Using One-Dimensional Geomechanical Model for Determining the Safe Wellbore Orientation of Zubair Reservoir, Southern Iraq

Abstract


Introduction
Wellbore instability can be considered as a critical phenomenon while drilling oil and gas wells because it stops the progress of the operations, which is so-called Non-productive time (NPT).The high NPT definitely leads to over cost the well budget which may cause abandoning the operations, in the worst-case scenario, before achieving the wells' production or injection objectives (Zhang, 2019).Every year about Eight billion dollars are spent trying to recover the wells after the wellbore instability occurs (Peng and Zhang, 2007), which can be led to an overall increase in drilling expenditure by up to 10 % (Aadnoy and Ong, 2003).One of the causes of the borehole instability is the rock mechanical failure in the wellbore because of the unbalanced stresses between the earth and the wellbore.The well Trajectory and the mud weight are playing a vital role in the wellbore stability (Zhang, 2019).Despite utilizing different modern technologies to control the downhole problems, wellbore instability is still an ongoing issue that faces drilling operations.And because of the high drilling costs, these problems should be investigated accurately and extensively during the well planning (Mohammed et al., 2018).Historically, Bradley (1979) designed a theoretical model to predict the wellbore failure with the pressure-induced lost circulation and hole collapse under normal and in-situ stress conditions.The developed model showed the influence of the hole orientation on the wellbore stability and the influence selection of mudweight windows.The model was considered as the first attempt to involve the earth geomechanics in the analysis of the stresses around the wellbore.Al-Wardy and Urdanets (2010) constructed a geomechanical model for Nahr Umr reservoir in one of the oilfields in northern Oman by using lab and field measured data.The model outcomes (wellbore orientation and mud weight) have contributed to reducing well delivery days from 36.8 in 2009 to 30.1 days in 2010.In the south of Iraq, wellbore instability is the most common and severe problem and it may encounter in many different forms, e.g., breakouts, caving, stuck pipe, hole collapses, loss of circulation, and inaccurate quality of logging (Abbas et al., 2018;Alsubaih and Nygaard, 2016).By using Schlumberger Techlog software (Version 2015), the mechanical earth model (MEM) was constructed to estimate the overburden stress, pore pressure, rocks mechanical properties, and the horizontal stresses magnitude.In each step of MEM construction process, it was validated with the laboratory measurement from the well information and core analysis to correlate and approve the output of the Techlog calculations.The stability assessment was described for developing the wellbore plan with wellbore orientation for safe drilling operations.

Field of Case Study
Zubair oilfield is one of the gigantic and mature oilfields around the world.It was discovered in 1949 by Basra Petroleum Company and went on stream at the beginning of 1951 (Dahab et al., 2020).The field is in the south of Iraq and it is about 20 km southwest of Basra city as shown in Fig. 1.Mishrif and Zubair formations are the reservoirs in Zubair oilfield.The structural trap of the Zubair field forms about 60 kilometers in length and 10 kilometers in width as the anticline extends from northwest to southeast.The anticline consists of four domes, which are Hammar, Shuaiba, Safwan, and Rafidyah, separated by saddles.Fig. 2, shows the Stratigraphy column for Zubair field which extends from Dibdiba to Zubair Formation (Jassim and Goff, 2006;Al-Ameri et al., 2011).

Materials and Methods
The One-Dimensional geomechanics model is constructed as follows: • Processed the data and generated the model by importing the basic information (e.g., total depth).
• Calculated the vertical (overburden) stress from the bulk density log.
• Pore pressure profile was computed based on vertical stress and sonic compressional log.The profile was calibrated with formation pressure points taken by the repeated formation test (RFT).• Calculated the rock mechanical properties (elastic and strength parameters) from sonic (shear and compressional) and density logs and validated the same with the laboratory core test results.• Calculated the magnitude of minimum and maximum horizontal stresses from the static rock properties, overburden stress, and pore pressure.Then, it is validated with the mini-frac test points.• The orientation of horizontal stresses is used based on an interpretated formation-image log (FMI).
• The estimated wellbore failure by the software is validated with the actual borehole failure (from caliper log and bit size) with different failure criteria to choose the best match.
• Run the model with different scenarios of wellbore inclinations to identify the safe wellbore orientation and the minimum required mud weight to achieve stable drilling operations.

Determination of Vertical Stress
The overburden stress is considered as the main input for constructing the geomechanical model and it is determined by integrating the bulk density, which is extracted directly from the bulk density log, with the column of formations by using equation ( 1) (Eaton, 1975): Where: Sv: overburden stress (psi).ρ: bulk density (gm/cm3 ).Z:verticaldepth (m).g: constant of gravity (m/s2) In Zubair oilfield, bulk density log is only available from the top of Sadi Formation to the end of Zubair Formation.The upper intervals, which are from surface to Sadi Formation, are not logged, therefore, the density was calculated by extrapolation method in equation ( 2) recommended by Schlumberger (2015): (2) Where: : density at the ground level (The density of the soil is 1.65 gm/cm3).Air Gap: distance between the ground level and the rig floor (m).TVD: true vertical depth (m).A and α: are fitting parameters.

Pore Pressure Prediction
Pore pressure is another main input for the geomechanical model which is used later to anticipate the horizontal principal stresses (Zhang, 2011).The pore pressure profile was predicted as follows:

Formation hydrostatic pressure
Hydrostatic pressure is defined as the pressure resulting from the average water in the formation column (Bjorlykke, 2010).The hydrostatic of the water is mainly dependent on water salinity and rarely depends on water temperature (Hantschel and Kauerauf, 2009).The average water-specific gravity in Zubair oilfield is 1.0772 gm/cm3.It was input to compute and predict the pore pressure for Zubair oilfield and the resulted hydrostatic pressure gradient is (0.4699 psi/ft), as shown in first track of Fig. 3.

Formation geo-pressure
The geo-pressure can be measured directly or calculated by using an empirical equation for the interval of interest.The indirect geo-pressure was calculated by using the Eaton's equation to estimate the pressure for all the intervals, from surface to bottom by using equation (3) (Schlumberger, 2015): Where: Ppg: the gradient of pore pressure (psi/ft).OBG: vertical stress gradient (psi/ft).Ppn: normal pore pressure gradient (psi/ft).NCT: the normal compacted trend line which fits DTC measurements (μs/ft).DTC: the compressional transit time (μs/ft).
The resulted geo-pressure was validated and confirmed by using the available pressure points from RFT across 9 points in Mishrif, 5 points in Nahr-Umr, and 23 points in Zubair formations (EOWR, 2019).The geo-pressure prediction from Eaton's equation shows a good matching and agreement with measured pressure points by RFT across Mishrif, Nahr-Umr, and Zubair formations.The only observation is across Zubair upper sand, which is the pay zone, where RFT records are lower than the calculated pressure profile and that is because of the production operations.Thus, the pore pressure profile was corrected only across Zubair/Upper sand, as shown in the first track of Figs. 3, 4, and 5.

Rock Mechanical Properties
The rock mechanical properties include elastic and strength properties and the accurate calculations of these parameters are vital input for the geomechanical model and wellbore stability (Zoback, 2010).Rock strength is defined as the rock's ability to resist the in-situ stress conditions around the borehole.The unconfined compressive strength (UCS), the friction angle (φ), and the tensile strength (To) are the rock strength parameters that are dominating the formation stability.As shown in Figs. 3, 4, and 5, Schlumberger Techlog software suggests an empirical linear relationship to estimate the friction angle (FANG_FromGR) profile from the Gamma-Ray log.The unconfined compressive strength (UCS_YM) for Zubair oilfield intervals is estimated by using the correlation of Static Young's Modulus.Equation ( 4) was used to calculate the Tensile strength (TSTR) from UCS (Schlumberger, 2015).
To = K * UCS (4) Where: UCS: unconfined compressive strength (psi).To: tensile strength (psi).K: is the facies and zone interval factor (0.1 is the default value).K factor is the tensile strength to the UCS ratio and its default settings as per the theory of Griffith Elastic brittle which ranged K value between 8 to 12 as a ratio between unconfined compressive strength to tensile strength (Zhang, 2019).
The rock elastic properties are Shear Modulus, Bulk modulus, Young Modulus, and Poisson ratio.The elastic properties that obtained from the well logs are dynamic parameters because the sonic log is reading at high frequencies and the wellbore failure is relatively a slow process.The static properties refer to results obtained directly from laboratory tests on formation cores which are accurate.And because of that, the dynamic elastic properties should be converted to the static form (Fjaer et al., 2008).However, the static properties consider limited data and only for short intervals because it is from the core and it does not cover all the well profiles due to, for example, the core operations cost (Aziz and Hussein, 2021).Because of that, the elastic properties which are estimated from the dynamic method (well logs) for all the well profiles, are correlated and checked with the laboratory data (static method).In the dynamic method, sonic logs (shear and compression logs) and bulk density log are utilized to estimate the elastic moduli, which is called the sonic model and it is assuming an isotropic, homogeneous, and elastic formation.The Dynamic Poisson ratio and Young's Modulus are computed as the property of bulk and shear moduli as expressed in equation ( 5) to equation ( 8) ( Zoback, 2010).Where: Gdyn: shear modulus in (Mpsi).Kdyn: bulk modulus in (Mpsi).
To convert the resulted dynamic Young's Modulus to static form, John-Fuller correlation was used, (YME_STA_JFC) because it is the most accurate correlation for shale as well as the sand formations (Schlumberger, 2015).The static form of Poisson's ratio (PR_STA) is equivalent to the dynamic Poisson's ratio, which is commonly used in rock mechanics (Archer and Rasouli, 2012).The resulted profiles of the rock mechanical properties are in agreement with the estimated rock mechanical properties profiles, published recently by Issa and Hadi in 2021, with using wireline logging and laboratory testing in Zubair sand reservoir in the same region of this case study.The rock mechanical properties (Elastic and plastic properties) were validated by using the available data Triaxial and Brazilain tests on core plugs taken from Mishrif and Zubair formations (upper sand layer and lower sand layer).The calculated rock mechanical properties have shown a good match with core data (ZFOD, 2013) as shown in Figs. 3, and 4 for Mishrif and Zubair formations, respectively.

Horizontal Stresses
The last requirement for constructing the mechanical earth model is calculating the principal horizontal stresses (minimum and maximum horizontal stresses) and determining its orientations by considering that vertical stress is also principal stress.The minimum and maximum horizontal stress magnitudes are computed by using the input of the static Poisson's ratio, the static form of Young's Modulus by John-Fuller correlation, the overburden pressure (vertical stress), and pore pressure.The Techlog software ( 2015 Where: σv: overburden stress (psi).Pp: pore pressure (psi).σH and σh: maximum and minimum stresses (psi).α: Biot's coefficient (α=1 as it is conventionally treated).εH and εh: maximum and minimum principal horizontal strains.
The strains are used to match and validate the values of the horizontal stresses until achieving an acceptable match between the calculated minimum horizontal stress and the mini-frac test, as shown in last track of Figs. 3, and 4 for Mishrif and Zubair formations, respectively.Additionally, validating maximum horizontal stress is not discovered yet and the only check that can be done is the match of wellbore failure measured by the caliper log which can be considered as a complementary calibration for both determined horizontal stresses (Zoback, 2010).
The directions of field horizontal in-situ stresses are important to understanding the stresses field which is essential for borehole failure analysis (Zoback et al., 2003).Caliper and micro-image logs are used to identify the orientation of the wellbore breakout which is in the direction of minimum horizontal stress (Shmin) and perpendicular to the maximum horizontal stress (SHmax) (Moos and Zoback, 1990).Fig. 5 shows the regional director of the SHmax which is at about 40-50 degree which was driven by many physical data (e.g., wellbore breakouts, earthquakes…etc.)(Carafa et al., 2015).The interpretated formation micro-image log, indicated that the direction of the breakouts is at about 130-140 (310-320) degrees (SE-NW) which is the Shmin direction, and the direction of the SHmax is at 40-50 (210-220) degrees (SW-NE) as it is shown in Fig. 6.The directions of the Shmin and SHmax, are in agreement with the regional SHmax direction.Fig. 7 shows the final elimant of the 1-D MEM for Zubair oilfield from Sadi Formation ot bottom of Zubair Formation.

The development plan
To achieve safe drilling operations without instability problems, several scenarios with different well inclinations are implemented by using of Mogi-Failure criterion.The development plan is summarized in Table 1.All scenarios are executed by changing the minimum mud weight, or the equivalent static mud weight (ESMW), with the equivalent circulation density (ECMW) to investigate the hole failure.Based on the single depth sensitivity analysis in Zubair Formation, the preferred directional drilling is in the minimum horizontal stress direction which is at +/-140 degree (or +/-320 degree), as shown in Fig. 9.The goal of all the scenarios is set to achieve stable drilling operations with the minimum breakout and no breakdown failure (no tensile failure) based on the selected hole angle and the minimum mud weight and regardless of the shape and type of the well (e.g., S-shape, J-shape).The first and second plans are applied to investigate the minimum mud weight that is required to drill the vertical and nearvertical wells without shear and/or tensile failure.The shale stabilization was achieved by changing the mud weight from 10 ppg (the original used density) to 11.8 ppg with the observations of spikes of knockout in the lower shale layer of Zubair Formation and no tensile failure, as shown in Fig. 10 and Fig. 11, respectively.The wellbore stability was also achieved in the third plan, which is performed with a 30-degree inclination from the vertical, by changing the minimum required mud weight up to 12.5 ppg, as shown in Fig. 12.The inclination of the wellbore trajectory was increased up to 40 degree, in the fourth plan, and the mud weight-adjusted up to 12.6 ppg accordingly to achieve the minimum possible level of breakouts (Fig. 13).The breakout spikes increased at this stage in the upper shale of the Zubair Formation which may lead to more complications in failure estimation.The next two plans were checked by increasing the well inclination to 50 degree (Fig. 14) and 75 degree (Fig. 15), respectively.Although the mud weight was adjusted, the breakout failure increased significantly in the upper shale, middle shale, and lower shale of Zubair and Nahr-Umr formations.The tensile failure prediction also appeared which introduces the risk of breaking down the formation and wellbore instability.

Conclusions
The vertical and directional wells (up to 40 degree) are more stable than higher deviation trajectories (above 40°) and horizontal wells where the instability issues start to appear in both forms, tensile and shear failures.The well trajectory towards the minimum horizontal stress direction is the preferred path to drill the deviated wells with a larger scale of mud weight window.The experienced failures in the well were due to the rock shear failures from using a low mud weight.Thus, it is mandatorily to increase the mud weight up to 11.7 ppg for drilling the vertical wells into Zubair Formation to avoid the rock shear failures.Increasing the well deviation results in a narrowing in the mud weight window and thereby the mud weight?should be increased with increasing the inclination of the well.The predicted rock mechanical properties showed a good matching with the properties that measured based on the laboratory core testing.

Fig. 3 .
Fig.3.The results and the Data validation of the 1-D MEM across Mishrif Formation

Fig. 4 .
Fig.4.The results and the Data validation of the 1-D MEM across upper and lower sand layers of Zubair Formation

Fig. 9 .Fig. 10 .Fig. 11 .Fig. 12 .
Fig.9.The sensitivity analysis for Zubair Formation shows the preferred direction of the drilling which is in the direction of the minimum horizontal stress (140) for a bigger scale of mud weight window: (a) Represents the breakdown vs. wellbore orientation; (b) represent the breakout vs. wellbore orientation (a) (b)

Table 1 .
Well orientation development plan