Friction Angle Prediction of Carbonate Rocks: A Case Study, Rumaila Oil Field

Abstract


Introduction
When exposed to very high stress, rock will fail and lose its capacity to support loads.Rock fracture and permanent rock shape distortion are both examples of this failure (Al-Khafaji, 2019, Issa andHadi, 2021).Rock failure is regarded as a primary rock mechanics phenomenon since it can generate a variety of issues for the oil industry, such as solid production and well bore instability (Mahdi and Alhaleem, 2023).Consequently, it is crucial to foresee the rock characteristics that lead to formation failure (Al-Kattan and Al-Ameri, 2012;Fjaer et al., 2008).Especially, when creating the mechanical earth model, a good evaluation of the geomechanical failure characteristics is essential (Aziz and Hussein, 2021b;Issa and Hadi, 2021).Once mechanical earth model is completed, various information about the reservoir can be gathered, and many issues can be avoided both during drilling and afterward by managing the reservoir more effectively (Issa and Alrazzaq, 2022).Elastic and rock strength parameters represent the main characteristics of a rock's mechanical characteristics (Al-Kattan, 2015, Aziz andHussein, 2021a;Hassan and Hussien, 2019).Knowing these characteristics is crucial for fracturing operations, wellbore stability analysis, preventing sand production, optimizing drilling operations, and developing geomechanical models to address the minimum required mud weight to drill a stable well (Kidambi and Kumar;2016, Zoback et al., 2003)).The geomechanical characteristics also have a significant impact on the selection of drilling bit, prediction of suitable mud window, optimization of well trajectory, and fracturing design (AbdulMajeed and Alhaleem, 2020;Guo et al., 2015;Li and Tang, 2016;Najibi et al., 2017;Zhang et al., 2010).One of these geomechanical characteristics is the friction angle.This is crucial for the assessment of rock strength, wellbore fluid in the beginning of production, and pore pressure.As formation strength and stability naturally vary around the wellbore in various levels within the interval of interest, the continuous friction angle profile offers a useful signal of these variations.The natural alteration of the wellbore stability and formation strength in various regions within the interval of concern is well signaled by the continuous friction angle profile.Friction angle is affected by mud weight, inclination angle, and azimuth.also effect on friction angle typically, cylindrical plug samples are subjected to gentle uniaxial or triaxial strains until failure occurs in order to determine the friction angle.The most direct and accurate method of establishing friction angle is through laboratory tests (Fjaer et al., 2008).As a result of its simplicity and low cost, tilt testing is probably the most popular technique for obtaining the friction angle.However, laboratory methods are very costly and Overburdened layers' core samples are nearly never available for analysis.Even if rock samples are retrieved from the depths of concern, the action of the drill bit during coring processes, as well as improper sample preparation and conditioning, may result in additional damage to the cores.This could have a significant impact on the outcome of the rock mechanical analysis.Additionally, only a small portion (a few feet) of the formation interval may be covered by experiments conducted in laboratories.Although well logging cannot be used to directly estimate friction angle, it is regarded as a good method for forecasting friction angle profiles throughout the whole interval of the formation for two primary causes.First, well logging provides precise measurements of the rock's petrophysical characteristics.Second, well logging is one of the few deep underground measurement methods available across the whole formation.Hence, in this article, we developed a correlation that can estimate the friction angle for carbonate formations from well logs using the typically accessible well log data (i.e.neutron porosity, gamma ray, bulk density, and sonic logs) and core data.Following that, laboratory experimental data, primarily from triaxial testing, is used to calibrate the generated correlation from well log data.

Materials and Methods
For assessing the formation's deformation and stability, friction angle prediction is crucial (Wang and Akeju, 2016), and it is critical for drilling operations and oil and gas production (Zhang and Yin, 2013).Several studies have shown that friction angle and the formation lithology are related in the first order.The lowest friction angles are actually found in rocks with a high volume of shale, while the highest friction angles are obtained in low porosity rocks.Additionally, it is possible to create a relationship between the confining pressure and friction angle, which are both influenced by the shale volume.For instance, the friction angles measured at 5 MPa confining pressure are as much as 50% greater than those recorded at 50 MPa for a given shale volume (Lama, 1978).Little efforts were made to create correlations for friction angle from well log data.Furthermore, since the relationship between strength points and confining pressure are typically not linear, there is a low probability that a rock has a single value of friction angle.The range of confining stress that the data are fit over determines the friction angle.This shown that friction angle rises as confining pressure falls (Weingarten and Perkins, 1995).Different correlations were created to calculate the rock's friction angle (Plumb, 1994) succeeded in correlating neutron porosity with internal friction angle.This was then enhanced by (Jaeger et al., 2009), to take shale into account, which increased the correlation performance.A linear relationship between porosity and the friction angel was developed by Weingarten and Perkins (1995) for sandstone rocks.Moreover, (Abbas et al., 2018) link the friction angle to the gamma ray and compressional wave logs.Some of the formulas created for predicting friction angle are shown in Table1.The accuracy of predicting friction angle of these previous correlations for the carbonate formation of Rumaila oil field have been evaluated using well log data and core sample measurements collected from an oil well of this carbonate formation.The used core samples are extracted from Limestone (i.e.Sadi) reservoir at depth of 2139 m to 2155 m with a recovery of 99.4%.Seven carbonate reservoir with one are used in this study including Hartha (Limestone and Dolomite), Sadi (Limestone), Tanuma (Shale and Limestone), Khasib (Limestone and Shale), Mishrif (Limestone), Rumaila(Limestone), Ahmadi (Shale and Limestone), Mauddud (Limestone), as shown in Fig. 1.A total of 5197 well log data points were collected from carbonate formation with depth interval of (1920 m to 2711 m) from Rumaila oil field.For all 5197 data points neutron porosity, and gamma ray logs were recorded as a function of depth, and the corresponding shale volume and total porosity were estimated.In addition to these well log data, 20 data core points with 9 different values of friction angle were collected (Figs. 2 and 3).

Results and Discussion
In this section, the estimated friction angle from equations (1 to 4) were compared with the measured friction angle from core samples.The results indicate that all tested correlations are unable to accurately predict the friction of carbonate formation of Rumaila oil field (Table 2 and Fig. 4).The reason of this is that all these correlations were created to compute the friction angle for sandstone and shale formations.Thus, a new correlation for predicting the friction angle of carbonate formation is required.Here, a new correlation is developed to predict the friction angle from the carbonate formation using the measured friction angle from core sample and the correspondent gamma ray from well log.The results show that the following equation represents the best form for the relationship between the friction angle and gamma ray (Equations 5): (5 Where θ is the friction angle for carbonate formation (Deg), and GR is the gamma ray from well log (gAPI).The ranges for the parameters that were used to create the new correlation (Eq.5) are presented in Table 2.The new correlation has a correlation coefficient (RSQ) of 0.9067 and can accurately estimate the friction angle (Fig. 4).The statistical accuracy (i.e.average absolute error (AAERR)) of the new correlation for predicting the friction angle (Eq.5) is compared with published correlations (Eqs. 1 to 4).The results indicate that the new correlation is better than published correlations in estimating the friction angle for carbonate formations.The results show that the new correlation has the highest accuracy (i.e. the lowest AAERR; Table 3).Figure 5 shows the measured and estimated friction angle from the previous correlations (Eqs 1 to 4) and new correlation (Eq.5).It indicates that the new correlation (Eq.5) is the best in predicting the friction angle with the highest accuracy.

Correlation
AAERR % (Abbas et al., 2018) 49.10 ( Zoback et al., 2003) 47.66 (Weingarten and Perkins, 1995) 27.66 (Plumb, 1994) 8.76 (This study) 1.66 Lastly, the new correlation is used to produce a continuous profile for friction angle for the depth interval of (1920 m to 2711 m) for carbonate formation of Rumaila oil field (Fig. 6).Fig. 6 indicates that the created friction angle profile for carbonate formation using the new correlation has an excellent match with the measured Friction angle.

Conclusions
Friction angle (φ) is the angle between the normal and resultant force that is achieved when failure just occurs as a result of a shearing stress.For the optimization of drilling operations, monitoring of the reservoir, and production of hydrocarbons, the prediction of friction angle is essential.
From laboratory measurements or wireline logging data, this parameter can be empirically predicted.However, taking this measurement in the lab takes time.So, in this study, we created a new correlation to forecast the Friction angle for carbonate formations as a function of the of Gamma Ray from well logging.20 experimental Friction angle data points that are obtained from laboratory are used to develop the new correlation.The developed correlation is then used with 5197 Gamma ray data point that are obtained from well logging to generate a continuous friction angle profile for carbonate formation.The calculated Friction angle from the developed correlation has been compared with the measured Friction angle from the laboratory.The results show that the correlations predict friction angle with excellent precision.With extremely high RSQ (0.9067) and very small average absolute errors (1.6%), the new correlation accurately predicts the Friction angle.We, therefore, draw the conclusion that the recently obtained correlations are superior to forecast the friction angle for carbonate formations.

Fig. 1 .Fig. 2 .
Fig.1.Stratigraphic column of the studied section from the well of Rumaila oil field.

Fig. 4 .
Fig.4.The new developed correlation for friction angle prediction as a function of Gamma Ray for carbonate formations.

Fig. 5 .
Fig.5.The predicted friction angle from the previous correlations and from new correlation with the measured friction angle as a function of Gamma ray

Fig. 6 .
Fig.6.Friction angle profile predicted for carbonate formation from the new developed correlation

Table 1 .
Previous correlations to estimate friction angle from rocks physical properties

Table 2 .
Statistical summary of the used well log and core data from carbonate formation.

Table 3 .
The comparison of the average absolute error for the previous and new correlation for predicting friction angle.