Introduction

Drilling through overpressure formations poses numerous challenges and risks to operations if the properties of the material are not accurately predicted prior to drilling (Zhang 2019). Adequate knowledge of the geomechanical properties of hydrocarbon reservoirs play an important role in designing recovery well, enhance recovery, and in safe drilling (Abijah and Tse 2016; Saikia et al. 2018). From previous studies (e.g. Streit and Hillis 2004; Archer and Rasouli 2012; Eyinla and Oladunjoye 2014, 2018; Eshkalak et al. 2014; Vilarrasa et al. 2016; Abijah and Tse 2016; Kumar et al. 2017; Turner et al. 2017; Feng et al. 2018), these applications often include the predictions of overpressure and sand production, modeling of rock's fracability during hydraulic fracturing, and in the estimation of injection-induced seismicity during fluid injection. Thus, the ability to safely plan hydraulic fracturing program and drill through abnormal pressure intervals require a multiple approach to understand the dynamics of the overpressure mechanisms (Zhang 2019).

With hydraulic fracturing stimulation of unconventional reservoirs, production is optimized through the creation of a connected stimulated rock volume for higher conductivity (Maulianda et al. 2019). Hydraulic fracturing treatment stands out as one of the most efficient matrix stimulation techniques being adopted for enhanced oil recovery (Shafiq and Mahmud 2017; Kolawole and Ispas 2019). Formation fracturing pressure is one of the key parameters used in hydraulic fracturing design, and the magnitude of this parameter depends on formation depth and the material properties (Guo et al. 2007). Generally, the unconventional (tight) reservoirs differ greatly from conventional reservoirs as a result of their deeper depth of burial, strong diagenetic properties, huge heterogeneity, reduced porosity, abnormal pressure with low permeability, and poorly developed natural fractures (Xue et al. 2014; Wang et al. 2016; Feng et al. 2018). Therefore, the nature of fracture propagation and hydraulic fracture initiation in a naturally fractured reservoir is influenced by the properties of the natural fractures, pore pressure and in situ stresses. Failure to present an accurate measurement and estimations of these parameters for a reservoir subjected to hydraulic fracturing might result in well instability, poor initiation of hydraulic fracture, poor fracture propagation, well perforation failure, casing collapse, sanding, and suboptimal production level (Cook et al. 2007; Denney 2011; Taheri-Shakib et al. 2019). Also, formation damage is harmful to the recovery process as this could lead to massive pressure drop around the vicinity of the wellbore (Shafiq et al. 2019).

While it is possible to carry out laboratory measurement of these properties, the amount of sample size being considered using this method is small in most cases. Meanwhile, the isolated samples may not be sufficient to represent the elastic regime throughout the reservoir owing to the sample size (Saikia et al. 2018). Consequently, geomechanical studies are performed often on a well correlational basis, which could later be used as calibration points in converting 3D seismic data to create geomechanical models. Overpressure in hydrocarbon unit represents one of the major challenges facing production and enhanced recovery processes because of their impact on drilling safety, well placement, cost-effective drilling and field development strategies (Kukla et al. 2011). Geomechanical analysis and reservoir modeling are tools employed to study the difference between the fluid pressure measured in a stratigraphic unit and the ‘normal’ hydrostatic fluid pressure in the pore structure. A technique for predicting pore pressure and associated fracture gradient would be helpful in selecting adequate mud weight to ensure well and drilling safety, in preventing the use of excess mud weights leading to fracture or losses, in preventing hole collapses and to assist in correct designing of casing scheme to ensure optimum completion and maximum productivity (Basu et al. 1994; Law and Spencer 1998; Babu and Sircar 2011). The geomechanical knowledge and pressure level would also afford the opportunity to pre-determine any sand production into a borehole, a problem which has been identified in drilling operations for long as it affects well productivity and the drilling equipment (Ispas et al. 2012; Zhou et al. 2016; Kolawole et al. 2018).

The origin of overpressures in the field of study has been attributed mostly to disequilibrium compaction of sediments (Swarbrick and Osborne 1998; Chukwu 2017; Nwozor et al. 2017; Ogunsakin et al. 2019). Thus, an appropriate design of a stable wellbore, especially when high-volume fluid injection is proposed, can only be achieved when the effects of the overpressure in the targeted zone have been thoroughly considered during the stages of well planning. The production from low permeable or unconventional reservoirs like tight sands, shale gas and carbonates, has become possible and more successful primarily because of various injection and hydraulic fracturing processes which have greatly improved the fault permeability, creating room for more recovery. As formation pressure in rocks changes due to the varying tectonic history and burial conditions, the resulting effect is often seen in the response of the reservoir to fluid injection and artificial fracturing (Feng et al. 2018; Eshkalak et al. 2014; Fan et al. 2016; Abijah and Tse 2016; Eyinla and Oladunjoye 2018). Nevertheless, the inherent strength of rocks has a direct correlation with the elastic properties, which has been observed to be a good source of information regarding the pressure state and sanding rate during production (Dresser Atlas 1982; Eyinla and Oladunjoye 2014).

Another important useful tool in studying rocks and their features is the acoustic impedance, which can be obtained from seismic data (Saputro and Haris 2017), and from wells using sonic and density logs (Dresser Atlas 1982). While shale strength is primarily controlled by the degree of compaction (Lal 1999; and Eyinla and Oladunjoye 2018), the rock saturation condition has a great effect on the compressional velocity (Maleki et al. 2014). Hence, as acoustic impedance relates the velocity of wave travel in rocks and the density of the material, the level of compaction of the sediments can indirectly correlated with the value of the acoustic impedance, and thus, the problem of overpressure and fluid saturation in sedimentary rocks can be similarly be addressed using this property. Additionally, reports have established that in most sedimentary environments, velocities and densities of siliciclastic rocks increase with depth, and this trend is often due to progressive mechanical compaction which in turn would yield porosities reduction (Avseth et al. 2003). With this knowledge, a more robust geomechanical study which can link the velocity of rocks with the degree of overcompaction of sediments and overpressure can be achieved.

Previous report from the same study area by Eyinla and Oladunjoye (2018) has considered the interrelationship between formation strength and fracture pressure, and the various patterns of the cross-plots proposed an interplay of disequilibrium compaction. However, several drilling problems which are related to wellbore stability are also linked to improper study of the pore pressure regime. Thus, this study presents a further systematic approach for predicting overpressured zones in the formation by interpreting the correlation and specific trends of geomechanical properties and rock physics parameters estimated from each sampled interval based on empirical correlations using physical properties derived from wireline logs data. Trend analyses in this work involve depth variations of porosity, elastic properties, densities and acoustic impedances of the formation.

The study area is Akas Field which falls within Tertiary sediments of the Niger Delta Basin in Nigeria with three distinct Formations Akata Formation, Agbada Formation and the Benin Formation (Tuttle et al. 1999). The Akata Formation (base of the delta) is of marine origin composed of thick shale sequences (including turbidite sand, and minor amounts of clay and silt) serving as potential source rock. The Agbada Formation is the major petroleum-bearing unit, consisting of paralic siliciclastics, mainly shelf deposits of alternating sands, shales and mudstone over 3700 meters thick, which also represents the actual deltaic portion of the sequence. In the lower Agbada Formation, shale and sandstone beds were deposited in equal proportions, however, the upper portion is mostly sand with only minor shale interbeds. The Benin Formation is a continental latest Eocene to Recent deposit of alluvial and upper coastal plain sands that are up to 2000 m thick. The topmost layer is predominantly nonmarine upper delta plain sandstone. The various units of the Niger Delta are shown in Fig. 1. Considering the geological history of the study area where overpressure has frequent occurrence, virtually all the geologic events which contribute to the accumulation and preservation of overpressure are available in the basin (Owolabi et al. 1990; Stacher 1995; Udo et al. 2015). The rate of sediment instreaming to the basin is very high which makes the basin unstable, and obviously still subsiding till date. The resulting high sedimentation rate and burial history prevent adequate settlement and dewatering, which causes the formation to develop abnormally high porosity and high fluid content leading to a buildup of overpressured intervals when lithification begins (Stacher 1995). The Akata Formation consists of highly undercompacted and overpressured marine shales (Fig. 1) with fluids which is constantly subjected to high overburden stress. Based on the depositional sequence, even a little overburden stress exerted on the Akata shale would yield considerable quantity of fluid to the adjacent reservoir rocks. Also, having established that the prevailing trapping mechanism in the Niger Delta is the growth fault, the implication of this is that the post-depositional processes will build up excess reservoir pressure (Osinowo et al. 2015).

Fig. 1
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Modified after Tuttle et al.1999 )

Events chart for the Niger Delta (Akata/Agbada) Petroleum System (

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Basic theory and methodology

The various kinds of reservoir pressure usually encountered while drilling have been broadly divided into three main components: Hydrostatic pressure, Overburden pressure and Formation pressure as shown in Fig. 2. The reservoir fluid pressure found in the rock pores is regarded as the formation pressure while the overburden pressure is the combined pressure exerted by the rock formation (rock matrix) and the reservoir fluid (fluids in the pore space) overlying the formation. This pressure increases with depth and is also called the vertical stress (Chopra and Huffman 2006). Reservoir pressure controls the gas capacity and the overall reservoir behavior, and it consists of two main components: lithostatic pressure and hydrostatic pressure (Satter and Iqbal 2016). The lithostatic pressure is a consequence of overburden stress, while hydrostatic pressure is the component of the reservoir pressure resulting from the effect of pore fluid. Additional, lithostatic pressure is a function of rock density and is mostly ranges between 22.7 and 25 KPa/m (that is, 1.0 and 1.1 psi/ft) in coal-bearing reservoir (McKee et al. 1984), whereas in normal hydrostatic gradient, the value in fresh water is 9.77 KPa/m (0.43 psi/ft), while the value in sea water is somewhat higher at 10.45 KPa/m (0.46 psi/ft). This research adopted hydrostatic gradient threshold value at 0.445 psi/ft, as shown in Fig. 2, being the reported average value for the study area. Pore pressure gradient is regarded as the ratio of the formation pressure to the depth and is often expressed in units of psi/ft or the equivalent of mud weight units in pounds per gallon (Chopra and Huffman 2006). Thus, pore pressures which are found to lie above or below the normal level of pore pressure gradient line are called abnormal pore pressures. From past works (Nwozor et al. 2013; Ichenwo and Olatunji 2018; Emudianughe and Ogagarue 2018), these formation pressures may be either subnormal (i.e. less than 0.445 psi/ft) or overpressured (i.e. greater than 0.445 psi/ft). The mechanisms which generate these abnormal pore pressures in subsurface reservoirs can be somewhat complex depending on the tectonic history, fluid expansion mechanism, and material constituents (Kukla et al. 2011; Satti et al. 2015).

Fig. 2
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Modified from Ismail 2010)

Components of Pressure and their Relations (

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Well logs obtained from well drilling are the most applicable and extensively used in the construction of rock models in rock strength study, and in delineating geopressures (Dutta 2002; Abijah and Tse 2016). Adopting wireline logs for estimating elastic and inelastic properties of rocks produce satisfactory results because the logs present a representation of the entire vertical section of the reservoir rocks, hence, they give a direct measurement of the petrophysical properties, and an ideal method of obtaining geomechanical data (Azizi and Memarian 2015; Abijah and Tse 2016). The works of Liu et al. (2012) and Eyinla and Oladunjoye (2014, 2018) reported that sonic (acoustic) log contain information which can be helpful in determining the mechanical properties of rock. The velocity of compressional wave depends on the elastic properties of the matrix rock and fluid (Garia et al. 2019), therefore the measured slowness also varies, depending on the composition and microstructure of the matrix, the type and distribution of the pore fluid and the porosity of the rock (Dresser Atlas 1982).

Before geomechanical parameters are predicted, certain petrophysical properties are generated from the well logs. These parameters include: Porosity (from Density log and Sonic log), volume of shale, interval transit time of compressional sonic, and overburden gradient. The elastic properties of rocks and its relationship with velocity of wave provided a relationship through which geomechanical parameters are estimated using already established equations. A comprehensive study by Eyinla and Oladunjoye (2018) have presented clear procedures for estimating these rock properties from well logs, when sonic, density and gamma ray logs are available. Thus, this study adopted same procedure and approach for the estimation of the geomechanical parameters. The values represent change in the properties vertically along each wellbore, with no emphasis on lateral inhomogeneity. The three suites of well data used for the study contain wireline logs of density, sonic, gamma ray and resistivity data. Porosity values were estimated from porosity logs (density and sonic log) while the density values of each material were obtained from density log. Gamma ray log served for lithologic control which helped to distinguish the two major lithologic units (sands and shales). Compressional and Shear wave velocities and geomechanical properties (Bulk modulus, Shear modulus, Young’s modulus, and Poisson’s ratio) were thus estimated using Eyinla and Oladunjoye (2018) method.

Additionally, this study introduced certain rock physics analysis, which involves the study of the relationships between elastic parameters and petrophysical properties of the subsurface formation. Therefore, for this study, the parameters considered are: Density, P-wave impedance, P-wave velocity, S-wave velocity, Bulk modulus, Shear modulus, among others. The products of density and velocity (ρ and V) known as impedances (Telford et al. 1990) was calculated for the compressional wave as shown in Eq. 1.

$$I_{P} = \rho \times V_{P}$$
(1)

Shales can be distinguished from other lithology by using Vp/Vs ratio and the impedance of the compressional wave (\({I}_{P})\). Hence, reservoir with shale formation can be separated from non-reservoir shale by using these parameters (Kumar and Hoversten 2012). Consequently, cross-plots were designed using the estimated parameters to enable proper understanding of the different rock materials in the reservoir, the governing rock physics laws in place. Thus, these trends afford proper geological inference which have implications on overpressure prediction.

Results and discussion

The resulting geomechanical computations and pressured intervals are presented in Tables 1, 2 and 3 for the three wells while correlations of specific parameters from the evaluted results are made. From the results, it was observed that mechanical strength of the material varies with depth, and the order of this varaition depends on the material constituents at each sampled interval. Also, a consistent trend in rock properties plots is observed, however, deviation from any expected trend is believed to be a resulting effect of abnormal pressure in the field.

Table 1 Estimated results for Well 1
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Table 2 Estimated results for Well 2
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Table 3 Estmated results for Well 3
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Figure 3 shows that the shear wave velocity is linearly related to the compressional velocity across the three wells. That is, with an increasing value of shear wave velocity, the corresponding compressional wave velocity increases. This relationship gives a clearer understanding of how the elastic properties of rocks relate in terms of the seismic responses and material porosity. It suggests that as the porosity of the material increases, shear and compressional velocities decrease in an almost linear fashion (Castagna and Batzle 1985). In addition, the relationship of wave velocity of the material and porosity of the sediments has been established through the plot in Fig. 4. The trend plot showed that compressional wave velocities decrease with increasing porosity, which implies an inverse relationship. Dolberg et al. (2000) reported that velocities are mostly sensitive to changes in porosity than change in fluid type or pressure in the reservoir. Thus, several reports have identified this relationship between wave velocities and the petrophysical properties of sedimentary rocks (e.g Assefa et al. 2003; Kahraman and Yeken 2008; Zhang et al. 2009; Al-Dousari et al. 2016 and Garia et al. 2019).

Fig. 3
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P-wave velocity (Vp) vs S-wave velocity (Vs) for Well 1, Well 2 and Well 3

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Fig. 4
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Compressional velocity (Vp) vs porosity showing an inverse relationship

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This study also revealed that both compressional velocity and shear velocity are dependent on porosity, since Vp and Vs have a similar decrease as porosity increases. From the trend plot of these two parameters, an imperfectly linear correlation is established, especially in Well 3. This is probably due to the variations in the values of elastic properties and pressure regime. A general rule is that with lower velocity (implying higher transit time), there is a corresponding rise in pore pressure (Zhang 2019). Figure 5 shows the plot of compressional velocity against density for the three wells, where velocity values increase with increasing density. The relationships between density and velocity provide an essential tool for geological analyses involving rock property parameters (Nwozor et al. 2017). The linear trends observed in this result indicate that the density and velocity of sands and shales increase with depth in normally pressured formations. However, the points which deviate from the supposed linear trend at certain intervals on the plot connote abnormal pressure zones. These points also correspond to the intervals which are observed to deviate from the linear trend in Fig. 4. In Well 1, these intervals with anomalous trend correspond to depth 7179 ft, 7549 ft, 7900 ft, 8900 ft, 9000 ft and 9250 ft. In Well 2, the intervals deviating from the linear trend are depth 6395 ft, 7195 ft, 7400 ft, 7600 ft and 8800 ft. In Well 3, these intervals are found at depth 6625 ft, 8025 ft and 8400 ft.

Fig. 5
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Compressional velocity (Vp) vs density for the three wells

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The plot of Shear modulus against Bulk modulus revealed that a linear correlation exists between the two elastic variables. Thus, in the three wells, materials which possess increased frictional resistance against shear stress also yield high resistance to compressibility (Fig. 6). Similarly, in Figs. 7 and 8, Bulk modulus and Shear modulus increase with decreasing porosity. This trend implies that the intervals with lesser porosities appear to be stiffer than highly porous layers, which agrees with the earlier reports by Gidley et al. (1989) and Tenthorey et al. (2003). Seemingly, the strength of any subsurface earth material is inversely correlated to porosity, which means that the ability of formation to support shear deformation and resist compression decrease with increasing porosity. The mechanical properties play a significant role in hydraulic fracturing of tight reservoirs, in terms of initiation and propagation of the hydraulic fracture (Josh et al. 2012; Li et al. 2015). Zones with high moduli strength and lower porosities would yield narrow fractures during hydraulic fracturing, whereas intervals with low moduli and high porosities would yield wider fractures. Report have suggested that hydraulic fractures are best when they are longer and narrower (Donaldson et al. 2013). Therefore, in this case, the intervals with higher moduli are best targeted, as this would yield the narrow fractures for best performance. Another implication of the lower values of elastic strength is in the magnitude of seismicity during injection (Gudmundsson 2004). Moreover, since the elastic properties of rocks are a significant parameter that best describe the mechanism that promote mechanical behavior of fault under rupture processes, the deformation of faulted block in terms of slip tendency and induced seismicity is therefore a fundamental evidence of the elastic state of the rock. The intervals where lower elastic moduli are recorded would be highly unstable. Such soft matrix requires placement of multiple layers of proppant around the wellbore area. Whereas intervals with hard matrix, where there is no embedment of the proppant, the fracture opening can be enhanced by using a monolayer of proppant (Donaldson et al. 2013). So far, the subsurface conditions that affect fractures orientations, failure modes and brittle behavior include the tectonic stresses and variability of elastic properties of the rock (Li et al. 2013). Thus, materials with low elastic properties would have higher magnitude of mechanical failure than formations with high elastic moduli.

Fig. 6
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Plot of shear moduli and bulk modulus showing a linear relationship

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Fig. 7
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Plot of shear modulus and porosity indicating a linear relationship

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Fig. 8
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Plot of Bulk modulus and porosity showing inverse relationship

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The plots of Bulk and Shear moduli against density (Figs. 9, 10) both showed a direct relationship, indicating that dense materials are more rigid and incompressible than those which are less dense. Clearly, a slight increase in density increases the Shear and Bulk moduli largely, which shows how the elastic strength of the materials is highly sensitive to the material density. The changing behavior of these materials would play a major role in their response to injection and fracturing. Notably, previous study from the same wells by Eyinla and Oladunjoye (2018) showed that pore pressure and fracture gradient decrease as the three elastic moduli (Bulk, Young and Shear) increases. The intervals where the lower elastic properties have been observed are also the same as the overpressured zones in this study. Thus, the pressured zones have been successfully linked with intervals where geomechanical strength is lowered.

Fig. 9
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Shear modulus against density showing direct relationship

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Fig. 10
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Plot of Bulk modulus and density showing direct relationship

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Additionally, this study explored the gamma ray log to distinguish the geologic beds into sand and shale, however, the lithology was further characterized into geological beds using the ratio of compressional velocity to shear velocity (Vp/Vs). For this study, the velocity ratio was employed to make distinctions between the formation lithology and the result was compared with gamma ray lithology log. There was a good correlation between the two results, which established the validity of the calculated velocity ratio. Meanwhile, from the velocity ratio values in Tables 1, 2 and 3, and as shown in Fig. 11, the depth plot of Vp/Vs and Poisson’s ratio revealed a perfectly linear correlation. This implies that both parameters have a relationship which can been adopted for lithology identification to discriminate the already established lithology of the formation (Wang et al. 2009). The values of Vp/Vs are consistently lower in sands than shales, and these shaly formations are already classified as overpressured sediments because of their properties and trends in other rock physics parameters. From Pickett (1963) reports, values of Vp/Vs ratios for different rock types vary (about 1.9 for limestone, 1.8 for dolomite, and 1.6–1.75 sandstones), and this velocity ratio is independent of the density of the rock. Therefore, this parameter be adopted with Poisson’s ratio to compliment lithology identification. The correlations between the Vp/Vs and the corresponding Poisson's ratio values can also be applied in modeling and interpreting seismic data in terms of the particle’s chemistry and lithology (Wang et al. 2009).

Fig. 11
figure 11

Vp/Vs against Poisson’s ratio showing linear relationship

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Also, Crain (2013) stated that low values of Poisson’s ratio, about 0.10–0.30, are indicative of most sandstones and carbonates, hence, any rock materials which fall within these values are assumed to fracture relatively easily. However, those with higher values, ranging from about 0.35 to 0.45, are classified as shales, very shaly sandstone, and coal. Notably, a combined depth plot of Vp/Vs and P show increasing and decreasing sequence depending on the material encountered down depth (Figs. 12, 13 and 14). Generally, result shows that the intervals with high values of Vp/Vs and P indicate shale or shaly sands, and they are the points indicated by black arrows on the plot. Meanwhile, these intervals also correspond to the highly pressured zones reported in other plots. Thus, an increase in Vp/Vs corresponds to increase in P, also, increase in shale content lowers VP and VS but increases VP/VS according to the report by Miller and Stewart (1990). It is believed that the materials present in the overpressured zone would be harder to fracture, thus, if hydraulic fracture is initiated without considering the material properties, these intervals would result in producing wider fractures during hydraulic fracturing. Nevertheless, the other intervals where Vp/Vs and P are not abnormally enhanced are classified as sandy or less shaly formations. Consequently, their material constituents are expected to yield narrow fractures with less fracture pressure during hydraulic fracturing (Eyinla and Oladunjoye 2014; Chen et al. 2016; and Eyinla and Oladunjoye 2018). The intervals with overpressure could also cause problem during hydraulic fracturing such as well bore instability, blowouts during drilling, diversion of hydraulic fracture path, poor fracture propagation and lost circulation are related to these geostatic/hydrostatic pressure gradients issues in oil field rocks, and may be addressed and controlled by the adequate monitoring/adjustment of drilling fluid density during drilling operations.

Fig. 12
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Vp/Vs and Poisson’s ratio against depth for Well 1 (Black arrows point at zones with high Vp/Vs values corresponding to shaly intervals and over pressure zones)

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Fig. 13
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Vp/Vs and Poisson’s ratio against depth for Well 2 (Black arrows point at zones with high Vp/Vs values corresponding to shaly intervals and over pressure zones)

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Fig. 14
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Vp/Vs and Poisson’s ratio against depth for Well 3 (Black arrows point at zones with high Vp/Vs values corresponding to shaly intervals and over pressure zones)

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Nevertheless, previous reports have indicated the possibility of identifying fluid or gas saturated reservoir using the Vp/Vs ratio. That is, a lower Vp/Vs may not only reveal an overpressured or shaly formation but may also be an indicative of a gas-bearing formation. This is because the presence of gas would increase the compressional transit time or slow down the compressional velocity of the material (Zhang 2019). The shear and compressional waves often give different response during passage through reservoir containing fluids and pressures, which implies that lower Vp/Vs can symbolize the presence of overpressure or gas saturation (Uyanik 2010). Thus, since compressional wave propagates in almost all kinds of medium (dry or saturated) whereas shear wave does not propagate in fluids, the porous medium saturated with fluids is expected to have a higher value of Vp above Vs, as rightly revealed in the result (Tables 1, 2 and 3). Consequently, the Vp/Vs ratio in a gas saturated environment is much lower than in liquid saturated reservoir (Tatham 1982). To clearly identify whether the interval with lower Vp/Vs in this formation is caused by overpressures or by gas effect, the shear transit time is examined, as described by Chilingar et al. (2002). The result in this study showed that gas in the reservoir has very little effect on the shear transit time, meanwhile, the effect of an overpressured formation causes both compressional and shear transit time to increase simultaneously (Fig. 3). Also, using the established behavior presented by Zhang (2019), overpressure in the formation is further identified where a very high shear wave velocity and shear transit time corresponds to a high pore pressure as shown in Figs 15, 16 and 17.

Fig. 15
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Plot of pore pressure and interval transit time against depth for Well 1 showing concurrent increase of both parameters

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Fig. 16
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Plot of pore pressure and interval transit time against depth for Well 2 showing concurrent increase of both parameters

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Fig. 17
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Plot of pore pressure and interval transit time against depth for Well 3 showing concurrent increase of both parameters

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In addition, P-wave impedance, which is directly related to material incompressibility (Bulk modulus), decreases with increasing porosity (\(\phi\)), as shown in Fig. 18.

Fig. 18
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Acoustic impedance against porosity for the three wells showing an imperfectly linear correlation

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This agrees with the study of Dolberg et al. (2000) and Chen et al. (2019), as their studies reported that acoustic impedance, acoustic resistance and acoustic reactance decrease as porosity increases. They also reported that the differences in acoustic impedance in a well formation correlate with the variations in the porosity in an inverse relationship. The result obtained from this field also showed that areas with high acoustic impedance are correlated with low porosity values, whereas materials with high porosities are observed in areas possessing low acoustic impedance. The trend plot of acoustic impedance shown in Fig. 19 indicates that under normal pressure conditions, acoustic impedance would increase linearly with depth, but certain intervals are abnormally pressured causing divergence of the supposed linear trend. This divergence away from the linear trend increases with depth in the three wells, meanwhile, Well 3 appears to be more linearly correlated than the other two. Seemingly, inhomogeneity of the rock types may account for the scatter around the established best fit lines of regression since acoustic impedance values vary for shales and sands. Moreover, Avseth et al. (2001) reported that sands can be discriminated from shales by running acoustic impedance inversion, and such model can be applied to seismic data in predicting important anomalies which are related to hydrocarbons overpressure, tectonic history, sediments compaction and cementation.

Fig. 19
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Depth trends of acoustic impedance for the three wells

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The overall result in this study agrees with literature reports (e.g. Dutta 2002; Chopra and Huffman 2006; Cibin et al. 2008) indicating that overpressured intervals generally show the following properties: higher porosity, lower bulk density, lower effective stress, and lower velocities, both shear wave and compressional wave. Shales often exhibit large variations in petrophysical and mechanical properties, and the materials are intrinsically anisotropic because of large volume of clay minerals, hence, they are typically overpressured due to trapped fluids in pores, presence of organic materials, and low porosity and very low permeability (Dutta 2002; Peacock et al. 2011; Wang et al. 2012). In this study, with an increasing shale content of the sediments, the effect lowers VP and VS but increases VP/VS. Overpressures in sedimentary basins are attributed to different mechanisms but the main causes are related to increasing formation stress and in-situ fluid generating mechanisms. It is believed that the tendency of these mechanisms and their processes to generate overpressure is dependent on the rock materials and fluid properties in the sedimentary rocks. Another important factor is the rate of change in properties and features under the normal basin conditions (Chopra and Huffman 2006). The dominant materials in Niger Delta Basin belong to Tertiary sediments. During the deposition of the materials, there was an increasing effect of vertical stress. Also, it is believed that the pore fluids escape while the pore spaces attempt compaction. Meanwhile, during sedimentation, grains of sediments are continuously building up on top of each other, and as the thickness of the layer of sediment increases, the grains of the sediment are packed closer together, and at this time, some of the water is expelled from the pore spaces. Consequetly, the most acceptable mechanism of overpressure generated in these processes is disequilibrium compaction. This phenomenon is responsible for the uneven distribution of rock physics and mechanical properties, thus, resulting in pore pressure rise and fall.

Generally, increase in pore pressure correspond to decrease in both shear and compressional velocities across the three wells. Seemingly, this effect is observed in the corresponding lowering of the impedance at these zones as the velocities and impedances of sands are much higher than for the overpressured layer which contains more of shale material (Avseth et al. 2001). The decrease in the P-wave velocity producing increased pore pressure has been used for detecting overpressure, consequently, the intervals showing abnormal trend in acoustic impedance plots are similarly assumed to have resulted from the abnormal pressure in the reservoir. Figures 20, 21 and 22 show composite plots of Vs, Vp, Y, B, S and PP against depth, where critical intervals corresponding to the zones with low velocities and high pore pressure encountered across the three wells have been identified using the black arrows. In Well 1, these intervals correspond to depth 7179 ft, 7700 ft, 7900 ft, 9350 ft, 10400 ft, and at greater depth. In Well 2, the abnormal pressure is found in depth 6595 ft, 7400 ft, 8566 ft, 9420 ft, and down depth. In Well 3, the intervals are found in depth 6000 ft, 6625 ft, 8025 ft, 8400 ft and 9036 ft, 9600 ft.

Fig. 20
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Composite Plot of Well 1 showing critical intervals with low elastic moduli and velocities yielding high pore pressure (arrows point at critical intervals)

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Fig. 21
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Composite Plot of Well 2 showing critical intervals with low elastic moduli and velocities yielding high pore pressure (arrows point at critical intervals)

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Fig. 22
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Composite Plot of Well 3 showing critical intervals with low elastic moduli and velocities yielding high pore pressure (arrows point at critical intervals)

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The recurring subnormal pressure and overpressure noticed throughout in this field suggest non-uniform compaction of the Niger Delta formation. An inverse relationship which exists between pore pressure and elastic properties as well as velocities of waves is further established from results obtained. It is revealed that with increasing pore pressure, there is a corresponding decrease in the elastic properties of the rock and the velocities of waves. Hence, at every point where such decrease in Vs, Vp, Y, B, S commensurate with an increase in pore pressure, creating an abnormal pressure zones, such intervals must be drilled carefully. Reports have shown that at such zones, there would be sanding problem when drilling, meanwhile, intervals with high geomechanical strength are strong enough to produce at high flow rates without sand. Therefore, sand control is highly essential for the intervals with low mechanical competency (Eyinla and Oladunjoye 2014), and it is highly essential to select adequate mud weight to ensure drilling safety, and to prevent hole collapses leading to fracture or losses.

Conclusions

This study has considered the behavioral patterns of material geomechanical properties in identifying overpressured intervals. It has been established that these overpressured intervals could be a serious threat to the successful implementation of enhanced recovery programs if not properly investigated. The values of estimated pore pressure from this study vary from well to well, but the general trend behaves the same across the three wells. Cross-plots of relevant rock properties such as density, velocity, mechanical properties, acoustic impedance, Vp/Vs and pore pressure produce patterns which confirm that the formation has been subjected to disequilibrium compaction. This is because of the uneven distribution of pressure across the three wells in which most of the intervals are abnormally pressured. It is concluded that pore pressure has a huge effect on the elastic moduli of the formations, as increase in pore pressure causes a decrease in the elastic properties. Elastic strength and velocities of the materials which ordinarily should follow an increasing order down depth varies at certain intervals because of the dominating abnormal pressure. In general, more stiff materials are at deeper depth, indicating that the less porous formations are stiffer than the porous layers.

The values of Vp/Vs were not only applicable for lithology identification, the correlation of both Poisson’s ratio and the Vp/Vs has helped to ascertain the classification of lithology across the wells where high values indicate shale and overpressured intervals. Although the presence of gas can show the same signature as overpressure while interpreting Vp/Vs values, however, interval transit time has served as a useful tool in confirming the presence of overpressure as observed in this study. The velocity of shear and compressional wave is related to the material porosity, and the relationship has also helped in promoting overpressure detection. This study has reported that an obvious deviation from existing trends give a pointer to the type of reservoir material at such interval, and a possibility of overpressure have been inferred. From the overall geomechanical properties analyzed, it is safe to adduce that divergence of any supposed trend is an indication of abnormal pressure and optimum production can be achieved by targeting intervals with high geomechanical strength, less shaly zones and normal pressure in the reservoir.

Nevertheless, the abnormal intervals can be carefully drilled safely and economically by adopting appropriate and suitable mud and casing. The drilling fluid’s density must also be increased to preserve the wellbore pressure above the formation pore pressure in order to maintain hole stability, to prevent borehole collapse and to prevent the influx of formation fluids into the wellbore. This careful consideration can help to reduce downhole problems, loss of reserves, environmental pollution and loss of life which might be resulted from the abnormal pressure. However, the proper prediction and characterization of subsurface formations, the geomechanical characteristics and overpressure are important to know the landing interval for the lateral wells and how the fractures will propagate while maintaining stability during hydraulic fracturing. Also, if this method is carefully utilized, it can serve as an easy tool for predicting subsurface mechanical properties of formation, pressure study and understanding the relationships between each parameter, consequently, the problems associated with drilling petroleum wells in over-pressured sedimentary basins including blow out and wellbore instability can be prevented by taking the necessary precautions and using the required tools.

Conclusively, since this study has revealed various geomechanical and pressure properties as a result of changing state of sediments compaction, for any hydraulic fracturing program, a careful well planning and consideration of the pressured intervals is suggested, in order to improve the stimulation performance and well productivity. Correct designing of casing scheme can be employed to ensure optimum completion and maximum productivity. Meanwhile, although this study only considered vertical change in material properties of rocks, assuming homogeneities of the material laterally, it might be essential to investigate how lateral heterogeneities of rock would affect the material properties and possible pressure change, and their consequence during fluid injection or hydraulic fracturing program .