Estimation of Rock Mechanical Properties of the Hartha Formation and their Relationship to Porosity Using Well-Log Data

Abstract


Introduction
Since rock failure is the cause of serious issues such as borehole instability and the production of solids, it is also a significant occurrence for rock mechanics in the context of petroleum.Therefore, knowing the circumstances in which rock is most likely to fail is useful (Raaen et al., 1996;Rabbani et al., 2012).It is defined as the amount of axial stress that a specific rock cylinder can withstand before failing, and it depends on several factors such as lithology, compaction, porosity, cementation factor, and fluid content (Nabaei et al., 2010;Awadh et al., 2019;Boschetti et al., 2020;Fayyadh, and Ismail, 2021).According to the proposed method, rock strength can be calculated utilizing the most used variables, including neutron porosity, bulk density, and gamma-ray for clay volume (Rabbani et al., 2012).Data from previous studies are gathered to create a statistical analysis of the relationships between Young's modulus, Uniaxial Compressive Strength (UCS), porosity, density, tensile and strength (Abdaqadir and Alshkane, 2018).Young's modulus represents the hardness of the rock ther is a clear vertical and horizontal heterogeneity.(Steer et al.,2023)Seismic waves have been widely used in various investigations to measure rock mechanical characteristics.In general, the velocity of seismic waves is determined by the ratio of rock moduli to density.Velocity variations are caused by the elastic moduli by density term, which is affected by rock characteristics, including fluid saturation and rock texture.The rocks elasticity concept demonstrates that seismic wave propagation provides two mechanisms in which the waves propagate independently (Durrani et al., 2014;Fadjarijanto et al., 2016;Jaeger et al., 2009).It has been clearly demonstrated that the shear wave velocity can be estimated from P-wave velocity, porosity and density if the dipole sonic log is not available (AbdulMajeed and Alhaleem, 2020) .The Compressional wave (Vp) of rocks is influenced when exposed to fluids.(Aziz and Hussein, 2021).shear wave velocity decreases with increasing porosity while Vp is less sensitive to porosity, also Vs decreases more than Vp with increasing Shale content.(Al-Kattan, W. M., 2015 Constructed a set of empirical equations that link the UCS physical parameters of sedimentary rocks (velocity, modulus, porosity).These equations can be used to calculate rock strength given well-logging parameters.They concern the advantages of compressional waves (Vp) (Zhang, 2005).
From the point of view of paleontologists, stratigraphers an sedimentologists, the Hartha Formation was stuied by several researchers in terms of biostratigraphy and depositional environment; for instance, Mousa and Shakir, 2023;Ismail et al., 2022a;Ismial et al., 2022b;Abed,. andAl-Jaberi, 2023. Boschettie et al., 2020).The reservoir properties require being evaluated by combining petrophysical and geomechanical rock properties (Farouk and Al-haleem, 2022;Al-Dabbas et al., 2014).The properties of the rock are not uniform as they vary horizontaly and vertically according to the type of rock (Al-jawad and kareem, 2016).The resistivity and porosity logs can predict the total organic carbon (TOC) (Idan, 2017).(Davies et al. (2019) using the geophysical well logs data, and sonic log for hydrocarbon well in Niger Delta Basin to estimate the dynamic rock mechanical parameters from established empirical relations.Their findings reveal that the trend of Young's modulus (E), unconfined compressive strength (UCS), bulk modulus (K), and shear modulus (G) increases as one moves down the well, whereas the Poisson ratio drops.The average values received from E, UCS, K, G, and  are 3.72*10⁹ Pa, 3.56*10⁹ Pa, 2.68*10⁹ Pa, 1.48*10⁹ pa and 0.3732, respectively.Multiple researchers have established many empirical correlations to estimate mechanical properties (Pickett, 1963;Ameen et al., 2009;Hadi and Nygaard, 2018;AbdulMajeed and Alhaleem, 2020;AbdulMajeed and Alhaleem, 2020;Aziz and Hussein, 2021;AbdulMajeed and Awadh, 2022).Various petrophysical parameters are used as input data for each of these estimating methods, as illustrated in the following equations: / = 1.8   = 1.8 (Pickett, 1963) (1)  = 62.567 −0.0203∅ (Ameen et al., 2009) (2)  = 0,1026 + 0.44104  + 0,1215  (Hadi and Nygaard, 2018 However, some studies which use multiple regression come up with positive outcomes.Considering the utilization of conventional well-logs,.Regression analysis, which is a statistical technique for predicting rock mechanical parameters and porosity characteristics in limestone formation (carbonate reservoir), is presented using JMP software.It will be covered how to create empirical models using measurable well logs to estimate mechanical properties as well as how to use single regression for accurate mechanical property forecasting in the studied reservoir.

Geological Setting
The Missan Oilfield is situated near Iraq-Iran borders in southeast Iraq.The field comprises the oilfields Abu Ghirab, Buzurgan, and Fauqi, all in production.The Fauqi oil field is roughly 30 km by 7 km.It has two domes tending NW-SE along the anticline axis.The Hartha Formation includes important carbonate reservoirs that are producible in Central and Southern Iraq.It gained significance due to significant amounts of hydrocarbon (Dunnington and Morten, 1953).The Hartha Formation was first described by Rabinit (1952) from well Zu-3, south of Iraq (Owen and Nasir, 1958).It is composed of organic detrital, glauconitic limestone interbedded with green and grey shale (Jassim and Goff, 2006).The thickness of the Hartha Formation is variable because it passes laterally and vertically with the marly limestones Shiranish Formation.Harth formation was influenced by channel system when it deposited and subsequently exposed at the surface.(Bashara et al.,2023).The thickness of the formation in southern Iraq varies from 200 to 250 m; in northern Iraq, the thickness reaches up to 350 m.It is conformably contacted with the Shiranish Formation, and unconformable with the Sadi Formation marking with a basal conglomerate (Jassim and Goff, 2006).The current study targeted the Hartha depth interval extending from 2622 to 3699 m.The detailed stratigraphic column of the Fauqi oil field is illustrated in Fig. 1 (Aziz and Hussein, 2021).

Statistical Evaluation
The current study employs multivariate regression analysis with the JMP program to develop a new correlation to predict rock mechanical parameters and their relationship to porosity of the productive carbonate reservoir.The creation of empirical models for estimating mechanical characteristics from well-log data was done.Multiple regressions are a type of regression analysis where the predicting equation includes an additional independent variable.(AbdulMajeed and Alhaleem, 2020).

Calculations and Analysis
A set of reservoir observations, including well logs and core evaluations, can be connected to the findings of the regression analysis in order to predict the output function.Regression analysis, either simple or multiple, can be used; simple regression analysis is frequently employed to model the relationship between two variables.The JMP soft program used this sample data to find the correlations between mechanical characteristics and NPH.Table .1 displays the estimated mechanical characteristics from log data.

Single Linear Regression Analysis
Various engineering challenges show that specific data fluctuates in an increasing or decreasing trend.For instance, numerous studies have shown that increased mechanical characteristics require increased rock samples.As a result, it is advantageous to investigate whether mechanical rock characteristics are connected to petrophysical characteristics when inspecting carbonate rocks using single linear regression analysis.

Relation between velocity ratio (Vp/Vs) and NPHI
The velocity ratio VP/VS ratio in Fig. 2 shows a proportionate inclination versus the observed porosity.The velocity ratio is unaffected by the degree of consolidation or the porosity of the dry sediment.However, it is noted that even in a dry state, the VP/VS ratio may be significant in estimating the rock's porosity by R 2 =0.709.The ensuing correlations provide: Where NPHI is porosity, fraction.

Relation between UCS and NPHI
Fig. 3 shows the correlation between UCS and porosity.In the basalts used in this research, porosity is a governing variable influencing rock strength.As porosity increases, the UCS reduces.This figure highlights that there is scattering surrounding the curve that has been assigned to the heterogeneity of carbonate since the void fractions and pore size distributions are complex throughout the rock fabric.The link between UCS and porosity yields R 2 = 0.746, and the formula for the relationship is provided:  = 14.86 − 0.1978  (9)

Relation between Young modulus and NPHI
By equation 10 and for limestone with a determination coefficient of 0.85, the regression lines of Young modulus on the NPHI for carbonate rock of the data set are presented in Fig. 3. Since the strength parameters depend on the physical, textural, and mineralogical characteristics of the rock, the points are dispersed uniformly throughout the diagonal line rock.These relationships suggest that NPHI increases with decreasing Young's modulus. = 68.4− 2.212  (10)

Relation between bulk modulus and NPHI
It is clear from the bulk modulus, which is the ratio of hydrostatic stress to volumetric strain, that bulk modulus typically varies when hydrostatic stress develops in voids.In other words, it makes the bulk volumetrically expand to the porous rock within its elastic limit.Fig. 6 displays the regression lines for the combined data for the bulk modulus vs. NPHI of carbonate rock.Equation 12 presents a relationship between an increase in NPHI and a decrease in bulk modulus with determination coefficients of 0.849 for limestone. = 43.52 − 1.444 (12)

Model Outcome
The newly developed UCS prediction framework given in equation 9 was validated further by comparing it to actual field data and previous correlations in Table 1., as shown in Fig. 7.The created model achieves more significant agreement between field data and the newly developed equation than empirical models and has a good match with the Abdulmajeed and Awadh (2022) correlation.However, it differs from the Ameen et al. ( 2009) correlation.Because The reservoir consists of various carbonate rock types and related to the heterogeneity of formation because of the depositional environments and dolomitization processes,due to difference the new correlation.

Results and Discussion
The predicted mechanical characteristics (UCS, Es) utilizing equations 9 and 10 have an excellent agreement with the evaluated (UCS and Es) using well-log data (Figs.8 and 9) with approximately R 2 of 0.8024 and 0.8204, respectively.The relevant UCS is calculated using equation 9, and the log UCS is calculated based on the actual field data from well 28 in the Fauqi oil field.Multiple regressions revealed a significant association in estimating UCS from well-log data.To anticipate (UCS, Es) of the carbonate reservoir, empirical and single regressions have been employed to log data.Regarding estimating, the statistical technique surpasses empirical approaches and could be used entirely to acquire a substantial degree of (UCS and Es).Fig. 10 depicts both geomechanical and petrophysical characteristics results.At 3671-3672 m depths, porosity increases, resulting in a drop in UCS and dynamic elastic modulus of rock due to the direct link between rock strength and elastic modulus.

Conclusions
In the current study, well-log data were used to perform a single regression analysis to identify the mechanical and elastic properties of the rock.Rock mechanical properties have been correlated with NPHI using a field case study at the Fauqi oil field in the Harth Formation.The following are the significant conclusions: The reported correlations can be used to calculate UCS, Vp/Vs, Es, K, and G using log data, resulting in a cost-effective relationship if core samples are constrained or unavailable.Both the bulk modulus, K, and the shear modulus, G, have exceptional precision coefficients of determination and are consistent with empirical equations.
It can be extrapolated from the study of rock behavior under the impact of porosity that petrophysical and mechanical parameters have a similar trend, which rises from porosity due to reduced mechanical properties values.The seismic waves can be beneficial in measuring and analyzing petrophysical parameters, mechanical characteristics, and behavior of rocks subject to the porosity effect.

Fig. 7 .Fig. 8 .
Fig. 7. Comparison between Equation 9 and other empirical Relation to predicted UCS for the Hartha Formation from log data

Fig. 9 .Fig. 10 .
Fig.9.Es predicted using a single regression equation vs measured Es from the log data for the Hartha Formation well 43

Table . 1
. Results of mechanical properties of the Hartha Formation, well-Fauqi 43