Compressive failure behaviour of friable rocks
Rock failure occurs under various stress states and is classified as being brittle, transitional (brittle to ductile) and ductile (e.g. M Khoshini, Khoshghalb, et al. 2019; Petley 1999). The post-peak behaviour of the stress-strain curve can be used to determine the type of failure that the rock experienced (e.g. Evans, Fredrich, and Wong 1990; Ishii et al. 2011; Iyare, Blake, and Ramsook 2021). Brittle failure is characterized by a rapid stress drop after the rock attained peak strength. Transitional failure is characterized by a gradual stress drop after the peak strength. Ductile failure occurs when there is no stress drop after the peak strength (that is, the peak strength remains constant). In the Erin Formation, ductile failure is prominent for both sandstone and thin-bed lithofacies in the perpendicular and parallel directions to bedding, under dry and saturated conditions, as no stress drops were observed after the specimens attained peak strength (Fig. 8 and Fig. 9). Ductile failure is predicted for the few specimens that did not reach peak strength because of the limits of the axial loading within the apparatus was met. For these specimens, the shape of the stress-strain curves was replicating the curves of ductile failure. The microstructural development in Fig. 10 and Fig. 11 supports ductile failure, as it shows that while the quartz grains are predominantly fractured, the fractures did not coalescence to form a failure plane, which is evidence for ductile failure.
The Effect Of Saturation On The Compressive And Tensile Strengths
It is well documented that water saturation causes the compressive strength of rocks to reduce (Cai et al. 2019; e.g. Baud, Zhu, and Wong 2000; Dyke and Dobereiner 1991; Hawkins and McConnell 1992; Van Eeckhout 1976; Wasantha and Ranjith 2014). Several studies have suggested that the primary control on the reduction in strength is the mineralogy, where the water weakening effect is considerably dominant in a clay- rich rock compared to a rock that is mainly composed of quartz (Cai et al. 2019; Hawkins and McConnell 1992). While it is known that saturation reduces the strength of rock, we assess if the effective pressure and the strength direction play a role in the reduction. The compressive strength of the sandstone and thin-bed shale lithofacies are significantly affected when saturated with water (Fig. 8 and Fig. 9). The reduction in strength is greater under confined conditions and perpendicular to the outcrop bedding. Confined compressive strength recorded a maximum reduction of 96% in the sandstone and 98% in thin-bed shale specimens, which were more prominent at lower effective pressures. Under unconfined conditions, the sandstone experienced a 71% and 49% reduction in strength when measured perpendicular and parallel to the outcrop bedding, respectively, whereas the thin-bed shale strength reduced by 37% and 54% when measured perpendicular and parallel to the outcrop bedding, respectively.
Several studies have shown that the tensile strength is affected by water saturation where the water weakening effect caused the tensile strength to reduce (Ojo and Brook 1990; Vutukuri 1974; L.N.Y. Wong and Jong 2014). The tensile strength reduction due to saturation is dependent on the lithofacies and the strength direction. The reduction is greater when measured parallel to the outcrop bedding for sandstone specimens, where the tensile strength recorded a 31% reduction compared to a reduction of 21% perpendicular to the outcrop bedding (Table 2). The thin-bed shale specimens experienced a 69% reduction in the tensile strength in both perpendicular and parallel directions to the outcrop bedding.
When the specimens are water saturated, the reduction in the compressive and tensile strength may be due to the water chemically altering the mineral composition and microstructural properties of the rock, which caused the cohesive strength and frictional coefficient of the grains to reduce (Cai et al. 2019; Wasantha and Ranjith 2014). The quartz minerals present in high quantities in both sandstone and thin-bed shale lithofacies (Fig. 5) may have experienced hydrolysis of the Si-O-Si bonds causing the stronger bonds to be replaced by weaker hydrogen bonds (Cai et al. 2019), while the thin-bed shale experienced swelling of its highly dominant clay minerals (Fig. 5) (Baud, Zhu, and Wong 2000). It is reported that the water weakening effect is prevalent when the rock sample is clay-rich (Cai et al. 2019; Hawkins and McConnell 1992), which explains the greater strength reduction in the thin-bed shale specimens compared to the sandstone specimens.
Compressive And Tensile Strength Anisotropy
Figure 12 shows that strength anisotropy exist in the sandstone and thin-bed shale. We defined anisotropy as the ratio between the strength perpendicular to the outcrop bedding and strength parallel to the outcrop bedding. The ratio is one for an isotropic rock. Under dry conditions, the compressive strength anisotropy is moderate (ratios ranging between 0.8 and 1.5) for both sandstone and thin-bed shale. However, when saturated, the strength anisotropy for sandstone is large (ratio of less than 0.3) at 10 to 50 MPa effective pressure, and moderate (ratio between 0.6 and 1.1) at uniaxial conditions and effective pressures greater than 50 MPa. The saturated thin-bed shale has a moderate strength anisotropy (ratio of 1.4) at uniaxial conditions and large strength anisotropy (ratio less than 0.4) under confined conditions. The sandstone has a tensile strength anisotropy of 1.2 under dry conditions and 1.4 under saturated conditions, whereas the thin-bed shale has a tensile strength anisotropy of 1.5 when dry and saturated.
In this study, we were unable to measure the strength of the Formation at angles between 0 and 90° to the outcrop bedding plane due to the difficulties and practicability of plugging the friable rocks. Numerous studies that carried out compressive strength measurements on consolidated rocks revealed that: (i) the maximum strength occurred at either 0 or 90° to the bedding or foliation plane, and the minimum strength occurred at between 20 and 45°; and (ii) the minimum and maximum strength occurred at 0 and 90°, respectively, to the bedding or foliation plane (Al-Harthi 1998; Gatelier, Pellet, and Loret 2002; Baud et al. 2005-c. Hu et al. 2017; Louis, Baud, and Wong 2009). As we observed that the compressive strengths of the friable rocks (Fig. 8, Fig. 9, and Table 1) are significantly different when they were measured perpendicular and parallel to the bedding plane, we assumed that these are the maximum and minimum strengths. The possible mechanism responsible for the strength anisotropy in these friable rocks may be due to the bedding plane acting as a strengthening or weakening plane. Under dry conditions, the compressive strength is generally greater perpendicular to bedding (θ = 90°) suggesting that the bedding plane acts as a strengthening plane. However, when the rocks are saturated the bedding plane acts as a plane of weakness where it causes the compressive strength to reduce when θ = 90°.
The Behaviour Of The Compressive Strength At High Effective Pressures
Unlike the tensile strength, the compressive strength is more intricate as it is highly dependent on the confining pressure. The compressive strength of a typical consolidated rock (that is, a well cemented rock) follows three distinct failure stages as the confining pressure increases (Y. Hu et al. 2015; Kohlstedt, Evans, and Mackwell 1995; Yuan et al. 2020). In the first stage, the compressive strength increases linearly with increasing confining pressure (Fig. 13). A non-linear form characterizes the second stage, with the gradient gently decreasing as the confining pressure increases. In the final stage, the compressive strength is approximately constant with increasing confining pressure. The three stages are as a result of the rock failure behaviour changing from brittle to ductile (Iyare, Blake, and Ramsook 2021; Petley 1999; H. Wang, Wu, et al. 2019-f. Wong and Baud 2012; Zhao et al. 2018). There is also a special case where the compressive strength does not follow the three stages. Instead, the compressive strength remains constants with increasing confining pressure (Fig. 13). This special case occurs for rocks that are friable or unconsolidated (that is, a poorly cemented rock), under undrained conditions where the pore fluid is not allowed to flow out of the sample, and therefore, the pore pressure increases and fully counteracts the increasing confining pressure (Das and Sivakugan 2015).
Figures 14 and 15 show the behaviour of the compressive strength as a function of effective pressure for sandstone and thin-bed shale lithofacies, respectively. We observed a linear trend for the compressive strength of dry sandstone and thin-bed shale specimens (Figs. 14a, 14b, 15a and 15b). A linear increase in compressive strength was also seen in saturated sandstone specimens where strength measurements were made parallel to the outcrop bedding (Fig. 14d). The compressive strength of saturated sandstone, that was measured perpendicular to the outcrop bedding, and thin-bed shale, that was measured parallel to outcrop bedding, followed the typical strength trend where the strength increases and becomes constant at high effective pressures. However, at high pressures the friable rock strength gets significantly larger and deviates from the typical strength trend. The strength of the saturated sandstone and thin-bed shale is considerably high at effective pressures greater than 50 MPa and 90 MPa, respectively. The significant increase in the strength may be due to high compaction of the grains, which denotes a rock that is consolidated and has a strength of a very weak consolidated rock.
We observed the aforementioned special failure envelope case, where the compressive strength is independent of the effective pressure, for the thin-bed shale that was measured perpendicular to the outcrop bedding (Fig. 15c). The thin-bed shale specimens are layers of shale, which are less than 1 cm thick, alternating with sandstone layers (Fig. 3c). Even though a constant pore pressure of 5 MPa was applied to the specimens under saturated conditions, the applied pore pressure had no effect on the thin-bed shale specimens that were tested perpendicular to the outcrop bedding. This is because the permeability of the shale layer is very low and acts as a barrier to fluid flow (O. O Blake et al. 2022). The pore fluid within the sandstone layers cannot escape because it is trapped between the shale layers and the sides of the PVC jacket that is used to separate the confining fluid from the pore fluid. As the strength is independent of the confining pressure, we would expect the microfracture development within the thin-bed shale specimens to also be constant. In Fig. 15c, we also observed that the strength significantly increased at effective pressure greater than 90 MPa and did not follow the strength trend of this special case. This suggests that the high compaction of the rock caused the solid matrix to act like that of a consolidated rock and carries a portion of the confining pressure.
During compressive strength testing, the rock undergoes an initial elastic deformation stage, followed by plastic deformation region where it accumulates permanent inelastic strain (Fig. 16a.). The transition point between the elastic and plastic deformation is the yield strength (C*). It is reported that C*/\({\sigma }_{c}\) ratio for consolidated rock range between 0.3 and 0.8 (Bieniawski 1967; S. Wang, Xu, et al. 2019). In order to understand the deformation of the friable rocks and the pressures at which the strength denotes that of a consolidated rock, we analysed C*/\({\sigma }_{c}\) ratio of the stress strain curves presented in Fig. 8 and Fig. 9. We observed multiple transient stress drops for test conducted under confined conditions, from 10 to 130 MPa effective pressures. These stress drops are associated with grain crushing and pore collapse, leading to deformation bands (Baud, Klein, and Wong 2004; Fossen et al. 2007; Griffiths et al. 2018). The deformation bands were not seen in the tested specimens because of the high axial strain (an average of 20%) accumulated, which potentially could have eliminate earlier evidence of deformation bands. The friable rocks experienced much larger axial strains when compared to consolidated porous sandstones (Baud, Klein, and Wong 2004; Bedford et al. 2019). Under uniaxial conditions, when the rocks are very weak, the C*/\({\sigma }_{c}\) ratio for all the specimens ranges from 0.3 to 0.8, which is in similar range as the consolidated rocks (Figs. 16b and 16c). The C*/\({\sigma }_{c}\) ratio reduced to less than 0.2 for the sandstone and less than 0.1 for the thin-bed shale lithofacies when specimens are subjected to confinement (from 10 to 130 MPa effective pressures), under dry conditions. This suggests that strain hardening is prominent in the plastic deformation region that caused the strength to be very high. Figures 16b and 16c show that the C*/\({\sigma }_{c}\) ratio is less than 0.17 for saturated specimens at effective pressures greater than 50 MPa, which explains the significant increase in the strength at these high pressures causing a deviation from the typical strength trend (Figs. 14c, 15c and 15d).
Safe Mud Weight Window Prediction For Friable Reservoirs
Wellbore stability is a critical challenge encountered during drilling and production operations and costs oil industries over US$500–1000 million annually (Abbas et al. 2019). Instability in a wellbore can result from the inability to balance the redistributed stresses in and around the borehole leading to stress concentrations and eventual hole failure. Two failure mechanisms that may be detected in a borehole are; breakout failure and tensile failure (A Darvishpour, Masoud, et al. 2019; Abbas et al. 2019). These failures are experienced in the well as fluid flows into the well, mud losses and drilling induced tensile fracture initiation. To sustain the stress concentration around the borehole and reduce failure effects, it is filled with drilling fluid of an appropriate weight, which provides the necessary pressure to equalize the stresses. The safe drilling fluid pressure for a borehole is managed within a safe operating mud weight window, which is governed by an upper and lower limit. The fracture gradient or upper limit describes the pressures that can cause tensile failure and is determined using in-situ principal stress field data and tensile strength measurements (Aghighi Ali and Asgari 2020). The lower limit controls the critical pressure to prevent shear failure and is determined from in-situ principal stress field data, compressive strength and failure criterion measurements.
Friable Formations pose a threat to drilling as it can be difficult to manage the hole’s integrity. It is therefore imperative to use accurate rock strengths and in-situ stresses to calculate the SMWW to prevent undesired wellbore instability issues. Compressive and tensile strength measurements (Table 1 and Table 2) were used to calculate the lower and upper mud weight limits for future vertical and horizontal wells drilled in the oil prolific Erin Formation. Table 3 shows the in-situ principal stresses and pore pressure that were determined from measurements made in Well B of the Starfish Field that is located in the ECMA (Ramjohn, Gan, and Manoj 2018). According to Ramjohn, Gan, and Manoj (2018), the minimum (\({S}_{hmin}\)) and maximum horizontal (\({S}_{Hmax}\)) principal stresses were estimated from extended Leak-off tests and Stress Polygon analysis, respectively. Overburden pressure (\({S}_{v}\)) was determined from the integration of density logs, and pore pressure (\({P}_{p}\)) was determined from Modular Formation Dynamics Tester (MDT) measurements from the reservoir sections.
Table 3. In-situ and reservoir conditions interpolated from Well-B Borehole Stability Model for the Starfish Field, Trinidad
The SMWW was calculated for wells aligned in the three principal in-situ stress directions (\({S}_{v}, {S}_{Hmax } and {S}_{hmin}\)) using Equations 1 to 6 (Fjaer et al. 2008; Zoback 2007), with the assumption that the wellbore is lined with the perfect mud cake, and therefore the Formation pore pressure is not influenced by the pressure of the drilling mud fluid.
For wells aligned in the \({S}_{v}\) direction, the lower and upper mud weight limits are calculated using Equations 2 and 3.
$${P}_{m,min}= {P}_{p}+\frac{\left(3{\sigma }_{H}-{\sigma }_{h}\right)-2{P}_{p}-{\sigma }_{O}}{1+ {tan}{\left(\phi \right)}^{2}}$$
2
$${P}_{m,max}= 3{\sigma }_{h}- {\sigma }_{H}-{P}_{p}+{\sigma }_{t}$$
3
For wells aligned in the \({S}_{Hmax}\) direction, the lower and upper mud weight limits are calculated using Equations 4 and 5.
$${P}_{m,min}= {P}_{p}+ \frac{\left(3{\sigma }_{v}-{\sigma }_{h}\right)-2{P}_{p}-{\sigma }_{O}}{1+ {tan}{\left(\phi \right)}^{2}}$$
4
$${P}_{m,max}= 3{\sigma }_{h}- {\sigma }_{v}-{P}_{p}+{\sigma }_{t}$$
5
For wells aligned in the \({S}_{hmin}\) direction, the lower and upper mud weight limits are calculated using Equations 6 and 7.
$${P}_{m,min}= {P}_{p}+ \frac{\left(3{\sigma }_{v}-{\sigma }_{H}\right)-2{P}_{p}-{\sigma }_{O}}{1+ {tan}{\left(\phi \right)}^{2}}$$
6
$${P}_{m,max}= 3{\sigma }_{H}-{\sigma }_{v}-{P}_{p}+{\sigma }_{t}$$
7
Where \({\sigma }_{O}\) is the UCS, \(\phi\) is the internal friction angle, \({\sigma }_{t}\) is the tensile strength, \({P}_{p}\) is the pore pressure,\({P}_{m,max}\) is the maximum mud pressure, \({P}_{m,min}\) is the minimum mud pressure, \({\sigma }_{h}\) is the minimum horizontal stress, \({\sigma }_{v}\) is the vertical stress and \({\sigma }_{H}\) is the maximum horizontal stress.
Well-B was drilled to a depth of approximately 7500 ft, which corresponds to an effective pressure range of about 50 MPa if a density of 2200 kgm− 3 is assumed. The Mohr-Coulomb failure envelope was used to determine the strength parameters (internal friction angle and cohesion) that are required to calculate the safe mud weight window. To determine the strength parameters up to depths of up to 7500 ft, we established the Mohr-Coulomb failure envelope using Mohr’s circles at 0, 10 and 50 MPa effective pressures (Fig. 17). Furthermore, at effective pressures greater than 50 MPa, the saturated friable specimens generally behave as a very weak consolidated rock due to the high degree of grain compaction, which significantly increases the strength of the rock matrix resulting in a large peak strength (Fig. 13c and Fig. 14c and 14d).
The Effect Of Strength Anisotropy On The Safe Mud Weight Window
Table 4 shows the effect of strength anisotropy on the lower mud weight limit for wells aligned in \({S}_{v}, {S}_{Hmax } and {S}_{hmin}\) directions in both dry and saturated conditions. The variation of the lower mud weight limit, that was determined from the maximum and minimum compressive strengths, increased as the wells are drilled to lower depths. We assumed that the maximum and minimum compressive strengths are perpendicular or parallel to the bedding plane due to difficulties and practicality when plugging the friable rocks at angles between 0 and 90° to the bedding plane. Therefore, the analysis on the effect of the anisotropy on the SMWW can be considered to be conservative, as there is a possibility that the strength is even weaker if measured between 20° and 45° to the bedding plane. A strength value that is weaker than the values reported in this study will result in an increase in the strength anisotropy and therefore, there will be a larger impact on the SMWW.
Table 4. Lower mud weight (LMW) limit for future vertical and horizontal wells in friable Erin Formation sandstone and thin-bed shale aligned in the principal in-situ stress directions
We observed that the variation of the lower mud weight limit due to the strength anisotropy is less than 1%, under dry conditions. When the friable sandstone is saturated, the variation of the lower mud weight limit is approximately 7% for wells that are aligned in the \({S}_{v}\) directions, 8% for wells that are aligned in \({S}_{Hmax}\) direction, and 5% for wells aligned in \({S}_{hmin}\) direction. The variation of the lower mud weight limit is between 1 and 3% for the friable thin-bed shale, under saturated conditions. Table 5 shows that the variation of the upper mud weight limit due to tensile strength anisotropy is less than 0.3%. The effect of the tensile strength anisotropy on wells drilled in all directions is very minimal because the tensile strength of the friable rocks is extremely small and therefore, the upper mud weight limit will be mainly influenced by the in-situ principal stresses.
Table 5. Upper mud weight (UMW) limit for future vertical and horizontal wells in friable Erin Formation sandstone and thin-bed shale aligned in the principal in-situ stress direction
Implication Of Drilling Future Wells In The Erin Formation
Drilling through the Erin Formation friable rocks can be difficult as these rocks are very weak making it challenging to maintain the integrity of the hole. It is therefore imperative to use accurate strength and in-situ principal stresses data when evaluating the SMWW in friable rocks. Even if the in-situ stresses are accurately determined, anisotropy in rocks may lead to wellbore failure. Most rocks are anisotropic because of preferred orientated fractures and minerals, and bedding, which caused the strength to vary in different directions and ultimately affecting the prediction of the SMWW. For these reasons, the effect of the compressive and tensile strength anisotropy on the lower and upper mud weight limits of future wells that penetrate the friable sandstone and thin-bed shale were evaluated. The results of this study highlighted that strength anisotropy can be significant, up to 8%, for the lower mud weight limit, and is negligible for the upper mud weight limit.
The SMWW is very narrow for these friable rocks, especially for proposed wells drilled in the maximum horizontal principal in-situ stress direction that penetrates the thin-bed shale (Table 4 and Table 5, and Figs. 18 and 19). This study gives an insight of how rock strength anisotropy affects the SMWW. However, care should be taken when using these safe mud weight values for drilling future wells in the Erin Formation. The in-situ stresses that were used in the analysis of this study, represented a normal faulting tectonic stress regime, where \({S}_{v}\) > \({S}_{Hmax }\)> \({S}_{hmin}\). Nevertheless, Trinidad underwent numerous tectonic regimes, where the latest (during the Early Pleistocene) is normal faulting and strike-slip (Fig. 1). Despite the Erin Formation being a prominent oil producing Formation in the Southern Basin, Trinidad, there are no published data on the in-situ principal stresses from the producing fields. It is pertinent to determine the magnitude of the in-situ principal stresses within the field(s) of interest, in order to accurately determine the SMWW, and therefore prevent wellbore instabilities in future vertical and horizontal wells.