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WELL LOGGING AND INTERPRETATION TECHNIQUES                    The Course For Home Study        I. Log Interpretation Funda...
FOREWORD          Lop, Interpretation Fundamentals: Open Hole is a home study course       which covers the important basi...
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TABLE OF CONTENTS   LESSON 1   Introduction to Rock Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
TABLE OF CONTENTS CONTINUED   LESSON 18   Overview of Shale Content Evaluation                             136   LESSON 19...
INTRODUCTION TO ROCK PROPERTIES                                                                                           ...
Sorting                        Grain Shape                                                                                ...
record. The great majority of all shales are deposited         tant producing horizons have been explored in     in near s...
In clastics, grain shape, size, sorting and energy         physically and chemically with drilling and comple-level of the...
X                                       X                      L-                                 _-J                     ...
exhibits a permeability of one darcy when a single                Therefore, a fracture 0.01 in. wide has a permeability p...
ABSOLUTE, EFFECTIVE AND RELATIVE                            where:PERMEABILITY                                            ...
80   r---------r----...-.......- -......- -.....- -.....- - - - - - - - - - -                                    .....7060...
80,..---------~----                                 ...                                                               ~---...
QUESTIONS                                                                                                      1(1) Which ...
BASIC RESISTIVITY CONCEPTS                                                                                           2INTR...
resistivity of the formation water. In Figure 2.3 the                                                                  inv...
taminated formation. The conductivity in the transi-                        profile exists. This invasion pattern is usual...
QUESTIONS                                                                                                 2(1) The resisti...
FORMATION FLUID PROPERTIES                                                                                              3F...
T,                      (OF)              450              400                                                            ...
+2.0 ...- ....- . . . - - - - -....----------------------------~- I - - - -..                     - .....                 ...
400                        100 200 300 400 500 600 700 800 900 1000                           1 - Temperature In Degrees F...
SUBSURFACE PRESSURE REGIMES                                                          PFG   =   0.433 x p              (3) ...
early formation of impermeable barriers prior to                        BIBLIOGRAPHYcompaction and consolidation or other ...
QUESTIONS                                                                                               3(1) What is the A...
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Well logging and interpretation techniques asin  b000bhl7ou
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Well logging and interpretation techniques asin b000bhl7ou

  1. 1. FFF
  2. 2. WELL LOGGING AND INTERPRETATION TECHNIQUES The Course For Home Study I. Log Interpretation Fundamentals: Open Hole II. Study Guide III. Induction Logs IV. Electrolog(st) V. Laterolog and Dual Laterolog VI. Flushed Zone Resistivity Devices VII. Spontaneous Potential Log VIII. Gamma Ray Log IX. Compensated Densilog" x. Acoustic Logs XI. Neutron Logs
  3. 3. FOREWORD Lop, Interpretation Fundamentals: Open Hole is a home study course which covers the important basic elements of open hole log interpretation. The emphasis is on log interpretation, not on tool measurement theory. The first few lessons introduce relevant rock and fluid characteristics. Subse- quent lessons present progressively more complex log interpretation tech- niques. The number of interpretation techniques is kept to a minimum. This is a lesson-by-Iesson course. Participants should study each lesson and then answer the related questions. (A study guide has been provided). Supplementary reading is suggested throughout the text. The text, along with the supplementary reading, should provide a sound basis for basic open hole log interpretation. Comments or questions, regarding any of the course material, should be made to Dresser Atlas sales or log analysis personnel worldwide.
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  5. 5. TABLE OF CONTENTS LESSON 1 Introduction to Rock Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 LESSON 2 Basic Resistivity Concepts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 11 LESSON 3 Formation Fluid Properties 15 LESSON 4 How Subsurface Temperature Affects Formation Evaluation. . . . . . . . . . .. 22 LESSON 5 The Archie Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 32 LESSON 6 Induction Log 39 LESSON 7 uterolog . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 52 LESSON 8 Additional Resistivity Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 60 LESSON 9 Spontaneous Potential (SP) Log. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 69 LESSON 10 Gamma Ray Log . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 79 LESSON 11 Spectralog" ····· · · · . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 84 LESSON 12 Densilogs 88 LESSON 13 Acoustilog" 94 LESSON 14 Compensated Neutron Log 102 LESSON 15 Lithology 118 LESSON 16 Crossplotting Porosity Logs (Mixed Lithology) 123 LESSON 17 Tri-Porosity Interpretation .. · · · · · · 129 iii
  6. 6. TABLE OF CONTENTS CONTINUED LESSON 18 Overview of Shale Content Evaluation 136 LESSON 19 Porosity and Clay Content Determination (Sand-Shale Sequences) 141 LESSON 20 Rwa Method: Fast Formation Evaluation 146 LESSON 21 Conductivity Derived Porosity (COP) 152 LESSON 22 The Formation Factor-Movable Oil Plot 161 LESSON 23 Hingle Crossplot 165 LESSON 24 Pickett Crossplot 175 LESSON 25 Water Saturation Determination (Sand-Shale) 179 LESSON 26 Predict Water Cut from Well Logs 188 LESSON 27 Computer Processed Interpretation 197 LESSON 28 Computer Generated Log Data 207 iv
  7. 7. INTRODUCTION TO ROCK PROPERTIES 1INTRODUCIlON THE NATURE OF SEDIMENTARY ROCKS Throughout geologic time, global tectonic activity Sedimentary rocks may be classified as having beenaltered and continues to alter the earths crust. This formed primarily by mechanical weathering (e.g. sand-process has distilled out the lighter lower melting stones, conglomerates) or by chemical weatheringpoint materials which have accumulated on the sur- and/ or precipitation from solution. These altered parti-face forming the continents. Sedimentary rocks have cles may then be transported or dissolved in a fluid andevolved as a result of mechanical and chemical altera- deposited mechanically or precipitated chemically ortion of these rocks through exposure to the surface biogenetically under specific chemical and physical con-environment. Today, a thin veneer of sediments ditions. Sedimentary rocks are composed primarily ofalmost entirely covers the earths surface. The those minerals which are stable under normal conditionsgeneration of petroleum within this sedimentary rock of stress, temperature and pressure. Minerals normallyhas been occurring on the earth since life evolved. A associated with igneous and metamorphic rocks whichsmall percentage of the total organic remains has were formed under abnormal conditions of stress,escaped oxidation by burial beneath the surface in temperature or pressure may also occur with thesediments. These organic remains, when sufficiently sedimentary rock. Of the 2,900 naturally occurringconcentrated and subjected to moderate levels of minerals now known, less than 200 occur in sufficientgeothermal heat and overburden pressure in an ox- amounts to be classified among the common rock-ygen free environment, have evolved to form forming minerals. Of these, only two dozen or sopetroleum. The movement of pore fluids from source characterize the majority of sedimentary rocks.rocks into porous and permeable reservoir rocks Sedimentary rocks may be grouped conveniently where they were accumulated and trapped has into mechanically derived rocks, or clastics and resulted in the hydrocarbon bearing reservoirs found chemically precipitated rocks. Chemically precipi- today. tated rocks may be further subdivided into car- Most of the worlds petroleum occurs in sedimen- bonates and evaporites. (Fig. 1.1) tary rocks. The location of petroleum reserves re- quires an understanding of the nature of the rocks in Source Rock which these reserves occur, and well logs are one of the primary sources for such data. Well logs are par- I I I ticularly useful in the description and characteriza- Chemical Mechanical tion of sedimentary rocks and their pore fluids. Weathering Weathering Well logs are a fundamental method of formation I I analysis since they measure the physical properties of the rock matrix and pore fluids. They provide forma- Plant Extraction I Solution I New Minerals tion data not directly accessible by means other than coring. Well logs can be used to extend data obtained from core analysis to wells from which only logs are available. Utilizing log-derived measurements of such petro-physical properties makes it practical to Precipitation determine, for example, lithology, porosity, shale Biologic Extraction volume, water and hydrocarbon saturation and type, and Precipitation when oil and/or gas are present and to estimate permeability, to predict water cut, calculate residual Peat Shale oil saturation, and detect overpressured zones. Coal The primary purpose in the analysis of most well Evaporites Conglomerate logs is to describe the lithology of the reservoir rock (Some Limestone) Sandstone and fluid properties for the section cut by that par- Limestones Chert ticular well. A set of logs representative of an area Diatomaceous Shales Phosphates can be used as an exploration tool to describe local stratigraphy, structure, facies relationships and en- FIGURE 1.1 Simplified chart showing origins of sedimentary rocks. vironments of depostion.
  8. 8. Sorting Grain Shape C1 °8° ~o~ Angular: having sharp corners and edges Very Well o Q and, therefore. showing little or no effects 000 of abrasion or wear. C68b 0 ~D{? Subangular: having edges and corners Well slightly rounded. so that wear is evident. 000 OPeO Subround: having most of the corners and Q~ l?~ Moderat~~y 00 °00 edges worn down to smooth curves, thus. showing extensive abrasion. 00°0 o 0 0 • 00 Round. having all edges and corners 0:)0 Poorly 1) 0°0 0 smoothed off to gentle curves by prolonged wear. 080FIGURE 1.2Texture of clastic rocks. Clastic rocks, principally sandstones and shales, comprise up to 40 alo or more of sands formed nearare those sediments composed of distinct grains granitic source areas in arid climates. A multitude ofwhich have been mechanically deposited. Their other minerals may occur in minor amounts (usuallycharacter is dependent upon the composition of the less than one percent of the rock). Some, such asgrains, their relative abundance, grain size and hematite, dolomite and siderite serve as cementingshape, orientation and packing of grains, cornposi- agents. Calcite is also quite common as a cement andlion and distribution of cement and nature of the a rock forming mineral. Textures can vary fromfluid content of the pore system. Typical clastic rock poorly sorted conglomerates as found in the granitenomenclature indicates the relative size of grains or wash to highly rounded, well sorted, fine blankettexture. For example, a siltstone is composed of silt- sands. A marl is usually 40 to 60070 carbonate withsized grains and a sandstone is composed of sand- the other 60 to 40 07 usually clay with silt or sand. 0sized grains. Greater than 60070 carbonate is considered a shaly The texture of clastic rocks is determined largely limestone or chalk. Less than 40 010 carbonate is oftenby grain shape and sorting. (Fig. 1.2) Grain shape or considered as a calcareous or dolomitic shale.sphericity is principally a function of the energy of Shale generally refers to a rock composed pri-the environment of transport reworking and deposi- marily of clay minerals, minor quartz silt with sometion. A grain which has been reworked through the feldspar, and from 0 to 20 070 organic matter. The car-sedimentary cycle several times generally has a higher bonate equivalent of shales are often called marls.sphericity. Younger grains near their source are They are composed primarily of calcite, clay, andusually very angular. Sandstones deposited in minor silica, and are occasionally dolornitized. Themoderate to high energy environments tend to be extensive "oil shale" deposits in Utah, Colorado andwell-sorted while those formed in low energy en- Wyoming are marls.vironments have poor sorting. Clay minerals are essentially hydrous aluminum The composition of sandstone is highly dependent silicates in which magnesium and/or iron mayupon the source, climate and environment of substitute for aluminum, and aluminum maytransport and deposition. Sandstones are usually substitute for silica within the structure. Claycomposed of quartz. Numerous sandstones contain minerals are formed by the weathering of silicateigneous or metamorphic rock fragments, some minerals from igneous and metamorphic rocks. In-feldspar and a few carbonate grains. Feldspar is the dividual particle size is of the order of 10 microns.most abundant mineral in igneous rock and may Shales comprise 50 to 60070 of the sedimentary 2
  9. 9. record. The great majority of all shales are deposited tant producing horizons have been explored in in near shore marine environments along continental California. margins. The remainder are deposited as deep marine muds or in fluvial, and lacustrine environments. CHEMICAL ROCK CLASSIFICATION The color of gray to black shales is due primarily to organic content. Red or green shales have a high From the preceding brief discussion of the prin- iron content and relatively low organic content. cipal features of sedimentary rocks, it is evident that Yellow and brown shales have a low iron and low a simplified classification system for log interpreta- organic carbon content. tion is needed. Logging tools respond primarily to Shales have a low effective porosity and extremely the chemical nature of matrix and pore fluids. For low permeabilities. They have usually been bypassed this reason, a chemical rock classification has beenI.. by drillers even when good mud shows were en- countered. The Woodford shale in Oklahoma is a typical black organic-rich shale with beds of dark pyritic chert, siliceous shale and some siltstone. adopted. All rocks composed primarily of silica, in- cluding cherts, are called sandstones. All calcium car- bonate rocks are called limestones. All calcium magnesium carbonate rocks are called dolomites. Where relatively brittle zones have developed natural Rocks composed primarily of clay are called shale. fracture systems, good gas production and some oil Silt or siltstone is sometimes used as the calculated have been found. difference between shale volume and clay volume. Anhydrite, gypsum, halite and coal all have suffi- Carbonates comprise approximately 10010 of the stratigraphic section. Their importance as reservoir ciently unique log responses which are easily iden- rocks should not be underestimated. Approximately tified. SOOfo of the world hydrocarbon reservoirs are in car- RESERVOIR ROCK PROPERTIES-POROSITY bonate rocks. These consist primarily of calcite or dolomite with mica amounts of aragonite, ankerite, A thorough understanding of basic reservoir siderite, pyrite, chlorite. quartz and clays. parameters is a must for the analysis of any well log. The ultimate storage capacity of any reservoir is Evaporite sequences are deposited in marine basins defined as the percent of space not occupied by the having restricted circulation. Halite or salt beds ex- rock matrix. Total porosity, 0, is defined as: ceeding 3,000 ft thick are known in the geologic record. Sylvite (KCl) and other salts occur in lower f2S = pore volume/total volume (1) volumes, but are more important economically. Gyp- sum and anhydrite are the common sulfates. Gypsum or is altered to anhydrite by loss of water with increas- ing depth of burial and these deposits are frequently interlayered with shale, limestone, or dolomite. I2l l I-matrix volume ) Anhydrite may also crystallize directly under certain ~ total volume conditions. Primary porosity is the porosity that is built into the Phosphatic rocks also occur in complex mixed rock matrix during original deposition and includes lithologies. They include carbonate as well as clastic its reduction by subsequent cementation and com- mixtures. They frequently have high organic carbon paction. (Fig. 1.3) content and are thought to be the source rock for several major oil fields. Extensive deposits of chert have been formed in deep marine basins from the remains of siliceous micro-organisms. Chert also occurs as replacement deposits in shales and limestones. Cherts are general- ly not porous or permeable except where fractured. Depth An exception is the Mississippian "chert" zone in South Central Kansas and Northern Oklahoma which is a weathered chert with porosity of 30-40010 in places. The zone is also fractured which increases 1 the permeability. Diatomites and diatomaceous shales are accumula- tions of thin-walled unicellular siliceous micro- organisms with varying amounts of shale. These FIGURE 1.3 deposits have very high porosities (25-60010), but their Porosity vs. well depth. permeabilities are comparatively low. Several impor- 3
  10. 10. In clastics, grain shape, size, sorting and energy physically and chemically with drilling and comple-level of the environment of deposition determine the tion fluids reducing permeability.packing arrangement. In general, fine-grained sand- Carbonate rocks usually show little evidence ofstones with poorly sorted angular grains will have physical compaction. Carbonate rocks are cementedlower porosity than sandstones composed of coarse, very quickly both during and soon after deposition.well-sorted grains. Angular grains tend to fit together Porosity reduction is primarily due to continuedand develop more intimate grain-to-grain contacts. growth of cement in the pore space.(Fig. t .4) In poorly sorted sediments, the smaller Secondary porosity is that porosity developed subsequent to original deposition, compaction and cementation. Secondary porosity includes fracture Porosity porosity, solution porosity and porosity caused by 47.6% dolomitization. 47.6% TRAPS The occurrence of accumulations of petroleum in nature requires the existence of an organically rich source rock, a porous and permeable reservoir rock 25.9% and a seal. Traps are classified as structural, stratigraphic or a combination. Structural traps include domes, faults and an- ticlines. Stratigraphic traps may be formed by lateral ~ <25.9% variations in lithology. The presence of fractured limestone stringers within impermeable shales is anFIGURE 1.4 example of a stratigraphic trap. (Fig. 1.5) In someGrain shape and size effects on porosity. cases, inclined bodies of rock have been eroded at the surface and overlain by impermeable bodies of rockgrains tend to fill the spaces in between the larger to form stratigraphic traps.grains. Packing is independent of absolute grain size.Rocks composed of grains of identical shape whichare equally well-sorted will theoretically have the PERMEABILITYsame porosity. However, sediment ranging from siltto very fine-grained sandstone frequently exhibit The interconnective porosity in a rock is called itslower porosities. Very small grains tend to have lower effective porosity. The degree to which this naturalsphericity and form smaller pores which are more plumbing system can conduct fluid is calledeasily cemented. The degree of sorting and average permeability. It is the key parameter in determininggrain size are directly related to the duration of the the rate of production.sedimentary process and the energy level present dur- Based on flow tests, Darcy determined that theing deposition. value of permeability, k, can be expressed by the After deposition, compaction and cementation equation:greatly reduce porosity. Shales exhibit the greatestdegree of compaction through the expulsion of in- k QJA/ A(AP/L) (2)terlayer pore fluids. This expulsion of fluids by com-paction at an increased temperature is the basic where:mechanism for primary migration of petroleum fromsource to reservoir rocks. Q flow per unit time Compaction effects in sandstones are less signifi-cant. The initial fabric of the grains is primarily JA = viscosity of flowing mediumdetermined at deposition. With increasing pressure, asand will compact no more than 10 to 15070 principal- A cross section of rockly due to grain rearrangement. At greatly increasedpressure and some increase in temperature, pressure L length of rocksolution occurs at stress points. Porosity reduction is primarily due to cementation ~P pressure differential (drop)and crystallization of certain minerals in the porespace. Clean sandstones and carbonates are relatively The unit of permeability is the darcy (D), equal tostable. Some clay minerals tend to react both 1,000 millidarcies (mD). By definition, a porous rock 4
  11. 11. X X L- _-J b. Normal Fault X Limestone a.Dome Shale Sandstone 0 0 0 0 0 0 <0 CO 0 0 -- CO <0 XXl c -- - 8 A - -- B C J II Oil sand I I I I I J. . . . . . ..- ---r - - I / 1".--1---1 . . . . . . . 1, : ---f ,--,I I I ----------~~~~~------ -------------~---~-- d. Fractured limestone stringers within impermeable shales. c. Anticlinal TrapFIGURE 1.5Structural traps. 5
  12. 12. exhibits a permeability of one darcy when a single Therefore, a fracture 0.01 in. wide has a permeability phase fluid of one centipoise viscosity (viscosity of of 5,440 darcys. water at 68 OF) which completely fills the entire pore In other words, solution channels, interconnectedspace will flow through it under viscous flow condi- vugs and fractures can significantly affect the pro- tions at the rate of one cm 3/sec per square centimeter duction behavior of potential reservoir rocks. of cross section area under a pressure gtadient of one Permeability can be determined from well resting atmosphere per centimeter. Potential hydrocarbon.. operations, wireline or DST, measurements on bearing rocks exhibit a wide range of perrneabilities. sidewall samples, core analysis using plug type or (Fig. 1.6) Frequently, permeability increases with whole (full) core measurements, or estimated through correlation to well log data. (Fig. 1.7) ffi High Permeability Area Rock ~ Low Permeability 0-)) )_ Pl , . - - L ~I P2 LengthFIGURE 1.6Range of permeability. Area of Core Permeability / . - - Pressure Drop porosity. However, even very low porosity rocks may "k x Q =. A-- be highly permeable. This is caused by natural frac.. L (P1 - P2) tures and/or solution channels. On the other hand, Flow / Fluid -, Core Length high porosity rocks, such as chalk, may have very Rate Viscosity low matrix permeability. A practical rule of thumb for classifying FIGURE 1.7 permeability is: poor to fair, k = < 1.0 to 15 mD; Determination of permeability. moderate k = 15 to 50mD; good k = 50 to 250 mD; very good k = 250 to 1,000 mD; and excellent k, in Reservoir permeability is a directional rock proper- excess of one darcy. ty. Cross bedding, ripple marks, bioturbation, cut Besides the typical matrix permeability, some and fill structures as well as variation in cementation, potential reservoir rocks, particularly low-porosity grain size, sorting and packing contribute to varia- carbonates, may have solution channels and vugs tion in permeability with a depositional unit. and/or natural fracture systems, which g~eatly Permeability in the direction of elongation of the enhance reservoir permeability. component grains is considerably greater than in any Permeability of solution channels, which exhibit other direction. Horizontal permeability (k h ) , circular or near circular openings, can be directly measured parallel to bedding, is the major con- related to and calculated from the size of the chan- tributor of fluid flow into the wellbore. nels: Vertical permeability (k-) is frequently lower than horizontal permeability. Bedding planes, the k(darcy) (3) presence of muscovite or other platy minerals and shale laminations act as barriers to vertical where: permeability. The ratio of kh/k v generally ranges from 1.5 to 3.0 and may exceed 10 for some reservoir d = diameter of channels rocks. Sometimes, however, unusually high vertical For example, the permeability of a solution channel permeability occurs in unconsolidated clean and having an opening of 0.001 in. is 20 darcys. coarse sandstones or due to fracturing or develop- ment of vertical jointing. Joints may occasionally be For typical fracture permeability, the above equa- filled with clay or other minerals which act as barriers tion becomes: to horizontal permeability. This condition (kh/k v ~ 1.0) greatly affects reservoir behavior due to bypass- k{darcy) (0.544)( 10 8) (,2) ing and coning effects in producing wells. where: w fracture width, in. 6
  13. 13. ABSOLUTE, EFFECTIVE AND RELATIVE where:PERMEABILITY o and Swi are expressed in 010 Taking certain analytical precautions, a specificrock sample is characterized by a unique permeabilityvalue, regardless of whether gas or liquid has beenused in the measurement. (5) Provided only a single medium such as water, oilor gas flows through the rock (So or Sw or S = 1.0),the term absolute permeability is used. g 250 for oil However, since petroleum reservoirs contain gas C ={and/or oil and water, the effective permeability (k , 80 for gasko k w ) for a given medium in the presence of othe:smust be considered. Effective permeability is the where: 0, Swi are decimal fractions.permeability of the rock to a medium when anothermedium is present in the pore space. It is important For a graphical solution to the Timur equation andto realize that the sum of effective permeabilities will Morris and Biggs equation, refer to Figures 1.8 andalways be less than the absolute permeability. This is 1.9.due to mutual interference of simultaneous flows ofmore than one liquid. When dealing with flow of more than one fluidthrough a permeable reservoir rock, it is necessary toconsider relative permeability (krg~ k ro, k rw). Relative permeability is defined as the ratio of BIBLIOGRAPHYrelative permeability of one phase, during multiphasefluid flow, to the absolute permeability of that fluid Blatt, H., Middleton, G., and Murray, R. Origin ofduring single phase flow through the reservoir rock. Sedimentary Rocks, Second Edition. Prentice-Hall, Inc., 1980. Relative permeability = effective permeability/absolute permeability. Fertl, W.H. Knowing Basic Reservoir Parameters First Step in Log Analysis. Oil and Gas Journal, Porosity and water saturation are commonly used 1979.to predict production potential. It is apparent thatunless the relationship between porosity and Folk, R.L. Petrology of Sedimentary Rocks, Austin,permeability is known, as well as the relative Texas: Hemphills, 1968. (A "syllabus" periodicallypermeability, this practice entails considerable risk. revised, and used as a laboratory manual at the The importance of the presence of clay minerals as University of Texas).a determinant of permeability is often related notonly to their abundance, but also to their mineralogy Levorsen, A.I. Geology of Petroleum, Second Edi-and the composition of the pore fluid, principally its tion. W.H. Freeman & ce., 1967.salinity. In an undisturbed sandstone, the clayminerals are attached to or coat the grain surfaces Potter, O.E., Maynard, J.B., and Pryor, W.A.reducing the pore space. If the clays should be ex- Sedimentology of Shale. New York: Springer-Verlag,panded due to changes in the chemistry of the pore 1980.fluids, mud filtrate invasion or become dislodged tofloat through the pore channels and block porethroats, the permeability win be further reduced. There are several methods of determining reservoirpermeability from log data. Two commonly used em-pirical methods are the Timur equation and the Mor-ris and Biggs equation.Timur Equation: 0 4 .4 k (mD~ = 0.136 ~ (4) WI
  14. 14. 80 r---------r----...-.......- -......- -.....- -.....- - - - - - - - - - - .....706050 I4030 1000 / 2000 /20 4000 /10 O~ ............ ~ ...... ._.._ ...._ __.l"__ ~ o 5 10 15 20 25 30 35 40 Porosity. +(%) FIGURE 1.8 Reservoir permeability estimate from log data (Timur equation). 8
  15. 15. 80,..---------~---- ... ~--------------------------- ... 70 k = 0.1 60~ 50 i(/)C~~jCiS(J) 40~CG~~.0u j 30t)!~ 20 10 0 ... .... .... ..... ...- - - -.....- - -..... .... .... o 4 8 12 16 20 24 28 32 36 40 Porosity. +(0/0) FIGURE 1.9 Reservoir permeability estimate from log data (Morris and Biggs equation).
  16. 16. QUESTIONS 1(1) Which of the following rock types arc usually clastics? a) limestone b) evaporites c) sandstones d) dolomites(2) Calculate the permeability of a fracture whose width is 0.2 in. a) 10 darcy b) 11 x 106 darey c) 2 x 106 darey d) 544 darcy(3) Sandstones are usually cornposed of: a) feldspar b) mica c) quartz d) calcite(4) Shales have (high, low) effective porosity and very (high, 10) permeability.(5) Relative permeability equals: a) effective permeability/absolute permeability b) absolute permeability/effective permeability c) absolute permeability x primary porosity d) primary porosity/effective permeability(6) Determine the reservoir permeability for a gas-bearing formation with 0 15ctJo and Swi 20% using both the Timur equation and Morris and Biggs equation. k (Timur) = k (Morris & Biggs) = 10
  17. 17. BASIC RESISTIVITY CONCEPTS 2INTRODUCTION ticular case may violate the rule. Figure 2.1 il- lustrates the various symbols and terms used. Resistivity Concepts in Well Logging Resistance is the property of a substance that of-fers opposition to the electrical current flow. Ohms Aslaw describes the behavior of electrical current flow Mut1.----.......- - - Cakethrough a material. hmLI E (1) r = Flushed Zone s;: Undisturbed Formation Invaded Zone .--Ri---t-.... • 8, ~ r resistance, ohm E electromotive force, volts current, amperes R - ResistiVity xo - Flushed zone Resistivity is a measure of the resistance of a given S - Saturation me - Mud cake s - Shoulder bed h - Thicknessvolume of material. me - Mud cake w • Formation water A i-Invaded zone d - Diameter R = r - L (2) t - Non-invaded zone FIGURE 2.1 R resistivity, ohms m 2/m Formation parameters. r resistance, ohms The flushed zone, next to the borehole, is created A cross-sectional area, meters/ by the mud filtrate passing through it during the pro- cess of invasion. The hydrocarbon saturation in the L = length of material, meters flushed zones is at a minimum, and all the virgin for- mation water is replaced by mud filtrate. The invaded In practice, the resistance of a certain volume of zone is that portion of the formation which has beenthe formation is measured. The volume of formation penetrated by drilling fluids. (Fig. 2.2)measured is a function of the configuration of the in- Moving through the flushed zone next to the wellstrument, which is a constant, therefore, the bore, deeper into the transition zone, water satura-measurement is expressed in terms of resistivity. tion can vary. In a water zone there is no change in The resistivity of any formation is a function of the water saturation, only a change in water resistivity oramount of water in that formation and the resistivity salinity. In a hydrocarbon bearing lone, theof the water itself. Ion-bearing water is conductive; hydrocarbon saturation is reduced in the flushedthe rock grains and hydrocarbons are normally in- zone and increases in the transition zone until thesulators. original saturation in the undisturbed formation isFORMATION FLUIDS reached. These changes in water saturation" combin- ed with changes in the resistivity of the fluids filling Changes in resistivity that occur in porous and the pores, create resist ivity pro files.permeable beds between the wen bore and the virgin In fresh drilling muds, the mud resistivity is nor-zone influence most resistivity logs. The following mally higher than the formation water, In a water-discussion assumes that some invasion occurs during bearing zone, the formation resistivity is higher in thethe drilling process. The depth of invasion is a func- flushed zone due to R lll f > R w and decreases withtion of the mud and formation properties. In general, movement out into the undisturbed formation. In alow porosity formations invade more deeply than hydrocarbon-bearing zone . drilled with fresh mud, high porosity formations. Explanations as to why the resistivity behind the flushed zone may be higher are, at best, rationalizations. In general, any par- or lower depending on the water saturation and the 11
  18. 18. resistivity of the formation water. In Figure 2.3 the invasion profiles are indicated with the relative posi- tion of the deep, medium and shallow resistivity curves. This assumes the shallow resistivity curve reads mostly the flushed lone, the medium reads some of the transition lone and the deep reads mostly the undisturbed formation. With a salt water based mud, the flushed zone nor- mally has a lower resistivity. With the undisturbed zone, resistivity is either the same or higher, if the formation contains equivalent or higher resistivity water . The virgin zone will have a higher resistivity, if there are hydrocarbons. Notice that the resistivity curve positions arc reversed because of the reversal of the resistivity profile. STEP PROFIL.: The step profile of invasion assumes the simplest geometry between the invading mud filtrate and undis- turbed formation. This invasion profile consists of a cylindrical interface moving laterally into a porous and QOAl _ - - [ ...... ., ... permeable homogeneous formation. The diameter of Distance from Borehole this cylindrical interface is d i- The formation within theFIGURE 2.2 interface is the flushed zone, with resistivity R xo •All resistivity/saturation profiles relate to this model. Beyond the interface lies the undisturbed zone, with a resistivity of Rt • Figure 2.4 shows a schematic diagram for this invasion profile. a: • Fresh Mud } cf....-. _Fresh Mud v Invaded System rl Formation A Undisturbed rf Formation 1 rl ~adius 9f _I Invaslo,;-J --Distance - -......Salt Mud System A FIGURE 2.4 Step profile of invasion.FIGURE 2.3• Schematic resistivity log response. The transition profile of invasion assumes that a D - Deep transition zone exists in a porous and permeable M-Medium homogeneous formation between the portion of the S -Shallow formation flushed by mud filtrate and the uncon- 12
  19. 19. taminated formation. The conductivity in the transi- profile exists. This invasion pattern is usually refer-tion zone is assumed to vary linearly between the con- red to as a low resistivity zone or annulus profile, andductivity of the flushed zone and the undisturbed for- its existence is an indication of moveable hydrocar-mation. (Figure 2.5) bons. The width of this transition zone is dependent Due to the current patterns of the logging devices,upon the type of formation, rate of invasion by mud the induction devices are affected to a greater degreefiltrate and the length of time the formation has been by the low resistivity zone. The low resistivity zoneexposed to the invading fluid. has a more severe effect upon the medium induction device. Computations show that in the case of a severe annulus, existing in a shallow to moderately cS invaded formation, the medium induction may A record lower resistivity than the deep induction J Undistrubed device when the ratio of Rxo/R t is less than five. Formation When ratios of Rxo/R t are greater than five, or deeper invasion exists, the effect decreases and the 0 1 - Inner Boundary of medium curve will record resistivity approximately Transition Zone equal to or greater than the deep induction curve. ~ - Outer Boundary Calculations show that the deep induction curve is only slightly affected by an annulus, and the record- "Co Translnon ed resistivity is only about lOC1Jo low for Rxo/R t ratios ~~ Zone ,~ ~ E of three to five and S% low for Rxo/R. ratios greater v LL 0 than five. Figure 2.6 shows a low resistivity annulus V u.. 01 profile. Induction devices are covered in detail in J Chapter 6. D i s t a n c e - - - - - - - -.. 01 - Inner Boundary of cf Invaded V Transition Zone Formation 02 - Outer Boundary r! Rxo Undisturbed -05 Formation ~; U)«S ~ s 2E Low Resistivity Zone :; LLO LL iii Q) a: Transition Undisturbed Zone 0 1 O2 rf Formation O2 ~ 1.4 0, 1 rl 0, - - Distance - - - - - - - - . II---Distance----.. FIGURE 2.6 Low resistivity annulus profile of invasion.FIGURE 2.5Transition profile of invasion,ANNULUS PROFIL.: Since it is possible for mud filtrate invasion 0 f ahydrocarbon-bearing formation to create a zone offormation water which is displaced ahead of the inva-sion front by a process of miscible drive, considera-tion must be given to the response of the loggingdevices in the event this particular type of invasion 13
  20. 20. QUESTIONS 2(1) The resistivity of the formation is a function only of the resistivity of the formation water. a) True b) False(2) A step profile of invasion assumes -- a) invading fluids are intermixed with the formation fluids, b) invading fluids are never mixed with the formation fluids. c) invasion seldom occurs and, as such, need not be considered in regard to resistivity devices(3) In a transitional profile the width of the transition Lone is assumed to vary only with the type of formation. a) True b) False(4) When an Annulus invasion profile exists and RXll/R. ratios are greater than five, a) deeper invasion exists b) the medium curve will record a resistivity approximately equal to or less than the deep induc- tion curve c) the medium curve will record a resistivity approximately equal to the deep induction curve d) the deep curve will record a resistivity approximately equal to the medium induction curve or less than the medium induction curve 14
  21. 21. FORMATION FLUID PROPERTIES 3FORMATION WATERS the same water in a reservoir at a higher temperature. Subsurface waters represent a diversity of sources. Likewise, water-base drilling mud changes resistivitvThey are mixtures of newly formed waters, at- with depth, due to the change in temperature. Figur~mospheric waters, ocean waters and waters produced 3.1 shows how to correct the resistivity of mud, for..from diagenetic reactions. The history of any specific marion water, etc. for the effects of temperature.sample is exceedingly complex. Throughout geologic When the temperature of a solution is increased it istime, formation waters have undergone continuous assumed that the salinity stays constant, makingmodification by filtrations through clays, by ion ex- resistivity t he only other variable.change, by precipitation of minerals and by reactionwith rock matrix and other fluids. Example: Draw a straight line on Figure 3.1 from 139 0 and a resistivity at 0.06 Q-lll; the salinit v of this The initial fluid in most sedimentary rock was sea mixture is 62,000 ppm as shown on the center stringwater. Although it cannot be assumed that the com- of the nomograph. An increase in temperature toposition of sea water has remained constantthroughout geologic time, most data suggest that its 179 0 (the salinity stays constant so the line still goescomposition has not undergone significant change through 62,000 ppm) changes the resistivitv to 0.046over the past few billion years. Q-m. All aqueous solutions are handled in the same manner. The salinities shown are for sodium chloride The salinity of subsurface waters generally in- solutions, but the nomograph works well for mostcreases with depth. Reversals, however, are not un- practical well Jogging applications.common. Considerable variation within the same In many cases. brines are encountered with totalformation may occur within a basin. Studies ofcementation in sandstones indicate that significant solid concentrations composed of ions other than Nasalinity variation can occur over very short distances, and Ct. To accurately correct the Rw R In or Rmf" • • ,U~-both horizontally and vertically. Filtration through tng FIgure 3.1. the total ionic concentration must beclay membranes appears to be one of the key expressed as equivalent NaCl concentration. Fiauremechanisms capable of producing the gradients 3.2 is used to correct ionic concentrations toobserved. equivalent NaCI concentrations. The density of water depends upon its salt content, Example: If a brine with 50,000 ppm total solidstemperature and pressure. The specific gravity of a which includes 10,000 ppm Nat J6,000 ppm Cit 7,000 ppm Mg, 5~O(){) ppm Ca and 12,000 ppm S04 is en-substance is the ratio of its density to that of water at countered, Chart 3.2 can be used to determine aspecified temperatures. The density of water value for equivalent NaCI concentration to enter indecreases with increasing temperature, but increases Chart 3.1. From the chart read K -= 0.92 for Mg , atwith higher total solid concentration and pressure. 50,000 ppm, K ::: 0.18 for Ca at 50,000 ppm, and All porous rocks contain some water. Bv virtue of K = 0.36 for S04 at 50.000 ppm, noting thationized salts contained in solution, these -fonnation K = ).0 for the Na and C } at 50,000 ppm. Then add ..waters are electrically conductive, exhibiting (10,000 xl) + (16,000 xl) ,. (7,000 x 0.92) +resistivities ranging from 0.02 Q-m to several ohm- (5,000 x 0.78) + (12.000 x 0.36) -= 40,660 ppmmeters at formation temperature. The predominant equivalent NaCI. This value is used at the ppm NaCIsalt in these solutions is sodium chloride. Resistivity entry in Chart 3.1 when correcting R w R In or R mt. forof such an electrolyte normally decreases with in- the temperature.creasing salt concentration due to the higher amountsof ions which carry electric charges and highertemperature which affects the mobility of the ions.The resistivity of formation water may be determined OIL & GAS PROPERTIESby direct resistivity measurement on a sample, Specific gravity of oil is related to its API gravitychemical analysis, or an estimation of R or by the relationship:equivalent NaCI (in ppm) from well logs. The resistivity of an aqueous solution, which is water plus a salt such as sodium chloride. varies with 141.5 temperature . The resistivity of a water measured at p (1) °API + 13].5 surface conditions is different from the resistivity of 15
  22. 22. T, (OF) 450 400 Aw.R m or Rmf (Q-m) NaCI 10 300 9 275 (ppm) 8 7 200 6 250 300 5 400 4 500 225 600 3 700 800 200 900 2 1000 190 180 2000 170 1 0.9 160 3000 150 4000 0.7 5000 140 6000 0.5 7000 130 8000 0.4 10.000 0.3 120 110 20.000 0.2 30.000 100 Equivalent NaGI in ppm 40.000 1.645 x ppm GI = ppm NaGI 50.000 0.1 90 60.000 0.09 80.000 0.07 100.000 80 0.06 150.000 0.05 200.000 0.04 70 300.000 003 60 0.02 Equations: 0.01 50 0.009 0.008 0.007 Salinity (ppm at 75°F) = 10x 3.562 - log (RW75 - 0.0123) x = ----~----- 0.955 3647.5 Rw = 0.0123+ --- 75 [NaCI (ppm)]0.955FIGURE 3.1Resistivity of saline solutions. 16
  23. 23. +2.0 ...- ....- . . . - - - - -....----------------------------~- I - - - -.. - ..... Mg .....- . , I I .- --._. - J. I I I / .. I .. -- :/ I "Mg Ca •• -....... __ • . _.·A~ . ,/r- ... ,/ .. .. .. . . . .~ <, / . . . .,........ _... ----------.1 Na and CI~ +1.0 ~---~ , - .... -...... ..........~......~...----~~ ~..... -------..---------~-~...... - - - - - -......3::E -- ---- -- K -- ~ .. ~~ .. - ............ -. "~ ........ Ca ... ~ - ...".". "-" .. . . .---._----- .............. ---"- - .- ...... HCOa - .-- ....... - HC~ . ~ . " .-i..:. O... ..._ ...._ .........__.....lI-A. . . . . . . . . . . ._ - . . . _. . . . . . . .--A............~ ....._ . . . ._ . a . _......................_..._j~ . . . . 100 1000 10.000 100.000 200,1 Total Solids Concentration. ppm FIGURE 3.2 Equivalent NaCI concentrations from Ionic concentrations. where p is the specific gravity of oil at 60 OF. When 1.0 dissolved gas is present in oil, the specific gravity of the mixture decreases as the gas/oil ratio increases. M Figure 3.3 can be used for determining reservoir den- E 09 ~ sity of oil in g/cm for a known value of GOR. ~ Figure 3.4 shows the variation of specific gravity of <5 0 0.8 oils with temperature. Dry gas density as a function ?: of reservoir pressure and temperature is illustrated in iii c Q) Figure 3.5. C 0.7 ~ The viscosity of gas-free crude oil also decreases 0 e with temperature. (Fig. 3.6) From a knowledge of (J) en 0.6 (1) crude oil °API gravity and formation temperature, a: the viscosity of gas-free crude oil can be determined. The amount of gas dissolved in oil has an important 0.5 10 20 30 40 50 60 bearing on viscosity at reservoir conditons, figure Oil Gravity (OAPI) 3.7 shows how to correct the viscosity of dead oil, at reservoir temperature and atmospheric pressure, to Example: °API qravitv » 39 the viscosity of gas-saturated oil for the known GOR GOR = 1000 at reservoir conditions. Oil Density = 0.66 g/cm 3 FIGURE 3.3 Reservoir oil density as a function of oil gravity (OAPI) and gas·oil ratio (GOA). 17
  24. 24. 400 100 200 300 400 500 600 700 800 900 1000 1 - Temperature In Degrees Fahrenheit Example: The specific gravIty of an oil at 60°F IS 0.85. The specific gravity at 10QoF = 0.83. --. ..... -- -- ~H6 = Ethane C:3Ha = Propane 20 30 40 50 60 C4 H 10 = Butane Crude Oil Gravity (OAPI) at 60°F and Atmospheric C4H 10 = Isobutane Pressure, C4H 10 = IsopentareTo find the weight densrty of a petroleum oil Ibs/ff~ at its FIGURE 3.6flowing temperature when the specific gravity at 60°F is ViSCOSity of gas-free (STO) crude oils.known. multiply the specific gravity of the oil at flowingtemperature (see chart above) by 62.4 lbs/It: the weightdensity of water at 60° F.FIGURE 3.4Specific gravity-temperature relationship for petroleum oils 100 .......- - - - , , - - - - - - - - - . . . . . - - - - - - - - - 80 60 Q) ~ 40 tJ) 0 C/) ~£ -c: 20 2000 ==0 o ~ 1O~---I__------_lfA__.........__,... ~OOg (j) 4000 ~~ ~ .>.. ~ ;j au ~ s 4 ~~ ,,~ C/) C/) Q) 6000 I ~ Ii: ~ ~ 2 ,.(o.... SOlution Gas/Oil 8000 C)Qi ,0".1 Ratio CU ft/bbl - a. -,,fOOo ~~ 1 t-----~~~ ......,........I«-" 00°;-.---------4 10,000 :~ .... 0.8 ",,~ 0 0.1 0.2 0.3 8 6 0.6 rz,r:fJ Density of Dry Gas (g/cm 3 ) 5 ~ 0.4 C/) ,,~$ ",~ C2 ~GOOFIGURE 3.5 ~O.2Density of dry gas as a fu nction of reservoir pressure andtemperature. Viscosity of Dead Oil (cP) (at Reservoir Temperature and Atmospheric Pressure) FIGURE 3.7 Viscosity of gas-saturated crude oils (J,l) at reservoir temperature and pressure. 18
  25. 25. SUBSURFACE PRESSURE REGIMES PFG = 0.433 x p (3) Hydrostatic pressure is caused by the unit weight where p is the specific gravity of a representative col-and venical height of a fluid column. The size and umn of water.shape of this fluid column has no effect on the Overburden pressure originates from the combinedmagnitude of this pressure. Hydrostatic pressure, weight of the formation matrix (rock) and (he fluids (water, oil, gas) in the pore space overlying the for-P H• equals the mathematical product of the average yfluid density and its vertical heights, such as: mation of interest. Mathematically, the overburden pressure can be expressed as:P Hy = P X g x D (2) P = weight (rock matrix + fluid) (4) o area where: p average density g gravity value D height of the column Generally, it is assumed that overburden pressure increases uniformly with depth. For example, The hydrostatic pressure gradient is affected by the average Tertiary deposits on the U .5. Gulf Coast,concentration of dissolved solids (i.e., salts) and and elsewhere, exert an overburden pressure gradientgases in the fluid column and different or varying of 1.0 psi/ft of depth. This corresponds to a force ex-temperature gradients. In other words, an increase in erted by a formation with an average bulk density ofdissolved solids (i.e., higher salt concentration) tends 2.31 g/crrr. Experience also indicates that the pro-to increase the normal pressure gradient, whereas in- bable maximum overburden gradient in clastic rockscreasing amounts of gases in solution and higher may be as high as 1.35 psi/ft.temperature would decrease the normal hydrostatic Worldwide observations over the last few yearspressure gradient. For example, a pressure gradient have resulted in the concept of a varying overburdenof 0.465 psi/ft assumes a water salinity of 80,000 gradient used for fracture pressure gradient predic-ppm NaCI at a temperature of 77 of (25 O(~). tions in drilling and completion operations. Typical average hydrostatic gradients which may Formation pressure (P f) is the pressure acting uponbe encountered during drilling for oil and gas are the fluids (formation water, oil, gas), in the poreshown below: space of the formation. Normal formation pressures in any geologic setting will equal the hydrostatic head Equivalent Total (i.e., hydrostatic pressure) of water from the surfaceHydrostatic Mud Wt. Chlorides Basin to the subsurface formation. Abnormal formation Gradient ppg ppm Location pressures, by definition, are then characterized by any departure from the normal trend line. 0.433 8.33 Fresh Rocky Formation pressures exceeding hydrostatic pres- water Mountains sure (Pr > PH,,) in a specific geologic environment 0.442 8.5 20,000 Beaufort, are defined as abnormally high formation pressure Brunei, (surpressures) whereas formation pressures less than Malay, hydrostatic are called subnormal (subpressures). Sverdrup, These subsurface pressures and stress concepts are N. Slope in related. Alaska In normal pressure environments (PI = PH ) , the (most of . ~ matrix stress supports the overburden load due to worlds grain-to-grain contacts. Any reduction in this direct basins) grain-to-grain stress (0 -+ 0) will cause the pore fluid 0.452 8.7 40,000 North Sea, to support part of the overburden, the result being Delaware abnormal formation pressures (P f > PH,,). In other (older words, the overburden may effectively be "floated" portion- by high formation pressures. prePenn.) There are numerous factors that can cause abnor- 0.465 9.0 80,000 Gulf Coast mal formation pressures, such as surpressures and 0.478 9.2 95,000 Portions of subpressures, Frequently, a combination of several Gulf Coast causes superimposed prevails in a given basin and as such is related to the stratigraphic, tectonic and In general, the hydrostatic pressure gradient (in geochemical history of the area.psi/ft) can be defined as: In most cases, abnormal pressures are caused by 19
  26. 26. early formation of impermeable barriers prior to BIBLIOGRAPHYcompaction and consolidation or other geologic anddiagenetic processes. Figure 3.8 shows subsurface Beal, C. The Viscosity of Air, Water, Natural Gas,pressure concepts. Crude Oil and Its Associated Gases at Oilfield Temperature and Pressure. A/ME, Vol. 165, 1946. Pressure (1000x psi) 2 4 6 O---.--......-----.-........- -.........----i---.---.---- Brown, K.E. The Technology of Artificial Lift Methods. Tulsa, Oklahoma: The Petroleum Publishing ce., 1977. 2 Dresser Atlas. Log Interpretation Charts. 1980. Fertl, W.H. Abnormal forma/ion Pressures. New £ 4 York-Amsterdam: Elsevier Scientific Publishing Co., o 8 1976. s: 0.. 6 Q) Katz, D.L., Cornell, D., Kobayashi, R., Poetman, c F.H., Vary, J.A., Elenbaas, J.R., and Weinaug, Surpressures C.F. Handbook of Natural Gas Engineering. (Abnormally 8 McGraw-Hill Book Co., 1959. High Pressure) Schowalter, T.T. Mechanics of Secondary Hydrocar- 10 bon Migration and Entrapment. AAPF Bulletin, May 1979.FIGURE 3.8 Standing, M.B. Volumetric and Phase Behavior ofSubsurface pressure concepts. Oil Field Hydrocarbon Systems. New York: Reinhold Publishing Corp., 1952.FLUID SATURATION DISTRIBUTION Fluid saturation is the percentage of the porosityof a rock occupied by a specific fluid. For example, awater saturation (Sw) of 50070 means that half thepore space is filled with water. In a water-oil system100070 - S" = So (oil saturation). The same logicwould apply to a water-gas system. Water saturation, a key parameter determinedfrom well logs, controls the reservoir productionbehavior and the amount of hydrocarbons in place.An oil reservoir at irreducible (non-movable) watersaturation produces water free, but with increasingwater saturation the percent of water production willincrease. There is no unique, single water saturationvalue to use as a cutoff for commercial or water-freeproduction. Each reservoir has its own uniquecharacteristics. 20
  27. 27. QUESTIONS 3(1) What is the API gravity of an oil whose specific gravity is 0.85 g/cm 3? a) 65 b) 35 c) 40 d) 50(2) Viscosity of gas-free crude oil (increases, decreases) with increasing temperature.(3) Higher salt concentrations tend to (increase, decrease) the normal pressure gradient, whereas in- creasing amounts of gases in solution would (increase, decrease) the normal pressure gradient.(4) If Sw = 720/0 So = ---(5) If the total solid concentration of a Cae) water is 5,000 ppm, of which 2,500 ppm is Ca, and 2,500 ppm is CI, determine the R w at 160 OF. a) 0.06 b) 0.4 c) 0.6 d) 0.03 21

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