Fig. 7 Output of 1D basin modeling process in terms of reservoir elastic properties and pressure regim.
In other words, it shows the time versus thickness relationship for all the layers including the layers that have been eroded or periods of non-deposition (Hiatus). Based on the lithology information of the 1D model inputs, depth–porosity relationship is also calculated while establishing burial history. The depth–porosity relationship is then converted to calculate the effective stress regime and temperature profile of each layer through the geological time. The effective stress thus derived for each layer of the basin provides crucial information for calculation of geomechanical properties of the reservoir rock.
Fig. 8 Geohistory plot (burial history)—output from 1D basin modeling process.
The final stage of the current integrated approach is to combine the result of classical 1D basin model (burial history) with geostatistical 3D geocellular model to generate discretized geomechanical model of the study area. Lithology identifier of each cell from 3D facies model provides the link of this integration. Each element of burial history model has also been assigned a lithological identifier to define (1) mechanical compaction, i.e., porosity versus depth relationships, (2) pore pressure relationships, i.e., porosity versus effective stress, (3) fluid transport properties, i.e., porosity versus permeability and capillary threshold pressure, and (4) matrix properties such as thermal conductivity. The lithology identifiers available in both the models enable populating layer-wise distribution of effective stress for each cell in the 3D geocellular grid (Fig. 9). The effective stress estimation is obtained during the process of burial history modeling of the sedimentary basin. The burial (or geo) history model provides information on rate of sedimentation including depth and age of deposition. While calculating effective stress regime of the basin, we assume that sedimentation and subsidence is the primary cause of pressure and stress; stresses generally increase with depth and rock stress generally interacts negatively with porosity and compaction (Hantschel and Kauerauf 2009). In 1D basin modeling approach, Terzaghi’s (1923) effective stress concept is widely used as the fundamental relationship for effective stress modeling (Hubert and Rubey 1959).
In this relationship, lithostatic pressure (equaling the sediment weight) is considered as total stress and additional stresses due to compaction or extensional forces are neglected (Hantschel and Kauerauf 2009). Biot (1941) established the theory of poro-elasticity for rocks and introduced Biot’s coefficient in the definition of the effective stress (Schneider et al. 1996).
In these models, pore pressure of formation is related to incomplete mechanical compaction and a fixed relation between porosity reduction and sediment compaction is assumed (Hantschel and Kauerauf 2009). Studies by various other researchers established a number of empirical relationships of porosity versus depth versus compaction. These relationships show that changes in porosity with increasing depth is a function of lithology of the sediments. Thus, in basin modeling process these lithology-wise empirical relationships are used to satisfy the depth–porosity function and pore pressure calculation. The complete mathematical explanations of these relationships and numerical solutions to complex equations can be obtained from Hantschel and Kauerauf (2009) and Schneider et al. (1996).
Once the effective stress distribution model is generated for the entire reservoir geocellular grid, rock mechanical properties such as Vp , Vs , UCS, BRI, OCR, Young’s modulus, Poison’s ratio, and bulk modulus are calculated at each cell locations of geocellular grid using empirical formula as provided below (Eberhert-Phillips et al. 1989; Ingram and Urai 1999; Horsrud 2001; Yarus and Carruthers 2014):
where Vp = P-wave velocity, Vs = S-wave velocity, ϕ = Porosity, C = Clay content, Pe = Effective stress, UCS = Unconfined compressive strength, OCR = Over consolidation ratio, BRIT = Brittleness, NC = Unconfined, ρ = Density, E = Young’s modulus, ν = Poisson’s ratio, K = Bulk modulus.
For each of the calculations lithology, porosity and effective stress serve as main input parameter. Figure 9 displays a representative view of the geocellular grid with discretized geomechanical property derived from the integration of result of basin and geocellular modeling.
Fig. 9 Distribution of geomechanical properties in the final integrated reservoir grid.
Well coverage in the study area is not adequate as revealed in Fig. 4c. The wells are mostly clustered in the central and north-eastern part. Furthermore, in the study area conventional cores were collected in only five wells out of 27 wells made available. Thus, physical measurement and interpolation of geomechanical properties of these core samples were not considered as reliable source of information for future drilling and investment decision. Additionally, due to non-availability of 3D seismic data, interpolation of well-based geomechanical properties beyond well control could not be validated through seismic attribute correlation and integration as secondary input. As a result, attempts to use the conventional approach of using well core sample analysis-based geomechanical property interpolation in the study area provided inappropriate information for full field appraisal and development planning.
However, use of current geostatistics-based modeling approach explained in this study helped to nullify these restrictions and provided a full field geomechanical property distribution model with the integration of parameters from basin modeling approach. Such integrated models are highly flexible and appropriate for full field development with reliable distribution of geomechanical property in 3D space of unconventional reservoir.
The model developed in the current study clearly indicates that elastic moduli decrease with increasing porosity; therefore, such models would aid in the understanding of the distribution of brittle versus ductile zones in the reservoir. Statistical analysis in terms of correlation coefficient of Young’s modulus and porosity reveals a value of − 0.86. Figure 10 displays a plot of Young’s modulus and porosity at K-level 23 of 3D reservoir grid. Based on the spatial distribution pattern of geomechanical properties, the lower part of the Bakken formation in the study area has been identified as zone of prime importance with favorable values of geomechanical properties to maximize hydrocarbon production. In the absence of 3D seismic coverage in the study area, such information aids operators tremendously for effective design of depletion strategies with minimal geological risks and associated costs. Furthermore, for a variety of other subsurface operations, including flow simulation, history matching, fluid typing, and hydrocarbon production, these models serve as main input.
Fig. 10 Plot showing correlation of Young’s modulus and porosity for K-level 23 of 3D reservoir grid.
Understanding the burial history of the reservoir is a step forward in modeling unconventional resources (Yarus and Carruthers 2014). As part of full field development project, a realistic picture of the depositional history of the reservoir through geological time provides a more solid foundation to build a knowledge base for economic forecasting and maximum return of investment. In the unconventional upstream oil and gas industry, spatial distribution modeling of rock mechanical properties of matured reservoir has always been a major challenge. However, 3D spatial distribution of model of geomechanical properties created in the current study provides an easy way of knowing prevailing rock elastic properties and stress regimes of the reservoir rocks.
Field development planning, in the current study area, involves the use of horizontal wells with multistage hydraulic stimulation in shale sweet spots as the primary production strategies. Knowledge of in situ stress conditions and facies is therefore very important for these operations as it guides the stimulation design which will in turn control the fracture propagation. Earlier studies on Bakken formation clearly elaborated the use of velocities and strains measured on samples from the core which are not sufficient enough to optimize field development strategy using hydraulic fracturing. This is because small sample plugs or slabs may not be always sufficient to describe elastic properties for the entire reservoir. For instance, V p measured from one core sample may not be very diagnostic of lithology as it cannot be used to map shales and sandstones across a reservoir with accuracy.
The current integrated approach incorporates wireline logs in the form of hard data covering entire sediment sequence. This provides a true representation of the subsurface geological condition of the reservoir even if there are no 3D seismic data available. In this approach, use of geostatistical techniques results into highly accurate 3D facies model resembling real geological condition of deposition of sediments. The geostatistical techniques via spatial covariance models of sample values helped in quantifying and mapping of geological heterogeneity in sediment deposition in unconventional reservoirs. Additionally, conditional simulation algorithms used in geostatistical modeling approach honor the sample values at location of measurements and produce minimum biasness of interpolation of rock properties from well data.
Thus, results generated from final integrated model are not only reliable, but also capable of providing accurate local error of estimation (i.e., heterogeneity) within them. Similar studies made elsewhere (Yarus et al. 2016; Yarus and Yarus 2014; Yarus and Carruthers 2014) indicated how combining geostatistics with basin modeling techniques accurately identifies sweet spots in unconventional reservoirs. Verification and comparison of results obtained from such integrated models with actual and blind wells provided high accuracy and reliability score with minimum deviation of results. Such convincing results are also true validation of consistency of result of current integrated technique over conventional approach.
Traditional modeling methods for identifying good and poor reservoir quality in shales have not been successful as reported by many authors. It is mainly due to lack of geospatial understanding of shales properties and difficulty of quantifying their heterogeneity. However, the current integrated geostatistics-based geomechanical models with higher degree of confidence show how the velocity and elastic moduli are decreasing with increasing porosity throughout the reservoir. As a result, in the current study area the concerned field team was able to identify target locations or sweet spots with high degree of accuracy within the shale for fracturing and completion. Furthermore, these models can be used alongside other reservoir characterization methods in shale play workflows to aid in the planning of unconventional well bores for enhanced production.
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