Calculation of Relative Permeability from

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。

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。

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。

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。

Professor Lee Barbour•The modeling of unsaturated flow through soils is the most commonly used application of unsaturated soil mechanics.•Emphasis upon the environmental and geo-environmental engineering areas, in addition to classical soil mechanics problems, has resulted in the development of severalcomprehensive software computer codes.•This chapter deals with the flow of the fluid phases (i.e., air and water) through an unsaturated soil.•The analysis of fluid flow through an unsaturated soil requires the definition of the driving potential and a flow law associated to each fluid phase.•The diffusion of air through water is also discussed as a phenomenon associated to unsaturated soils.Additional notes:•The analysis of fluid flow requires a law to relate the flow rate to the driving potential through the use of appropriate coefficients.•Air in an unsaturated soil can occur either in an occluded form or a continuous form depending upon the degree of saturation of the soil.•A knowledge of the driving potentials that causes air and water to flow through an unsaturated soil is necessary for solving geotechnical engineering problems.•The movement of air through the water phase is referred to as air diffusion and its driving potential needs to be defined.•Water flow is caused by a hydraulic head gradient, where the hydraulic head consists of an elevation head plus a pressure head.•The flow of air in the continuous phase form is governed by a concentration or pressure gradient. The elevation gradient has a negligible effect.Additional notes:•What is the driving potential for the flow of water through an unsaturated soil?•Several concepts, such as water content gradient, pressure head gradient, soil suction gradients, and hydraulic head gradient have been used to explain the flow of water through an unsaturated soil.•The above figure illustrates some hypothetical cases which demonstrate that matric suction gradient is not the driving potential that causes water to flow through an unsaturated soil.•Case 1 illustrates that water can flow through an unsaturated soil from a region of low matric suction to another region at a relatively high matric suction.•Case 2 illustrates that the flow of water through an unsaturated soil can occur between regions with equal matric suctions.•Case 3 illustrates that water can flow through an unsaturated soil even when the left-hand side (i.e., departing region) is at a matric suction higher than the right-hand side (i.e., target region).•Water flow can be defined most appropriately in terms of a hydraulic head gradient. •The special case where the air pressure is zero, which is the common situation in nature, the matric suction gradient is numerically equal to the pressure gradient in the water.•The elevation head can be omitted then the matric suction gradient is equal to the hydraulic head gradient and all points in the soil mass are at the same elevation (i.e., horizontal flow).Additional notes:No suctiongradient•A point (e.g., an elemental volume) in the water phase has three primary components of energy; namely, gravitational, pressure, and velocity.•Point A has a gravitational potential energy, Eg , which is a function of the water element mass and the distance, y , relative to a datum.•When the water density, ρw , is constant, the pressure energy can be expressed as a function of the pore-water pressure, the water volume, and the water density at point A .•The flow rate of water at point A gives rise to a velocity energy that can be expressed as a function of the mass of water and the velocity of water at point A .•The total energy (i.e., mechanical energy) at point A is the summation of thegravitational, pressure, and velocity components.•Potential or hydraulic head is defined as energy per unit of weight. Therefore, the hydraulic head consists of three components; namely, the gravitational head, the pressure head and the velocity head.•The velocity head in a soil is commonly negligible in comparison to the gravitational and the pressure heads.Additional notes:•The heads used in the definition of hydraulic potential have the dimensions of length. •Hydraulic head is a measurable quantity, the gradient of which causes flow in saturated and unsaturated soils.•Piezometers and tensiometers can be used to measure the in situ pore-water pressure at any point in a soil mass.•A piezometer can be used to measure positive pore-water pressures at a point in a soil mass.•A tensiometer can be used to measure negative pore-water pressures at a point in a soil mass.•In the above figure, point A has a higher total head than point B [i.e., hw (A) > h w (B)] and therefore water will flow from point A to point B due to the hydraulic head gradient.•The driving potential causing flow in the water phase through a soil mass has the same form for both saturated (i.e., point B ) and unsaturated (i.e., point A ) soils (Freeze & Cherry, 1979).Additional notes:•Darcy’s law describes the flow of water through an unsaturated soil. However, the coefficient of permeability in an unsaturated soil need not be a constant.•The coefficient of permeability in an unsaturated soil is a variable that is predominantly a function of the water content or the matric suction in the unsaturated soil.•Water can be visualized as flowing only through the pore space filled with water. The air filled pore spaces are nonconductive channels to the flow of water.•To verify Darcy’s law for unsaturated soils, experiments were conducted using acolumn of unsaturated soil, with a uniform water content and a constant water pressure head subjected to various gradients of gravitational heads.•The results indicated that at a specific water content, the coefficient of permeability, k w , is constant for various hydraulic head gradients applied to the unsaturated soil.•The rate of water flow through an unsaturated soil is linearly proportional to the hydraulic head gradient, with the coefficient of permeability being a constant, similar to the situation for a saturated soil.•Therefore, Darcy’s law can also be applied to unsaturated soils.However, themagnitude of the coefficient of permeability is a function of volumetric water content, θw .Additional notes:•The coefficient of permeability depends upon the properties of the fluid and the properties of the porous medium. Different types of fluids (e.g., water and oil) ordifferent types of soil (e.g., sand and clay) produce different values for the coefficient of permeability, k w .•The intrinsic permeability of a soil, K , represents the characteristics of the porous medium and is independent of the fluid properties.•In geotechnical engineering, the term coefficient of permeability, kw , is a commonly used term.•In an unsaturated soil, the coefficient of permeability, k w , is affected by changes in void ratio and more significantly by the degree of saturation (or water content).•As a soil becomes unsaturated, air first replaces some of the water in the large pores, and this causes water to flow through the smaller pores, with an increased tortuosity to the flow path.•Additional increases in matric suction leads to further decreases in the the pore volume occupied by water, and the air-water interface is drawn closer and closer to the soil particles.•As a result, the coefficient of permeability with respect to the water phase decreases rapidly as the space available for water flow reduces.Additional notes:•Change in void ratio in an unsaturated soil may be small. However, the effect of a change in degree of saturation may be highly significant.•As a result, the coefficient of permeability is often described as a singular function of the degree of saturation, S,or the volumetric water content, θw.•A change in matric suction can produce a more significant change in the degree of saturation than can be produced by a change in net normal stress.•Degree of saturation has been commonly described as a function of matric suction. •Numerous semi-empirical equations for the coefficient of permeability have been derived using the matric suction versus versus degree of saturation curve.•In these equations, the pore-size distribution forms the basis for predicting the coefficient of permeability.•The residual degree of saturation,Sr , is defined as the degree of saturation at whichan increase in matric suction does not produce a significant change in the degree of saturation.Additional notes:•The matric suction versus degree of saturation curve exhibits hysteresis and thedrainage curve is most commonly used. In addition, the soil structure is assumed to be incompressible.•The air entry value of the soil, (u a -u w )b , residual degree of saturation, S r , and the pore size distribution index, λ, are three parameters commonly used when deriving equations for predicting the coefficient of permeability, k w .•Using the concept of effective degree of saturation, S e , the above figure illustrates a procedure for determining the air entry value, the residual degree of saturation, and the pore size distribution index.•The effective degree of saturation can be computed by first estimating the residual degree of saturation.•Plotting the effective degree of saturation versus matric suction and adjusting a horizontal and a sloping line to the calculated data permit the use of a new assumed residual degree of saturation.•The procedure is repeated until all points on the sloping line constitute a straight line. The pore size distribution index, λ,is defined as the negative slope of the effective degree of saturation, S e , versus the matric suction, (u a -u w ), curve.•The intersection point between the straight sloping line and the saturation ordinate (i.e., S e = 1.0) defines the air entry value of the soil.Additional notes:•The above figure shows an equation for effective degree of saturation as a function of the matric suction for values of matric suction greater than the air entry value of the soil.•The figure also illustrates typical matric suction versus degree of saturation curves for various soils.Additional notes:•The above figure illustrates typical λvalues for various soils that have been obtained from matric suction versus degree of saturation curves.•Soils with a wide range of pore sizes have a small value for λ. The more uniform the distribution of pore sizes in a soil, the larger the value for λ.Additional notes:•Brooks and Corey (1964) proposed an equation for the coefficient of permeability, k w , by using the matric suction versus the degree of saturation curve and the concepts of effective degree of saturation and pore-size distribution index , λ.•The coefficient of permeability, kw , for a sandstone is expressed in terms of the relative permeability as compared to the coefficient of permeability of the soil at saturated conditions, k s .•The figure also presents the air permeability of the soil to illustrate its decreasing value as the soil approaches a degree of saturation equal to 100%.Additional notes:•The above table presents several empirical constant, δvalues (i.e., Brooks and Corey, 1964 parameter) and their corresponding pore size distribution indices,λ, for various soil types.(Note that δ= (2+3λ) / λ)•The above values can be used in practice as a first estimation for different soils.Additional notes:•The above figure presents the equation proposed by Gardner (1958) for predicting the coefficient of permeability for an unsaturated soil as function of matric suction.•The equation provides as flexible permeability function that is defined by two constants (a and n ) where “a”is related to the breaking point (i.e., air entry value) and “n ” is defined by the slope of the function.•Four typical functions, with differing values of “a”and “n”illustrates the forms produced by Gardner’s (1958) equation.Additional notes:Gardner’s equation(1958)•The above table summarizes several of the proposed relationships between the coefficient of permeability and matric suction.•The equations illustrate the relationship between coefficient of permeability and matric suction by using soil constants that can be evaluated from the matric suction versus degree of saturation curves.Additional notes:•A coefficient of permeability function, k w (θw ), was proposed using the configurations of the pore space filled with water (Childs and Collis-George, 1950).•The soil-water characteristic curve can also be presented in terms of volumetric water content, θw , versus the matric suction. Therefore, k w can also be expressed directly as a function of matric suction.•The permeability function, k w (θw ), is derived based on Poiseuille’s equation.•The above permeability function has a similar form to the function presented by Kunze et al., (1968) and is slightly modified to use SI units and matric suction is used in the equation instead of pore-water pressure head.•The calculation of the permeability function, k w (θw ),at a specific volumetric water content involves the summation of the matric suction values that correspond to the volumetric water content at and below the value under consideration, (θw )i .Additional notes:Childs andCollis-George(1950)•The calculation of the permeability function, k w (θw ),at a specific volumetric water content involves the summation of the matric suction values that correspond to the volumetric water content at and below the water content under consideration, (θw )i .•A matching factor, (k s /k sc ), based on the saturated coefficient of permeability is necessary in order to provide a more accurate representation of the unsaturated permeability function.•The shape of the permeability function is determined by the terms inside thesummation sign portion of the equation as obtained from the soil-water characteristic curve.•The magnitude of the permeability function needs to be adjusted with reference to the measured saturated coefficient of permeability, k s , by using the matching factor.•If the saturated coefficient of permeability is measured, the permeability function can be predicted directly from the soil-water characteristic curve because all of the terms in front of the summation sign in the equation can be considered as an adjusting factor.•Therefore, the permeability function, k w (θw ), can be written as shown at the bottom of the slide.Additional notes:Childs andCollis-George(1950)•The soil-water characteristic curve can be visualized as an indication of theconfiguration of water-filled pores in the soil mass.•The coefficient of permeability is obtained by dividing the soil-water characteristic curve into “m” equal intervals along the volumetric water content axis.•The matric suction corresponding to the midpoint of each interval is used to calculate the coefficient of permeability.•This computational procedure for obtaining the permeability function appears to be most successful for sandy soils having a narrow pore size distribution (Nielsen et al., 1972).•The soil-water characteristic curve and the prediction of the permeability function for a fine sand (Lakeland sand) are shown on the next slides.Additional notes:•The soil-water characteristic curve for the Lakeland fine sand is shown above. •The figure shows a low air entry value for the soil specimens tested [i.e., (u a -u w )b around 3 kPa] and an estimated residual degree of saturation around 10 kPa.Additional notes:•A comparison between the permeability function, kw (θw ),computed from theproposed equation and experimental data is shown for a fine sand.•There is a satisfactory match between the measured and calculated values.Additional notes:•The coefficient of permeability, k w , is generally assumed to be uniquely related to the degree of saturation, S , or the volumetric water content, θw .•This assumption is reasonable since water flows through the pore-water phase.•The degree of saturation or volumetric water content shows significant hysteresis when plotted versus matric suction.Additional notes:•The relationships between the water content (i.e., S or θw ) and thecoefficient of permeability appear to exhibit little hysteresis (Nielsen and Biggar, 1961).•The permeability function, k w (or θw ), for coarse-textured soils isapproximately the same for both wetting and drying (Nielsen et al., 1972.)Additional notes:No hysteresis•Since there is hysteresis in the relationship between water content and matricsuction, there is also hysteresis in the relationship between the coefficient ofpermeability and matric suction.•The hysteresis in the relationship between the coefficient of permeability andmatric suction depends upon the distribution of pores in the soil.Additional notes:•Air in an unsaturated soil can be present in two forms; namely, a continuous form or as occluded air bubbles.•Air phase is generally continuous when the degree of saturation is below 85%.•Air phase becomes occluded bubbles as the degree of saturation is higher than 90% and the air flow is reduced to a process of diffusion through the pore-water.•Concentration or pressure gradient can be used as the driving potential for the flow of the continuous air phase through an unsaturated soil.•Fick’s law is often used to describe the diffusion of gases through liquids.•A modified Fick’s law, as shown above, relates the mass rate of flow, Ja , to theconcentration gradient, (dC /dy ), by using the transmission constant for air flow through a soil, D a .•The negative sign in the relationship indicates that air flows in the direction of a decreasing concentration gradient.•The concentration of the air, C , in a soil can be expressed as a function of the air pressure by using the air density which is related to the absolute air pressure in accordance with the gas law.Additional notes:•The modified Fick’s law, as shown above, can be used to express the mass rate of flow, Ja , to the pore-air pressure gradient, (d ua /d y ), by using a modified coefficient oftransmission for air flow through soils,D a *.•It can be observed that D a *is a function of the volume-mass properties of the soil.•This modified form of Fick’s law has been used in geotechnical engineering to describe air flow through soils (Blight, 1971).•Air flow, under steady-state conditions, can be measured through a soil mass. At the exit point, the mass rate of the air flow is measured at a constant air density, ρma .•This particular steady-steady condition permits the establishment of a relationship between the flow rate, v a , and the air pressure gradient, d u a /d y .Additional notes:•The pore-air pressure, u a , can be expressed in terms of pore-air pressure head, h a , using a constant air density (i.e., by neglecting the elevation head gradient).•Therefore, the equation for air flow through an unsaturated soil mass has the same form as Darcy’s equation for air phase, when the term k a is used for D a * g , and the hydraulic head gradient consists of the pore-air pressure head gradient as the driving potential.•The coefficient of permeability for the air phase is a function of the fluid (i.e., air) and the soil volume-mass properties.•Air flows through the air phase and as the matric suction increases, or the degree of saturation increases and the air coefficient of permeability increases.•Relationships between air coefficient of permeability and matric suction or degree ofsaturation reflect the pore size distribution and the matric suction versus degree of saturation curve of the soil.•The relationship at the bottom is obtained when the effective degree of saturation, S e , is expressed in terms of matric suction.•The air coefficient of permeability, k a , is essentially the inverse of the water coefficient of permeability function, k w .(Brooks and Corey, 1964)Additional notes:•The relationships between ka and degree of saturation or matric suction are also validfor the air coefficient of transmissivity, Da *, since the two coefficients are related bythe constant, “g”.•Experimental verifications have been performed for Fick’s and Da1971) and some results are presented.•The tests were performed by establishing steady-state air flows through dry soils.The soils were assumed to have a rigid structure because no measurable volume change occurred during the tests.•In order to use the bulk soil as a reference, the mass rate of air flow must be multiplied by the air porosity, na.•The above figure illustrates the applicability of Fick’s law to air flow. For a small change in the pore-air pressure gradient, the mass flow rate,J, is almost linearlyproportional to the pore-air pressure gradient, with Da * being the coefficient ofproportionality.•The air pressure gradients used in the experiments were high, and the pressures applied could affect the soil structure (i.e., altering the pore-soil distribution) and themagnitudes for both the Da * and kacoefficients.Additional notes:Fick’s Law•The above figure illustrates the applicability of Darcy’s law to air flow. For a smallchange in the pore-air head gradient, the flow rate of air, va , is almost linearlyproportional to the pore-air head gradient, with ka being the coefficient ofproportionality.•The above results were calculated using a constant air density, ρa , at a pressure of 101.3kPa and a temperature of 20 o C (i.e., 1.20 kg/m3). Additional notes:Darcy’s Law•The above figure illustrates the agreement between measured data and the theoretical air coefficient of permeability function by using the air permeability equation defined with effective degree of saturation expressed in terms of matric suction.•The results are presented in terms of relative permeability with the maximum air coefficient of permeability corresponding to the dry soil conditions.Additional notes:•The above figure presents air and water coefficients of permeability for a soilcompacted at different water contents or matric suction values.•The air coefficient of permeability, ka , decreases as the soil water content ordegree of saturation decreases (Ladd, 1960; Barden and Pavlakis,1971).•The air and the water coefficients of permeability were measured on the same soil specimens under steady-state flow conditions induced by small pressuregradients applied to each phase.•The air coefficient of permeability , ka , decreases rapidly as optimum watercontent is approached. At this point, the air phase becomes occluded and the flow of air takes place as diffusion of air through water.•The coefficient of permeability decreases and the water coefficient ofpermeability increases with increasing water content, however, the aircoefficients of permeability remain significantly greater than the watercoefficients of permeability.•The difference in air and water viscosities (i.e., water viscosity is about 56 times the air viscosity at atmospheric conditions) is one of the reasons for the aircoefficient of permeability being greater than the water coefficient ofpermeability.Additional notes:•The diffusion process occurs in response to a concentration gradient. Ionic or molecular movement take place from regions of higher concentration to regions of lower concentration.•There are two common diffusion mechanisms of interest in unsaturated soil mechanics, the first is the flow of air through the pore-water in a saturated or unsaturated soil, the second process is related to air flow through the water in a high air entry ceramic disk. •Fick’s law, which is shown above, is often used to describe the first diffusion process. The concentration gradient provides the driving potential for the diffusion process and is expressed with respect to the soil voids (i.e., air and water phases).•Fick’s law equation can also be written in terms of the partial pressure of a constituent gas diffusing through the pore-water in a soil, by expressing the concentration of the gas constituents in terms of partial pressures.Additional notes:•The mass rate of the gas constituents diffusing across a unit area of the soil voids (i.e., J a ) can be determined by measuring the volume of the diffused constituents under constant pressure conditions.•The ideal gas law is applied to the diffusing constituents.•A change in concentration of the diffusing constituent relative to a change in partial pressure is obtained by using the change in density of the dissolved constituent in the pore-water.•Using the ideal gas law yields the equation at the bottom of the slide which expresses the change in concentration of the diffusing gas in terms of the partial pressure of the diffusing constituent and the volume of the dissolved constituent, V d i , through the pore-water.Additional notes:•The ratio of the volume of dissolved constituent to the volume of water, (i.e., V di /V w ) is referred to as the volumetric coefficient of solubility, h .•The flow rate of the diffusing constituent across a unit area of the soil voids, v f i , can beexpressed as a function of the partial pressure gradient, (i.e.,in this case in the y-direction) by combining the previous equations.•The equation for the diffusing constituent, vf i , can be applied to air or gas diffusion through the pore-water in a soil or through free water or some other material such as a rubber membrane (Poulos, 1964).•The equation for the diffusing constituent, v fi , can also be developed in terms of the partial pressure head, h fi , with respect to the constituent density ρfi , which corresponds to the absolute constant pressure,u fi , used in the measurement of the diffusing constituent volume.•By defining the diffusion coefficient of permeability for air through an unsaturated soil with occluded air bubbles, the equation for the flow rate of the diffusing gas can be expressed as a modified form of Darcy’s law, as shown at the bottom of the slide.Additional notes:。

黄河口凹陷相渗曲线构建方法及其应用陆云龙;王明方;李兴丽;崔云江;赵书铮【摘要】针对岩心实验成本高、非均质差异及数据量有限,难以大范围获取及使用相渗数据的难题,根据黄河口凹陷相渗实验数据特征,通过对数据归一化处理,引入反映储层孔隙结构差异的特征指数λ对归一化数据进行特征值提取,通过特征指数消除孔隙结构差异等因素,使得不同相渗曲线变化规律趋于一致,进而拟合相对渗透率与含水饱和度之间关系,构建出黄河口凹陷相渗曲线.结果表明,特征指数λ与束缚水饱和度具有很好的相关性,构建的油、水相渗曲线与黄河口凹陷实验数据吻合度较高.在缺少相渗实验数据时,该方法可以作为估算油水相对渗透率的有效方法.%Because of high core experiment cost,core heterogeneity difference and limited core experiment data,it is difficult to obtain and use a wide range of relative permeability data.For this reason,taking Huanghekou Sag as an example,a construction method of relative permeability curve was presented.The relative permeability experiment data are normalized,the features of the normalized data are extracted by introducing the characteristic indexλreflecting reservoir pore structure difference,and the relationship between relative permeability curve and water saturation can be fitted.Introducing the characteristic indexλ is for eliminating the difference in reservoir pore structure and makes the variation laws of different relative permeability curves tend consistent.The result shows that there is a good correlation betweenλ and irreducible water saturation,the relative permeability curve of Huanghekou Sag obtained using the method has high coincidence degree with core experiment data.This method canbe used as an effective method to estimate the oil/water relative permeability in the absence of relative permeability data.【期刊名称】《西安石油大学学报（自然科学版）》【年(卷),期】2017(032)002【总页数】5页(P59-63)【关键词】相渗曲线;黄河口凹陷;特征指数λ;自由流体饱和度;比采油指数【作者】陆云龙;王明方;李兴丽;崔云江;赵书铮【作者单位】中海石油(中国)有限公司天津分公司,天津300452;天津大学精密测试技术及仪器国家重点实验室,天津300072;中海石油(中国)有限公司天津分公司,天津300452;中海石油(中国)有限公司天津分公司,天津300452;中海石油(中国)有限公司天津分公司,天津300452【正文语种】中文【中图分类】TE122.2+3相渗曲线是油水两相渗流的重要曲线，在油田开发中发挥着重要作用。

储层油水两相动态毛管力测试方法谢志勤【摘要】针对目前毛管力测试方法无法准确反映出渗流过程中毛管力的动态变化问题,在借鉴气水两相动态毛管力的基础上,提出了油水两相动态毛管力的概念,并制作了动态毛管力测试装置.利用半渗透薄膜分别制作了单独测量油相和水相的压力传感器,在人工胶结岩心两个表面对称制作了8个压力测试点,采用环氧树脂将油相压力传感器与水相压力传感器紧密固定在人工胶结岩心上,采用类似稳态法测相渗曲线的实验流程,注入比例恒定的油水混合液体,测试不同饱和度条件下的毛管力.利用动态毛管力测试仪,对人工胶结岩心的动态毛管力进行了测量,得到了3条不同驱替速度条件下的动态毛管力曲线,分析发现,不同驱替速度条件下的毛管力数值存在差异,并且会对水驱油过程的数值计算带来较大影响.%At present, the capillary force test method cannot reflect the dynamic change of capillary force in the process of porous flow. To solve this problem, the concept of oil-water two-phase dynamic capillary force was put forward on the basis of gas-water two-phase dynamic capillary force, and the dynamic capillary force test unit was prepared. The pressure sensor to measure oil phase and water phase independently was developed respectively by using the semi-permeable membrane. 8 pressure testing points were set symmetrical-ly on two surfaces of the artificial core, and oil-phase pressure sensor and water-phase pressure sensor were fixed firmly to the artificial core with epoxy resin. The experimental process was similar to the one that is used to measure relative permeability curve by means of steady state method. Oil-water mixture was injected at the constant proportion and the capillaryforce under different saturations was measured. The dynamic capillary force on the artificial core was measured by means of the dynamic capillary force testing unit, and the dynamic capillary force curves corresponding to 3 displacement velocities were plotted. It is indicated that the numerical value of capillary force varies with the displacement velocity and has more effect on the numerical calculation of water displacing oil process.【期刊名称】《石油钻采工艺》【年(卷),期】2018(040)001【总页数】4页(P137-140)【关键词】毛管力测试;动态毛管力;驱替速度;测试装置;数值计算;半渗透薄膜【作者】谢志勤【作者单位】中国石化胜利油田分公司石油工程技术研究院【正文语种】中文【中图分类】TE311毛管力是毛细管压力的简称，是指毛细管中弯液面两侧两种流体（非湿相流体与湿相流体）的压力差［1］。

船用钢板高频感应加热热源简化计算方法张正星;赵耀;胡小才;杨振【摘要】[目的]在钢板感应加热的数值计算中,通常采用磁热耦合计算方法.该方法虽然结果准确,但建立的模型非常复杂,且计算需耗费大量时间.为此,[方法]通过计算和理论推导,提出一种高频感应加热热源的简化计算方法,以一个空间函数形式的热源模型来代替复杂的电磁热耦合计算.使用COMSOL Multi-physics软件建立钢板静止式感应加热有限元模型,运用磁热耦合计算方法和简化方法分别计算钢板加热后的温度场,并对采用2种方法得到的温度场分布结果进行比较,以验证简化方法应用到热源模型的可靠性.[结果]结果表明,运用所提简化计算方法得到的热源模型具有可靠性.[结论]相比于磁热耦合的方法,采用热源简化方法计算钢板感应加热过程,可以有效缩短计算时间,且在钢板移动式感应加热的计算中,能很好地解决模型过于复杂、计算时间过长等问题.【期刊名称】《中国舰船研究》【年(卷),期】2018(013)005【总页数】7页(P18-24)【关键词】船用钢板;高频感应加热;热源模型;磁热耦合;简化计算方法【作者】张正星;赵耀;胡小才;杨振【作者单位】华中科技大学船舶与海洋工程学院,湖北武汉430074;华中科技大学船舶与海洋工程学院,湖北武汉430074;华中科技大学船舶与海洋工程学院,湖北武汉430074;华中科技大学船舶与海洋工程学院,湖北武汉430074【正文语种】中文【中图分类】U671.60 引言在造船工业中，船舶外板的加工通常采用线加热工艺。

该工艺是一种沿预定的加热线对板材进行局部线状加热的方法，采用水跟踪冷却（或自然冷却），使板材产生局部塑性变形，从而将其弯成需要的曲面形状。

传统的线加热工艺使用的是氧乙炔火焰作为热源对钢板进行加热。

随着技术的发展和造船模式的转变，高频感应加热因效率高、精度较易控制和更环保等特点，在很多工业领域得到了广泛应用。

作为一种线加热工艺的热源，高频感应加热也受到越来越多研究人员的关注。