UCS Amireg Paper Kelessidis

3rd AMIREG International Conference (2009): Assessing the Footprint of 212 Resource Utilization and Hazardous Waste Management, Athens, Greece

Need for better knowledge of in-situ unconfined compressive strength of rock (UCS) to improve rock drillability prediction

V.C. Kelessidis Department of Mineral Resources Engineering, Technical University of Crete, Hania, Greece ABSTRACT Rock - drill bit interaction while drilling has been modeled for many years but a complete understanding of the phenomena occurring has yet to materialize. Successful models will allow the prediction of rate of penetration in a given environment and optimal selection of drill bit and drilling parameters thus minimizing explo-ration costs. In most rock-drilling models the value of the unconfined compressive strength of the rock (UCS), one of the most important engi-neering properties of rocks, is used in the pre-dictive equations, within the concept of specific energy, and the value of UCS is the percentage of the value of the stress applied on the drilling bit in order for the bit to advance. While the ex-act percentage depends on the model used and it is not known with certainty, good knowledge of UCS is never-the-less required before any de-cent prediction can be made on rate of penetra-tion. Determination of UCS, normally done via destructive testing, requires not only availability of sound core samples, but also performance of expensive testing and significant time for the test, which many times is not available for rou-tine drillability predictions. Hence, a multitude of methods and techniques has been proposed to estimate UCS from various indirect and/or not-destructive measurements, or combination of measurements using neural networks, such as point load index, block punch index, unit weight, apparent porosity, water absorption by weight, P-wave velocity and Schmidt hardness. The many proposed approaches are critically re-viewed and the results are compared and what becomes apparent is that after many years, not only in mining but also in oil-well drilling, ac-

curate indirect determination of UCS is still an elusive property. Various approaches are sug-gested to enable better indirect determination of UCS.

1. INTRODUCTION The prediction of drilling time when designing a drilling campaign for any type of well, hydro-carbon, mining, geothermal, even water-well, for different subsurface conditions and using va-riety of equipment could be very beneficial for estimating drilling costs and for safe drilling practices. This could be accomplished if a full model which takes into account drilling parame-ters and formation properties is available. How-ever, such a model is not available and industry as well as researchers attempt to predict drilling times via the concept of Specific Energy (SE), defined by Teale (1969) as the minimum energy required by the drilling rig to cut a unit volume of rock. Teale went a step further and indicated that the units of specific energy were essentially units of stress and identified similarities be-tween Specific Energy and Unconfined Strength of rocks (UCS). Thus, Teale’s model, which has been used by many researchers and practitioners in the years that followed (Bilgin, 1982; De-tournay and Tan, 2002, among many others) is given as,

( ) ( )( )

AbitWOB

effUCS

AbitWOBDRPMROP

−=

/)(8 μ (1)

where, (ROP) is the rate of penetration, (RPM) is the rotational speed, (D) is the bit diameter, (WOB) is the applied weight on bit, (Abit) is the


cross sectional area of the hole, (μ) is the coeffi-cient of friction between drill string and forma-tion converting applied WOB to torque, and (eff) is the efficiency of transmitting the de-struction power of the drilling rig to the rock. The value of (eff) is not known a-priori, but could be estimated from existing data. Other au-thors proposed to use additional rock properties, besides UCS, such as tensile strength, modulus of elasticity, stiffness of the rock, as parameters of drillability. Rock drillability, defined as the time spent to drill one meter of rock, has been widely used as rock classification in mining (Tanaino, 2005) but it is not objective, as it does not take into account the drilling equipment.

A great deal of testing has thus been under-taken via standard methods (ISRM, 1978; Brown, 1981) to gather representative mean val-ues of the properties of the drilled rock types. The results have indicated that rock properties are influenced by anisotropy and orientation of discontinuities related to the direction of testing or drilling, spacing of discontinuities, mineral composition and equivalent quartz content, moisture and finally pore volume and porosity of the micro fabric (Thuro, 1997; Chen and Hu, 2003).

From the literature cited, UCS could be used as a rough estimate of rock drillability. A criti-cal bibliographic search has thus been under-taken on the reported values of UCS from repre-sentative rock types that could be encountered while drilling in shallow and deep horizons for water, geothermal, mineral and hydrocarbon ex-ploration. Therefore, since rock property meas-urements are usually performed in the labora-tory, there is a strong need to access such data in the field to run drillability models. There is a continuous search for optimum methods to pre-dict UCS from field measured parameters with sufficient accuracy. Thus, a review of these ap-proaches is also performed. Finally, the implica-tions of the findings with respect to variability of the reported measured and predicted values of UCS on the prediction of rock drillability are discussed.

2. ROCK UNCONFINED COMPRESSIVE STRENGTH AND ITS MEASUREMENT Uniaxial compressive strength of rocks (UCS) is a property very often measured and used by en-

gineers to design surface and underground structures and to drill wells for mineral explora-tion and exploitation. Standard procedures to accomplish this have been presented both by American Society for Testing and Materials (ASTM, 1984) and by International Society for Rock Mechanics (ISRM, 1978) who have classi-fied UCS into seven grades designated by the codes R0 to R6, with R0 being the weakest rock.

Variability, however, of the reported UCS values for different rock types and from various places around the world is extremely high. Searching for data on UCS from several differ-ent publications, from the mining and petroleum industry, one realizes that, for a given rock unit, there are as many UCS values reported as probably the number of particles comprising a m3 of the particular rock. Variability of a pa-rameter, defined as the standard deviation over the mean value and expressed as a percentage, (Roxborough, 1987), could indicate the spread of data. Roxborough gives rock variability, based on 40 sandstone samples, at 20% while Zhorlu et al., (2005) reported variability for 61 sandstone samples was 44%,. Negative correla-tion between UCS and variability of the meas-ured values has been reported (Rohde and Feng, 1990) stemming from the fact that stronger rocks have fewer imperfections.

It is interesting to note the point raised by Tanaino (2005) that the geological name of a rock is not a criterion for strength determina-tion, as it is evident from Figure 1. The data categorizes maximum UCS measured from ap-proximately 1000 rock samples, from igneous, metamorphic and sedimentary rocks and ores. The author found that the most influential factor was weathering. UCS values for the same rock but different weathered conditions could have one order of magnitude difference. For example, non-weathered basalt could have UCS values in

Figure 1: Rock classification by intervals of compressive strength (from Tanaino, 2005).


the range of 350-400 MPa, while UCS for weathered basalt has been reported at 35-50 MPa.

Furthermore, one always addresses the issue of weak and strong rock. But how can one de-fine hard and weak rock? What are the decisive parameters for characterizing a rock mass like this? Many years of research and field work cannot really answer what constitutes hard rock, even with a +/-100% margin of error. In the case of weak sandstones, UCS is usually be-tween 0.5 and 25 MPa (Brown, 1981). Factors affecting the properties of weak rock include poor cementation, weathering, tectonic distur-bance and large pore spaces (Olivera, 1993). In addition, the mineral composition of the rock is also important, as well as porosity, water con-tent, density and particle size, the properties that are known to influence the wave velocity, com-pressive strength and slake durability (Bell and Culshaw, 1993).

A factor very influential for the magnitudes of compressive strength values is the confining stress. Several studies, using triaxial testing, have shown an increase in UCS with increasing confining pressure, typically called Confined Compressive Strength. CCS may be very impor-tant for oil well drilling, but not as significant for mining, particularly for shallow drilling. Use of CCS takes into account the change in pore volume with increasing pressure thus mimicking better what is happening in the field during drilling (Walker et al., 1986). Studies (Peng and Zhang, 2007) have shown that for CCS up to 10% of UCS, UCS has increased dramatically by almost 80% (80 to 145 MPa). Even stronger influence has been reported for oil-well drilling, as it can be seen in Figure 2 for different sedi-mentary rock types.

3. UCS PREDICTION Measurements of UCS can be time consuming and expensive, while they require core data. In-formation about rock strength could be derived from measurements on cuttings (Uboldi et al., 1999) and some success has been reported. A point not addressed, though, is that the actual horizon where cuttings are generated is not known with certainty which may hinter identifi-cation of the rock horizon. Hence, industry has addressed several different ways to predict, in-cluding Schmidt hammer test, point load test, impact strength test, sonic velocity.

Fener et al., (2005) tried to relate UCS with the Schmidt hammer test, the point load test and the impact strength test for 144 samples, but found no good correlations with either. The highest value for regression coefficient was 0.77 for UCS versus the point load test. The reported UCS values ranged between 61 and 202 MPa, with igneous, metamorphic and sedimentary rocks. Fener et al., (2005) also evaluated prior relationships for the prediction of UCS, with 20+ correlations regarding UCS and point load test and 15+ correlations regarding the Schmidt hammer test and reported no agreement. They have attributed the inability of UCS predictions to the differentiation of rock types, rock micro-texture and even to test conditions, which then indicates that standardization procedures are not as definite as they should have been.

Kahraman (2001) also evaluated several sim-ple methods such as the ones mentioned above, to assess UCS using data from 48 different rocks. The least variability was observed with the point load test, but indicating not large vari-ability when compared with the other methods. Reported regression coefficients ranged be-tween 0.4 to 0.86.

One of the basic techniques to estimate UCS via non-destructive testing is by using sonic data, as velocity of elastic waves in rock de-pends on rock density, stiffness and hence to rock strength. It is also known that velocity de-pends strongly on rock mineralogy, grain size, porosity, weathering, stress level, water absorp-tion, water content and temperature, all of which complicate the issue and thus, no simple corre-lations exist or have been suggested. In oil-well drilling, UCS is also estimated from porosity logs. Khaksar et al., (2009) have listed 26 corre-

Figure 2: Effect of confining pressure on rock compres-sive strength for thre different rock types (adapted from Black et al., 2008).


lations for sandstones, 11 for shales and 7 for carbonates, for estimating UCS from various logged parameters.

An extensive literature search has indicated as many correlations between UCS and sonic data as research work undertaken. For e.g. D’Andrea et al., (1965) derived an expression from UCS - Vp data from rock samples from USA, while McCann et al., (1990) derived simi-lar relationship for British rocks, with both of them being of the type:

bpVaUCS ⋅= (2)

with reported regression coefficients in the range of 0.80. Both works reported significant data scattering especially at low porosity values, not to be expected, because at low porosities homogeneity of rock mass is greater. Similar re-sults were also reported for volcanoclastic rocks exhibiting strong UCS variation at porosities as low as 2% (Entwisle et al., 2005). The authors attributed this variation to structural differences among the samples. Using data from 144 sam-ples with porosity ranging between 0.01 to 15.7%, the authors have suggested the following correlation:

( ) 882.0783.0 pVUCS = (3)

with a very low correlation coefficient, 533.02 =cR . Prior work has also attempted to

separate the sonic responses according to rock type. Soroush and Fahimifar (2003) have meas-ured Vp and UCS, together with other proper-ties in 2000 cylindrical specimens, with the re-sults shown in Figure 3.

For the indicated rock types, e.g. claystone, cogglomerate, marl, sandstone and slate, sig-nificant variation is seen even among similar rock types. Similar significant variation from various data sources and areas in USA is also evident from the data presented by Oyler et al., (2008), reproduced here in Figure 4, with travel time being the reciprocal of p-wave velocity. The classical McNally equation (McNally, 1987), given as:

pVeUCS /035.0000,143 −⋅= (4)

is also shown, where UCS is in (psi) and Vp is in (ft/μs). It can be seen that the data is widely scattered while equation (4) does a decent pre-dictive job. On the contrary, Sharma and Sing (2008) reported good correlation between sonic velocity and UCS for a range of rocks, one ig-neous, three sedimentary and three metamorphic rocks for a total of 43 samples. They proposed a linear equation,

99.1170642.0 −⋅= pVUCS (5)

with a fairly high, for the given data, regression coefficient of 90.02 =cR .

In oil-well and rock drilling, sonic and den-sity logging is always performed, particularly in difficult to drill wells. Hence, data of sonic ve-locity and porosity or density is available. For this reason and for many years industry tried to find good correlations of UCS versus sonic ve-locity or bulk density in order to assess in situ rock strength and develop the drilling strategy accordingly. What is necessary of course is high quality of the field drilling data for a first hand approximation of UCS. Onyia (1988) performed several experiments and concluded that the sonic model may be used to develop a continu-

Figure 3: Variation of UCS with sonic velocity according to rock type (from Soroush and Fahimifar, 2003).

Figure 4: Variation of UCS with sonic travel time from USA data (from Oyler et al., 2008).


ous rock strength model. However, extensive data gathering using wireline logs, like the ones shown in Figure 5, gathered from 10 wells from the Alberta Canada region (Andrews et al., 2007) show significant variability the estimate of UCS, derived from sonic velocity. The UCS values are estimated form:

( ) 240_ 1

Kct

KUCSA−Δ

= (6)

where, UCSA _ is the estimated apparent rock strength, ctΔ is sonic travel time and 21, KK are constants.

Zhou et al. (2005) attempted to get better re-sults than from only simple exponential correla-tions, attempted to get better correlations, utiliz-ing all available geophysical logs, and two methods of data processing, SOM and RBF. Their predicted UCS results versus UCS data from cores from 3 boreholes are shown in Fig-ure 6, where the large data scatter is evident.

Also, one can see that the simple McNeally correlation performed as well as the more exag-gerated approaches presented by Zhou et al. The authors indicated that the regression coefficients between measured and predicted values were 0.62, 0.65 and 0.72 for the McNally equation, and their two approaches. Furthermore, the es-timated relative error ranged between a mini-mum of 0.1% to a maximum of 157%, with av-erages around 30% for all three approaches. Hence, even use of most available data to pre-dict UCS has not been sufficient to provide a fair estimate of UCS. Thus, data are site specific and if decent predictions are expected, meas-urements coupled with site calibration are es-

sential. We have attempted to gather sonic-UCS data

to see whether any correlation could be devel-oped from a variety of sources. The data is plot-ted in Figure 7, where the McNally equation is also shown. The results represent data of 187 samples, of different rock types and various places around the world and one can notice that variations are larger than +/-100%. Worth not-ing is the narrow range of sonic velocities for carbonates spanning a range of 50 to 200 MPa, a fairly flat response (wide variation in sonic ve-locity for a very narrow range of UCS) for some limestones, and a generally fairly linear trend between UCS and sonic velocity for sandstones. The McNally equation also seems to pass through most of the data, thus doing also here a decent job.

Figure 5: Data of predicted UCS values, from sonic data, from 10 wells versus sonic travel time (from Andrews et al., 2007).

Figure 6: Predicted UCS versus measured UCS for a vari-ety of samples from 3 wells (adapted from Zhou et al., 2005).

Figure 7: UCS - sonic velocity correlations for various rock types and from a variety of sources. S: sandstone, M: marble, C: carbonates, L: limestone, Si: ith site; data from: Kahraman (2001), Papanacli (2007), Moradian and Behnia (2009), Sharma and Singh (2008), Vogiatzi (2008).


4. DISCUSSION The variability of UCS with rock type empha-sizes the importance of local calibration before performing any logging, in hydrocarbon drill-ing. But researchers have been suggested a mul-titude of correlations, which, in the absence of other data can give a very vague idea about rock properties from sonic data (Chang et al., 2006). The issue is to narrow down the uncertainty so that we can estimate UCS, the ever sought after rock property, from indirect measurements, and also, how we can combine it with other avail-able data for better estimates.

Of course the question is how, an error in es-timation of UCS, impacts the predictions of rock drillability. An answer could be given with a fair degree of accuracy if an appropriate rock-bit interaction model is available, which is not true. Fair estimates of the effect could, however, be given with the use of simulators which can be fine-tuned using real field data. Such a test case has recently been presented (Kelessidis and Dalamarinis, 2009) using an accurate enough drilling simulator, Payzone, shown in Figure 8.

One can see that an error in the value of UCS by 50% could have significant effect on the pre-diction of drilling time for the given formations. For the specific case at hand formations drilled were shale, soft and hard sand. The error may range between 58 and 96%, giving an overall increase in total drilling time of 82%.

Recently, researchers, particularly in hydro-carbon drilling (Andrews et al., 2007) follow the reverse path, having a good drilling model which could predict the rate of penetration to continuously run it in order recover a field de-rived UCS. This is the so called apparent rock strength, which is used to design future work or take drilling decisions on the spot when changes in drilling performance are observed. Of course

this is the reverse of what has been suggested above. It could be useful while on the job and while drilling, so that a continuous update on formation strength is given. But it necessitates the availability of a good drilling model, i.e., translation of the rig cutting and drilling power to rock crushing, which is not yet available. What is then necessary, for a job drilling design, is availability of good UCS data, predicted with fair accuracy. Furthermore, a good rock-bit in-teraction model is also needed, incorporated into an accurate drilling model which could integrate all information and allow for better drilling de-sign better job implementation.

5. CONCLUSIONS Drilling rate models require information related to rock drillability which in the past has been approximated by the Unconfined Compressive Strength. Many of the reported results on UCS of almost any rock type show wide scattering, not following particular trends.

Measurements of UCS require rock core samples, not always available because they are expensive to get from drill sites and are also time consuming and costly. Thus, researchers attempted to relate UCS to other, easier to per-form measurements with minimum to fair suc-cess.

Sonic velocity is mostly used for the indirect measurement of UCS. Several works have been reviewed and the results show wide scattering, with predictions of UCS from sonic velocity with a low of 0.50 to a high of 0.70 regression coefficient. Attempts to integrate additional logging parameters from hydrocarbon wells did not provide any significant improvement, thus pointing out to additional work to get better UCS estimates.

The impact of variability of UCS on predict-ing rock drillability or drilling time can be quite dramatic, thus better UCS estimates are needed as well as better rock-bit interaction and drilling models.

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Figure 8: Normal drilling time plot [2] and simulated drilling time plot [1] when UCS for all formations en-countered is estimated as increased by 50% (adopted from Kelessidis and Dalamarinis, 2009).


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UCS Amireg Paper Kelessidis