Challenges of Coupled Geomechanical Modeling: I. Stress Initialization

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Figure 1. This simple schematic demonstrates the generic process of coupled thermos-poro-mechanical modeling along with fracture propagation.
Figure 1. This simple schematic demonstrates the generic process of coupled thermos-poro-mechanical modeling along with fracture propagation (Source: Soltanzadeh, 2015).

Reservoir-scale models usually integrate different physics like rock mechanics, multi-phase fluid flow, heat transfer, fracture mechanics and sometimes geochemistry and geophysics. Considering all these physics at the same time and solving their filed equations simultaneously (fully-coupled modeling), if possible, seems to be an ideal case but usually it is less practical for different reasons such as being computationally intensive, costly, complex, unstable, and difficult to learn, run, and troubleshoot. Therefore, instead, models developed based on coupling of separate modules are much more popular in industry. In this modeling scheme, each module handles only one or two physics at a time and feeds its results to the other modules in every step of modeling. Figure 1 shows a generic illustration of geomechanical models that couple rock mechanics, fluid flow, heat transfer, and fracture effect on fluid flow. This type of coupling is very attractive to the users as it allows them to find the most practical, advanced, available, and affordable software packages in each discipline and tie them to each other. Although attractive, coupling of different modules has the risk of leading to erroneous results mainly due to the lack of an integrated perspective of how these modules interact with each other. This series of posts briefly discusses some of the issues that may show up and need to be looked after in the process of coupled modeling.

 The Stressful Stage of Stress Initialization

Figure 2.
Figure 2.

Probably one of the most challenging tasks of modeling of complex geologies is applying the right initial stresses to the model. Ideally, in case you run a model with the proper initial in-situ stresses in a stationary or steady state (no external loading or deformation applied), it is not suppose to show any further deformation or stress changes. In other words, it must be and stay in the equilibrium state since the beginning. Unluckily, in the real world of geomechanical modeling of complex structures, this is not an easy condition to hold as the in-situ stresses are usually determined by the user separately and without really caring about the static equilibrium of the 3D or 2D models. These data usually come from different sources such as field tests, frictional equilibrium, simplistic poroelastic models, or wellbore stability analysis and they come in the form of single data points or well profiles that need to be populated in model’s volume. So, when the model  is running, the first thing it tries to do is taking the stresses to an equilibrium state that is usually accompanied by inducing new deformations and stress changes in the model. Eventually, the initially introduced stresses may change to a different stress state that can be different from the initially introduced stress state to the model and note that all of these happen without applying any loading, drilling, fracturing or injection/production.

Figure 3. In linear elastic modeling, it is assumed that the stress changes are independent of stresses and strains. The linear trends on this figure developed based on data from the classic example of Ekofisk field (after Teufel, 1989) are showing that change in minimum horizontal stress only depends on pore pressure change. Remember finding such a linear relation is not always easy.
Figure 3. In linear elastic modeling, it is assumed that the stress changes are independent of stresses and strains. The linear trends on this figure developed based on data from the classic example of Ekofisk field (after Teufel and Rhett, 1991) are showing that change in minimum horizontal stress only depends on pore pressure change. Remember finding such a linear relation is not always easy.

There are different ways to tackle this problem. One simple way is ignoring the effect of initial stresses in numerical modeling, run the model without any initial stresses (zero-stress model) and simply superimpose the induced stress changes by field operations to the initial stress state. As much as off beam this method sounds, in fact, it can be working fine if i) you do not care about initial stress state of your model to be in equilibrium and ii) if your rock lives in a linear elastic life where its behaviour is not dependent on its past or current stress/strain state (see Figure 3 for an example). This might be the case for some consolidated sandstones or carbonates or even less consolidated rocks that undergo limited changes in loading, pressure and temperature.

Some modellers may prefer to apply their acquired initial stress data and run the initial model (without any external loading) to an equilibrium stress state where no further changes observed and, then, consider the newly developed stresses as their initial stress state for modeling. This is only correct if the changes in stress state from initial to equilibrium are not significant and can be ignored.  Another, probably more reasonable, approach is applying the tectonic strains (deformations) derived from back analysis of stress measurements to the model and let the stresses develop (Figure 4). Minimizing the difference between the developed stresses and initial stress state based on user’s data can help with finding the best tectonic strain approximation.

Figure 4. Applying tectonic strains calculated by reverse analysis of field stress measurements to a geomechanical model for the purpose of stress initialization.
Figure 4. Applying tectonic strains calculated by reverse analysis of field stress measurements to a geomechanical model for the purpose of stress initialization (Source: Soltanzadeh, 2015).

To Remember

No matter what approach is used for stress initialization, there are always some uncertainties that come along at this stage of the job. We need to remember that it is always important to verify the equilibrium state of the model before applying further changes in terms of drilling, fracturing, or pressure or temperature. We need to let our model run in its initial condition for a while and make sure the changes are trivial. If not, we need to take action and come up with a solution. When dealing with a complex geometry with several different formations which are not simple flat layers, the problem becomes more cumbersome. Presence of faults, makes the issue even more challenging.

A more complex issue shows up when the initial disequilibrium of the in-situ stresses in thermo-poro-mechanical models is not just the result of imbalanced stress initialization but it is also caused by the unsteady fluid flow or heat transfer in the initial model. For instance, having a non-steady pore pressure state in the model may lead to fluid flow from one zone to another leading to pore pressure change and, consequently, perturbation of initially introduced stresses.

In case of having no data or a small amount of data to compare with our model’s results, or when we are simplifying our geometry, or in cases when we are ignoring the effects of pressure and heat imbalance, we might get the impression that stress initialization is not a big deal as the model is doing the initialization job for us automatically but, in reality, it is the ignorance of the model that makes it look easier to handle and this is nothing to be excited about. Sometimes we cannot or decide not to do anything about the issue; this is fine as long as we acknowledge the shortcomings and potential errors that may arise from our decisions and lack of certainty.

Read part II of this series.

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