关是因为磁导率体现了磁通量在材料中的渗透情况）- The magnetic field can permeate the ferromagnetic material easily.（磁场能轻易地渗透铁磁材料。
）2. magnetic（形容词，磁的；有磁性的）- magnetic field（磁场）五、用法1. 作主语- The permeability of this material is very high.（这种材料的磁导率非常高。
）2. 作介词宾语- Scientists are studying the change of permeability in different environments.（科学家正在研究不同环境下磁导率的变化。
）3. 与形容词搭配使用- The relative permeability of the alloy is an important parameter.（这种合金的相对磁导率是一个重要参数。
）六、双语例句1. The magnetic permeability of iron is much higher than that of air.（铁的磁导率比空气的磁导率高得多。
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EXPERIMENTAL VERIFICATION O F T H E METHOD I n one application of the new method water and oil relative permeabilities were calculated from flooding data obtained on a glass-bead packing. Three floods were run o n the glass-bead system at oil-water viscosity ratios of 1: 1, 5: 1 and 37: 1. Because flooding behavior is dependent on viscosity ratio the calculated relative permeability curves cover a different range in saturation for each of the floods. The results of these calculations are presented in Fig. 1. It can be seen that the three segments of the relative permeability curves are in close agreement. This indicates that the new calA
A B S T R A C T
A method is presented for calculating individual gas and oil or water and oil relative permeabilities f r o m data obtained during a gas drive or a waterflood experiment performed o n a linear porous body. T h e method lrm been tested and found both rapid and reliable for normal-sized core samples.
foil
= -
. . . . . . . . (4)
ห้องสมุดไป่ตู้
K k r , Sp
- ,
-
. . . . . . . .
(5)
The cited relationships provide the means for calculating individual relative permeabilities. Specifically, for any instant in the displacement, i.e., for any value of cumulative injection Wi, the derivative in Eq. 8a can be evaluated from data collected during the experiment. For a given value of W, the fraction of oil in the effluent, f., can be evaluated separately by Eq. 3. The k,,, which is then obtained by dividing f. by the derivative from the left-hand side of Eq. 8a, is the relative permeability to oil at the outlet face saturation, S:. The S , for the Wi under consideration is obtained by rearranging Eq. 4: The expression for the relative permeability of the displacing phase at S , is obtained by solving Eq. 2 for k,,.
INTRODUCTION Individual oil and gas or oil and water relative permeabilities are required for a number of reservoir engineering applications. Chief among these is the evaluation of oil displacement under conditions where gravitational effects are significant, such as a water drive or crestal gas injection in a steeply dipping oil reservoir. Numerous proposed methods of obtaining relative permeability data on reservoir core samples have been too tedious and time consuming for practical use, o r have yielded questionable and sometimes inconsistent results. A method has been developed by which the individual relative permeability curves can be calculated from data collected during a displacement test. The method is based on sound theoretical considerations. Using this method, with a properly designed experimental procedure, relative permeability curves can be obtained using core samples of normal size (i.e., 2 to 3 in. in length and 1 to 2 in. in diameter) within a few days after receipt of the core. In a recent publication D. A. Efros' describes an approach to the calculation of individual relative permeabilities that is based on the same theoretical considerations. We believe the approach described in the present paper is more adaptable to practical application than the method implied by Efros. In addition, comparisons with independently determined relative permeabilities are furnished to substantiate the reliability of the new method.
PETROLEUM TRANSACTIONS, A l M E
cross sect~ons requires that the phases behave as immiscible incompressible fluids. When one of the phases is gas. essentially incompressible behavior can be obtaincd by maintaining a pressure level high enough that the expansion of the gas accompanying the pressure drop across thc system can be neglected. Some of the relations presented previously by Welge are needed for the calculation of individual relative permeabilities. These are given as follows.
Calculation of Relative Permeability from Displacement Experiments
E. F. JOHNSON D'
I
JERSEY PRODUCTION RESEARCH C(1.
JUNIOR MEMBER AlME V. 0.NAUMANN MEMBER AlME
A A INDEPENDENTLY
DETERMINE0
=
0
$
>
FROM R O O D AT
I
1
e0
C
2
a
W W
m
6 0
I
4 0
6
W
20
0 20 40 WATER SATURATION-%
80 60 PORE VOLUME
100
FLOOD
FIG. 1-WATER-OIL RELATIVE PERMEABILITIES FROM WATERSUSCEPTIBILITY TEST DATA. DRI-FILMED GLASS SPHERES, LINEAR CELL PERMEABILITY = 11.5 DARCIES.