Revisiting the Rock Physics Basis for Fracture Stress in Oil and Gas Exploration

International Journal of Research in Engineering & Science ISSN:(P) 2572-4274 (O) 2572-4304 Available online on http://rspublication.com/IJRES/IJRE.html volume 9 Number 6, 2025 DOI: 10.5281/zenodo.17818104 Original Article ©2025 RS Publicaon, rspublica[email protected]m 131 Revisiting the Rock Physics Basis for Fracture Stress in Oil and Gas Exploration Pratap V. Nair 1 and Dilip Mahata 2 1 Retired Exploration Petroleum Geologist, Devidarshan, Kawdiar, Thiruvananthapuram - 695003, Kerala, India 2 Junior Research Fellow, Department of Petroleum Engineering, IIT (ISM) Dhanbad - 826004, Jharkhand, India ARTICLE INFO ABSTRACT ©2025 RS Publicaon Paper ID: IJRES692FE2FBEA1BD Published: 2025-12-04 DOI: https://dx.doi.org /10.5281/zenodo.17 818104 Page No: 131-142 Evaluating the extent of the minimum in situ total stress within rock formations is crucial across various domains of petroleum engineering, especially for maintaining wellbore stability and forecasting fracture geometry during well stimulation. We highlight the importance of a thorough understanding of rock behaviour regarding retention capacity in the context of hydrocarbon entrapment and the exploration drilling window. The phrase "fracture gradient" is understood differently across various subsurface fields. This discrepancy may stem from the lack of standardised terminology and from differing emphasis on specific elements of stress measurements in boreholes. This paper examines the exploration, drilling, stimulation, and development sectors to integrate existing knowledge, standardise terminology, and define current best practices. Keywords: Fracture gradient, Shear failure, Tensile failure, Minimum stress, Lithological effects, Stress ratio, Weak zones, Salt, Carbon capture and Mud weight window. Corresponding Author: Pratap V Nair; ([email protected]) INTRODUCTION The fracture pressure is the pressure required to initiate and extend fractures in a rock formation, typically expressed as a gradient in pressure per unit depth (e.g., psi/ft or kPa/m). I The fracture pressure gradient is affected by the mechanical properties of the rock, in-situ stresses, and pore pressure. For practical applications, fracture pressure is defined as the fluid pressure at which losses from the borehole become evident. In cases where the formation is already fractured, fluid loss will occur when the existing fractures can be opened further – generally when the mud pressure, Pmud, surpasses the minimum stress. Conversely, if the Interna%onal Journal of Research in Engineering & Science Available online on h*p://rspublica%on.com/IJRES/IJRE.html ISSN:(P) 2572-4274 (O) 2572-4304 Cite This Paper: PRATAP V NAIR AND DILIP MAHATO (2025). "Revisiting the Rock Physics Basis for Fracture Stress in Oil and Gas Exploration". INTERNATIONAL JOURNAL OF RESEARCH IN ENGINEERING & SCIENCE (IJRES), vol. 9, no. 6, 2025, pp. 131-142. DOI: https://dx.doi.org/10.5281/zenodo.17818104 International Journal of Research in Engineering & Science ISSN:(P) 2572-4274 (O) 2572-4304 Available online on http://rspublication.com/IJRES/IJRE.html volume 9 Number 6, 2025 DOI: 10.5281/zenodo.17818104 Original Article ©2025 RS Publicaon, rspublica[email protected]m 132 formation remains intact, new fractures must form, necessitating that the pressure exceed the fracture initiation pressure, Pfrac init, which is typically greater than the minimum stress. A comprehensive fracture pressure model must address both of these conditions. The significance of a comprehensive understanding of rock behaviour regarding retention capacity in relation to hydrocarbon entrapment and the exploration drilling window is crucial as oil and gas exploration moves into deeper, higher-pressure, higher-temperature territory. Assessing the degree of the minimum in situ total stress within rock formations is essential in multiple areas of petroleum engineering, particularly for ensuring wellbore stability and predicting fracture geometry during well stimulation. We revisit this crucial aspect, summarise the current industry standards, and bring forth the best practices . Failure Models In the simplest models, there are two modes of failure for intact rock (Figure 1). II In tensile failure, the rock is merely pulled apart, and the required pressure must exceed the confining stress and the rock's tensile strength. Typically, tensile strength is relatively minor compared to the total pressures and their associated uncertainties; thus, assuming that tensile failure occurs when the force exceeds the confining stress is a reasonable approximation. The second mode is shear failure, where the rock on either side of the failure moves in opposite directions. This type of failure occurs when the difference in perpendicular stresses exceeds the formation's shear strength. Given that there are three principal stresses, there are also three stress combinations that need to be evaluated for shear failure; however, the procedure for each remains consistent. The amalgamation of potential failure modes yields four possible fractureinitiation pressures – one corresponding to tensile failure and three to shear failure. As the pressure within the borehole escalates, fractures will develop as soon as any of these pressures are surpassed, so Pfrac init = min (Ptensile , Pshear S1-S2 , Pshear S1-S3 , Pshear S2-S3 ). Figure 1: Two modes of failure of intact rock The interplay of different shear and tensile failure mechanisms leads to a fracture gradient model referred to as the mixed-mode fracture gradient. This model begins with an estimate of in-situ stress, which is crucial for determining both the pressure required to reopen fractures and the pressure necessary to initiate tensile fractures. The Mohr-Coulomb failure model governs the formation of shear fractures; it not only accounts for stresses but also considers the International Journal of Research in Engineering & Science ISSN:(P) 2572-4274 (O) 2572-4304 Available online on http://rspublication.com/IJRES/IJRE.html volume 9 Number 6, 2025 DOI: 10.5281/zenodo.17818104 Original Article ©2025 RS Publicaon, rspublica[email protected]m 133 compressive strength and friction angle of the formation. III In the context of the mixed-mode model, these two rock characteristics are inferred from established rock-mechanics correlations between the formation's acoustic velocity and the strength and friction angle. The comprehensive model produces two possible 'fracture pressures' to evaluate at any specified depth: fracture re-opening pressure and fracture creation pressure. The observed strengths of formations exhibit a bi-modal distribution, clustering closely around these two pressures, even though re-opening and creation pressures usually vary by several hundred psi (or several MPa). Although this model is more intricate than standard fracture-pressure methodologies like effective stress models, it effectively captures the influence of the primary factors affecting formation strength: stress, pore pressure, and rock matrix strength. Consequently, this leads to predictions with reduced uncertainty and a superior ability to extrapolate to environments with minimal or no well data for calibration. Estimating Minimum Horizontal Stress The minimum stress (S min ) of the formation is a fundamental factor influencing borehole fluid pressures (Pmud), which are essential for maintaining a stable borehole (Figure 2). IV Alternatively, these pressures can lead to formation break-out or fracturing. Consequently, S min is a vital component in estimating fracture pressure and borehole stability pressure. Direct measurements of Smin are pretty uncommon. Its assessment is based on the principle that when fractures occur—whether by design or accident—they will remain open as long as the fluid pressure exceeds the minimum stress that would close them. Casing shoe tests, mini-frac tests, and lost circulation events can all be utilised to estimate this pressure, albeit with varying degrees of precision. Figure 2: Cross-section of a wellbore with a fracture that is normal to the minimum stress IV Although shoe tests are generally conducted at various depths within a specific well, only those equipped with specialised flowback apparatus or those that undergo repeated cycles can yield a well-defined minimum stress range (Figure 3). Traditional leak-off pressure measurements only establish an upper limit on the stress. V At the same time, a formation integrity test may yield values either above or below Smin, offering no constraints on its actual value. Mini-frac tests are more commonly used to obtain the essential data for accurate minimum-stress estimates; however, they are typically conducted only in sands designated for production, resulting in a scarcity of data. Instances of lost circulation can occasionally provide reliable stress estimates, provided that comprehensive downhole pressure profiles are recorded. Still, such occurrences are (ideally) infrequent and are only accessible after the relevant interval has International Journal of Research in Engineering & Science ISSN:(P) 2572-4274 (O) 2572-4304 Available online on http://rspublication.com/IJRES/IJRE.html volume 9 Number 6, 2025 DOI: 10.5281/zenodo.17818104 Original Article ©2025 RS Publicaon, rspublica[email protected]m 134 been drilled. Consequently, for the majority of intervals slated for drilling, we predominantly depend on calculated estimates of S min . Figure 3: Typical extended Leak-off test The assessment of minimum stress initiates with the understanding that solids subjected to a load in one direction will generally expand or extend in the perpendicular direction. Within the subsurface, any sediment volume is enclosed by surrounding sediments and cannot grow, thereby generating a confining stress (refer to Figure 4). In a straightforward uniaxial system, the magnitude of the confining stress is directly correlated to the load through Poisson’s ratio of the formation, expressed as S confine = v/(1-v) * S load , assuming the formation is elastically isotropic. Figure 4: Stress confinement and spreading In tectonically relaxed environments, the load is simply the weight of the sediments above – in this case, the overburden stress and the confining stress represent the minimum horizontal stress. The overall stress within the formation can be divided into the (isotropic) fluid pressure and the (anisotropic) effective stress acting on the formation matrix. The relationship above applies to the matrix; therefore, the total horizontal stress in this simplified context is expressed as International Journal of Research in Engineering & Science ISSN:(P) 2572-4274 (O) 2572-4304 Available online on http://rspublication.com/IJRES/IJRE.html volume 9 Number 6, 2025 DOI: 10.5281/zenodo.17818104 Original Article ©2025 RS Publicaon, rspublica[email protected]m 135 S h , min = v/(1-v) * (Svertical – P) + P Poisson's ratio can be derived from sonic logs or seismic velocities or approximated based on regional trends. VI This approach is adequate for generating reliable estimates of minimum stress in numerous areas of interest. Additionally, more complex formulations are available to account for the effects of elastic anisotropy and other stresses arising from tectonic loads, saltinduced stress, and other factors. Although the straightforward method mentioned above can be readily computed along a wellbore manually or in a spreadsheet, more complex scenarios may require a numerical solution within a specialised computer model. Lithology Effects on Stress and Fracture Pressure The material's elastic stiffness influences the stresses induced by a specific load. Softer materials tend to undergo considerable deformation and require a relatively substantial restoring force (stress) to inhibit it. In contrast, harder materials exhibit less deformation under the same load and require a lower restoring force (see Figure 5). As a result, complex formations, such as many carbonates, typically exhibit comparatively low minimum stress, while a soft shale tends to display a relatively high minimum stress. Shales that possess greater hardness due to increased silt content, compaction, cementation, and other factors may fall somewhere in between. Variations between high and low stress can be significant and sudden; notable changes on the order of meters have been recorded in numerous wells. The pressure required to initiate fractures, which depends on the formation's stress and strength, will also vary with lithology. Figure 5: In response to loading, soft materials undergo significant spreading, whereas hard materials display comparatively minor deformations The variations arising from lithology are inherently represented in models that utilise formation measurements. When considering basin-scale or pre-drill estimates at a specific well site, property estimates may be derived from offset well logs, seismic velocity information, or lithology-dependent trends. VII The degree to which particular variations are correlated across different locations depends on the anticipated continuity of the sediment packages. In the context of log-based analysis, less continuous formations may yield estimates of background variability (including expected ranges or uncertainties), while highly continuous formations establish a baseline trend. International Journal of Research in Engineering & Science ISSN:(P) 2572-4274 (O) 2572-4304 Available online on http://rspublication.com/IJRES/IJRE.html volume 9 Number 6, 2025 DOI: 10.5281/zenodo.17818104 Original Article ©2025 RS Publicaon, rspublica[email protected]m 136 Fracture pressure estimation Fracture pressure refers to the fluid pressure necessary to either reopen or create a new fracture within the rock at the wellbore at a specified depth. Estimating fracture pressure is often based on the minimum principal component of the in situ stress tensor. The deformation and fracturing of rock are influenced by effective stresses, which are defined as the difference between the total stress S and the pore pressure PP. Both fracture pressure and pore pressure are critical factors in well design. Breckels and van Eekelen VIII , along with other researchers, demonstrated that due to the influences of hoop stress, borehole conditions, geometry, and other factors, the fracture gradients obtained from leak-off tests fall between the fracture initialization pressure— which, in relaxed conditions, is nearly equivalent to the minimum horizontal stress— and the fracture propagation pressure, which can reach [2σh – PP], where σh represents the minimum horizontal stress and PP denotes the pore pressure, under the assumption that the in situ tensile strength is negligible. In practical applications, it is frequently assumed that the lower limit of leak-off data is nearly equivalent to the minimum horizontal stress. Nevertheless, it is crucial to maintain the integrity of leak-off data and to refrain from utilising incomplete formation integrity tests or substandard data, which often fall below the lower limit of fracture pressure. In a manner akin to the overburden relationship, horizontal stress can be categorised into two components: matrixsupported horizontal effective stress and pore fluid pressure: S h = HES + PP where S h = minimum horizontal stress, HES=horizontal effective stress, and PP = pore pressure. Based on elastic theory, the horizontal effective stress for a confined, vertically-transversely isotropic block can be expressed through Poisson’s ratio and vertical effective stress HES = {PR/ (1 - PR)}*VES The equation used for calculating fracture pressure is (Eaton IX ): FP = PP + {PR/ (1 - PR)}*(OBP-PP) where, FP = fracture pressure; PP = pore pressure; PR = Poisson’s ratio; OBP = overburden pressure Stress Ratio (Ko) Estimation The ratio PR/(1 - PR) is referred to as the matrix stress ratio (Ko). Holbrook X and others have demonstrated that this equation is valid only in fully recoverable, linear-elastic environments, and its application to actual Poisson’s ratios derived from dipole sonic logs or core measurements may result in inaccuracies. To address this concern, an apparent Poisson’s ratio is typically utilised for predicting fracture pressure rather than the actual elastic constant. A wide range of models has been published and employed by practitioners in pore pressure prediction (PPP). These models can be categorised into four groups: 1) Purely empirical depth-dependent models. Some of these (e.g., Breckels and van Eekelen) VIII are applicable for regional fracture pressure estimates. International Journal of Research in Engineering & Science ISSN:(P) 2572-4274 (O) 2572-4304 Available online on http://rspublication.com/IJRES/IJRE.html volume 9 Number 6, 2025 DOI: 10.5281/zenodo.17818104 Original Article ©2025 RS Publicaon, rspublica[email protected]m 137 2) Empirical models that rely on effective stress ratio trends derived from LOT and/or minifrac data are generally dependable. However, they frequently fail to distinguish between the minimum horizontal stress and the fracture initiation pressure, which is typically greater than the minimum stress. 3) Log-based fracture pressure gradients assist in qualitatively assessing lithology effects, but they often lack accuracy. 4) Models that integrate empirical calibration with log-derived parameters tend to be successful; these models may help account for lithology effects and, in certain instances, can clarify both minimum horizontal stress and fracture initiation pressure. A typical fracture stress model is shown in Figure 6. Figure 6: A typical Fracture stress profile Weak Zones and Fault Shear Failure Values from leak-off tests (LOTs) or drilling losses at certain mud weights that are lower than expected stress levels may be due to several reasons. These include fluid losses into porous formations, new fractures forming in shear rather than tension, or the reactivation of nearby faults. Factors that favour shear fractures include low frictional resistance and high shear stress, which reflect differences among the principal total stresses. The in-situ stress regime affects fracture initiation or reactivation, influenced by factors such as fault type, wellbore orientation, thermal effects, drilling fluid characteristics, and operations such as LOTs. These factors can lead to either tensile or shear conditions, requiring individual assessments. Chan et al. XI studied normal-faulting regimes, while Couzens-Schultz and Chan XII explored applications of reverse faulting. An example is given for calculating Smin from loss data in a normal-faulting regime at the ‘P’ Field offshore Australia, which may transition to strike-slip faulting at greater depths (Figure 7). International Journal of Research in Engineering & Science ISSN:(P) 2572-4274 (O) 2572-4304 Available online on http://rspublication.com/IJRES/IJRE.html volume 9 Number 6, 2025 DOI: 10.5281/zenodo.17818104 Original Article ©2025 RS Publicaon, rspublica[email protected]m 138 Losses were seen in shallow formations of nearby wells at effective circulating densities (ECDs) slightly above hydrostatic pressure. These ECDs were within the expected fracture gradient range for P1. The fracture pressure (FP) is the pressure at which fluid first enters the formation during a leak-off test (LOT) or during drilling, regardless of the mechanism of loss. The minimum stress (Smin) was calculated using critical stress analysis for fault reactivation, with specific values for friction angle and cohesion defined in the study. Here, FP is described in the general drilling context as the pressure at which fluid initially begins to seep into the formation during an LOT or while drilling, irrespective of the loss mechanism. XIIi,XIV The calculation of Smin was derived from critical stress analysis for fault reactivation within a normal-stress regime (Smin = Sh and most incredible compressive stress S max = Sv), with cohesion Co set to 0, and a presumed value for the friction angle (or friction coefficient μ = tan Ǿ ) as elaborated by Couzens-Schultz and Chan XI,XII : S h = [S V (1 – sin Ǿ) + 2 · FP(loss) · sin ] / (1 + sin Ǿ ) Figure 7: Pre-drill PP-FG plot XV This method assumes that faults either intersect the well or connect through a permeable pathway, allowing hoop stresses around the wellbore to be ignored. The equivalent circulating density (ECD) at which losses occur is linked to the formation pore pressure (PP) around the faults that cause their reactivation. Values of S V are derived from a regional overburden model, in which the shallow overburden contains a mix of sandstones, siltstones, claystones, and carbonates. A friction angle of 30° was chosen to represent these intervals. The fracture pressures from losses determined mud weights for shallow drilling, and values of Sh were used for borehole stability assessments. The Sh curve on the PP/FG plot meets the Design of Engineering Practice requirements, representing the maximum-case FG. The resistivity-based real-time PP prediction and wireline pressure measurements from the discovery well are also indicated. International Journal of Research in Engineering & Science ISSN:(P) 2572-4274 (O) 2572-4304 Available online on http://rspublication.com/IJRES/IJRE.html volume 9 Number 6, 2025 DOI: 10.5281/zenodo.17818104 Original Article ©2025 RS Publicaon, rspublica[email protected]m 139 Fracture Pressure in Salt In certain petroleum basins, multiple wells need to be drilled through extensive salt formations to reach hydrocarbon reservoirs. The fracture gradient in salt formations varies significantly from that in other sedimentary rocks. In the Gulf of Mexico and various other petroleum basins, subsalt wells require drilling through substantial salt formations to access hydrocarbon reserves. The occurrence of salt creep poses a significant challenge to borehole stability; therefore, it is essential to use a heavier mud weight (e.g., 80%–90% of the overburden stress) to effectively manage it. XVI The elevated mud weight necessitates a higher fracture gradient in the salt formation to prevent fracturing of the salt. LOT and FIT data from salt formations across 15 wells in the Gulf of Mexico (10 located in the Mississippi Canyon and 5 in the Green Canyon) were analysed by Zhang et al. and illustrated in Figure 8. Oil majors really do not have predictive models for fracture pressure in salt. Therefore, a fit-for-purpose model proposed by Zhang can be used with local alterations as required. Fracture pressure in Salt = Sv + C where C is a variable and varies from 0 to 1000 psi based on the data shown in Figure 8, and for the most likely case, C = 500 psi. This is the common planning practice in vogue. The findings indicate that in the majority of salt formations, the LOT and FIT pressures exceed the overburden stress. The fracture gradient within salt formations is suggested based on the collected data. It is frequently observed that certain LOT values obtained from leak-off tests surpass their corresponding overburden stress gradients (i.e., LOT[OBG). This phenomenon may be attributed to several factors: (a) the recorded LOT value represents the formation breakdown pressure, and (b) the formation exists within tectonic stress regimes. XVI Figure 8: Measured FIT and LOT data points (the dots, triangles, squares, etc. in the figure) plotted with the overburden stress (OBP) in 15 wells in the Mississippi and Green Canyons in the Gulf of Mexico XVI