1、Ingrain公司實驗分析技術介紹在Ingrain的巖石物理實驗室，利用X-CT巖石掃描技術，我們可以測量、計算巖石的物理性質和含油氣儲層巖石流體的流動特性。我們的分析測試技術領導著當今世界石油天然氣行業中泥頁巖、碳酸鹽巖、致密含氣砂巖和油砂的工業分析測量技術。關于Ingrain的數字巖石物理實驗室Ingrain的數字巖石物理實驗室，可以測量計算含油氣巖石的物理特性和流體流動性質，我們提供先進的砂巖、泥頁巖、碳酸鹽巖、致密含氣砂巖和油砂的巖石物性分析。使用巖心柱體或者鉆井巖屑進行分析，Ingrain實驗室在2周時間內提供精確的分析結果。甚至可以使用被鉆井液改變性質的巖心樣品進行分析測量，并提供

2、精確的分析處理結果。Ingrain實驗室的資深地質家使用微米CT和納米CT儀器掃描巖石樣品并形成數字化資料，對巖石樣品掃描的每個數據都形成一個vRock(即形成一個高分辨率的三維數字圖像)，并提供精確的分析結果。vRock可以反映巖石樣品的實際孔隙網絡分布和巖石顆粒結構等特征。利用vRock數據可以計算巖石的物理性質。這意味著巖石樣品的信息被轉換成可以被再度使用的數據體，不會出現在普通實驗分析中樣品被破壞或者改變巖石物理性質的情況。圖像的分辨率通常取決于樣品的類型，一般的巖石樣品，像致密的含油氣砂巖，其圖像的分辨率在微米級，對于泥頁巖和復雜的致密含氣砂巖，Ingrain實驗室使用納米CT掃描，

3、可以達到100納米的分辨率。這種高的分辨率是形成圖像和計算巖石孔隙網絡分布和巖石顆粒結構的關鍵。Ingrain實驗室的服務項目巖石物理性質分析：孔隙度分析（連通的孔隙和孤立孔隙）、絕對滲透率分析（在x、y、z三個方向上的滲透率）、地層的導電性和彈性參數（體積模量、壓縮波速度、楊氏模量、剪切模量、剪切速度、泊松比）多項流動分析：兩項相對滲透率，油-水、氣-油、氣-水在不同的濕潤相和粘度下的驅替性質；束縛水飽和度和殘余油飽和度；在三個軸向方向可選的兩項相對滲透率；Ingrain實驗室測量孔隙介質中低雷諾數流體的流動性能；表面張力、界面張力、毛管力。Ingrain實驗室使用幾種不同的Lattice

4、Boltzmann格子法進行多相流體測量； Rothman 和 Keller色譜模型； Shan 和 Chen的擬勢模型； Swift, Osborne, and Yeomans的自由能模型。Ingrain模擬物理實驗室的實驗過程測量巖樣中流體的傳遞性質，可人為管理實際巖心的實驗過程；邊界流動和全部流動條件模仿傳統的巖心實驗測量原理、動態的相對滲透率-排驅和吸汲過程、毛細壓力。精確的物理模型體現在單項和多項流體流動中，就像粘滯性指狀突進和導致毛管壓力突變行為。Ingrain實驗室的特色Ingrain實驗室與傳統的實驗室有什么區別？資深地質家管理和操作所有的分析項目；使用鉆井巖屑可以獲得未取心井

5、段地層的巖石物理性質；14天的快速的分析周期（即使是低滲透巖石的相對滲透率）；精確的獲得復雜巖石（油砂、泥頁巖、低滲透巖石）的分析資料；巖石樣品以數字化形式儲存成vRocks三維立體圖像（且樣品不被破環）； vRocks數據體可以重復使用，能夠在任何假設的油藏（儲層）條件下模擬分析；計算結果可結合目前存在的油藏（儲層）模型。Ingrain實驗室的分析項目孔隙度；孔隙度定義為巖石的孔隙體積與巖石的總體積的比值。沉積物是多孔的，這是非常重要的，孔隙可以充填石油、天然氣或者新鮮水等天然資源。孔隙的測量用百分比表示，沉積物（砂粒）的原始孔隙度大約為40%，由于上覆沉積物的壓實作用孔隙度減少到30%左右

6、，而后，由于化學成巖作用的加強孔隙度將進一步減少。剛沉積的粉砂和粘土，這種沉積物的孔隙度可達60%，甚至更高，這種沉積物在地質埋藏時期被快速的壓實，孔隙度很快達到30%，甚至更小。泥頁巖中的孔隙度比砂巖要小得多。如果砂、粉砂和泥質混合沉積在一起，由于粉砂和泥質顆粒充填于較大顆粒形成的骨架孔隙中，則使原始孔隙度要遠遠小于40%。孔隙度很大程度上取決于形成巖石的源巖，由于碳酸鹽巖的沉積往往由多孔的水生物骨架和生物礁等，這就是為什么產油的白堊系碳酸鹽巖具有50%的孔隙度。同樣，含有硅藻質類的巖石，由于含有硅質骨架這類礦物容易被水溶解而充填于孔隙中，導致孔隙度降低到30%以下。孔隙度的計算是根據高分辨

7、率的CT數字圖像進行的，就像前面所展示的那樣。計算的孔隙度是三維數字圖像體中孔隙空間像素（黑色-暗灰色部分）與三維數字圖像體總體積像素的比率。從一個由顆粒物體構成的三維體中分離孔隙的工作，稱為像素分離（image segmentation），在像素分離中主要的技術關鍵是在孔隙向孔洞的邊緣部位的漸變，即黑色向淺色的灰色調的過渡，Ingrain使用具有知識產權的圖像處理系統，包括統計分析和灰度色標圖像技術，這樣孔洞被精確地從礦物基質中分離開來，從而計算出孔隙度。絕對滲透率；指的是測量巖石樣品允許單一流體通過孔隙結構的能力。不像測量密度和聲速那樣簡單，在一口井中測量滲透率是困難的，在實驗室中，傳統的

8、測量滲透率是要用規則的樣品采用壓力使流體通過巖石，并記錄流體流動和壓力降低結果。Ingrain利用高分辨率三維圖像資料，通過數字模擬形成了直接用數據表示流體通過孔隙空間的流動特性，大大完善和拓展了滲透率的實驗數據庫。緩慢的滲流需要使用lattice Boltzmann method (LBM)方法進行模擬滲透率評估，LBM算法模擬納維-斯托克斯方程的滲流，把流體作為符合一定相互作用原理的一套質點束的流動來處理。它的最大優點是直接解決了流動方程，并且可以直接處理解決一個真實而復雜的孔隙界面的邊界條件問題。可以形成孔隙度與滲透率有關的數據、各種巖石類型的孔隙幾何形態，包括致密含氣砂巖、碳酸鹽巖及松

9、散的瀝青砂。關于滲透率測定的計算方法絕對滲透率的計算，實際上類似于實驗室測量；一個壓力差或者物體的作用力直接應用于數字樣品上產生流體流動，根據達西方程原理計算滲透率。電導率電導率（地層因子）是巖石的導電能力， Ingrain使用有限元方法（FEM）解決拉普拉斯方程電勢場內部數字樣品邊界電位差。孔隙內部的電流場被計算，并統計獲得通過樣品流量的總數。樣品的電導效率簡單地說就是單位長度電流對電位差的比率 彈性特征當巖石在不同的方向受壓所產生形時，在各個方向所測得的彈性傾向是不同的。Ingrain測量彈性模量是通過模擬三維數字巖石樣品靜態變形的實驗過程得到的。通過壓力使樣品骨架產生變形，使用

10、有限元方法計算局部產生的形變，這樣導致樣品的有效形變是與計算有效彈性模量樣品邊界上所施加的壓力有關的。這種方法認為在樣品內部線性彈性定律是有效的，因此，彈性模量的獲得可以被轉換成彈性波速。彈性模量的計算流程 不同的載荷壓力施加到相同的數字樣品獲得有效彈性模量（擠壓和剪切）相對滲透率是一個無量綱的測量值，它表示一種流體相通過巖石孔隙中另外開一種流體相時的滲透能力，相對滲透率的計算如下： 如果在巖石中只有單一一種流體，那么它的相對滲透率是1.0。對比先前存在的不同的流體相對滲透率具有不同的性能。后來的多于一種以上的流體產生相互制約的流動性質。影響相對滲透率的關鍵因素包括：孔喉幾何形狀（大

11、小吼道和形狀的分布）礦物表面的濕潤性流體相之間的表面張力、每個流體相和巖石之間的表面張力，這些參數定義為濕潤角、它在流體和礦物質之間形成一個界面，當濕潤角大于90度時為濕潤性，否則， 當濕潤角小于90度時為非濕潤性。濕潤性沿著平面逐漸擴展開來，最終的接觸角大約是140度，在Ingrain使用LBM方法可以進行數字模擬  緩慢的多項滲流需要相對滲透率評估，模擬使用LBM方法的多項滲流方程，將流體作為一個在相同流體顆粒之間、不同流體顆粒之間、流體和孔壁之間具有相互作用原理的質點集來處理。 LBM直接模擬靜態的和動態的考慮表面張力和接觸角這類流動相與孔隙壁接觸的類型，它

12、可以評估束縛水和含有飽和度。常見問題問答關于和Ingrain 公司的合作樣品分析周期是多少？樣品分析時間是比較靈活的，一般我們14天提供結果，特殊情況可7天提供結果。Ingrain 公司賣軟件嗎？不，我們提供先進的數字物理實驗室分析的巖石性質資料。Ingrain 公司使用什麼樣的軟件計算處理這些參數？我們使用Ingrain 公司內部自己開發的軟件計算處理巖石性質。為什么用戶更喜歡Ingrain 公司的圖像和計算處理的資料代替實驗分析測量的資料？Ingrain 公司提供一種全新的方法，常規巖石物理實驗室的分析測量是耗時的，Ingrain 公司評價鉆井巖屑和巖心是快速的，并且不毀壞樣品實物。在像致

13、密氣砂巖、泥頁巖和含油砂巖這樣困難的地層，也改善了回收過程，Ingrain 公司精確的計算、分類評價巖石的物理特性意味著比實驗分析法要快速的多。 Ingrain可以成像和分析泥頁巖和致密砂巖嗎？可以，使用納米CT掃描我們可以解決60納米級別大小的巖石特征，對于測量泥頁巖和致密砂巖這是基本的條件。我們可以成像泥頁巖內部的有機質并提供分析總的有機碳（TOC）含量。可以做油砂和重油的分析嗎？是的，Ingrain由于快速的成像處理過程，在處理含油砂是具有明顯的優勢，我們可以處理未固結的巖石，由于我們的測試具有非破壞性，可以測量沒有進行預處理的油砂的特性。還可以測量油砂中瀝青的百分含量。但是Ingrai

14、n不能提供煤層甲烷氣的測量。使用鉆井巖屑計算巖石特性的可信度有多少？如果樣品沒有物理損壞，它的精度同井壁取心是一樣的。就某一口井而然，進行儲層模擬需要掃描和分析多少巖心樣品？對于不同類型的儲層，我們建議至少每英尺一個巖心樣品。另外考慮油藏模擬的程度，通常，我們建議要分析足夠的巖心樣品，便于在油藏模型中建立流動單元或者建立巖相單元。Ingrain成像和計算的巖石樣品是否浸泡有汞？汞是有毒害物質我們的工作流程中不含有任何有毒害物質。巖石樣品的準備Ingrain不提供完全數字化的巖心。 我們能夠分析最小的巖心樣品是多大？我們首選的分析最小的巖心樣品是1立方英寸（16.4立方厘米），理由是這樣大小的巖

15、石樣品內部能夠具有非均質性，實際上分析樣品的最佳大小取決于巖石樣品的粒度和孔隙空間大小。誰來確定巖石樣品是使用微米巖心分析還是使用納米巖心分析？Ingrain受過培訓、據有經驗的地質家分析每塊巖石樣品，并確定處理方案。我們接受并處理冷凍的巖心（像含有砂巖），并且在分析處理過程中盡可能避免溫度有大的變化。微小的鉆井巖屑應避免過熱（烘干），最好保存于液氮中。巖心樣品的掃描Ingrain使用什麼樣的CT掃描巖心樣品？它們和醫院中的CT類似嗎？Ingrain使用工業級別的CT儀，我們的掃描儀器比醫用CT具有很高的分辨率。我們使用的納米級CT僅僅是全球石油工業中應用的一種，我們首先利用分辨率較低的CT儀

16、器把樣品全部成像，確定樣品的非均質性，然后利用這些低級別的CT圖像確定那些樣品或者樣品的哪個部位需要做較高分辨率的微米級CT掃描成像、那些樣品或者樣品的哪個部位需要做高分辨率的納米級的CT掃描成像。同一個樣品我們同時做微米CT和納米CT掃描碼? 不，關于進一步的納米CT掃描，我們使用更小型的樣品。標準的微米巖心樣品大小為2.5mm，納米巖心樣品大小為0.5mm。掃描樣品需要多少時間？致密巖心比多孔隙巖心需要更多的時間，微米級CT掃描需要1-8小時（取決于微米巖心樣品的大小和均質性程度），納米級CT掃描需要24-72小時（取決于納米巖心樣品的大小和均質性程度）。Ingrain提供3個軸向方向的掃

17、描切片成像、一個三維體成像透視圖，我們還提供巖石體的成像圖和孔隙體積圖。為計算巖石性質準備圖像，微米級CT成像需要掃描多少二維切片？在掃描過程中要有1024 個二維切片產生。這些切片集合起來創建一個三維數據體。每個三維數據體要經過圖像分割(image segmentation)的處理過程，最后進行計算處理。什么是圖像分割（image segmentation）？分割是指在x、y、z三個方向上處理每個三維數字巖石體，它包括轉換像黑色度、白色度及灰色梯度等信息成為包含巖石顆粒粒度和孔隙等內容的三維圖像像素的數字文件。利用這些很多的二維X射線的切片，我們創建一個來自于實際巖石顆粒和孔隙的三維數字圖像

18、。巖石物理性質計算如果我們有了測井數據，為什么還要做樣品分析？孔隙度可以根據中子、聲波和密度測井推斷，但是至關重要的滲透率參數不能直接從測井數據中推斷，需要巖石分析計算。可以從孔隙儲運性質之間的獲得接觸關系嗎？可以，使用Ingrain技術，我們揭示了孔隙空間形態，包括連通和孤立的孔隙形態，我們不使用模型。Ingrain提供什么類型的滲透率數據，我們提供三個方向的絕對滲透率，還提供相對滲透率曲線（通常是一個方向上的相對滲透率）。我們提供先進的巖石特性分析，包括砂巖、碳酸鹽巖、油砂、致密氣砂巖和泥頁巖。并提供量化的孔隙度（包括連通的孔隙和不連通的孔隙）。Ingrain如何計算巖石的彈性參數？被分割

19、的巖石樣品的圖像（稱為vRock），使用有限元方法數字化計算描述由于壓力導致變形的結果。由于相關的壓力到變形我們獲得巖石的彈性模量。Ingrain計算體積模量和泊松比嗎？是的，當我們計算巖石的彈性模量時，我們要考慮不同的礦物模量的。由于成像是在圍壓條件下進行的，那么，我們可以模擬儲層地下壓力情況下的壓縮性嗎？可以的。Ingrain怎樣獲得巖石顆粒的膠結特征？我們可以利用我們的成像處理來解決膠結特性。相對滲透率的計算Ingrain計算巖石的流體流動特性或者計算巖石的物理性質時，常常要計算巖石干樣的彈性系數，同時，孔隙度空間格架也要輸入流體模擬中。我們在流體模擬過程中使用地層原位流動性質進行模擬，

20、像原始地層的溫度、壓力、鹽度、油氣比等。當進行滲透率分析時，有時存在變化的流體飽和度，這對于致密氣砂巖是很重要的，這時含油飽和度的變化會很大程度影響氣的滲透率。Ingrain公司可以做油、氣、水的相對滲透率。附件原文Ingrain Delivers Fast，Accurate Rock Properties analysis At Ingrain's digital rock physics lab, we compute the physical properties and fluid flow characteristics of oil and gas reservoir ro

21、cks. Our technology leads the industry in measuring shales, carbonates, tight gas sands and oil sands.Using core plugs or drill cuttings, Ingrain can deliver accurate results as fast as 14 days.About Ingrain's Digital Rock Physics LabIngrain's digital rock physics lab computes the physical p

22、roperties and fluid flow characteristics of oil and gas reservoir rocks. We provide advanced rock properties analysis for sandstones, shales, carbonates, tight gas sands and oil sands. Using core plugs or even drill cuttings, Ingrain can deliver accurate results as fast as 14 days. Ingrain can

23、even provide accurate results using samples from core repositories that have been altered by drilling fluids.A degreed Ingrain geologist uses micro- and nano-resolution CT scanners to digitize the fabric of each rock sample.  Each set of scans is combined and segmented to create a vRock - a hig

24、h-resolution 3D image of the actual pore network and grain structure. Rock properties are then computed from the vRocks. This means that the rock samples are converted into reusable digital objects, not destroyed or altered as is the case with physical lab experiments.The resolution of imaging used

25、depends on the type of rock. Conventional rock samples, some tight gas sands and oil sands are imaged at one micron resolution.  For shales and complex tight gas sands, Ingrain uses nanometer-scale CT scanning to achieve a resolution of 100 nanometers. This high resolution is crucial to imaging

26、 and computation of pore networks and grain structure in these rock types.Ingrain servicesPhysical PropertiesIngrain computes physical properties of reservoir rocks using high resolution 3D images of the pore network and grain structure of rock samples.  Ingrain's process works equally well

27、 with samples taken from core plugs, oil sands samples or drill cuttings:· Porosity:  Vv/Vt (% total, connected and isolated porosity) · Absolute permeability:  Permeability (mD) in X, Y and Z directions · Electrical properties:  Formation factor (S/m) in X, Y and Z dir

28、ections · Elastic properties:  Bulk modulus (K), compressional velocity (Vp), Young's modulus (E), Shear modulus (G), Shear velocity (Vs), Poisson's ratio Multiphase Flow· Two-phase relative permeability: water-oil, gas-oil, and water-gas displacement at different wettability

29、indices and viscosity values· Irreducible water saturation and residual oil saturation· Optional two-phase relative permeability in three axes Ingrain computes multiphase flow at the pore scale in an accurate digital representation of the pore space. Our algorithms can operate at any desir

30、ed boundary and saturation condition, as well as varying fluid viscosity and wettability contrasts. 數字模擬水驅油Digital simulation of oil displacing water. 使用Lattice Boltzmann方法數字模擬油砂的相對滲透率曲線Relative permeability curves in oil sand digitally simulated using the multiphase lattice Boltzmann method.&#

31、160; Ingrain's Lattice Boltzmann methods incorporate several technical breakthroughs. · Ingrain's computations have been designed and developed specifically for low Reynolds number fluid flow in porous media (not strictly gas dynamics) and incorporate: o Surface Tensions (wetting/ fluid

32、-surface interactions) o Interfacial Tensions (fluid-fluid interactions) o Capillary forces· Several different Lattice Boltzmann schemes are employed for multiphase fluids: o Chromodynamic model of Rothman and Keller o Pseudo-potential model of Shan and Chen o Free energy model of Swift, Osborn

33、e, and Yeomans · Ingrain simulates the experimental processes used in a physical laboratory to measure fluid transport properties in core samples, allowing us to conduct virtual core laboratory experiments: o Boundary and general fluid flow conditions mimic traditional experimental core measure

34、ments o Dynamic relative permeability drainage and imbibition processes o Capillary pressure· Accurate modeling of the physics exhibited in single-phase and multi-phase fluid flow, such as viscous fingering and capillary-induced “snap-off” behaviorThe Ingrain DifferenceWhat makes Ingrain's

35、digital rock physics lab different from a conventional core lab?  · Degreed geologists conduct all analyses · Use of drill cuttings means rock properties information can be obtained for wells in which coring is not an option · Rapid turnaround time (as fast as 14 days, even for r

36、elative permeability in low perm rocks) · Accurate in difficult formation types (oil sands, shales, low perm rocks) · Rock samples are digitized, not destroyed, and archived as vRocks (segmented 3D digital images)· vRocks are reusable, enabling "what-if" analyses under varyi

37、ng reservoir conditions · Results are ready to integrate with existing reservoir models The science PorosityPorosity is defined as the ratio of the void volume in the rock to the total volume of the rock. Sediments are porous.  This fact is practically important, because the pores may

38、 be filled with natural resources, such as oil, gas, and/or fresh water.Porosity is measured in percents of fractions of one.  For example, if one cubic centimeter of rock contains 0.25 cubic centimeters of void, the porosity is 25% or 0.25.Freshly deposited sand on an ocean beach or a river ba

39、nk has porosity about 0.40.  As this sand is buried under a column of other sediments delivered by wind or water, its grains are pressed together and compacted, such that the porosity may reduce down to about 0.3.  Further porosity reduction occurs due to chemical dissolution of the minera

40、ls and their redeposition in the original large pores. 左圖為高孔隙度砂巖，右圖為致密氣砂巖；孔隙為黑色、石英礦物呈灰色、方解石為白色Left: High-porosity sand (Porosity 0.39) Right: Tight gas sandstone. Pores are dark, quartz is gray, and heavier minerals (calcite) are white. (Porosity 0.05)The porosity of freshly deposited silt or clay m

41、ay be as large as 0.60 and more.  This sediment quickly compacts during geologic burial, such that even at small depths its porosity reaches 0.30 and may become much smaller.  The pores in shale are usually much smaller than in sand.   Shale - The pores are green.  (Porosity

42、 0.08)If sand is deposited together with silt and clay, its original porosity may be much smaller than 0.4, simply because the small silt and shale particles occupy the pore space inside the large-porosity framework formed by large sand grains. Poorly sorted sand.  The grains are light-gra

43、y while the pores are dark.Porosity strongly depends on the source of mineral that builds the solid part of rock.  The source of carbonate sediment is hollow skeletons of water organisms, as well as coral reefs.  This is why the porosity of oil-producing chalk may reach 0.50.  The sam

44、e is true for diatomaceous rock that carries silica skeletons.  Such sediments are very reactive with water.  As a result, their minerals can rapidly dissolve and fill the pores thus reducing porosity to 0.30 and lower.  Porosity is directly calculated from high resolution digital ima

45、ges such as those shown above.  This calculation is the ratio of the number of voxels that fall into the pore space (black and dark-gray) to the total number of voxels in a 3D image.  The task of separating the pores from grains in such 3D objects is called image segmentation.  The ma

46、in technical challenge in image segmentation is the gradual transition from dark to light shade of gray at the edges of the pore space. Ingrain uses proprietary image-processing algorithms that include statistical analysis of the gray-scale images.  As a result, the pore space is accurately sep

47、arated from the mineral matrix and the porosity is computed.Segmented nano-resolution image of tight sandstone.  The pore space is blue. (Porosity 0.02)Absolute PermeabilityPermeability is a measure of the ability of a rock to transmit a single fluid phase through its pore structure.Unlike the

48、bulk density and sonic travel time, it is difficult to measure permeability directly in a well. It is traditionally measured in the laboratory on regularly shaped rock samples by forcing a fluid through the rock and recording the resulting fluid flux and pressure drops.Ingrain complements and vastly

49、 expands laboratory permeability data sets by numerically simulating fluid flow through a direct digital representation of a real pore space obtained by high-resolution 3D imaging. Such imaging and simulations can be rapidly and massively conducted on physical samples of irregular shapes and sizes t

50、hat are impossible to handle in the physical laboratory.The slow viscous flow needed for such permeability estimates is simulated using the lattice Boltzmann method (LBM). LBM mathematically mimics the Navier-Stokes equations of viscous flow by treating the fluid as a set of particles with certain i

51、nteraction rules. Its great advantage over directly solving the equations of flow is that it directly handles the boundary conditions on a complex realistic pore surface. The outcomes are consistent datasets of permeability versus porosity correlations and pore geometries for various rock types, inc

52、luding tight gas sandstone, carbonates, and friable tar sands.Computational set-up for permeability determinationThe absolute permeability is computed in a manner analogous to a laboratory measurement: a pressure head or body force is directly applied to a digital sample. The resulting fluid flux is

53、 then computed and permeability is calculated according to the Darcy's equation.Electrical ConductivityElectrical conductivity (formation factor) is the rock's capacity to transmit electrical current.Ingrain uses the finite element method (FEM) to solve the Laplace equation for the electric

54、potential field inside a digital sample for a specified potential difference at the boundaries. The electrical current field in the pores is computed and then summed-up to obtain the total current through the sample. The effective conductivity of the sample is simply the ratio of this current to the

55、 potential drop per unit length. Elastic PropertiesAn elastic property is the measurement of the tendency of a rock to deform non-permanently in various directions when stress is applied.Ingrain determines elastic moduli by simulating a static deformation experiment on a 3D digital rock sample.

56、The application of stresses to the faces of the sample generates strains in the rock frame that are computed locally using the finite element method (FEM). The resulting effective deformations of the sample are related to the stresses applied at the boundaries to calculate the effective elastic modu

57、li. This application assumes linear elasticity laws are valid within the sample. Therefore, the elastic moduli thus obtained can be converted into the elastic-wave velocities.Computational setup for elastic moduli determinationVarious loading configurations are applied to the same digital sample to

58、obtain the effective elastic moduli (e.g., the bulk and shear). Relative Permeability Relative permeability is a dimensionless measure of the permeability of a fluid phase as it flows through porous rock in the presence of another fluid phase.  Relative permeability is calculated as follow

59、s:  If a single fluid is present in a rock, its relative permeability is 1.0. Relative permeability allows comparison of the different abilities of fluids to flow in the presence of each other, since the presence of more than one fluid generally inhibits flow.Key parameters that affect relative

60、 permeability include: · The pore-space geometry (the distribution of large and small conduits and their sizes) · Viscosity of the fluids· Wettability of the mineral surface, and · The surface tension between the fluid phases and between each fluid phase and the minerals.  These parameters define the wetting (or