Mechanical Rock Properties Estimation for Carbonate Reservoir Using Laboratory Measurement: A Case Study from Jeribe, Khasib and Mishrif Formations in Fauqi Oil Field

Estimation of mechanical and physical rock properties is an essential issue in applications related to reservoir geomechanics. Carbonate rocks have complex depositional environments and digenetic processes which alter the rock mechanical properties to varying degrees even at a small distance. This study has been conducted on seventeen core plug samples that have been taken from different formations of carbonate reservoirs in the Fauqi oil field (Jeribe, Khasib, and Mishrif formations). While the rock mechanical and petrophysical properties have been measured in the laboratory including the unconfined compressive strength, Young's modulus, bulk density, porosity, compressional and shear -waves, well logs have been used to do a comparison between the lab results and well logs measurements. The results of this study revealed that petrophysical properties are consistent indexes to determine the rock mechanical properties with high performance capacity. Different empirical correlations have been developed in this study to determine the rock mechanical properties using the multiple regression analysis. These correlations are UCS-porosity, UCS-bulk density, UCS-Vs, UCs-Vp Es-Vs, Es-Vp, and Vs-Vp. (*). For example, the UCS-Vs correlation gives a good determination coefficient (R2= 0.77) for limestone and (R2=0.94) for dolomite. A comparison of the developed correlations with literature was also checked. This study presents a set of empirical correlations that can be used to determine and calibrate the rock mechanical properties when core samples are missing or incomplete.


Introduction
Rock mechanical properties are significant in establishing the plans associated with drilling, completion, stimulation, production, and reservoir monitoring processes (Meehan, 1994;Bjorlykke and Hoeg, 1997). When a piece of rock is subjected to sufficiently large stresses, some kinds of failures will occur. This implies that the rock shape will permanently change, and possibly fall apart. This condition is accompanied by reducing the ability to carry loads. Carbonate rocks are complex and thus rock mechanical properties are heterogenous (Tawfeeq and Al-Sudani, 2020). While rock mechanical laboratory testing is the most accurate method for calculating the rock strength (Rabbani et al., 2012). Core testing, unfortunately, can never lead to a continuous profile of rock strength along the wellbore.
The coring is very expensive, and it is very sensitive to stress unloading. The number of core samples is also restricted due to time limitations as well as the availability of good quality core. Besides that, the lab results may not be fully representative of the entire reservoir section due to complex variations in rock composition (Rabbani et al. 2012). Rock failure is also an important phenomenon for petroleum related rock mechanics, as it is the origin of severe problems such as borehole instability and solids production. It is therefore useful to be able to predict under which conditions a rock is likely to fail (Raeen, et al. 1996;Rabbani et al. 2012). The unconfined compressive strength (UCS) is the essential parameter for planning the mud weight window, bit selection and wellbore stability analysis. Besides, it is very important for reservoir subsidence and reservoir acidizing studies. When using this parameter, it is important to choose the proper weight on bit, evaluate drilling operation efficiency, bit wear and efficient bit lifetime in use (Nabaei et al. 2010, Rabbani et al. 2012. Several authors have been established many empirical correlations to estimate the mechanical properties (Militzer and Stoll, 1973;Sharma and Singh, 2010;Karamia et al. 2012;Castagna et al. 1993;Ameen et al. 2009;Chamge, 2004;Smorodinovet, et al. 1970;Khandelwal and Singh, 2009;andKaramia et al. 2012. Hadi andNyaagred, 2018;Abdulmajeed and Alhaleem, 2020). Table 1 lists these studies along with the equations of the rock mechanical and petrophysical properties. The prediction of mechanical properties using petrophysical properties is more reliable, especially in carbonates rocks. Most of these models are empirical correlations established based on geophysical well logs, such as acoustic porosities or velocities porosities, to determine laboratory-derived mechanical rock properties (Yagiz, 2011). These correlations are based on the fact that several same factors that affect mechanical rock properties also affect physical properties, such as porosity, velocity, and elastic moduli (Chang et al. 2006). Generally, the relationships of mechanical rock properties and physical rock properties established for specific formation depending on the calibration of laboratory tests on rock samples from a specified field. The aim of this study is to correlate the rock mechanical properties with petrophysical properties using experimental work of many core samples that have been taken from three formations which are Jeribe, Khasib and Mishrif formations. This study has been conducted in the production section of the Fauqi oil field (South East Iraq). A major issue of this field is that no local empirical correlations can be used to determine the rock mechanical properties in terms of petrophysical for many applications related to geomechanics.

Geological Setting of the Study Area
Missan Oilfield is located in southeastern Iraq and close to the Iraq-Iran border. The field consists of three producing oilfields, namely Abu Ghirab, Buzurgan and Fauqi oilfields. Stru Fauqi oilfield has two sets of reservoirs, Tertiary Asmari and Cretaceous Mishrif. Three pay zones are divided in the Asmari reservoir which is A, B and C. The pay zone A of Asmari consists of mainly dolomite. The pay zone B is dolomite intercalated with sandstone, limestone and thin shale. The pay zone C is mainly the sandstone, intercalated with a few dolomite, mudstone and limestone. The main reservoir in the Fauqi oilfield is cretaceous Mishrif. Seven pay zones are divided in the Mishrif reservoir, which are MA, MB11, MB12, MB21, MB22, MC1 and MC2. More details about the studied formations are listed in Table.

Materials and Methods
In this study, mechanical rock properties were determined using core samples collected from different reservoir intervals from different wells. Seventeen core samples of limestone and dolomite were obtained from Jeribe, Khasib and Mishrif formations in the FAUQI oil field. The length of studied cores is ranged from 2.3 cm to 4.43 cm, while the width is ranged from 2.34cm to 2.5 cm.

Uniaxial Compressive Strength (UCS) Test
The uniaxial compressive strength, or UCS, test is a destructive technique for determining the uniaxial compressive strength of intact rock core specimens. In rock mechanics and engineering geology, the UCS test considered to be the most widely used methods to obtain rock strength properties. Uniaxial compressive strength values (σf) were calculated using the following simple formula: (1) where Ff is the force applied by the hydraulic cylinder to the sample at the time of catastrophic failure, A is the area of the ends of the sample, and is uniaxial compressive stress at failure that is equal to the UCS. Under the assumption that the material is isotropic one can also determine the Young's modulus E.
(2) and Poisson's ratio ν where ε axial and ε radial are provided by the strain gauges mounted parallel and perpendicular to the cylindrical sample's axis, respectively. The lab apparatus used in this study for measuring the UCS, is shown in Fig.1. The experiment started with putting the core sample between two plates contacted with the top platen. An axial load about 100 N is applied to core sample using the loading frame for fixing the core sample. The results are recorded with different axial forces until the core is crushed or fractured.

Ultrasonic Test
The velocity of propagation (Vp) and shear velocity (Vs) of core samples were measured with an ultrasonic device according to standard ASTM (1986) (Fig. 2). Measure the length or height of the specimen. Clean the upper and lower surfaces of the specimen and put little amount of any kind of grease on them to have complete adhesion between the specimen surfaces. put the specimen between the two transducers. Put the tester on to generate the pulse move the certain kind of P-waves and shear waves velocity could be obtained by using the two kinds of transducers each one specified fore wave shape on the oscilloscope to read out the arrival time of the wave the pointer must be the begin point of pulsation when recording the time. Measuring of primary waves velocity. The velocities of either P or S wave are calculated as follows: (4) where VP is the P-wave velocity (km/s), VS is the S-wave velocity (km/s), S is the distance traveled by the wave (mm), and t is the travel time in this method, the wave frequency must be high, and the rock specimens must have infinite extent compared to the pulses' wavelength. This test is performed following the ISRM (2007). Fig. 3 shows several samples that were used before and after testing. Table 3 represents experimental results of mechanical and physical rock properties for carbonate reservoir. Table 4 presents the JMP software's statistical output in terms of mean and standard deviation parameters for thirteen samples of limestones and four samples of dolomites for the involved properties.   In the following sections, correlation between individual mechanical and physical properties will be presented separately as follows: Fig. 4 shows the laboratory measured ultrasonic S-wave velocity (Vs) along with UCS results for limestone and dolomite samples. Two relationships between UCS and Vs have been presented where UCS in MPa and Vs in Km/sec. The results revealed that there is a scattering around the UCS-velocity curves. This can be attributed to the heterogeneity of carbonates formation which are mixed of dolomite intercalated with argillaceous dolomite in addition to conglomerate and locally anhydrite argillaceous (Jeribe Formation), and limestone interrelated with thin argillaceous limestone (Khasib and Mishrif formations). In other words, this scattering is related to the complexity of pore rock system. Two correlations (Eqs. 5 and 6) have been constructed in this section, obtaining correlation coefficients (R2) of 0.77 for limestone and (R2) of 0.94 for dolomite, respectively. According to the results of Fig. 4, the results showed that UCS increases linearly with Vs (inversely with sonic travel times).

Correlation between (UCS)and P-wave velocity (Vp)
Fig. 5 presents the relationships between UCS and compressional wave velocities for both limestone (13 samples) and dolomite (4 samples). The relationship between UCS and Vp is expressed in MPa and Km/sec, respectively. The results showed a clear scattering around each fit curve. This can be attributed to the different geological setting of limestone and the effect of the diagenetic processes on dolomite which altering the rock framework and pure structures to varying degrees. In addition, this scattering is related to the heterogeneity of formation because of the depositional environments and dolomitization processes.

Correlation between uniaxial compressive strength and porosity
The relationship between porosity and UCS values is presented in Fig. 6. the porosity is a controlling factor of rock strength in the basalts that conducted in this study, most of the samples with relatively high porosities tend to be broken at very early stages in the load cycle which exhibit a very low UCS. On the other hand, most of the strong solid samples are associated with extremely low porosity. It also shows a strong correlation of R2=0.84 between UCS and porosity for dolomite and R2=0.76 for limestone according to the Equations 9 for limestone and 10 for dolomite.

Correlation between compressional wave and shear wave velocity
The results of the laboratory ultrasonic measured velocities Vp and Vs for carbonate (limestone and dolomite) formations are presented in Fig. 8, where both Vs and Vp in Km/sec. Equations 13 and 14 outline the presented fit curve, obtaining equal R2 of 0.88 for both limestone and dolomite, respectively. There is a scattering around each curve which can be attributed to the heterogeneity of carbonate samples in which the void proportions and pore size distributions within the rock fabric are complex. To validate our model, we compare the Equation from the core with the log data, as shown in Fig.  9 with R2=0.88 for limestone and R2=0.91 for dolomite. Fig. 9. Plots of predicted Vs. using core data versus measured Vs. from log Fig. 10 shows the relationship between S-wave velocity and bulk density of carbonate rocks. there are good relationships between S-wave velocity and bulk density with R2 = 0.76 for limestone and R2=88 for dolomite. The scatter in the data can be attributed to sample heterogeneities, matrix is mainly composed of particles. According to Equation 15 for limestone and Equation 16 for dolomite, S-wave velocity increases linearly with increasing bulk density. the equations of the relation are:

Correlation between S-wave velocity and bulk density
Vs=3. 175×P-5.46 (15) Vs=3. 033×P-5.532 (16) Fig. 10. Relationship between vs. and bulk density Fig. 11 shows the relationship between P-wave velocity and bulk density of limestone and dolomite. The results support good relationships between P-wave velocity and bulk density with R2 =0.73 for limestone and R2= 0.81 for dolomite, Where Vp in km/sec and bulk density in gm/cc. The scatter of even the mean values around the regression lines is due to the complex depositional environments and digenetic processes of carbonate rocks. According to Equation 17 for limestone and Equation 18 dolomite P-wave velocity increases linearly with increasing bulk density. the equations of the relation are:

Correlation between young modulus and shear wave velocity
The regression curves between Young's modulus on S-wave velocity of carbonate rocks are shown in Fig. 12

Correlation between young modulus and P-wave velocity
The regression lines of young modulus on the P-wave velocity of carbonate rock for the combined data are shown in Fig. 13

Comparison between new correlations with the previous Empirical correlations
In this section, the developed correlations have been compared with some previous correlations in Table 1. The new correlation gives an excellent matching with Ameen (2009) and Castagna (1993) correlation but relatively less matching with Al-Kattan (2015) correlation for limestone formation. The results show an excellent matching between the developed correlation, Ameen (2009) and Castagna (1993) correlations but it has a little difference with Al-Kattan correlation (2015), (Fig. 15). The new correlation is matched the Ameen (2009) and Castagna (1993) correlations but less relative matching with the Kattan correlation (2015). The new correlation gives an excellent matching with Ameen (2009) and Castagna (1993) correlations but have some differences with Kattan correlation (2015) (Fig. 17).

Conclusions
This study presents a set of correlations to estimate the rock mechanical and elastic properties based on lab experimental works using the multiple regression analysis technique. A field case (FAUQI oil field), located in southeast Iraq, was conducted to correlate the rock mechanical with petrophysical properties. The greatest difference between this study and previous studies is that there are no local studies to estimate the rock mechanical properties in this field of interest. The conclusion of this study can be summarized in the following points: • Petrophysical rock properties including porosity, compressional shear aves, and bulk density are consistent indexes to estimate the rock mechanical properties. • The results are more conservative in estimating UCS rather than using previous correlations.
• The results of Vs and Vp are well matched well log data when the core plugs are saturated with diesel oil than when the core plugs are dried. • The presented correlations can be used to estimate UCS, Vs, and Vp from well log data if the core samples are limited or not available, which is a cost effective correlation. • Even though all of Vs correlations (previous and developed) show a good match with well log data, their prediction ability is different. For example, Castagna and Ameen correlations show a closely match with the developed correlations while AlKattan correlation showed an overestimation of Vs magnitudes. • The developed correlations in this study can be locally used with high performance capacity, but it requires a calibration when it will be used in another field of interest.