Basic Relationships of Well Log Interpretation PDF

CH01_v2.qxd 8/5/04 10:42 AM Page 1 1 Asquith, G., and D. Krygowski, 2004, Basic Relation- ship...

CH01_v2.qxd 8/5/04 10:42 AM Page 1 1 Asquith, G., and D. Krygowski, 2004, Basic Relation- ships of Well Log Interpretation, in G. Asquith and D. Krygowski, Basic Well Log Analysis: AAPG Meth- ods in Exploration 16, p. 1–20. Basic Relationships of Well Log Interpretation INTRODUCTION puter software, is intentional. It is only through expe- rience with such manual methods that the reader can This chapter provides a general introduction to well gain an appreciation for the effects of parameters on logging principles and methods that will be used the calculations, and gain a better understanding of the throughout the book. Succeeding chapters (2 through accuracy and precision of the techniques discussed 6) introduce the reader to specific log types. The text here. discusses how different log types measure various When the first edition of this book was published, properties in the wellbore and surrounding formations, virtually all well-logging data were acquired through what factors affect these measurements, where on a the use of wireline-conveyed tools; that is, logging standard log display a particular curve is recorded, and tools lowered in the borehole on a 7-conductor cable how interpreted information is obtained from the logs over which power, operating instructions, and data using both charts and mathematical formulas. Unlike were sent. Since the mid-1980s, a second formation- many other logging texts, the logging tools are evaluation technique, measurement while drilling grouped according to their primary interpretation tar- (MWD) or logging while drilling (LWD), has devel- get, rather than their underlying measurement physics. oped. In this method, the logging sensors are imbed- Spontaneous potential (SP) and gamma ray logs are ded in the thick-walled drill collars used at the bottom discussed first, as their primary use is correlation and of the drill string (near the bit), and measurement of their primary interpretive target is gross lithology (the formation properties is done continuously during the distinction between reservoir and nonreservoir). The drilling process (hence the name, MWD). Initially, porosity logs (i.e., sonic, density, and neutron logs) are MWD logging technology borrowed heavily from covered next, then the resistivity logs. Nuclear mag- wireline technology, with the goal being to produce netic-resonance logs, although they provide porosity LWD measurements comparable to wireline measure- (among other quantities of interest), are presented after ments. As LWD technology has progressed, sensor resistivity logs. This is due in part to their recent design and other features of LWD have been incorpo- arrival and to their relative absence in historical data rated back into wireline technology, for the improve- archives. ment of those measurements. The final four chapters again deal with interpreta- Unless specifically noted in the text, the interpreta- tion of the data, this time in detail with example prob- tion of borehole data is the same irrespective of the lems and their solutions. These chapters bring the source of the data, either wireline or LWD sensors and introductory material of Chapter 1 together with the measurement systems. The techniques shown here are specific measurement information and are intended to applicable to both data sources and can even be provide a coherent view of the interpretation process. extended to incorporate equivalent core measure- The reader is encouraged to work the examples to gain ments. familiarity with the interpretation techniques and to begin to understand the limitations on interpretation that are present due to the nature of subsurface infor- GENERAL mation. As logging tools and interpretive methods are The use of charts and simple calculations through- developing in accuracy and sophistication, they are out the text, rather than the use of petrophysical com- playing an expanded role in the geological decision- 1 CH01_v2.qxd 8/5/04 10:42 AM Page 2 2 ASQUITH AND KRYGOWSKI making process. Today, petrophysical log interpreta- some property in the rock surrounding the wellbore tion is one of the most useful and important tools (see Society of Professional Well Log Analysts, 1984). available to a petroleum geologist. For the reader unfamiliar with petrophysical logging, Besides their traditional use in exploration to corre- some confusion may develop over the use of the word late zones and to assist with structure and isopach log. In common usage, the word log may refer to a par- mapping, logs help define physical rock characteristics ticular curve, a suite or group of curves, the physical such as lithology, porosity, pore geometry, and perme- (paper) record of the measurements, a logging tool ability. Logging data are used to identify productive (sonde), or the process of logging. zones, to determine depth and thickness of zones, to Rock properties or characteristics that affect log- distinguish between oil, gas, or water in a reservoir, ging measurements are: porosity, lithology, mineralo- and to estimate hydrocarbon reserves. Also, geologic gy, permeability, and water saturation. Additionally, maps developed from log interpretation help with the resistivity of the rock is important because it is determining facies relationships and drilling locations. directly measured and is an essential part in the inter- Increasingly, the importance of petrophysics and well- pretation process. It is essential that the reader under- log analysis is becoming more evident as more atten- stand these properties and the concepts they represent tion is being devoted to the ongoing management of before proceeding with a study of log interpretation. reservoirs. The industry is realizing the importance of detailed petrophysical analyses, based on the details of the available data in monitoring, simulating, and Porosity enhancing reservoir performance to maximize the Porosity can be defined as the ratio of voids to the return on investment. total volume of rock. It is represented as a decimal Of the various types of logs, the ones used most fre- fraction or as a percentage and is usually represented quently in hydrocarbon exploration are called open- by the Greek letter phi, φ. hole logs. The name open hole is applied because volume of pores these logs are recorded in the uncased portion of the porosity, φ = 1.1 total volume of rock wellbore. All the different types of logs and their curves discussed in this text are of this type. The amount of internal space or voids in a given A geologist’s first exposure to log interpretation volume of rock is a measure of the amount of fluid a can be a frustrating experience. This is not only rock will hold. This is illustrated by Equation 1.1 and because of its lengthy and unfamiliar terminology, but is called the total porosity. The amount of void space also because knowledge of many parameters, con- that is interconnected, and thus able to transmit fluids, cepts, and measurements is needed before an under- is called effective porosity. Isolated pores and pore vol- standing of the logging process is possible. ume occupied by adsorbed water are excluded from a Perhaps the best way to begin a study of logging is definition of effective porosity but are included in the by introducing the reader to some of the basic con- definition of total porosity. cepts of well log analysis. Remember that a borehole represents a dynamic system; that fluid used in the Lithology and Mineralogy drilling of a well affects the rock surrounding the bore- hole and, therefore, log measurements. In addition, the In well-log analysis, the terms lithology and miner- rock surrounding the borehole has certain properties alogy are used with some ambiguity. Lithology is often that affect the movement of fluids into and out of it. used to describe the solid (matrix) portion of the rock, The two primary parameters determined from well generally in the context of a description of the primary log measurements are porosity and the fraction of pore mineralogy of the rock (e.g., a sandstone as a descrip- space filled with hydrocarbons (i.e., hydrocarbon satu- tion of a rock composed primarily of quartz grains, or ration). The parameters of log interpretation are deter- a limestone composed primarily of calcium carbon- mined directly or inferred indirectly and are measured ate). In the early days of log interpretation (with limit- by one of three general types of logs: ed measurements), this was usually a sufficient electrical description. Probably the first instances of lithologic nuclear effects on the logs were observed in shaly or clay-con- taining sandstones. With the advent of multiple poros- acoustic or sonic logs ity measurements and the development of more The names refer to the sources used to obtain the detailed interpretive methods, it has become possible measurements. The different sources create records to estimate the primary solid constituents, normally as (logs), which contain one or more curves related to a mineral pair or triad. CH01_v2.qxd 8/5/04 10:42 AM Page 3 Basic Relationships of Well Log Interpretation 3 The literature has tended to follow the improved ferently, formation water takes up space both in pores understanding of the constitution of the solid part of and in the connecting passages between pores. As a the formations of interest, with most current literature consequence, it may block or otherwise reduce the referring to the determination of mineralogy instead of ability of other fluids to move through the rock. lithology. When one considers the physics of logging Relative permeability is the ratio between effective measurements, the ambiguity continues. Some meas- permeability of a fluid at partial saturation and the per- urements (primarily nuclear) are made as the result of meability at 100% saturation (absolute permeability). molecular-level interactions between the formation When relative permeability of a formation’s water is and the logging tool. These might be considered as zero, the formation produces water-free hydrocarbons being affected by the formation’s mineralogy. Others, (i.e., the relative permeability to hydrocarbons is especially the acoustic measurements, interact with 100%). With increasing relative permeabilities to the formation on a bulk or framework level, and could water, the formation produces increasing amounts of be considered to be more affected by lithology (S. L. water relative to hydrocarbons. Morriss, 1999, personal communication). The ambiguity between lithology and mineralogy is best seen in porosity crossplots which, through time, Water Saturation have moved from estimating lithology to estimating Water saturation is the amount of pore volume in a mineralogy, while the underlying measurements and rock that is occupied by formation water. It is repre- interpretive techniques have remained essentially the sented as a decimal fraction or as a percentage and has same. the symbol Sw. As noted above, the first lithologic effects were probably due to the presence of clays and shales in for- formation water occupying pores water saturation, S w = mations of interest. One parameter that has been used total pore space in the rock 1.2 consistently to account for these effects has been shale volume. As our understanding of geological processes Although hydrocarbon saturation is the quantity of matured, it became understood that shale and clay interest, water saturation is usually used because of its were different, and that shaly sands were usually not direct calculation in equations such as Archie’s equa- just sands with shales mixed in, but sands that con- tion, discussed in a later section in this chapter. Hydro- tained clays — clays that could be very different from carbon saturation is usually determined by the differ- the clays present in the shales near those sands of ence between unity and water saturation: interest. Again, the literature and our interpretive tech- niques often use the terms shale volume and clay vol- Sh = 1 − Sw 1.3 ume interchangeably. In this text, shale volume will be used preferentially because most of the interpretive Irreducible water saturation or Sw irr is the term techniques in which the volumes are used derive those used to describe the water saturation at which all the volumes from the properties of nearby shales. water is adsorbed on the grains in a rock or is held in the capillaries by capillary pressure. At irreducible water saturation, water does not move and the relative Permeability permeability to water is zero. Permeability is the ability of a rock to transmit fluids. It is related to porosity but is not always dependent Resistivity upon it. Permeability is controlled by the size of the connecting passages (pore throats or capillaries) Resistivity is the rock property on which the entire between pores. It is measured in darcys or millidarcys science of logging first developed. Resistivity is the (md) and is represented by the symbol K. The ability inherent property of all materials, regardless of their of a rock to transmit a single fluid, when it is com- shape and size, to resist the flow of an electric current. pletely saturated with that fluid, is called absolute per- Different materials have different abilities to resist the meability. Effective permeability refers to the ability of flow of electricity. the rock to transmit one fluid in the presence of anoth- While the resistance of a material depends on its er fluid when the two fluids are immiscible. shape and dimensions, the resistivity is an invariant Formation water (connate water in the formation) property; the reciprocal of resistivity is conductivity. held by capillary pressure in the pores of a rock serves In log interpretation, the hydrocarbons, the rock, and to inhibit the transmission of hydrocarbons. Stated dif- the fresh water of the formation are all assumed to act CH01_v2.qxd 8/5/04 10:42 AM Page 4 4 ASQUITH AND KRYGOWSKI as insulators and are, therefore, nonconductive (or at where m is the cementation exponent whose value least very highly resistive) to electric current flow. Salt varies with grain size, grain-size distribution, and the water, however, is a conductor and has a low resistivity. complexity of the paths between pores (tortuosity), The measurement of resistivity is then a measurement, and a is the tortuosity factor. The higher the tortuosity albeit indirect, of the amount (and salinity) of the for- of the formation, the higher the value of m. The tortu- mation water. The unit of measure used for the con- osity factor (a) is commonly set to 1.0, but is allowed ductor is a cube of the formation, one meter on each to vary by some petrophysicists. edge. The measured units are ohm-meters2/meter and Water saturation (Sw) is determined from the water- are called ohm-meters. filled resistivity (Ro) and the actual (true) formation resistivity (Rt) by the following relationship: r
A R= 1.4 1 L ⎛R ⎞n S w = ⎜⎜ o ⎟⎟ 1.7 where: ⎝ Rt ⎠ R = resistivity (ohm-m) r = resistance (ohms) where n is the saturation exponent, whose value typi- A = cross-sectional area of substance being meas- cally varies from 1.8 to 2.5 but is most commonly ured (m2) assumed to be 2. By combining equations 1.6 and 1.7, the water-sat- L = length of substance being measured (m) uration formula can be rewritten in the following form: Resistivity is a basic measurement of a reservoir’s 1 fluid saturation and is a function of porosity, type of ⎛ F
Rw ⎞ n fluid (i.e., hydrocarbons, salt water, or fresh water), S w = ⎜⎜ ⎟⎟ 1.8 amount of fluid, and type of rock. Because both the ⎝ Rt ⎠ rock and hydrocarbons act as insulators but salt water is conductive, resistivity measurements made by log- This is the formula that is most commonly referred to ging tools can be used to detect hydrocarbons and esti- as the Archie equation for water saturation (Sw). All mate the porosity of a reservoir. During the drilling of present methods of interpretation involving resistivity a well, fluids move into porous and permeable forma- curves are derived from this equation. In its most gen- tions surrounding a borehole, so resistivity measure- eral form, Archie’s equation becomes: ments recorded at different distances into a formation 1 often have different values. Resistivity is measured by ⎛ a
Rw ⎞ n electric logs, commonly known (in the West) as lat- S w = ⎜⎜ ⎟ m⎟ 1.9 erologs and induction logs. R ⎝ t
φ ⎠ Conrad Schlumberger in 1912 began the first exper- iments which led, eventually, to the development of Table 1.1 illustrates the range of values for a and m. modern-day petrophysical logs. The first electric log In first-pass or reconnaissance-level interpretations, or was run September 5, 1927, by H. G. Doll in Alsace- where there is no knowledge of the local parameters, Lorraine, France. In 1941, G. E. Archie with Shell Oil the following values can be used to achieve an initial Company presented a paper to the AIME in Dallas, estimate of water saturation: Texas, which set forth the concepts used as a basis for modern quantitative log interpretation (Archie, 1942). a = 1.0; m = n = 2.0 Archie’s experiments showed that the resistivity of a water-filled formation (Ro) could be related to the re- Now that the reader is introduced to some of the sistivity of the water (Rw) filling the formation through basic concepts of well log interpretation, our discus- a constant called the formation resistivity factor (F): sion can continue in more detail about the factors that affect logging measurements. Ro = F
R w 1.5 Archie’s experiments also revealed that the forma- BOREHOLE ENVIRONMENT tion factor (F) could be related to the porosity of the Where a hole is drilled into a formation, the rock formation by the following formula: plus the fluids in it (the rock-fluid system) are altered a in the vicinity of the borehole. The borehole and the F= 1.6 φm rock surrounding it are contaminated by the drilling mud, which affects logging measurements. Figure 1.1 CH01_v2.qxd 8/5/04 10:42 AM Page 5 Basic Relationships of Well Log Interpretation 5 Table 1.1. Different coefficients and exponents used to calculate formation factor (F). (Modified after Asquith, 1980.) a: Tortousity m: Cementation Comments factor exponent 1.0 2.0 Carbonates1 0.81 2.0 Consolidated sandstones1 0.62 2.15 Unconsolidated sands (Humble formula)1 1.45 1.54 Average sands (after Carothers, 1968) 1.65 1.33 Shaly sands (after Carothers, 1968) 1.45 1.70 Calcareous sands (after Carothers, 1968) 0.85 2.14 Carbonates (after Carothers, 1968) 2.45 1.08 Pliocene sands, southern California (after Carothers and Porter, 1970) 1.97 1.29 Miocene sands, Texas–Louisiana Gulf Coast (after Carothers and Porter, 1970) 1.0 φ(2.05-φ) Clean granular formations (after Sethi, 1979) 1Most commonly used is a schematic illustration of a porous and permeable tion pressure prevents blowouts. The density of the formation that is penetrated by a borehole filled with mud is usually kept high enough so that hydrostatic drilling mud. pressure in the mud column is greater than formation Some of the more important symbols shown in Fig- pressure. This pressure difference forces some of the ure 1.1 are: drilling fluid to invade porous and permeable forma- tions. As invasion occurs, many of the solid particles Hole Diameter (dh) (i.e., clay minerals from the drilling mud) are trapped on the side of the borehole and form mud cake (having The borehole size is determined by the outside a resistivity of Rmc; Figure 1.1). Fluid that filters into diameter of the drill bit. But, the diameter of the bore- the formation during invasion is called mud filtrate hole may be (with a resistivity of Rmf; Figure 1.1). The resistivity larger than the bit size because of washout values for drilling mud, mud cake, and mud filtrate are and/or collapse of shale and poorly cemented recorded on a log’s header (Figure 1.2), and are used porous rocks, or in interpretation. smaller than the bit size because of a build up of mud cake on porous and permeable formations Invaded Zone (Figure 1.1). Common borehole sizes normally vary from 7-7/8 The zone in which much of the original fluid is in. to 12 in., and modern logging tools are designed to replaced by mud filtrate is called the invaded zone. It operate within these size ranges. The size of the bore- consists of a flushed zone (of resistivity Rxo) and a hole is measured by a caliper log. transition or annulus zone (of resistivity Ri). The flushed zone occurs close to the borehole (Figure 1.1) where the mud filtrate has almost completely flushed Drilling mud Resistivity (Rm) out a formation’s hydrocarbons and/or water (Rw). The transition or annulus zone, where a formation’s fluids Today, most wells are drilled with rotary bits and and mud filtrate are mixed, occurs between the flushed the use of a special fluid, called drilling mud, as a cir- zone and the uninvaded zone (of resistivity Rt). The culating fluid. The mud helps remove cuttings from uninvaded zone is defined as the area beyond the the wellbore, lubricate and cool the drill bit, and main- invaded zone where a formation’s fluids are unconta- tain an excess of borehole pressure over formation minated by mud filtrate. pressure. The excess of borehole pressure over forma- The depth of mud-filtrate invasion into the invaded CH01_v2.qxd 8/5/04 10:42 AM Page 6 6 ASQUITH AND KRYGOWSKI zone is referred to as diameter of invasion (di and dj; Sh = 1 – Sw Figure 1.1). The diameter of invasion is measured in inches or expressed as a ratio: dj/dh (where dh repre- where: sents the borehole diameter). The amount of invasion Sh = hydrocarbon saturation (i.e., the fraction of that takes place is dependent upon the permeability of pore volume filled with hydrocarbons). the mud cake and not upon the porosity of the rock. In Sw = water saturation of the uninvaded zone (i.e., general, an equal volume of mud filtrate can invade the fraction of pore volume filled with water). low-porosity and high-porosity rocks if the drilling muds have equal amounts of solid particles. The solid The ratio of the uninvaded zone’s water saturation particles in the drilling muds coalesce and form an (Sw) to the flushed zone’s water saturation (Sxo) is an impermeable mud cake. The mud cake then acts as a index of hydrocarbon moveability. barrier to further invasion. Because an equal volume of fluid can be invaded before an impermeable mud-cake INVASION AND RESISTIVITY PROFILES barrier forms, the diameter of invasion is greatest in low-porosity rocks. This occurs because low-porosity Invasion and resistivity profiles are diagrammatic, rocks have less storage capacity or pore volume to fill theoretical, cross-sectional views of subsurface condi- with the invading fluid, and, as a result, pores through- tions moving away from the borehole and into a for- out a greater volume of rock are affected. General mation. They illustrate the horizontal distributions of invasion diameters in permeable formations are the invaded and uninvaded zones and their correspon- dj/dh = 2, for high-porosity rocks; ding relative resistivities. There are three commonly recognized invasion profiles: dj/dh = 5, for intermediate-porosity rocks; and dj/dh = 10, for low-porosity rocks. step transition Flushed zone Resistivity (Rxo) annulus The flushed zone extends only a few inches from These three invasion profiles are illustrated in Figure the wellbore and is part of the invaded zone. If inva- 1.3. sion is deep or moderate, most often the flushed zone The step profile has a cylindrical geometry with an is completely cleared of its formation water by mud invasion diameter equal to dj. Shallow-reading resis- filtrate (of resistivity Rmf). When oil is present in the tivity logging tools read the resistivity of the invaded flushed zone, the degree of flushing by mud filtrate zone (Ri), while deeper reading resistivity logging can be determined from the difference between water tools read true resistivity of the uninvaded zone (Rt). saturations in the flushed (Sxo) zone and the uninvaded The transition profile also has a cylindrical geome- (Sw) zone (Figure 1.1). Usually, about 70% to 95% of try with two invasion diameters: di (flushed zone) and the oil is flushed out; the remaining oil is called resid- dj (transition zone). It is probably a more realistic ual oil [Sro = (1.0 - Sxo), where Sro is the residual oil model for true borehole conditions than is the step pro- saturation, (ROS)]. file. At least three resistivity measurements, each sen- sitive to a different distance away from the borehole, are needed to measure a transitional profile. These Uninvaded zone Resistivity (Rt) three measure resistivities of the flushed (Rxo), transi- tion (Ri), and uninvaded zones (Rt) (see Figure 1.3). The uninvaded zone is located beyond the invaded By using these three resistivity measurements, the zone (Figure 1.1). Pores in the uninvaded zone are deep reading resistivity measurement can be corrected uncontaminated by mud filtrate; instead, they are satu- to a more accurate value of true resistivity (Rt), and the rated with formation water (Rw), oil, and/or gas. depth of invasion can be determined. Even in hydrocarbon-bearing reservoirs, there is This ability to estimate the invasion in a formation always a layer of formation water on grain surfaces. arrived with the wide introduction of the dual induc- Water saturation (Sw; Figure 1.1) of the uninvaded tion and dual laterolog tools in the 1960s. As the zone is an important factor in reservoir evaluation names imply, each tool made two induction or two lat- because, by using water saturation data, a geologist erolog measurements. These two measurements inves- can determine a reservoir’s hydrocarbon saturation. tigate different distances into the formation and are Equation 1.3 expresses the calculation and is repeated referred to as medium and deep measurements. The here: word dual in the names of these logging tools can be CH01_v2.qxd 8/5/04 10:42 AM Page 7 Basic Relationships of Well Log Interpretation 7 confusing, because each tool also made a third meas- Hydrocarbon-bearing Zones urement, which was shallower than the medium and deep measurements. In the 1980s, array resistivity Figure 1.5 illustrates the borehole and resistivity tools made their appearance. Through the use of more profiles for hydrocarbon-bearing zones where the sensors, they investigate more distances into the for- resistivity of the mud filtrate (Rmf) for a freshwater mation (usually 5 to 7), which provides for a more mud is much greater than the resistivity of the forma- detailed picture of the formation and its invasion. tion water (Rw), and where Rmf of a saltwater mud is An annulus profile is only sometimes recorded on a approximately equal to Rw. A hydrocarbon zone invad- log, because it rapidly dissipates in a well. The annu- ed with freshwater mud results in a resistivity profile lus profile is detected only by an induction log run where the shallow (Rxo), medium (Ri), and deep (Rt) soon after a well is drilled. However, it is very impor- resistivity measurements all record high resistivities tant to a geologist, because the profile can only occur (Figure 1.5). In some instances, the deep resistivity is in zones that bear hydrocarbons. As the mud filtrate higher than the medium resistivity. When this happens, invades the hydrocarbon-bearing zone, the hydrocar- it is called the annulus effect. A hydrocarbon zone bons are moved out first. Next, formation water is invaded with saltwater mud results in a resistivity pro- pushed out in front of the mud filtrate, forming an file where the shallow (Rxo), medium (Ri), and deep annular (circular) ring at the edge of the invaded zone (Rt) resistivity measurements separate and record low (Figure 1.3). The annulus effect is detected by a high- (Rxo), intermediate (Ri) and high (Rt) resistivities (Fig- er resistivity reading on a deep induction log than by ure 1.5). Figures 1.8 and 1.9 illustrate the resistivity one on a medium induction log. curves for hydrocarbon zones invaded with either Log resistivity profiles illustrate the resistivity val- freshwater or saltwater mud. ues of the invaded and uninvaded zones in the forma- tion being investigated. They are of particular interest BASIC INFORMATION NEEDED because, by using them, a geologist can quickly scan a IN LOG INTERPRETATION log and look for potential zones of interest such as hydrocarbon zones. Because of their importance, Lithology resistivity profiles for both water-bearing and hydro- carbon-bearing zones are discussed here. These pro- In quantitative log analysis, there are several rea- files vary, depending on the relative resistivity values sons why it is important to know the lithology of a of Rw and Rmf. All the variations and their associated zone (i.e., sandstone, limestone, or dolomite). Porosi- profiles are illustrated in Figures 1.4 and 1.5. ty logs require a lithology or a matrix constant before the porosity (φ) of the zone can be calculated. The for- mation factor (F), a variable used in the Archie water- Water-bearing Zones saturation equation, also varies with lithology. As a consequence, the calculated water saturation changes Figure 1.4 illustrates the borehole and resistivity as F changes. Table 1.1 is a list of several different val- profiles for water-bearing zones where the resistivity of ues for calculating formation factor and illustrates how the mud filtrate (Rmf) for a freshwater mud is much lithology affects the formation factor. greater than the resistivity of the formation water (Rw), and where resistivity of the mud filtrate (Rmf) for a salt- water mud is approximately equal to the resistivity of Formation Temperature the formation water (Rw). A freshwater mud (i.e., Rmf > Formation temperature (Tf) is also important in log 3 Rw) results in a wet log profile where the shallow analysis, because the resistivities of the drilling mud (Rxo), medium (Ri), and deep (Rt) resistivity measure- (Rm), the mud filtrate (Rmf), and the formation water ments separate and record high (Rxo), intermediate (Ri), (Rw) vary with temperature. The temperature of a for- and low (Rt) resistivities (Figure 1.4). A saltwater mud mation is determined by knowing: (i.e., Rw = Rmf ) results in a wet profile where the shal- low (Rxo), medium (Ri), and deep (Rt) resistivity meas- formation depth urements all read low resistivity (Figure 1.4). Figures bottom hole temperature (BHT) 1.6 and 1.7 illustrate the resistivity curves for wet zones total depth of the well (TD) invaded with either freshwater or saltwater mud. surface temperature CH01_v2.qxd 8/5/04 10:42 AM Page 8 8 ASQUITH AND KRYGOWSKI A reasonable value for the formation temperature y = 166° formation temperature at 8,000 ft can be determined by using these data and by assum- After a formation’s temperature is determined ing a linear geothermal gradient (Figure 1.10). The either by chart (Figure 1.10) or by calculation, the formation temperature is also calculated (Asquith, resistivities of the different fluids (Rm, Rmf, or Rw) can 1980) by using the linear regression equation: be corrected to formation temperature. Figure 1.11 is a y = mx + c 1.10 chart that is used for correcting fluid resistivities to the formation temperature. This chart is closely approxi- where: mated by the Arp’s formula: x = depth y = temperature Rtemp (Temp + 6.77 ) RTF = m = slope (In this example it is the geothermal gra- (T f + 6.77) dient.) 1.10 ⎛ Rtemp (Temp + 21.0) for depth ⎞ c = a constant (In this example it is the mean annu- ⎜= ⎟ al surface temperature.) ⎜ ⎝ (T f + 21.0) in meters ⎟⎠ An example of how to calculate formation temper- ature is illustrated here: where: RTF = resistivity at formation temperature Temperature Gradient Calculation Rtemp = resistivity at a temperature other than for- mation temperature Assume that: Temp = temperature at which resistivity was meas- y = bottom hole temperature (BHT) = 250°F ured (usually Fahrenheit for depth in feet, Celsius x = total depth (TD) = 15,000 ft for depth in meters) c = mean annual surface temperature = 70°F Tf = formation temperature (usually Fahrenheit for depth in feet, Celsius for depth in meters) Solve for m (i.e., slope or temperature gradient): Using a formation temperature of 166°F and assuming y −c an Rw of 0.04 measured at 70°F, the Rw at 166°F is: m= x Rw166 = 0.04
(70 + 6.77) / (166 + 6.77) Rw166 = 0.018 ohm-m Therefore, Resistivity values of the drilling mud (Rm), mud fil- 250° − 70° trate (Rmf), mud cake (Rmc), and the temperatures at m= which they are measured are recorded on a log’s head- 15,000 ft er (Figure 1.2). The resistivity of a formation’s water m = 0.012° / ft or 1.2° / 100 ft (Rw) is obtained by analysis of water samples from a drill stem test, a water-producing well, or from a cata- Formation Temperature Calculation log of water resistivity values. Formation water resis- tivity (Rw) is also determined from the spontaneous- Assume: potential log (discussed in Chapter 2), or it can be cal- m = temperature gradient = 0.012°/ft culated in water zones (i.e., where Sw =1) by the appar- x = formation depth = 8,000 ft ent water resistivity (Rwa) method (see Chapter 7). c = surface temperature = 70° COMMON EQUATIONS Remember: Table 1.2 is a list of common equations that are y = mx + c used for the log evaluation of potential hydrocarbon Therefore: reservoirs. These formulas are discussed in detail in y = (0.012
8,000) + 70 subsequent chapters. CH01_v2.qxd 8/5/04 10:42 AM Page 9 Basic Relationships of Well Log Interpretation 9 Table 1.2. Common equations of well-log interpretation Porosity, φ: Water saturation: 1 ∆t log − ∆t matrix Sonic log porosity φ Sonic = ⎛ a
Rw ⎞ n Water saturation in ∆t fluid − ∆t matrix (Wyllie time-average equation) S w = ⎜⎜ m⎟ ⎟ ⎝Rt
φ ⎠ the uninvaded zone 1 5 ⎛ ∆t log − ∆t matrix ⎞ Sonic log porosity ⎛ a
Rmf ⎞ n Water saturation in the φ Sonic =
⎜ ⎟ S xo = ⎜⎜ ⎟ m⎟ 8 ⎜⎝ ∆t log ⎟ (Raymer-Hunt-Gardner equation) ⎠ ⎝ R xo
φ ⎠ flushed zone 0.625 ⎛ R /R ⎞ S w = ⎜ xo t ⎟ Water saturation, ρ matrix − ρ bulk (log) ⎜R /R ⎟ φ Density = Density log porosity ⎝ mf w ⎠ ratio method ρ matrix − ρ fluid φ N2 + φ D2 Porosity in a gas zone Bulk volume water: φ NDgas = from neutron and density 2 BVW = φ
S w Formation factor, F: Permeability (estimated): F = a /φ m General form of the equation 2 Permeability in ⎛ ⎛ φ3 ⎞⎞ K e = ⎜250
⎜⎜ ⎟⎟ ⎟⎟ millidarcys, oil ⎜ F = 1.0 / φ 2.0 Carbonates ⎝ ⎝ S wirr ⎠⎠ reservoir F = 0.81 / φ 2.0 Consolidated sandstones ⎛ ⎛ φ3 ⎞⎞ 2 Permeability in K e = ⎜79
⎜⎜ ⎟⎟ ⎟⎟ millidarcys, gas ⎜ ⎝ ⎝ S wirr ⎠⎠ F = 0.62 / φ 2.15 Unconsolidated sands reservoir Formation-water resistivity: SSP = − K
log(Rmf / Rw) Basic SP response equation (K
log(Rmf ) + SP ) / K First-order approximation Rw = 10 of Rw from the SP CH01_v2.qxd 8/5/04 10:42 AM Page 10 10 ASQUITH AND KRYGOWSKI REVIEW tion by mud filtrate creates invaded zones around the wellbore. Shallow-, medium-, and deep-reading resis- 1. The four most fundamental rock properties used tivity measurements provide information about the in petrophysical logging are: invaded and uninvaded zones and about the depth of porosity invasion of the drilling fluid. permeability 5. The lithology of a formation must be known water saturation because: lithology A matrix value (usually sandstone, limestone, or 2. The Archie equation for water saturation is: dolomite) is needed to determine porosity from 1 logs. ⎛ a
Rw ⎞ n S w = ⎜⎜ m⎟ ⎟ The formation factor varies with lithology. ⎝ Rt
φ ⎠ The variation in the formation factor changes the water-saturation values. where: 6. The four fluids (and the symbols for their resis- Sw = water saturation of uninvaded zone tivity) that affect logging measurements are: Rw = formation water resistivity drilling mud (Rm) Rt = formation resistivity (uninvaded zone) φ = porosity mud filtrate (Rmf) a = tortousity factor formation water (Rw) m = cementation exponent hydrocarbons (assumed infinite resistivity, no n = saturation exponent symbol) 3. Where a porous and permeable formation is pen- 7. The resistivities of the drilling mud (Rm), mud etrated by the drill bit, the liquid part of the drilling cake (Rmc), mud filtrate (Rmf) and formation water mud invades the formation as mud filtrate. The mud (Rw) all vary with changes in temperature. Conse- filtrate resistivity is designated Rmf. quently, a formation’s temperature (Tf) must be deter- 4. The invasion of a porous and permeable forma- mined and all resistivities corrected to Tf. CH01_v2.qxd 8/5/04 10:42 AM Page 11 Basic Relationships of Well Log Interpretation 11 Figure 1.1. The borehole environment and symbols used in log interpretation. This schematic diagram illustrates an idealized version of what happens when fluids from the borehole invade the surrounding rock. Dotted lines indicate the cylindrical nature of the invasion. dh = hole diameter di = diameter of invaded zone (inner boundary of flushed zone) dj = diameter of invaded zone (outer boundary of invaded zone) ∆rj = radius of invaded zone (outer boundary) hmc = thickness of mud cake Rm = resistivity of the drilling mud Rmc = resistivity of the mud cake Rmf = resistivity of mud filtrate Rs = resistivity of the overlying bed (commonly assumed to be shale) Rt = resistivity of uninvaded zone (true formation resistivity) Rw = resistivity of formation water Rxo = resistivity of flushed zone Sw = water saturation of uninvaded zone Sxo = water saturation flushed zone Courtesy Schlumberger Wireline & Testing, ©1998 Schlumberger 1 Figure 1.2. Reproduction of a typical log heading. This is the first page of a typical log heading. Following pages contain details of the logging equipment used, the scales used to display the data, general information about the borehole direction, remarks about the logging job, and a disclaimer which outlines the responsibilities of both the acquisition 2 company and the client. 1. The title indicates the services that are associated with the data that appear on this log. 3 2. Basic well name and location information. 3. More detailed information about the physical surface 4 location of the well. 5 4. Other services that were run at the same time (during the same trip to the well) as the services in this log. 5. Information about location and elevation from which the well depths are measured. K.B. = kelly bushing elevation, D.F. = drill floor elevation, G.L. = ground level elevation, 6 T.K.B. = top of kelly bushing 6. Environmental information about the well. The drilling mud and borehole size values are especially important in applying the proper environmental corrections and interpretation parameters to the data. 7. General information about the logging equipment, the engineer, and any clients who witnessed the logging job. More detailed information about the specific logging tools is listed in the pages that usually follow this one and in tables that detail the calibration techniques and results. 7 CH01_v2.qxd 8/5/04 10:42 AM Page 12 12 ASQUITH AND KRYGOWSKI Figure 1.3. Resistivity profiles for three idealized versions of fluid distributions in Step Profile the vicinity of the borehole. As mud filtrate (Rmf) moves into a porous and permeable formation, it can invade the formation in several different ways. Various fluid borehole wall distributions are represented by the step, transition, or annulus profiles. All three profiles illustrate the effect of a freshwater mud; for profiles using saltwater mud see figures 1.4 and 1.5. Mud cake thickness is indicated by hmc. Rxo Step profile: Resistivity This idealized model is the one inferred by the use of three resistivity logs to esti- mate invasion. Mud filtrate is distributed with a cylindrical shape around the borehole Ro and creates an invaded zone. The cylindrical invaded zone is characterized by its abrupt contact with the uninvaded zone. The diameter of the cylinder is represented as dj. In the invaded zone, pores are filled with mud filtrate (Rmf); pores in the uninvaded zone are filled with formation water (Rw) and hydrocarbons. In this example, the uninvaded zone is wet (water saturated and no hydrocarbons), thus the resistivity beyond the invaded zone is low. The resistivity of the invaded zone is Rxo, and the resistivity of the hmc di dj uninvaded zone is Rt (where Rt reduces to Ro when the formation is water bearing). Distance from the borehole Transition profile: This is the most realistic model of true borehole conditions. Here again invasion is Transition Profile cylindrical, but in this profile, the invasion of the mud filtrate (Rmf) diminishes gradually, rather than abruptly, through a transition zone toward the outer boundary of the invad- borehole wall ed zone (see dj on diagram for location of outer boundary). In the flushed part (Rxo) of the invaded zone, pores are filled with mud filtrate Rxo (Rmf), giving a high resistivity reading. In the transition part of the invaded zone, pores are filled with mud filtrate (Rmf), formation water (Rw), and, if present, residual hydro- Ri Resistivity carbons. Beyond the outer boundary of the invaded zone, pores are filled with either formation water or formation water and hydrocarbons. In this diagram, hydrocarbons are not present, so resistivity of the uninvaded zone is low. The resistivity of the invad- Ro ed zone is Rxo, and the resistivity of the uninvaded zone is Rt (where Rt reduces to Ro when the formation is water bearing). Annulus profile: This reflects a temporary fluid distribution and is a condition that should disappear hmc di dj with time (if the logging operation is delayed, it might not be recorded on the logs at all). The annulus profile represents a fluid distribution that occurs between the invaded Distance from the borehole zone and the uninvaded zone and only exists in the presence of hydrocarbons. Annulus Profile In the flushed part (Rxo) of the invaded zone, pores are filled with both mud fil- trate (Rmf) and residual hydrocarbons. Thus the resistivity reads high. Pores beyond the borehole wall flushed part of the invaded zone (Ri) are filled with a mixture of mud filtrate (Rmf), for- mation water (Rw), and residual hydrocarbons. Rxo Beyond the outer boundary of the invaded zone is the annulus zone, where pores Ri are filled with formation water (Rw) and residual hydrocarbons. When an annulus pro- Rt Resistivity file is present, there is an abrupt drop in measured resistivity at the outer boundary of the invaded zone. The abrupt resistivity drop is due to the high concentration of forma- tion water (Rw) in the annulus zone. Formation water has been pushed ahead by the invading mud filtrate into the annulus zone. This causes a temporary absence of hydro- Ro carbons, which have been pushed ahead of the formation water. Beyond the annulus is the uninvaded zone, where pores are filled with formation water (Rw) and hydrocarbons. The resistivity of the invaded zone is Rxo, and the resis- hmc di dj tivity of the uninvaded zone is Rt (where Rt reduces to Ro when the formation is water bearing). Distance from the borehole CH01_v2.qxd 8/5/04 10:42 AM Page 13 Basic Relationships of Well Log Interpretation 13 Figure 1.4. Resistivity profile for a transition-style invasion of a water-bearing formation. Note: These examples are shown because freshwater muds and saltwater muds are used in different geographic regions, usually exclusively. The geologist needs to be aware that a difference exists. To find out which mud is used in your area, check the log heading of existing wells or ask your drilling engineer. The type of mud used affects the log package selected, as will be shown in later chapters. Freshwater muds: The resistivity of the mud filtrate (Rmf) is greater than the resistivity of the formation water (Rw) (remember, saltwater is conductive). A general rule when freshwater muds are used is: Rmf > 3 Rw. The flushed zone (Rxo), which has a greater amount of mud filtrate, has higher resistivities. Away from the borehole, the resistivity of the invaded zone (Ri) decreases due to the decreasing amount of mud filtrate (Rmf) and the increasing amount of formation water (Rw). With a water-bearing formation, the resistivity of the uninvaded zone is low because the pores are filled with formation water (Rw). In the uninvaded zone, true resistivity (Rt) is equal to wet resistivity (Ro) because the formation is completely saturated with formation water (Rt = Ro where the formation is completely saturated with formation water). Resistivity To summarize: in a water-bearing zone, the resistivity of the flushed zone (Rxo) is greater than the resistivity of the invaded zone (Ri), which in turn has a greater resistivity than the uninvaded zone (Rt). Therefore: Rxo> Ri > Rt in water-bearing zones. Saltwater muds: Distance from the borehole Because the resistivity of mud filtrate (Rmf) is approximately equal to the resistivity of formation water (Rmf ~ Rw), there is no appreciable difference in the resistivity from the flushed (Rxo) to the invaded zone (Ri) Resistivity to the uninvaded zone (Rxo = Ri = Rt); all have low resistivities. Both the above examples assume that the water saturation of the uninvaded zone is much greater than 60%. Distance from the borehole CH01_v2.qxd 8/6/04 7:26 AM Page 14 14 ASQUITH AND KRYGOWSKI Figure 1.5. Resistivity profile for a transition-style invasion of a hydrocarbon-bearing formation. Freshwater muds: Because the resistivities of both the mud filtrate (Rmf) and residual hydrocarbons are much greater than formation water (Rw), the resistivity of the flushed zone (Rxo) is comparatively high (remember that the flushed zone has mud filtrate and some residual hydrocarbons). Beyond its flushed part (Rxo), the invaded zone (Ri) has a mixture of mud filtrate (Rmf), formation water (Rw), and some residual hydrocarbons. Such a mixture causes high resistivities. In some cases, resistivity of the invaded zone (Ri) almost equals that of the flushed zone (Rxo). The presence of hydrocarbons in the uninvaded zone causes higher resistivity than if the zone had only formation water (Rw), because hydrocarbons are more resistant than formation water. In such a case, Rt > Ro. The resistivity of the uninvaded zone (Rt) is normally somewhat less than the resistivity of the flushed and invaded zones (Rxo and Ri). However, sometimes when an annulus profile is present, the invaded zone’s resistivity (Ri) can be slightly lower than the uninvaded zone’s resistivity (Rt). To summarize: Rxo > Ri > Rt or Rxo > Ri < Rt in hydrocarbon-bearing zones. Saltwater muds: Because the resistivity of the mud filtrate (Rmf) is approximately equal to the resistivity of formation water (Rmf ~ Rw), and the amount of residual hydrocarbons is low, the resistivity of the flushed zone (Rxo) is low. Away from the borehole, as more hydrocarbons mix with mud filtrate in the invaded zone the resistivity of the invaded zone (Ri) increases. Resistivity of the uninvaded zone (Rt) is much greater than if the formation were completely water saturated (Ro) because hydrocarbons are more resistant than saltwater. Resistivity of the uninvaded zone (Rt) is greater than the resistivity of the invaded (Ri) zone. So, Rt > Ri > Rxo. Both the above examples assume that the water saturation of the uninvaded zone is much less than 60%. CH01_v2.qxd 8/5/04 10:42 AM Page 15 Basic Relationships of Well Log Interpretation 15 Figure 1.6. Example of dual induction log curves through a water-bearing zone. Given: the drilling mud is freshwater based (Rmf > 3Rw). Where freshwater drilling muds invade a water-bearing formation (Sw > 60%), there is high resistivity in the flushed zone (Rxo), a lesser resistivity in the invaded zone (Ri), and a low resistivity in the uninvaded zone (Rt). See Figure 1.4 for review. (Figure 1.8 shows the response of these resistivity curves in a hydrocarbon-bearing zone.) Compare the three curves on the right side of the log (tracks 2 and 3). Resistivity increases from left to right. A key for reading this logarithmic resistivity scale is shown at the bottom of the log. Depth scale is in feet with each vertical increment equal to 2 ft. Log curve ILD: Deep induction log resistivity curves usually measure true formation resistivity (Rt), the resistivity of the formation beyond the outer boundary of the invaded zone. In water-bearing zones (in this case from 5870 to 5970 ft), the curve reads a low resistivity because the pores of the formation are saturated with low resistivity connate water (Rw). Log curve ILM: Medium induction log resistivity curves measure the resistivity of the invaded zone (Ri). In a water-bearing formation, the curve reads a resistivity between Rt and Rxo because the fluid in the formation is a mixture of formation water (Rw) and mud filtrate (Rmf). Log curve SFLU: Spherically focused log resistivity curves measure the resistivity of the flushed zone (Rxo). In a water-bearing zone, the curve reads a high resistivity because freshwater mud filtrate (Rmf) has a high resistivity. The SFL pictured here records a greater resistivity than either the deep (ILD) or medium (ILM) induction curves. CH01_v2.qxd 8/5/04 10:42 AM Page 16 16 ASQUITH AND KRYGOWSKI Figure 1.7. Example of dual laterolog curves through a water-bearing zone. Given: The drilling mud is saltwater based (Rmf ~ Rw). Where saltwater drilling muds invade a water-bearing formation (Sw > 60%), there is low resistivity in the flushed zone (Rxo), a low resistivity in the invaded zone (Ri), and low resistivity in the uninvaded zone (Rt). Because Rmf is approximately equal to Rw, the pores in the flushed (Rxo), invaded (Ri), and uninvaded (Rt) zones are all filled with saline waters; the presence of salt results in low resistivity. See Figure 1.4 for review. (Figure 1.9 shows the response of these resistivity curves in a hydrocarbon-bearing zone.) Compare the three curves on the right side of the log (tracks 2 and 3). Resistivity increases from left to right. A key for reading this logarithmic resistivity scale is shown at the bottom of the log. Depth scale is in feet with each vertical increment equal to 2 ft. Log curve LLD: Deep laterolog resistivity curves usually measure true formation resistivity (Rt), the resistivity of the formation beyond the outer boundary of the invaded zone. In water-bearing zones (in this case from 9866 to 9924 ft), the curve reads a low resistivity because the pores of the formation are saturated with low resistivity connate water (Rw). Log curve LLS: Shallow laterolog resistivity curves measure the resistivity in the invaded zone (Ri). In a water-bearing zone, the shallow laterolog (LLS) records a low resistivity because Rmf is approximately equal to Rw. Log curve RXO: Microresistivity curves measure the resistivity of the flushed zone (Rxo). In water-bearing zones the curve records a low resistivity because saltwater mud filtrate has low resistivity. The resistivity recorded by the microresistivity log is low and approximately equal to the resistivities of the invaded and uninvaded zones. CH01_v2.qxd 8/5/04 10:42 AM Page 17 Basic Relationships of Well Log Interpretation 17 Figure 1.8. Example of dual induction log curves through a hydrocarbon-bearing zone. Given: the drilling mud is freshwater based (Rmf > 3Rw). Where freshwater drilling muds invade a hydrocarbon-bearing formation (Sw < 60%), there is high resistivity in the flushed zone (Rxo), high resistivity in the invaded zone (Ri), and high resistivity in the uninvaded zone (Rt). Normally, the flushed zone has slightly higher resistivity than the uninvaded zone. See Figure 1.5 for review. (Figure 1.6 shows the response of these resistivity curves in a water-bearing zone.) Compare the three curves on the right side of the log (tracks 2 and 3). Resistivity increases from left to right. Log curve ILD: Deep induction log resistivity curves usually measure true formation resistivity (Rt), the resistivity of the formation beyond the outer boundary of the invaded zone. In hydrocarbon-bearing zones (in this case from 8748 to 8774 ft), the curve records a high resistivity because hydrocarbons are more resistant than saltwater in the formation (Rt > Ro). Log curve ILM: Medium induction log resistivity curves measure the resistivity of the invaded zone (Ri). In a hydrocarbon-bearing zone, because of a mixture of mud filtrate (Rmf), formation water (Rw), and residual hydrocarbons in the pores, the curve records a high resistivity. This resistivity is normally equal to or slightly more than the deep induction curve (ILD). But, in an annulus situation, the medium curve (ILM) can record a resistivity slightly less than the deep induction (ILD) curve. Log curve SFLU: Spherically focused log resistivity curves measure the resistivity of the flushed zone (Rxo). In a hydrocarbon-bearing zone, the curve reads a higher resistivity than the deep (ILD) or medium (ILM) induction curves because the flushed zone (Rxo) contains mud filtrate and residual hydrocarbons. The SFL pictured here records a greater resistivity than either the deep (ILD) or medium (ILM) induction curves. CH01_v2.qxd 8/5/04 10:42 AM Page 18 18 ASQUITH AND KRYGOWSKI Figure 1.9. Example of dual laterolog curves through a hydrocarbon-bearing zone. Given: The drilling mud is saltwater based (Rmf ~ Rw). Where saltwater drilling muds invade a hydrocarbon-bearing formation (Sw