**Abstract/Excerpt**

**Improving Petroleum Systems Modeling with Basin-Scale 3D Stress-Strain Models**

**Thomas Hantschel¹, Michael Fuecker¹, Tim Matava², and Armin Kauerauf¹**

*¹Aachen Technology Center, Schlumberger, Aachen, Germany
²ConocoPhillips, Houston, TX, USA
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**Introduction**

Petroleum systems modeling consists of thermal, geomechanical, and fluid-flow models. In the geomechanical model, the formation of rock stresses and fluid pressures are calculated. Both processes are closely interconnected.

Methods for calculating fluid pressure are well established and take into account basin scale effects such as overburden stress, mechanical compaction, cementation of sandstones and carbonates, and fluid expansion mechanisms such as aqua-thermal pressuring and pressure generated during the formation of hydrocarbons. The material parameters for pore pressure calculation, such as rock permeability and compaction parameters, are also well established. Pore pressure models are not only an important component in petroleum systems modeling. These models are also sometimes used as a separate application: pore pressures predicted from geologic processes (e.g., sedimentation type and rate) as a complementary method to the prediction of pore pressures from seismic velocities using Eaton type models.

The traditional method for calculating the rock stress is the Terzaghi model—a simple 1D model—with the maximum principle stress equal to the overburden load (lithostatic pressure), coupled with a 1D compaction law for the sediments. Lithostatic pressure is the only gravity force affecting pressure formation and the horizontal stress is assumed as a fixed ratio of the vertical stress. A simple Terzaghi model is often a good model for many geologic settings; however, it suffers from two general deficiencies. First, the calculated pore pressures in compressional basins are underestimated as the abnormally high horizontal stresses are not considered. Second, the stress derived fracture models are oversimplified. This paper shows how a three-dimensional stress model improves petroleum systems modeling by addressing the shortcomings of the Terzaghi model.

**The 3D Stress Model**

Three-dimensional stress-strain calculations and simulators are well established on a reservoir or wellbore scale to predict borehole stresses and strains for well design in appraisal and production settings. Two approaches are used on a regular basis: a simple poroelasticity model based on “irreversible nonlinear elasticity” and a more sophisticated poroplasticity (Drucker-Prager type) model that takes into account failure criteria and plastic deformation for shear failure and compaction. Poroelasticity models are standard in most well and reservoir models. Both models are used here and compared.

Several modifications are required before existing approaches to three-dimensional stress modeling can be used on basin scale. First, material parameters, such as elasticity moduli, have to be upscaled to a basin scale. Second, a yield surface has to be developed in a dynamic model on geological time scale. Third, basin scale boundary conditions are required. Fourth, basin evolution processes such as sedimentation, erosion, salt deformation, tectonics, and fault development are required in the model.

In our proposed poroelasticity model, a linear relationship between the effective stress and strain tensor is assumed. The lithological parameters of the formulation are the Biot coefficient, Young’s modulus of the bulk and the grain matrix, and Poisson’s ratio and the bulk density (see, for example, Jaeger, 2007). Young’s modulus is derived from the Terzaghi compressibility after Hantschel (2007). Porosity-dependent Terzaghi compressibilities are well established in many basin simulators. Standard data for the Young’s modulus of the grain matrix (which also gives the Biot coefficient) and the Poisson’s ratio are included for many lithology types. Our proposed poroplastic model limits the stresses by two yield surfaces for shear failure and compaction. Stress formation during shear failure is ideally-plasticity controlled with a volume preserving plastic flow law. During compaction, associated plastic flow is assumed with work hardening controlled stress formation. Additional material parameters are required: cohesion, friction angle, critical state stress, the cap mean stress, and the hardening parameter. The hardening parameter is derived from the compaction law, while the other failure parameters are treated as constant litho-type standards. The solutions of poroplastic equations are much more challenging compared to the poroelasticity equation. Each time step requires several iterations and a multi-dimensional Newton Raphson procedure to solve for the plastic strains.

The main advantages of the poroelastic approach are that only a limited number of known material parameters are needed and the calculated stresses and strains can be easily explained. The poroplasticity approach is physically more correct in the description of the compaction. It especially limits stresses in deeper parts of basins. The main differences in these two methods are the use of different material laws; both are mainly controlled by the same bulk modulus K, but which yield quite different directions for the stress path. Only in the case of normal compaction lines with no shear stress are the calculated vertical stress components similarly directed in both approaches. The proposed boundary conditions are a traction-free surface, fixed walls on the side boundary (zero horizontal displacements), and fixed basement (horizontal and vertical displacements are zero). Alternative conditions are positive and negative displacements at the lateral boundaries of the model for compressional and extensional tectonics.

The equations for pore pressure and rock stresses are coupled via the Biot term and gravity type overburden term. Coupling between fluid pressure and rocks stress means that the rock stress solution can only be as good as the pore pressure solution. This is a strong advantage of the implementation of the 3D stress module in basin and petroleum systems simulators rather than in reservoir simulators. Additionally a complete data model can be directly used: the paleo-geometries and meshes, the basin type cell properties such as porosities, compressibilities and permeabilities, and physical values such as temperatures and fluid pressures.

**Applications**

The new geomechanical model can result in significant differences for rock stress and pore fluid pressures compared to the Terzaghi model. This is particularly the case in salt basins and basins subject to significant compressional stress. Salt has a Poisson’s ratio that approaches 0.5 on a geologic time scale and results in higher horizontal stresses in salt than the Terzaghi model. There are also large gradients in the near salt stress field in the rocks suggesting that they may be at risk for shear failure. Basins under compression show high horizontal stresses in all rocks. These models result in higher pore pressure than predicted by the Terzaghi model for compaction and this appears to be more realistic.

Two applications are shown: a three-dimensional Gulf of Mexico model with complex salt domes and a two-dimensional model of the Monogas-Thrust Belt of Eastern Venezuela as an example for compressional tectonics. The structural reconstruction for the Monagas model included an early phase of subsidence, the main compressional over-thrusting from 24 to 10my accompanied by uplift and erosion, and a final phase of subsidence afterwards (L. and F. Maerten, 2006). A special modeling technique (TecLink) is used to take these predefined reconstructed sections into account during forward simulation.

The stress history through geological time in the salt-affected basin is complex and depends on the geometry of the salt through time. In general, this model shows that the minimum and maximum principle stresses differ from lithostatic pressures and the maximum stress is not necessarily vertical. Areas with high deviatoric stress generally coincide with significant overpressures that result from the low minimum principle effective stress. Another interesting result is that the overpressure increase due to basin compression is not uniform in the sediments, but instead shows strong local variation.

High deviatoric stresses also mean a higher risk of failure due to fracture. Moreover, calculated stresses and strains can be used to improve fracture orientations and fault property predictions through geologic time. A comparison of the two approaches indicates that the poroplasticity approach yields lower stresses in the part of the basin greater than 3 km deep.

**Conclusions**

The proposed basin-scale geomechanical model integrates for the first time (i) a dynamic model acting on geological time scales, (ii) a coupling of stress calculations with a basin scale fluid simulator, (iii) the adjustment of material parameters to larger scale cells, (iv) considerations of plastic and elastic yielding such as compaction and fault movements, and (v) the definition of suitable boundary conditions.

Implementation of 3D stress-strain formulation improves petroleum systems modeling as the models are more consistent with the processes occurring during sedimentation and compaction. These models also yield more realistic pore pressure and stress predictions in salt basins and in basins subject to lateral compression. Early results appear promising in that the three-dimensional rock stresses and related failure may be predicted by basin scale geological modeling rather than constructed from well data. The prediction of basin wide stresses in general suggests that other predictions may be improved (e.g., seal capacity) since seal risks are often perceived to be much higher than the risks related to charge, trap, and reservoir.

**Acknowledgments**

The authors would like to acknowledge the support of Chuck Shearer and Douglas Foster from ConocoPhillips and Fausto Mosca from Devon (now Nexen) for joint development of the physics of the geomechanical model. Further thanks go to Frantz Maerten, Laurent Maerten, and Martin Neumaier (Schlumberger) for providing the model data from the Santa Barbara section; Frantz and Laurent performed the structural reconstruction and Martin the petroleum systems modeling part.

**References**

Hantschel, T., Kauerauf, A.I. 2009: Fundamentals of Basin and Petroleum Systems Modeling. Springer-Verlag.

Hantschel, T., Fuecker M., Wygrala B., Neber A.: Modeling Basin-Scale Geomechanics Through Geological Time, IPTC Bangkok, 2012

Jaeger, J.C., et al., 2007: Fundamentals of Rock Mechanics, Blackwell Publishing, pp 168-197

Maerten, L., Maerten, F., 2006, Chronologic Modeling of Faulted and Fractured Reservoirs Using Geomechanically Based Restoration: Technique and Industry Applications, AAPG Bulletin, v. 90, no. 8 (2006), pp. 1201–1226.

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AAPG Search and Discovery Article #120098©2013 AAPG Hedberg Conference Petroleum Systems: Modeling the Past, Planning the Future, Nice, France, October 1-5, 2012*