(2009) SPE 121972 Khaksar- Rock Strength From Core and Logs

SPE 121972

Rock Strength from Core and Logs: Where We Stand and Ways to Go A. Khaksar, P.G. Taylor, Z. Fang, T. Kayes, A. Salazar, K. Rahman; SPE, Helix RDS

Copyright 2009, Society of Petroleum Engineers This paper was prepared for presentation at the 2009 SPE EUROPEC/EAGE Annual Conference and Exhibition held in Amsterdam, The Netherlands, 811 June 2009. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract Knowledge of accurate rock strength is essential for in situ stress estimation, wellbore stability analysis, sand production prediction and other geomechanical applications. Reliable quantitative data on rock strength can only be obtained from cores. However, cores are limited, discontinuous and often biased. Consequently, rock strength evaluation is primarily based on log strength indicators, calibrated where possible against limited core measured values. There are a number of published log-core strength correlations that can be used for rock strength modelling. These empirical relationships are developed for specific rock type, age, depth range and field. Their general applications, therefore, need to be critically assessed on a case by case basis. This paper briefly: (i) outlines the best practice for obtaining quality rock strength data from core tests; (ii) presents common empirical rock strength equations for sedimentary rocks and (iii) discusses ways of improving rock strength estimates.

While some equations such as porosity-based or sonic log-based rock strength models work reasonably well, rock strength variations within individual rock properties show considerable scatter, indicating that most of the empirical models are not sufficiently generic to fit all rocks in the database. Like any other physical rock properties, the variation in rock strength in a given sedimentary rock is controlled by mineralogy, sedimentology and micro-structure of the rock and simple log-derived rock strength models need further modification and classification incorporating these geological characteristics.

This paper has shown that when sufficient core rock strength data exists, applications of computing techniques, such as fuzzy logic and cluster pattern recognition, coupled with sedimentary facies analysis and diagenetic classification can improve strength estimation. Semi-continuous impact energy logs using portable non-destructive testing tools can be correlated with petrophysical logs to generate mechanical facies and improved sampling for conventional rock testing. Introduction Rock mechanical properties are essential for accurate in situ stress analysis and geomechanical evaluations including wellbore stability analysis, sand production prediction and management, hydraulic fracturing design, fault stability and reactivation analysis and other geomechanical applications. The rock mechanical parameters typically required to populate a geomechanical model based on the linear Mohr-Coulomb failure criterion are: Unconfined Compressive Strength (UCS or C0), Friction angle () or Coefficient of internal friction, (where = tan), as well as Thick Wall or hollow Cylinder strength (TWC) which may be needed for sanding evaluation and calibration. These properties are commonly known as rock strength parameters. Other essential rock mechanical properties are elastic moduli. The two most common required elastic constants are; Poissons ratio () and Youngs modulus (E) from which other elastic moduli such as shear and bulk moduli can be derived. While rock elastic moduli can be derived from well logs (bulk density, both compressional and shear sonic logs), reliable quantitative data on rock strength parameters can only be derived at specific depths from laboratory tests on core samples. Laboratory measurements of elastic moduli on core samples subjected to the in-situ stress condition are also needed to calibrate log-derived (dynamic) elastic moduli to static values measured on cores.

Laboratory-based rock strength values are typically determined through triaxial tests on cylindrical samples that are obtained from cores at depths of interest. Continuous profiles of rock strength against depth can be estimated using well logs and empirical core-log relationships. Ideally, log-derived strengths should be calibrated by direct laboratory measured values to ensure that the results are reasonable for the rocks under analysis. However, in most cases the core strength databases are limited, discontinuous and often biased toward stronger intervals. Quality core plugs of non-reservoir formations (for example, mudstones and shales), where most of hole instability problems occur, are rarely available for testing. In practice, many geomechanical problems are often addressed in the absence of core samples for laboratory testing. Consequently, rock strength evaluation is primarily based on log strength indicators, calibrated where possible against limited core measurements.

2 SPE 121972

There are a number of published log-core strength correlations that can be used to develop a rock strength model. These empirical relationships are developed for specific rock type, age, depth range, field or sedimentary basin and their applications to other rocks may not be reliable unless they are calibrated with specific field conditions. This paper first briefly outlines good practices for obtaining quality rock strength data from core tests then presents common empirical rock strength equations and discusses ways of improving rock strength estimates. Rock Strength from Core Tests Rock mechanics has traditionally carried an air of mystique; practitioners are frequently regarded as Rock Docs and, as a consequence, acquisition of important input data for geomechanics modelling has all too often been neglected in the oil and gas industry. Even in the early years of the twenty first century, a lack of awareness for good industry practice in planning for rock mechanics studies can result in costly well problems. This is then followed by rushed geomechanics studies with little useful data with which to fire fight. This section offers some advice on how best to plan in readiness for rock mechanics testing and the importance of good sample selection and plug preparation. The emphasis is on the workflow process prior to laboratory testing, because this will ensure the most representative samples from which the final model will be calibrated. Finally, a brief review is made of some of the supplementary testing that can help explain results of geomechanical empirical and analytical computations.

Planning for Sampling and Core Tests. Core is acquired at great expense and is a precious resource. This is recognised for the needs of petrophysics, but all too often samples for rock mechanics testing are forgotten about until after the initial slab cut is made. This reduces the core diameter and hence the plug length; usually making the length to diameter ratio unacceptable. Worse still, no samples for rock mechanics tests are cut and the core is allowed to dry out and possibly deteriorate, depending on mineralogy.

Planning the rock mechanics programme must be done well in advance of the core being cut, because there are many interests to accommodate and potential pitfalls to overcome. Good communications between different departments will help streamline the process, maximise the benefits of geomechanics and avoid repeated work. Quite often, wellbore stability (WBS) is considered by the drilling group and, separate to this, sand production issues by the reservoir engineering, production technology and completion design teams. For both studies a common geomechanical model will be required; its two essential elements being in situ stresses and rock strength. An interdisciplinary planning team should be assembled from drilling, geology, petrophysics, reservoir engineering, well engineering, production technology, geophysics and, geomechanics (assuming a geomechanics department or specialist exists) to plan coring, laboratory testing (rock mechanics, routine and special core analysis including formation damage) and logging (mud and wireline/LWD).

It is useful to speak with other operators of reservoirs producing from the same or similar formation(s). Even though such matters may only be discussed at a high level, guidance on rock strength and related rock mechanics issues can be sought and will help focus the needs of the laboratory test programme.

In summary the essentials of planning requirements are: Is core planned to be cut in the new well or is core from offset wells required? Is there suitable preserved core available for testing from offset wells? Can preserved samples be used for rock mechanics testing? If unpreserved core is all that is available, has it degraded on exposure to air or moisture? If unpreserved core is acceptable, can representative plugs be cut? Will it be necessary to scan the core/preserved core before cutting plugs? Should a plug fail, can a replacement plug of similar rock properties be taken? What is the availability and schedule of the rock mechanics testing laboratory?

It must also be highlighted that integral to rock strength from core testing is the chosen suit of wireline/LWD logs run through the overburden, reservoir and underburden. The calibrated rock strength algorithms, established between the core and equivalent logged interval, must accurately compute rock strength throughout the un-cored sections of the reservoir (or well) based on well log data alone. The accuracy of computation is then solely dependent on the type and resolution of well logs. It is therefore essential that the planning process takes account of these needs when determining the suites of logs to be run.

Sample Selection. Sample selection is a critical step in the rock strength workflow and must be afforded the time and effort in order to make the process robust. This process is the kingpin between two very costly stages: obtaining the core and rock strength determination (laboratory and modelling). The aim of sample selection is to supply the rock testing laboratory with a range of samples which represent all the facies, rock types and rock strengths present in the core. This is not a simple process and can seldom be done from visual recognition alone.

When choosing the sections of core from which the plugs are to be cut, as much information as possible should be available. This includes, but is not limited to, geological reports, including the depositional environment, petrology, mineralogy, sedimentology and structure. Basic core analysis may already have been conducted and so porosity and permeability data can be reviewed in context with the core. More recent workflows now include non-destructive tests (NDT); impact strength or scratch testing along the entire length of the core. This readily reveals the full range in relative strength and

SPE 121972 3

is the first direct measurement of rock strength, as opposed to geological, routine core analysis (RCA) data and wireline logs which are all indirect strength indicators. Visual inspection of the core is also important in conjunction with all previously mentioned methods, whereby rock textures, mineralogy and cements are quickly appraised, all in the context of rock strength from micro to bed scale.

When ready to select the sampling points, the person responsible should be clear as to what rock mechanics tests are to be performed, as to determine the type, amount and number of samples required. For example, a single stage triaxial compressive test will require a minimum of three or four plugs at each sample point. To summarise the essentials of sampling requirements:

Each facies or lithology type must be represented. Samples must be representative of the range in rock strengths throughout that facies or lithology type, based on NDT

testing, well logs, textures, cements, etc. The correct number of samples can be cut to meet the requirements of the tests. Sample sets to be as close to each other as physically possible; essential in heterogeneous formations. Core diameter or remaining pieces of core are of sufficient size from which to cut a plug of 1:2 diameter to minimum

length ratio. Clay-rich sandstones or mudrocks (e.g. shale) are best sampled from preserved cores.

The choice of samples should however take into account the following: In unpreserved core, is the state of preservation representative for strength tests? Avoid the temptation to only sample strong looking sections of core, i.e. from which good plugs can be cut. Avoid choosing only interesting looking sections of core. It is normally the mundane sections which are most

representative. Micro-fractures, joints, natural fractures and faults are usually not representative and should, in the main, be avoided Material from wide fault or fracture zones such as breccia, fault gouge or rock flour should be sampled too. Such

debris can range from loose to well cemented and can be tested for rock strength, grain size distribution and petrological properties.

Mud rock sections (claystone, siltstone, shale, etc.) should be sampled for rock mechanics tests, mineralogy and clay reactivity tests.

Reservoir rocks should be examined for cement mineralogy. This helps in typing the range in rock strengths and for a cements propensity for dissolution.

Pre-screening of whole core is commonly undertaken prior to drilling plugs for petrophysics and rock mechanics testing. Computed axial tomography (CAT) scanning is probably the most frequently used method and identifies changes in density in traverse and longitudinal sections of the core. This method produces internal images of bedding, structure, mineralogy, fractures, vugs, mud (barite) invasion, etc. and is ideal for identifying suitable sections for plugging. Other methods of pre-screening include acoustic velocity (sonic) measurements taken along the core and core gamma, although neither of these provide the resolution or amount of useful data as CAT scanning.

Plug Preparation. Clear instructions must already have been given not to slab the core prior to rock mechanics sampling. The problem with core that has been slab sawn is that the core plugs are likely to be under size, i.e. < 2:1 length to diameter ratio required for test purposes and quality control. Plugs must be cut and prepared to very exacting standards otherwise the subsequent strength tests will be invalid. Plugs should be cut either perpendicular or parallel to bedding depending on the test requirement. In heterogeneous and laminated rocks, plugs cut at an oblique angle to the bedding (true dip) may be necessary to determine strength anisotropy.

Supplementary Testing. Many other techniques and tests are performed on core samples which supplement the rock strength data set. The principal methodologies include special core analysis (SCAL) and petrographic analyses. This work is usually commissioned by the Petrophysics and Reservoir Geology departments and copies of these data should be acquired for input to the geomechanics process. If it has not been planned to undertake any SCAL or petrographic studies of particular interest to the rock mechanics study, then these should be commissioned. The following list is a summary of the principal supplementary methodologies that can be incorporated within a laboratory rock strength test programme:

Particle (or grain) Size Distribution (PSD) analysis, Thin Section (TS) analysis/point counting (petrographic microscope), Scanning Electron Microscopy (SEM), X-Ray Diffraction (XRD), Cathodo-Luminescence microscopy (CL).

4 SPE 121972

Common Rock Mechanics Tests Single Stage Triaxial Compressive Tests (SST). Triaxial compressive tests are typically conducted on identical samples (at least three sets, ideally four or five plugs) for a range of confining pressures in order to establish a relationship between the axial load at failure (1) and the confining pressure (3). As a sample is confined it reinforces the sample so that the axial stress required to cause failure increases. Axial and radial strain measurements are made during each test so that static Youngs modulus and Poissons ratio data are obtainable for each sample. An example of an axial stress vs. axial strain plot from a typical triaxial stress experiment is shown in Figure 1.

Initially, the sample is soft, but it stiffens as the axial load increases, and eventually the relationship is approximately linear. An inelastic behaviour reflects the onset of internal damage and the sample becomes ductile once past this yield point. Ultimately, if the axial load continues to increase, it will reach a maximum, followed either by a catastrophic brittle failure or a roll-over plastic behaviour continued with residual strength, for which an increase in deformation can be achieved with no change in axial load. Some techniques for wellbore/perforation stability and sanding evaluation require both peak and residual strength parameters. Hence it is important to document the rock behaviour beyond the peak strength as the difference between the peak and residual strengths determines the load bearing capacity of the rock beyond initial failure.

The linearized Mohr-Coulomb failure criterion is a simple, and the most commonly used, criterion to define the state of stress and rock failure (Jaeger and Cook, 1979). The Mohr-Coulomb criterion defines a linear relationship between the stress difference at failure and the confining stress using two parameters: the cohesion, So and the friction angle, or the coefficient of internal friction, i, where i = tan. The linear criterion Mohr-Coulomb failure equation is:

= So + i n (1) These parameters can be derived from triaxial strength tests on cylindrical cores, by measuring the stress at failure as a

function of confining pressure. Figure 2 shows a series of Mohr circles in a plot of shear stress to effective normal stress n. The failure line (with slope i and intercept So) that touches each of the circles defines the parameters of the linear Mohr-Coulomb strength. The lower diagram in Figure 2 is a plot of 1 vs. 3, which is normally used to derive Mohr-Coulomb parameters directly. In this plot the linear Mohr-Coulomb criterion, is expressed in terms of principal stresses as follows:

kC 301 += (2) where is the maximum principal stress (the axial stress at failure in the test configuration), 3 is the confining stress (3 = 2). The intercept on the 1 axis is the unconfined (uniaxial) compressive strength (C0 or UCS), which corresponds the peak strength at zero confinement. k is the slope of the linear best fit to the data where:

sin1sin1

+=k (3)

and is the angle of internal friction. The Mohr-Coulomb failure parameters are obtained from the failure stress-confining stress relationship where:

kCSo 2

0= (4)

kk2

1tan == (5)

Multi-Stage Triaxial (MST) Compressive Tests. Multi-stage triaxial compressive tests are often used as an alternative to single stage triaxial tests when there is a shortage of quality samples. The multi-stage method requires a triaxial cell and carries out a series of tests on a single sample and the technique avoids the potential effects of rock heterogeneity between samples used in single stage tests. The first stage of an MST test is to establish a low confining pressure and increase the axial stress until the sample begins to yield. Axial stress at this condition is recorded. The cell pressure is then increased to a new value and axial loading proceeds until the new yield point is achieved. The procedure is repeated to obtain a total of 4 or 5 yield strength values. At the final stage, the test is continued beyond peak strength until residual strength is achieved. Mohr-Coulomb failure envelope parameters are then determined for peak strengths but not for the residual strength. Figure 3 shows an example of multi-stage triaxial test results for a sandstone plug.

It is not possible to obtain residual Mohr-Coulomb parameters from the MST test as residual strength is only determined at the final test confinement. Generally, multi-stage test results are less reliable than single stage triaxial tests. This is due to the

SPE 121972 5

nature of multi-stage tests in which one sample is subjected to several cycles of loading close to failure, but not to complete failure. Therefore, the rock strength parameters derived from multi-stage tests could represent one single failure plane created during the first loading cycle which would be reactivated on the subsequent loading and therefore the overall test results may not represent the properties of an intact sample. Nevertheless multi-stage triaxial test results are superior to unconfined (uniaxial) test results but careful testing procedure and monitoring is crucial in order to achieve useful test results.

Unconfined Compressive Strength (UCS) Tests. Because triaxial tests are expensive and time-consuming to conduct, it is common to carry out uniaxial or unconfined compressive strength tests in which the confining pressure is zero. The axial stress at failure in a uniaxial test is a direct measure of UCS or Co. Generally, compressive strength tests, conducted under zero confining pressure, underestimate the true strength of the rock due to formation of micro-cracks in rocks during the coring process and sample preparation. This can cause the sample to fail prematurely under uniaxial loading and do not provide a good measure of Co for use with a Mohr-Coulomb model. Furthermore, it is often difficult to derive the internal friction angle using one test, unless the sample is failed in shear and the failure plane is well defined. For these reasons, a series of triaxial tests is preferred.

Figure 4 shows examples of unconfined compressive tests on two sandstone plugs. The upper sample pictured in Figure 4 shows a well defined failure point on the stress-time (related to strain) plot but the sample has failed on conjugate shear planes, making it difficult to determine the angle of internal friction. The lower example pictured in Figure 4 shows a poorly defined peak failure point on the stress-time plot and multiple failure planes on the sample possibly due to poor sample quality. Both samples shown in Figure 4 have been tested after the RCA programme as there was insufficient core remaining for rock mechanics tests. The mechanical response of the lower sample shown shown in figure 4 (which is weaker than the sample above) is affected and the Co strength weakened, by the plug quality and sample damage which could have occurred during core preparation and porosity-permeability testing in the RCA programme. This emphasises the need to take separate samples for rock mechanics tests. Thick Wall Cylinder (TWC) Tests. Thick wall cylinder tests are normally used in analytical and numerical sand production and sanding rate predictions. In these tests a hollow cylindrical core plug is loaded axially and laterally under increasing hydrostatic stress (1=2=3), until collapse occurs in the walls of the cylinder. The hydrostatic stress at which failure initiates in the internal wall is reported as the TWC-Internal and the stress that causes external wall failure is called TWC External or TWC collapse. The external wall catastrophic failure pressure corresponds to the perforation failure condition that causes continuous and catastrophic sand production. The internal wall failure pressure is less than the catastrophic failure pressure and normally corresponds to the onset of transient sanding. This is often assumed to be manageable without using downhole sand control installations. Identification of initial failure during thick wall cylinder tests however is not straightforward. TWC-Internal can be defined by an increase in fluid volume expelled during constant loading, or by monitoring the weight of detached (failed) sand grains by a digital balance (with respect to applied stress). Alternatively, monitoring and measuring the internal hole deformation during tests can be achieved more accurately using internal gauges (such as small callipers) or cameras, however such measures require large plug sizes which are not routinely available. Non-Destructive Strength Tests (Strength Indicators). A number of techniques have been developed to replace or supplement triaxial tests to measure the strength properties of rocks. Scratch and Schmitt hammer tests are examples of such techniques that have demonstrated the ability to provide continuous or semi-continuous, fine-scale measurements of rock mechanical properties. In contrast with conventional triaxial tests, both of these tests are non-destructive and do not cause significant damage to the core and no special core preparation is required. These tests can be conducted either in the lab, core store or, in principle, on the rig, almost immediately after recovery of core material.

Impact Testing. Various forms of impact testing have been used on cores for a number of years now, perhaps the first well known application being the Brinell test. In this test a standard size ball of hard material is pressed under a heavy load into the surface of the rock and the diameter of the depression measured using a microscope. The Brinell Number (BN) is the ratio between the load and area of the depression (kg/mm2). This test is somewhat slow to execute over long cored intervals and requires sections of core to be uplifted and carried to the instrument; i.e. the equipment is bench mounted.

Application of the Schmidt hammer, Taylor and Appleby (2006), to whole and half cut core allowed for impact measurements to be made directly on the core itself, providing the core was laid out on a rigid surface, such as a concrete floor. The Schmidt hammer, originally designed for concrete testing, contains a spring-loaded mass that is automatically released against an impact plunger when the hammer is pressed against the test surface. Elastic recovery of the rock is dependent upon its surface hardness. Since hardness is related to mechanical strength, the rebound distance travelled by the returning hammer mass is a relative measure of the surface hardness, and therefore the strength. The main disadvantage of this technique is the relatively high energy imparted to the core which can result in fracturing and breaks.

A new instrument by the inventors of the Schmidt hammer is the Equotip 3 hardness tester. This is a portable, low energy impact, NDT device for in situ hardness testing of metals. Aoki & Matsukura (2007) used this device for measuring rock strength on weathered and fresh surfaces of Aoshima sandstone blocks and concluded that the Equotip was a versatile and accurate tool for such field investigations. The authors of this paper used the Equotip 3 to characterise rock strength on a core from the Central North Sea in 2008 and Figure 5 shows it in use. Impact measurements were made and compared between

6 SPE 121972

matched depth sections of whole core, half cut core and slab sawn, resinated core, and all were found to correlate well with each other and many other petrophysical properties; e.g. GR, RHOB, NPHI, Dt, Dts, Helium porosity, air permeability and grain density.

Figure 5 shows an example of the Equotip 3 impact strength plotted against other petrophysical parameters for a cored interval. Four intervals of high rock strength can be clearly seen and correspond to zones of intense quartz cementation. Direct measurement, semi-continuous impact logs such as this provide an excellent pre-filtering tool for plug selection for rock strength laboratory testing. It also provides a direct indication of which wireline and laboratory measured petrophysical parameters most influence rock strength (either in depth space or when cross-plotted); valuable when selecting the initial UCS and TWC equations with which to build the strength model.

Scratch Testing.This test involves driving a sharp cutter across a rock surface. By monitoring the vertical and lateral forces required to maintain a certain depth of cut, it is possible to relate the applied force to the uniaxial compressive strength, C0, in rocks. The laboratory based equipment consists of a moving cutter with a sample holder and a loading fixture capable of scratching the rock sample. An example of scratch test system is described by Surez-Rivera et al. (2003). A load cell is mounted on the loading frame and measures the horizontal force (in the cutting direction) and the vertical force (normal to the cutting surface) typically in the range from 10 N to 4000 N, with an accuracy of 1 N. Computer controlled feedback allows variable cutter velocity, automatic data acquisition, and real-time data analysis. Measurements can be conducted on slabbed core sections with a pre-slab diameter of 4 inches and a length of 3 feet. The rock surface is typically scratched at a constant depth of cut from 0.2 to 0.5 mm, as appropriate for different rock types. Normal and tangential forces on the cutter can be measured, and automatic data processing provided estimates of rock strength (UCS) along the cut. A comprehensive discussion on the testing methodology can be found in Detournay et al. (1992 and 1996), Schei et al. (2000) and Surez-Rivera et al. (2002 and 2003). The advantage of this method is a continuous profile of rock strength that is sensitive to rock fabric and mineralogical composition. The main disadvantage is that there are currently only limited laboratory facilities for this type of test and core has to be transported to dedicated laboratories and specially prepared in short slabbed sections. It is often the case that core is not intact and this precludes a continuous strength log. Another disadvantage is that the scratch test cannot be considered totally non-destructive. Empirical Rock Strength Relationships Rock strengths are generally influenced by physical and elastical properties of rocks. Well logs such as density and sonic logs are often used to assess rock strength. Core strength-log integration can be used to define a continuous rock strength prediction model. Single variable analysis in which the measured core property (e.g. UCS) is correlated against a wireline log response (e.g. Dt, Rhob) or interpreted parameter (e.g. clay content and total porosity) using conventional regression analysis can provide useful strength prediction models. Calibration can be improved by using dynamic elastic moduli as they exploit two independent tool responses (sonic and bulk density) which are often more sensitive to strength variations than density or sonic alone, and are not overly reliant on interpreted logs (e.g. porosity) which can have uncertainties in log calibration inputs. In gas reservoirs, especially those with high porosity and at shallow depth, sonic and density data may require correction to account for gas effects on the log response before applying to rock strength modelling. Figure 6 shows the use of core and well logs to derive a continuous TWC profile computed from a correlation between measured TWC on core samples and log derived dynamic compressional modulus (M) from sonic and density logs for Tertiary reservoir sandstones in an offshore field, South Asia.

There are many published log-core strength correlations that can be used to develop a rock strength model. These empirical relationships have been developed for specific rock types and their application to other rock types should be verified before they are utilized. Chang et al. (2006) summarized 31 empirical equations that relate unconfined compressive strength and internal friction angle of sedimentary rocks (sandstone, shale, limestone and dolomite) to physical properties (such as acoustic velocity, elastic modulus and porosity). It is important to recognize that different rock types will have very different log-strength relationships, based on their lithology, age, burial history and consolidation state. Therefore, it is important to avoid applying a relationship calibrated for one rock type to another.

In Tables 1 to 5, rock strength models including UCS, TWC and Friction Angle are listed along with a brief description on their applicability and, where possible, the source of each equation. All equations are presented in imperial unit system. Some of these equations are well known and are commonly used by the geomechanics community, such as the Dt based UCS equation developed by Horsrud (2001) for North Sea shales and the UCS-Youngs modulus equation introduced by Plumb (1994) for sandstones. However, some other equations are field specific (such as the TWC-M equation shown in Figure 6) are therefore less known to the public. Rock Strength Controls and Model Comparison. In their review Chang et al. (2006) compared laboratory measured UCS data obtained from a range of published literature with UCS values predicted by a number of empirical equations listed in Tables 1 to 3 for sandstones, shales and limestones. Plots in Figure 7 show similar comparison for UCS strength versus porosity and Youngs modulus in sandstones for several empirical equations listed in Table 1. It can be seen that while some equations work reasonably well, rock strength variations with individual rock properties show considerable scatter, indicating that most of the empirical models are not sufficiently generic to fit all the data in the database.

SPE 121972 7

Figure 8 shows an example from a North Sea well where none of the empirical UCS strength models used to create a strength profile gives a reasonable match with the limited core-based UCS data available in Well-B. One possible reason for this mismatch could be that the empirical strength correlations based on single variable (X-on-Y) analysis, using porosity log or sonic travel time as a strength predictor for example, are often not robust enough. Similar to other rock properties in sedimentary rocks, rock strength is controlled by internal rock fabric structure, i.e. grain support versus clay support structure (Vernik 1994 and Plumb, 1994), cementation, pore geometry, grain contacts and other diagenesis and facies related characteristics.

A single variable such as total porosity or rock acoustic properties may not necessarily fully capture these petrographic features. Additional data and measures (listed under supplementary testing in pervious section) are needed for a more detailed rock classification far beyond a simplistic lithology classification such as sandstone versus shales or reservoir versus non-reservoir rocks. Detailed petrological characterisation is also required to understand rock failure mechanisms, give quality assurance to empirical, analytical and numerical modelling and provide an interface between the mathematical model and its practical application to wellbore construction or sandface completion design. A task of the geomechanics specialist is to make good use of all of the geologically orientated data that is normally available. If rock strength studies are being undertaken at an early stage in the field life, then the number of geological and core analysis reports may be somewhat limited. However, once the initial rush of field characterisation is completed, such data will be plentiful. A good overview of the qualitative influence of geology, petrology and mineralogy on geomechanics studies is given by Webster and Taylor (2007).

Multi-Variable, Fuzzy Logic and Clustering Analysis Standard single variable regressions are commonly poor at picking extremes and outliers and can have a significant impact on the derived correlations. Where there are sufficient core test data available (ideally more than 15 tests) multi-variable or soft computing techniques such as fuzzy logic and clustering analysis can be used to optimise the strength prediction. Such techniques in predicting rock strength in uncored intervals can provide a radical improvement over other techniques.

Fuzzy logic, a statistical technique, asserts that the formation consists of several litho-types each represented by data bins and each having characteristic distributions for strength and electrical log values (Cuddy, 1998). Each bin has a characteristic log response (e.g. porosity, Vclay, Dt) defined in terms of its mean and standard deviation. In this way the error bars or fuzziness of the predictions are captured. Fuzzy logic techniques quantify these errors and use them, together with the measurement, to improve the prediction. Whereas conventional techniques deal with absolutes, fuzzy logic methods carry the inherent error term through the calculation rather than ignoring or minimising it. In practice raw and derived logs are correlated against the input core data (e.g. UCS, TWC). Fuzzy logic techniques are then used to predict rock strength based on the input curves with the highest-ranked correlation coefficients. The resulting UCS curves are then checked against the core strength values.

Multi-resolution graph-based clustering (MRGC) of log and core test data can be used to model rock strength and K-Nearest Neighbours (KNN) methods can been used to propagate MRGC models for rock strength prediction. Similarity threshold modelling (STM) can been used to quality control cluster models used to predict rock strength values. This method is not constrained to simple UCS models but can be used to predict more useful rock mechanics parameters like friction angle, cohesion, peak strength and residual strength which are used in stability calculations.

MRGC and KNN techniques are a useful check and balance against single variate and fuzzy logic techniques because they are not statistical techniques and are constrained to work within the provided data set. Thevoux-Chabuel et al. (1997) and, Ye and Rabiller (2000) for further technical background on MRGC and KNN techniques. Fuzzy logic is able to extrapolate beyond the input data set. The combination of statistical fuzzy logic and non-statistical clustering or pattern recognition methods gives the Geomechanics Specialist a better description of rock strength variability. It is recommended that both techniques are used as complimentary rock strength predictors because fuzzy logic can extrapolate rock strengths outside the tested range and clustering predicts only within the tested range. It is therefore very important that the correct rock testing programme is designed as described earlier in this paper.

An example from a field in the North Sea is shown in Figure 9. The rock strength prediction in this case was thick wall cylinder strength for input into a sand production prediction and selective perforation strategy. This analysis was provided real-time. In order to have the greatest confidence of rock strength and to provide the least conservative perforation strategy the two techniques of fuzzy logic and clustering were compared and a decision was based on the complete picture.

Clustering methods require larger core test data sets and with the development of the laboratory-based portable impact testing techniques there will be considerably more data points for this method to use. At the time of writing an impact testing data set of approximately 200 ft of core is being added to a conventional core testing data set and the results of this analysis will be available in a follow up paper. Closing Remarks

Planning. Rock strength testing requires planning well in advance of the execution of a geomechanical study itself. Rock strength and the associated elastic properties are a common data requirement for many subsurface and well engineering disciplines. When planning rock mechanics work, it is therefore essential to ensure that other interested departments are included in discussions. Good communications at an early stage can eliminate unnecessary, repeated or staged work, avoid

8 SPE 121972

gaps in the data set and focus on common needs and goals. Supplementary testing including any laboratory process that is not directly considered a part of rock strength testing, are important in understanding the underlying micro and macro-mechanics of rock failure. The majority of such tests or analysis would normally fall under the remit of the Reservoir Geology or Petrophysics groups, but occasionally this work may not have been undertaken. It may therefore be necessary to have some of this work conducted in order to supplement verification of empirical, analytical or numerical geomechanical modelling.

Sample Selection and Screening. Sampling is a kingpin in the workflow and should not be underestimated. The correct choice of a representative range of samples for strength testing is not very often apparent when viewing a core, especially when a lot of core has been cut. The screening process must be adaptable to accommodate the variation in core material, but will typically incorporate visual inspection, a review of porosity and permeability data, wireline log data and, more commonly now, scratch testing or impact strength characterisation. Combinations of these techniques will help to clearly identify different mechanical facies, sometimes termed mechanical stratigraphy, and access the range in absolute or relative strength within each. Another important point during screening stage is the quality control throughout laboratory testing and the quality assurance of intermediate and final test results prior to further analysis and their incorporation into geomechanical modelling. All available raw and processed data should be requested from the rock mechanics laboratory, e.g. stress-strain plots, pre- and post-test colour photographs and visual inspection of tested plugs. These must be checked for potential problems inherent in the testing, as shown for the UCS tests illustrated in Figure 4.

Model Selection and Enhanced Log-Derived Strength Estimation. Choice of the best model for the computation of log-derived strength (UCS, TWC) can be focused and the process made more robust using a combination of conventional laboratory triaxial testing and emerging non-destructive methods such as impact and scratch strength measurements made along the core. The process described for model selection can be progressed to enhance log-derived strength estimation over both the cored interval and, more importantly, un-cored intervals. Simple correlation models can quickly be created by determining the regression between impact or scratch strengths (calibrated to laboratory measured rock strength) and any given continuous log. Also, non-calibrated impact strength (relative strength) or calibrated impact strength (absolute strength) can be input to fuzzy logic or cluster pattern recognition techniques together with any other parameters such as facies, cement type, and other petrological data to improve strength estimation in the un-cored sections of the well.

Downhole Rock Strength. Direct measurement of rock strength downhole is a highly desirable aspiration. Advantages include, but are not limited to: near wellbore stresses accounted for, the rock remains at in situ stress and at temperature, the measurement is made against semi-infinite half space, rather than small diameter core. Downhole scratch testers are currently under development and, if successful, may provide a continuous rock strength log. Although at a very early stage, impact strength testers are now being discussed and could probably operate in more difficult downhole conditions. Like with core, impact strength logs would be semi-continuous and would be able to provide a relative measurement of strength along the well path throughout the overburden and reservoir interval.

Nomenclature b = Bulk density, g/cc = Porosity, fraction = Poissons ratio = Coefficient of internal friction = Friction angle, degree 1 = Major principal stress 2 = Intermediate principal stress 3 = Minor principal stress n = Normal stress = Shear stress C0 = Unconfined compressive strength, psi CAT = Computer Axial Tomography CL = Cathodo-Luminescence Microscopy Dt = Compressional wave transit time, s/ft Dts = Shear wave transit time, s/ft E = Youngs modulus, psi Edyn = Dynamic Youngs modulus, psi Esta = Static Youngs modulus, psi GR = Gamma Ray

LWD = Logging While Drilling M = Dynamic compressional modulus, psi MST = Multi-Stage Triaxial test NDT = Non Destructive Testing NPHI = Neutron porosity PSD = Particle Size Distribution RCA = Routine Core Analysis RHOB = Bulk density, g/cc S0 = Cohesion SCAL = Special Core Analysis Laboratory SEM = Scanning Electron Microscopy SST = Single Stage Triaxial test TS = Thin Section TWC = Thick Wall Cylinder UCS = Unconfined (Uniaxial) Compressive Strength,

psi Vclay = Clay volume, fraction WBS = Well Bore Stability XRD = X-Ray Diffraction

SPE 121972 9

References Aoki, H. and Matsukura, Y., 2007. A new technique for no-destructive field measurement of rock-surface strength: an application of the

Equotip hardness tester to weathering studies. Earth Surface Processes and Landforms, Wiley InterScience. Bradford, I.D.R., Fuller, J., Thompson, P.J. and Walsgrove, T.R., 1998. Benefits of assessing the solids production risk in a North Sea

reservoir using elastoplastic modeling. SPE/ISRM 47360. Bruce, S., 1990. A mechanical stability log, SPE 19942. Chang, C., Zoback, M. D. and Khaksar, A., 2006. Empirical relations between rock strength and physical properties in sendimentary rocks.

Journal of Petroleum Science & Engineering, 51, 223-237. Coates, G.R. and Denoo, S.A., 1981. Mechanical properties program using borehole analysis and Mohrs circle, SPWLA 22nd Annual

Logging Symposiums Transactions. Cuddy, S.J., 1998. Litho-facies and Permeability Prediction from Electrical Logs using Fuzzy Logic. SPE 65411. Detournay, E and Defourny, P., 1992. A phenomenological model for the drilling action of drag bits. Int. J. Rock Mech. Min. Sci. and

Geomech. Abstr, 29(1):13-23. Detournay, E., Drescher, A., Defourny, P. and Fourmaintraux, D., 1996 Assessment of rock strength properties from cutting tests:

Preliminary experimental evidence. In Chalk and Shales Colloquium, Brussels. Fjaer, E., Holt, R.M., Horsrud, P., Raaen, A.M., and Risnes, R., 1992. Petroleum Related Rock Mechanics. Elsevier, Amsterdam. Freyburg, E., 1972. Der unterwer und mittlere Buntsandstein SW-Thuringens in seinen gesteinstechnischen Eigenschaften, Ber. Dte. Ges.

geol. Wiss. A; Berline, 17 6, 911-919. Golubev, A.A. and Rabinovich, G.Y., 1976. Resultaty primeneia appartury akusticeskogo karotasa dlja predeleina proconstych svoistv

gornych porod na mestorosdeniaach tverdych isjopaemych. Prikladnaja GeofizikaMoskva, 73: 109-116. Horsrud, P., 2001. Estimating mechanical properties of shale from empirical correlations. SPE Drilling & Completion, 6873. Jaeger, J. C. and Cook, N. G. W., 1979. Fundamentals of Rock Mechanics, Chapman and Hall, London. Jizba, D., 1991. Mechanical and Acoustical Properties of Sandstones and Shales, Ph.D. thesis, Stanford University. Khaksar, A., Rahman, K., Ghani, J., and Mangor, H., 2008. Integrated geomechanical study for hole stability, sanding potential and

completion selection: a case study from South East Asia. SPE 115915. Lal, M., 1999. Shale stability: drilling fluid interaction and shale strength. SPE Latin American and Caribbean Conference. Lashkaripour, G.R. and Dusseault, M.B., 1993. A statistical study on shale properties; relationship among principal shale properties. Proc.

Conference on Probabilistic Methods in Geotechnical Engineering, Canberra, Australia. McNally, G.H., 1987. Estimation of coal measures rock strength using sonic and neutron logs. Geoexploration, 24: 381-395. McPhee, C.A., Lemanczyk, Z.R., Helderle, P., Thatchaichawalit. D. and Gongsakdi, N., 2000. Sand management in Bongkot Field, Gulf of

Thailand: an integrated approach, SPE 64467. Militzer, H. and Stoll, R., 1973. Einige Beitrageder geophysics zur primadatenerfassung im Bergbau, Neue Bergbautechnik. 3: 21-25. Moos D., Zoback, M.D. and Bailey, L., 1999. Feasibility study of the stability of openhole multilaterals, Cook Inlet, Alaska. SPE 52186. Perkins, T.K. and Weingarten, J.S., 1988. Stability and failure of spherical cavities in unconsolidated sand and weakly consolidated rock,

SPE 18244. Plumb, R., 1994. Influence of composition and texture on the failure properties of clastic rocks. SPE 28022 Raaen, A. M., Hovem, K. A., Jranson, H. and Fjaer, E., 1996. FORMEL: A step forward in strength logging, SPE 36533. Rahman, K., Khaksar, A., and Kayes, T., 2008. Minimizing sanding risk by otimizing well and perforation trajectory using an integrated

geomechanical and passive sand-control approach. SPE 11633. Richard, T., Detournay, E. Drescher, A., Nicodme, P. and Fourmaintraux, D., 1998. The scratch test as a means to measure strength of

sedimentary rocks. SPE 47196. Rzhevsky, V. and Novick, G., 1971. The Physics of Rocks, MIR Publ., 320 pp. Sarda, J. P., Kessler, N., Wicquart, E., Hannaford, K. and Deflandre, J. P., 1993. Use of porosity as a strength indicator for sand production

evaluation, SPE 26454. Schei, G., Fjaer, E., Detournay, E., Kenter, C.J., Fuh, G.F and Zausa, F., 2000. The scratch test: an attractive technique for determining

strength and elastic properties of sedimentary rocks. SPE 63255. Surez-Rivera, R., Ostroff, G., Tan, K., Begnaud, B., Martin, W. and Bermudez, T., 2003. Continuous rock strength measurements on core

and neural network modelling result In significant improvements in log based rock strength predictions used to optimize completion design and improve prediction of sanding potential and wellbore stability. SPE 84558.

Suarez-Rivera, R., Stenebraten, J. and Dagrain, F., 2002. Continuous scratch testing on gores allows effective calibration of log-derived mechanical properties for use in sanding prediction evaluation. OilRocks. Paper No. 78157.

Taylor, P.G. and Appleby, R.R., 2006. Integrating quantitative and qualitative rock strength data in sanding prediction studies: an application of the schmidt hammer method. SPE/IADC 101968.

Thevoux-Chabuel, H., Veillerette, A. and Rabiller, P., 1997. Multi-well log data coherence characterization using the similarity threshold method. SPWLA, 38th Annual Logging Symposium Transactions, paper BB.

Vernik, L., Bruno, M. and Bovberg, C., 1993. Empirical relations between compressive strength and porosity of siliciclastic rocks. Int. J. Rock Mech. Min. Sci.& Geomech. Abstr., 30: 677-680.

Vernik, L., 1994. Predicting lithology and transport properties from acoustic velocities based on petrophysical classification of siliciclastics. Geophysics 59, 420-427.

Webster, C.McK. and Taylor, P. G., 2007. Integrating quantitative and qualitative reservoir data in sand production studies: the combination of numerical and geological analysis. SPE 108586.

Weingarten, J.S. and Perkins, T.K., 1995. Prediction of sand production in gas wells: methods and Gulf of Mexico case studies, Journal of Petroleum Technology, 47(7):596-600.

Ye, S.-J. and Rabiller, P., 2000. A new tool for electro-facies analysis: multi-resolution graph-based clustering. SPWLA, 41st Annual Logging Symposium Transaction, paper PP.

10 SPE 121972

Table 1: UCS Models for Sandstones Model and Reference Equation Remarks

Dt-McNally (McNally, 1987)

DteC 037.00 185213= Low to medium porosity sandstones, 65< Dt < 100

s/ft and UCS > 3000 psi, Permo-Triassic age SE Australia

Dt-Mod McNally (Modified McNally)

DteC 057.00 838825= A modified McNally equation for unconsolidated and

high porosity sandstones with UCS less than 3000 psi

Dt-HRDS (Rahman et al. 2008)

DteC 0268.00 40847= Tertiary sandstones,offshore gas field, South Asia

Dt-FORMEL (Raaen et al. 1996)

)0083.01.2140(145 20 DtDtC += 90< Dt < 140 s/ft

-FORMEL (Raaen et al. 1996)

)6314043(145 20 +=C 0.2< < 0.35

Dt Cubed-Sand (Chang et al. 2006)

390 1005.2

= DtC Gulf of Mexico,weak and unconsolidated rocks

Dt-Freyburg (Freyburg, 1972)

5.4567/1055.1 60 = DtC Consolidated Thuringia sandstones, Germany

-Sarda (Sarda et al. 1993)

6.1116172 = eCo Germigny-sous-Coulombs reservoir, with the < 0.35 -Vernik (Vernik et al.

1993) ( )27.2136830 =oC Reasonable for consolidated sandstones with < 0.30

-Vclay-Vernik ( ) ( )20 7.21204254145 = clayVC Modified Vernik equation with Vclay for shaly sandstones with < 0.30 -Literature1 (Chang et

al. 2006) 10

0 40165= eC UCS between 300 and 52000 psi and less than

0.33

M-Bongkot (McPhee et al. 2000)

14364.001182.00 = MC Bongkot Field, Gulf of Thailand, for UCS < 5000 psi

M-Hemlock (Moos et al. 1999) 304510745.1

30 = MC Cook Inlet, Alaska unconsolidated fine to coarse grained low strength sandstones, 10,000 ft depth

M-GOM (Chang et al. 2006)

MeC710862.7

0 15.561= Gulf of Mexico

M-Browse (Chang et al. 2006)

MeC71031.1

0 5.6104= Consolidated sandstone with 0.05 < < 0.12 and

UCS>12000 psi, Browse Basin, Australia

E-Plumb (Bradford et al. 1998) sta

EC 0041.07.3300 += Worldwide for 725 < UCS < 29000 psi

E-Everest (Bradford et al. 1998)

7.2140 10177.17.330 dynEC

+= Another form of the E-Plumb equation with dynamic Youngs modulus

E-Literature1 (Chang et al. 2006)

EeC71086.1

0 6700= Based on static Youngs modulus

Esta-C&D (Coates and Denoo, 1981) sta

EC = 30 1054.4 Linear relation between C0 and Esta

BRUCE (Bruce, 1990) ( )claybdyn VKEAC 0035.00045.010026.0 60 += Applicable to UCS > 4350 psi with ( ) sin1/cos2 =AW&P (Weingarten and

Perkins, 1995) ( ) dynbclay EKVC 9711410145 120 += unconsolidated sandstones, gas fields in USA

MECHPRO1 (Fjaer et al. 1992)

( )claydyn VKEC 78.01107.8 120 += Sandstones with UCS>4350 psi MECHPRO2 (Fjaer et

al. 1992) ( ) ( )[ ] ( )( clayVMC 78.01211/11027.2 22100 ++=

Sandstones with UCS>4350 psi

-Travis Peak 466.00 4697

= C Tight sandstone with 0.01 < < 0.18 M-Travis Peak MeC

71065.30 3648

= Tight sandstone with 0.01 < < 0.18

E-Travis Peak EeC71014.4

0 3668= Tight sandstone with 0.01 < < 0.18

SPE 121972 11

Table 2: UCS Models for Shales Model and Reference Equation Remarks

Dt- Horsrud (Horsrud, 2001) ( ) 93.20 /8.30465.111 DtC = High porosity North Sea Tertiary shales Dt-GOM (Chang et al. 2006) ( ) 2.30 /8.30435.62 DtC = Pliocene and younger shales Dt-Global (Chang et al. 2006) ( ) 6.20 /8.30475.195 DtC = Globally applicable

Dt Cubed-Shale (Chang et al. 2006) ( )30 /8.3045.72 DtC = Gulf of Mexico Dt-Lal (Lal, 1999) ( )1/8.30414500 = DtC High porosity Tertiary shales

E-Horsrud (Horsrud, 2001) 91.00 0232.0 EC = High porosity North Sea Tertiary shales

E-Literature1 (Chang et al. 2006) 712.00 221.0 EC = Strong and compacted shales

-L&D (Lashkaripour and Dusseault, 1993) 143.10 1.145

= C Compacted shales ( < 0.10) -Horsrud (Horsrud, 2001) 96.0

0 7.424= C High porosity North Sea Tertiary shales

-Literature1 (Chang et al. 2006) 762.10 47.41

= C Shales with > 0.27 Rhob-shale beC 89.40 0123.0= Developed from published data for density < 2.4 g/cc

Table 3: UCS Models for Carbonates

Model and Reference Equation Remarks

Dt-M&S (Militzer and Stoll, 1973) ( ) 82.10 /7682 DtC = Limestones Dt-G&R (Golubev and Rabinovich, 1976) ( )DtC /14.10944.20 10 += Limestones

-Rzhewski (Chang et al. 2006) ( )20 3140020 =C Similar to Vernik formula with different constants -Limestone1 (Chang et al. 2006) 8.4

0 5.19705= eC Strong limestones with low porosity (0.06 on average)

-Limestone2 (Chang et al. 2006) 95.60 20851

= eC UCS > 4900 psi in a field in Middle East E-Limestone (Chang et al. 2006) 51.0

0 66.4 EC = Moderately to very strong limestones (UCS > 2000 psi) E-Dolomite (Chang et al. 2006) 34.0

0 64EC = Dolomite with 8700 < UCS < 14500 psi Table 4: TWC Models

Model and Reference Equation Remarks

TWC-UCS 58.008765.80 CTWC = Global for sandstones

TWC-M (Rahman et al. 2008) 77.1810 MTWC = Tertiary sandstones, gas field in South Asia TWC- 54.362.20 = TWC Weak sandstones

12 SPE 121972

Table 5: Friction Angle models Model and Reference Equation Remarks

FANG-Dt (Lal, 1999)

+

= 1000304878/1000304878sin 1DtDt

Shales

FANG-M (McPhee et al. 2000)

51.28100691.1 6 += M Sandstone, Bongkot Field, Gulf of Thailand.

FANG-Vclay -1 (Plumb, 1994)

( ) ( )211.6214.375.26 clayclay VV += Both sandstones and shales FANG-Vclay -2 ( )clayV+= 1155.20 Sandstones

FANG-1 (Weingarten and Perkins, 1995)

1058.57 = Sandstones

FANG-2 (Perkins and Weingarten,1988)

13558 = Weak sandstones

FANG-b 85.21.0tan b = Sandstones

Axial deviatoricStress (1-3)

Axial strain

Increasingconfinement

Residual strength

Peak strength

3

1

3

1Before

After

n

Figure 1. Typical plot of axial deviatoric stress vs. axial deformation during single stage triaxial tests (SST)

Sample ID: BTA-2UCS = 4882 psiFric. Angle = 34.85 deg.Cohesion = 1275 psi

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

0 2,000 4,000 6,000 8,000 10,000 12,000Effective Normal Stress (psi)

Shea

r Str

ess

(psi

)

Peak StrengthUCS = 4882 psi


0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000


Shea

r Str

ess

(psi

)



0

1,000

2,000

3,000

4,000

5,000

0 2,000 4,000 6,000 8,000Effective Normal Stress (psi)

Shea

r Str

ess

(psi

)

Residual StrengthUCS = 2030 psi


0

1,000

2,000

3,000

4,000

5,000

0 2,000 4,000 6,000 8,000Effective Normal Stress (psi)

Shea

r Str

ess

(psi

)

Residual StrengthUCS = 2030 psi

Pp = 1 MPaPc = 6 MPa



Principal Stress Plot-Residual Strength

y = 3.167x + 2030R = 0.999

0

2,000

4,000

6,000

8,000

0 400 800 1,200 1,600 2,000

Effective confining stress - 3 (psi)

Effe

ctiv

e st

ress

- 1

(psi

)

Principal Stress Plot-Peak Strength

y = 3.67x + 4882R = 1

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

0 400 800 1,200 1,600 2,000

Effective confining stress - 3 (psi)

Effe

ctiv

e st

ress

- 1

(psi

)

= tan

S0

Figure 2. Example of Mohr circles in shear stress vs. effective normal stress space, with a fitted linear Coulomb failure envelope for both peak and residual strengths for a set of triaxial tests on three plugs. Also shown (right) are the plots of effective stress at failure vs. confining effective stress (1 vs 3).

SPE 121972 13

Sample ID: BTA-2 MSTUCS = 4694 psiFric. Angle = 42.54 deg.Cohesion = 1032 psi

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000


Shea

r Str

ess

(psi

)


Sample ID: BTA-2 MSTUCS = 4694 psiFric. Angle = 42.54 deg.Cohesion = 1032 psi

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000


Shea

r Str

ess

(psi

)


Pp = 1 MPaPc = 2, 4, 8, 10 MPa

Figure 3. Example multi-stage triaxial test (MST) results on a preserved sandstone plug (data source, Khaksar et al. 2008).

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 200 400 600 800 1000 1200

time (s)

axia

l loa

d (k

N)

0

0.1

0.2

0.3

0.4

0.5

0.6

0 200 400 600 800 1000 1200

t ime ( s)

Well defined failure point, ambiguous failure plane

Poorly defined failure (sample damage)

Figure 4. Examples of unconfined compressive tests on two sandstone plugs with ambiguous results.

14 SPE 121972

10000

10005

10010

10015

10020

10025

10030

10035

10040

10045

10050

10055

10060

10065

10070

10075

10080

10085

10090

10095

10100

10000

10005

10010

10015

10020

10025

10030

10035

10040

10045

10050

10055

10060

10065

10070

10075

10080

10085

10090

10095

10100

Figure 5. Example of the Equotip 3 impact strength indicator plotted against other petrophysical parameters for a cored interval. Also shown (left) are, Schmitt hammer (top) and Equotip 3 (below) impact testing tools in action.

Core TWC vs. Log - Derived Compressional Modulus (M)

TWC = 1E-08 M 1.77

R = 0.85

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

2.E+06 3.E+06 3.E+06 4.E+06 4.E+06 5.E+06 5.E+06

Dynamic Compressional Modulus (psi)

Cor

e TW

C (p

si)

Log-derivedcore data

7850

7900

7950

8000

8050

8100

8150

8200

8250

0 4000 8000 12000 16000TWC (psi)

Figure 6. Core-log correlation between measured TWC and dynamic compressional modulus M from well logs (left) and Log-derived TWC profile (right) for sandstones in a gas field, offshore South Asia (data source, Rahman et al. 2008).

SPE 121972 15

0

50

100

150

200

250

300

350

400

0 10 20 30 40 50 60 70 80

UCS dataUCS -E-EverestUCS-E-Literature 1UCS-E

sta-C&D

Young's Modulus (GPa)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35 40

UCS data

UCS-Phi -Vernik

UCS-Phi-Literature-1

UCS-Phi-Formel

UCS-Phi-Sarda

Porosity (%)

Figure 7. Comparison between different empirical equations for UCS strength in sandstones for porosity-based models (left) and Youngs modulus-based models (right), in SI unit system.

5505

5510

5515

5520

5525

5530

5535

5540

5545

5550

5555

5560

0 1000 2000 3000 4000 5000 6000

Sandstone UCS Profile-Well A

5555

5560

5565

5570

5575

5580

5585

5590

5595

5600

5605

0 1000 2000 3000 4000 5000 6000

UCS (psi)

Dep

th (M

D ft

)

Sandstone UCS Profile-Well BUCS (psi)

Mod McNally

Core UCS

Dt-McNally

M-Hemlock

Phi-Vclay-Vernik

Figure 8. Comparison between different empirical equations for UCS strength for the same reservoir sandstone in two nearby North Sea oil wells. In Well A (left) predictions by Vclay-Vernik model are consistent with UCS from core measurements whereas in Well B (right) the same model signficanlty underestimates UCS strength at depth of core sample.

16 SPE 121972

Figure 9. An example of rock strength prediction in the North Sea using the complimentary techniques of fuzzy logic and log clustering. Data shown in second track from right are as follows: TWC_1 is Thick wall cylinder strength from core test, TWCPRED_FM3 is predicted TWC strength based on clustering methods and TWCPRED_FL3 is predicted TWC strength based on fuzzy logic methods.

Model and ReferenceModel and ReferenceModel and ReferenceModel and ReferenceModel and Reference

Documents

(2009) SPE 121972 Khaksar- Rock Strength From Core and Logs