After encountering frequent misunderstandings of rock compressibility and its applications, I decided to write a series of posts on ‘geomechanics of compressibility’ to explain its rock mechanical definition, its different types, methods of compressibility measurement and their differences and the parameters affecting this property especially stress path and hysteresis. As an introductory post, let’s start with explaining why compressibility is important to us. But wait a moment! If you feel the equations are eyesores just ignore them, I don’t think it will really matter.
Fluid Flow Analysis
Pore volume compressibility (Cp) has long been recognized as an important factor in fluid flow simulation for aquifers and reservoirs as shown by the following fundamental equation of fluid flow in porous media:
[In this equation, Cl is fluid compressibility, ρ is pore fluid density, φ is rock porosity, g is gravity acceleration, q is the source term, k is permeability, t is time and z is the elevation measured in the vertical direction oriented downward.]
Generally, in either of fluid flow simulations or material-balance calculations, the role of pore volume compressibility coefficient (Cp) becomes increasingly important as the fluid compressibility decreases. The importance of pore volume compressibility is even more crucial for closed systems where, in absence of fluid flux, fluid flow and pressure changes are controlled mainly by pore volume changes.
Hydrocarbon Reserve Estimation and Storage Capacity Evaluation
Pore volume compressibility is also important in volumetric estimation of hydrocarbon reserves (find more in here) and evaluation of fluid storage capacity and efficiency in aquifers (for instance, waste fluid disposal or CO2 sequestration). As a simple example, in estimation of storage capacity of closed-system aquifers, the efficiency factor (Ei) for storage is introduced by Zhou et al. (2008) as:
[where Cw is the compressibility of water and Δp is the average pressure increase within the aquifer induced by injection.]
Approximation of Porosity Variation
Another application of pore volume compressibility is for the estimation of porosity change induced by pore pressure variation within a reservoir. The following equation is widely used for porosity approximation of consolidated and cemented reservoir rocks (e.g., Satter et al., 2008):
[where φ1 and φ2 are the values of porosity, at reservoir pressures of p1 and p2, respectively.]
Such relations are the most simplistic way of involving geomechanics in fluid flow simulation. However, as it can bee seen in Figure 3, such relations must be used with the most caution as I will discuss it in detail later in this series.
Estimation of Ground Deformation
Bulk volume compressibility coefficient, when measured using a uniaxial pore volume test, can be directly used for calculation of reservoir or aquifer contraction or expansion induced by production or injection.
In general, the expansion of ΔH induced by the average pore pressure increase of Δp in a reservoir or an aquifer with an average height (thickness) of H may be calculated from the following equation:
[where Cbu is uniaxial compressibility.]
Some rocks, such as consolidated sandstones, behave elastically when stresses are less than critical yield stresses. Rocks show more elastic responses when pore pressure is increased e.g., in the case of waste fluid disposal or CO2 sequestration (Fjær et al., 2008). When rock behaviour is isotropic and elastic, the following relation exists between uniaxial bulk compressibility and rock elastic parameters:
[where υ is Poisson’s ratio and E is Young’s modulus of the rock.]
Hence, in absence of other reliable data, bulk volume compressibility can be used as an auxiliary parameter for estimating elastic properties of the rock.
Calculation of Biot’s Coefficient
Bulk volume compressibility coefficient (Cb) may also be implemented in the following equation to estimate Biot’s coefficient (α) as a key parameter required for any geomechanical analysis:
where Cm is the matrix (or grain) compressibility and can be measured using an unjacketed hydrostatic test, or it can be estimated from the mineralogical composition of the rock (Zimmerman,1991).
Read the second part of this series here.
Zhou, Q., Birkholzer, J., Tsang, C.-F., Rutqvist, J., 2008. A method for quick assessment of CO2 storage capacity in closed and semi-closed saline formations. Journal of Greenhouse Gas Control 2, 626–2,639.
PDF version of this article: A Primer on the Geomechanics behind Fracturing Pressure
In this post, I will break an idealized pressure curve (like what is recorded during hydraulic fracturing or pressurize fracturing tests) in different segments and explain the geomechanics behind each. I will try to answer questions such as:
- Why does pressure increase, decrease or remain constant in each segment?
- At what pressure a fracture initiates? At what stage it can be considered a mature fracture? what pressure is required for a fracture to grow?
- What are the important pressure values on this curve and how they are representing the mechanical state of the rock? How well-known pressure values such as leak-off, initiation, breakdown, propagation, shut-in, and closure pressures are defined and what is their geomechanical significance?
I will deliberately avoid getting deep in explaining mechanical models behind fracture initiation and propagation for the sake of simplicity.
To avoid complexities that are out of the scope of this primer article, I will use an ideal case of hydraulic fracturing similar to pressurized fracturing tests such as mini-frac, extended leak-off, or DFIT tests (Figure 1). The curve in Figure 1 simply shows how fracturing fluid pressure (on the vertical axis) varies with time (on the horizontal axis). The rate of injection is assumed to remain constant before the pumps are turned off. Note that this is an ideal curve and similar to many other idealization in engineering, the real curves may not look as smooth as this one. Also, the graph has not been drawn to scale on any of its axes to ensure all the major details and variations could be demonstrated. In addition, it was assumed that no natural or induced fractures exist in the zone of interest prior to fracturing.
The operation is performed on an isolated zone of a wellbore that can be either cased or open. In a simple pressurized fracturing test, the fracturing fluid is injected at a specific and constant rate for a period of time (that is to be known by the response of the rock to injection during the test) and then pumping is stopped although the pressure measurement is continued. In massive hydraulic fracturing, the injection rate varies by time and varying volumes of proppants are also injected along with the fracturing fluid.
Fluid pressure is measured throughout the entire test most likely at the wellhead and occasionally downhole. If pressure is measured at the wellhead, it needs to be converted to downhole pressure by accounting for the hydrostatic column of the fluid and all the dynamic pressure losses caused by friction and other effects during injection. This conversion becomes more cumbersome in massive fracturing jobs performed with high injection rates, special fluids (viscose, energized, foam, nitrogen, etc.) and proppants.
Ascending Straight Up (A-B)
After injection is started, the low-permeability target interval is usually intact with no fractures to let the injected fluid escape. At this condition, by continuing injection in the isolated volume of the borehole, the fluid will be compressed and, as a result, pressure has to increase. The rate of pressure increase (e.i., the slope of the line A-B) depends on different parameters mainly the compressibility of fracturing fluid (e.g., you can inject a larger volume of a less compressible fluid with less increase in pressure) and the rigidity of your container (the well). The rigidity of the container varies based on whether the well is cased or not and, also, dependent on how packers used for zone isolation and other tools will deform in response to pressurization. This straight line might be affected by high permeability of the formation, pre-existing fractures, or fluid pathways related to the cement job.
A Little Bit Extra!
If injection is stopped at a desired pressure along this period , the test is called Formation Integrity Test (or FIT). This test is used to ensure the target formation is competent enough to stand the maximum pressure needed for drilling or enhanced recovery. Nowadays, however, conducting full-cycle tests is more favored as it provides much more useful information.
When It Bends (B) – Leakoff Pressure
The discussed straight line does not continue forever and there comes a so called ‘leak-off’ point where this line bends. This is the time when induced fractures are starting to form. Initiating fractures means there will be more room for the injected fluid to occupy. Having this extra room, fluid will not get as much pressurized as before and the slope of the line is reduced and it will appear as a bending point.
Although fractures are already initiated at this bending point, they should not be considered as maturely extended fractures. These initiated fractures are small in both length and width and they are not likely to propagate far without being exposed to greater pressures. Note that Leakoff pressure is usually greater than minimum in-situ stress and the reason is speculated to be the stress concentration around the borehole.
The Uphill (B-C)
By keeping on injection, the initiated fractures will open wider and extend farther from the well and, as a result, more room will be created for the injected fluid. This extra room means less pressure increase and more bending (the curve slope will reduce) in response to more fluid injection. This segment of the curve might be quite short for the highly brittle rocks. Fluid injection type, rate and viscosity along with the complexity of the fracture also play roles in forming this uphill segment.
An important point to remember here is that, at this stage, the fracture is ‘stable’ in contrast to what we will see soon in the next segment of the curve. A stable fracture needs higher pressure to overcome the rock’s resistance against propagation and if the pressure does not increase, the fracture will not grow anymore. At this stage, more injection and pressure is required to extend the fractures meaning that the operator is in full control of the fracture’s destiny. However, as soon as the climax of the curve is passed, we are going to lose control as will be discussed in the following.
The Climax (C) – Breakdown Pressure
This is a climax necessary for creation of a trustworthy fracture. For a long time, definition of breakdown pressure and its difference with fracture initiation pressure has been a source of debate mainly due to the complex physics behind the problem. There are some less popular theories that speculate that the time of breakdown is when a fracture actually initiates (e.g., Boone and Ingraffea, 1989). However, the commonly accepted theories in fracture mechanics believe in existence of fracture prior to this time. These theories, however, differentiate the status of the fracture before and after breakdown. According to these theories, breakdown is a point where the fracture moves from a ‘stable’ to an ‘unstable’ condition (Guo et al., 1993, is a great read on this if you are interested). They also sensibly argue that even the fluid entrance into the fracture and pressure distribution within the fracture are different in these two distinct states.
Breakdown pressure has been observed to be dependent on fracturing fluid type and viscosity, injection rate and borehole size. Efforts to simply calculate breakdown pressure from elastic models (commonly used in borehole stability and drilling models) have not been very successful. Also, there have been some efforts in the industry to use the recorded breakdown pressure in these models to estimate magnitudes of in-situ stresses using elastic models, mostly showing less success.
A Little Bit Extra!
The similarity between fluid pressure-time graphs recorded during fracturing (Figure 1) and stress-strain curves measured during compressive failure of rock (Figure 2) is interesting. It might have been the reason that, in earlier times, some experts (e.g., Morgenstern, 1962) theorized that breakdown of the rock might be the result of shear failure. Some experiments have also shown that geometry complexities of the curved or parallel fractures have major influences on the magnitude of breakdown pressure (see Figure 3 for an example).
Losing Control (C-D) – Relief-In Pressure
At the breakdown point, the energy provided by pressurization helps the fracture to become mature enough and grow unstably. This unstable fracture is not in control anymore and employs the previously stored energy along with the currently injected one to grow wider and farther. As a result of this extensive fracture propagation, the fracturing fluid has a lot of room to occupy and so, it relaxes some of its high pressure and the fluid pressure drops substantially. There is another reason for pressure drop: the unevenly distributed pressure in the previous immature fracture is now re-distributed much more uniformly in the current wide and long fracture.
As we will see in the next section, like any instability with a limited amount of energy, this one has to come to a stable state if given enough time.
A Little Bit Extra!
Based on several lab simulations of hydraulic fracturing for wells with different orientations , Abass et al. (1996) showed that the pressure loss during this unstable period (so called ‘relief-in pressure’) is related to fracture geometry complexities such as curving.
The Flat Ride (D-E) – Propagation Pressure
Ultimately, with no change in the rate of injection, fluid, fracture and rock will all come to a stable and balanced condition where, first, the existing pressure at the tip of the fracture is exactly what is required to extend the fracture and, second, the volume of the injected fluid is exactly in balance with the fracture volume generated by fracture extension.
Having everything in balance, pressure does not need to vary significantly if injection rate does not change. This equilibrium pressure is called fracture propagation pressure or fracture extension pressure or simply fracturing pressure. Fracturing pressure is higher than minimum in-situ stress and it is usually used to determine the allowable upperbound pressure during drilling or injection to avoid fluid loss or leakage.
Enough Pumping! (E)
So far, many things have been revealed throughout a course of injection of a fluid in an isolated interval of a well. Things such as how the wellbore as a container reacts to injection, how much pressure is required to initiate the first fractures in the rock, at what pressure we can create a ‘mature’ fracture, and finally, the balanced pressure at which the fracture keeps propagating. In case of hydraulic fracturing jobs, the operator has a desired fracture geometry in mind so s/he keeps injecting until s/he is convinced that the desired fracture geometry is achieved based on the designs (I leave it to him/her to tell us how much s/he trusts the results). In the case of formation tests, keeping on injecting for long is not going to reveal much more. In contrast, there is still so much valuable knowledge to be learned by stopping injection and simply observing the pressure response of the system.
Free Fall (E-F) – Instantaneous Shut-In Pressure (ISIP)
As soon as the pumps are off, a sudden drop will happen in the pressure curve and pressure will fall to a value called Instantaneous Shut-in Pressure (ISIP). This drop happens because the pressure caused by flow turbulence and friction during injection instantly disappears after pumping is stopped. With no influences from the dynamic flow, the mechanical characters of rock and fracture are probably less masked in ISIP in comparison to the previously recorded parameters. This is the reason that ISIP has gained so much popularity in the industry.
Some may argue that ISIP is the ‘real’ fracture propagation pressure as it does not include the dynamic effects of the flow. This reasoning might not be very convincing as fracture propagation pressure cannot be really considered valid if fracture does not propagate. In other words, existence of flow and its characteristics can hardly be separated from fracture propagation.
Curtains Closing (F and Beyond) – Closure Pressure
After shut-in, the fracture will stop propagating and instead, in absence of the required pressure for its propagation, it will start closing. Fracture closure is the consequence of pressure drop in the fracture as fluid flows back into the well and penetrates into the rock, simultaneously. This period is probably the most favorite part of the operation for geomechanics as it provides a great opportunity to find closure pressure, which is a great proxy for minimum in-situ stress. Let me emphasize here that closure pressure is not exactly minimum in-situ stress (i.e., a parameter that we might never be able to measure it exactly) but it can be very close to this stress component. One other thing to keep in mind is that the exact location of closure pressure on the curve is not always easily identifiable and industry has come up with several different approaches to estimate it.
After closure, pressure will still decline due to the permeable behaviour of the fracture and rock but contribution of geomechanics to the process becomes trivial. The rest of the curve is highly favored by the engineers who want to find out more about fluid efficiency, formation leakoff capacity, permeability, and reservoir pressure.
Abass, H.H., Hedayati, S., Meadows, D.L. 1996. Nonplanar Fracture Propagation From a Horizontal Wellbore: Experimental Study. SPE 24823.
Boone T.J. and lngraffea A.R. 1989. Simulation and visualization of hydraulic fracture propagation in poroelastic rock. The Report to NSF Grant 8351914.
Guo, F., Morgenstern, N.R., Scott, J.D. 1993. Interpretation of Hydraulic Fracturing Breakdown Pressure Int. J. Rock Mech. Min. Sci. & Geomeeh. Abstr. 30, 6, pp. 617-626.
Morgenstern N.R. 1962. A relation between hydraulic fracture pressure and tectonic stresses. Geofis. Pura Applic. 52, 104.
What do we know about the geometries of hydraulic fractures? Are they really as simple as the straight planes we usually assume in our reservoir simulations and fracture designs? What factors influence their geometries? What are the geomechanical mechanisms behind geometry complexities? How do our completion designs affect fractures geometries and what completion designs can reduce the adverse effects of geometry complications? What is the influence of fracture geometry on production?
Our recently published article in CDL’s Discovery Digest titled ‘Fracture Re-Orientation: The Impact on Completion and Production’ is trying to investigate these questions and present a general overview of the current knowledge of fracture re-orientation and curving in a simple language. The article briefly reviews several mechanisms responsible for fracture re-orientation and curving and their effects on the efficiency of hydraulic fracturing.
Below are some of the topics discussed in the article:
- Near-wellbore tortuosity and curving;
- Fracture bending, branching, merging and link-up;
- Curving potential in offset and infill wells;
- Effects of natural fractures and faults on hydraulic fracture geometry;
- Behaviour of fractures at lithological interfaces;
- Influence of production on fracturing and re-fracturing.
We may prefer to think different modules in coupled models are like matching pieces of a jigsaw puzzle and, by coupling, we are just fitting them to figure out the big picture. In reality, this is not probably the most accurate image of the problem as, usually, different modules in these models are for different physics with different field equations, different discretization methods, and even sometimes different time steps, a fact that modelers ought to remember to acquire precise results from their models. In practice, these unfitting pieces need to be stitched to each other by interfaces, i.e., the mediums with the role of transferring and translating data between these modules. Like any language translation, if translated loosely or if some data get lost in translation, misinterpretations and errors will dominate the solution. In this post, I will discuss some of the common communication issues that can threaten the accuracy of coupled modeling. Some others will be discussed in another post of this series to be published soon on geometry and gridding.
Cell-To-Node Projection, A Big Deal!
This is a less noticed (or better to say ‘less considered’) issue that has the potential of leading to significant errors especially in locations close to the boundaries of the permeable and low permeability rocks (for instance, a reservoir and its caprock). Most likely, for many justifiable reasons, your fluid flow/heat transfer module uses a version of finite volume method (FVM) for solving its field equations while your geomechanics model uses finite element method (FEM). These two methods are significantly different in the ways they discretize geometry and in how they treat the field equations, set aside the different physics involved. While in FVM the equilibrium equations are written for a volume (cell), in FEM, they are written for nodes of an element. As a result, in FVM, properties (e.g., pore pressure, temperature, or stresses) are assigned to the volume of discretized cells but, in FEM, they are assigned to the nodes of elements. As its name makes it evident, the cell-to-node projection becomes a concern when the common properties between these modules are transferred or projected between the cells of one module to the nodes of another. To get an idea of this process, see the simple example below.
Assume a basic fluid flow – geomechanics coupled model with very simple geometry as shown in Figure 3a for a reservoir and its caprock. For simplicity, both modules have the same mesh.
1. Imagine, as a result of production, pore pressure change of dp is given by the fluid flow module within the reservoir and, as expected, no pressure change is predicted by this module in the caprock (see Figure 3b).
2. The given cellular pressure needs to be translated into nodal properties of the geomechanics module. Using a simple technique, pore pressure at each node is calculated by averaging pore pressure in the cells around it (Figure 3c).
3. Now, let’s see how these nodal pressure changes are understood by the geomechanics module. This module simply calculates pore pressure change in each of its element by averaging the nodal properties and gives what we see in Figure 3d.
You see how a pore pressure change of dp/4 has been artificially introduced into the bottom layer of the caprock by just data transfer from one module to another. Also. pore pressure change within the top layer of the reservoir is 3dp/4 in the FEM model lower than the fluid flow module prediction . It works similarly for heat transfer.
To get a sense of the importance of this issue, imagine the model given in the example above has been developed for a caprock integrity assessment of an in-situ thermal project (e.g., SAGD). Having artificially created pore pressure and temperature in the riskiest location of the caprock easily leads to significant increase in the predicted chance of caprock failure and predicts lower maximum allowable pressure (MOP), something a producer does not like to hear. Goumiri and Prevost (2010) tried to quantify the error rising from cell-to-node projection.
Dealing with the cell-to-node projection is not probably the easiest task in modeling. One way to solve the problem is using specific numerical techniques such as using piecewise shape functions and low order integration in the FEM module. This is not the modeler’s job and must had been formulated in the software by the developer. This, of course, will take the load off your shoulders, so, if you are using a full thermo-poro-mechanical software suit, always check your software’s technical manuals to see how its interface treats the issue of data transfer between different modules. However, several modeling softwares have not been designed with this consideration, or in some cases, the modelers have to write their own interfaces to facilitate data transfer between different modules. In these cases, a solution is using very fine gridding at the vulnerable boundaries so you will be able to ignore the wrongly behaving elements with more confidence and, instead, track your model behaviour at the adjacent observation cells that are not significantly affected by the issue (see Figure 4, for an example). Splitting your thick caprock in 4 equal layers and tracking the response in the bottom cells, for instance, very likely will give you inaccurate results.
Strength of Coupling
Different coupling approaches may be used in modeling such as partly coupled, one-way, two-way, and iterative two-way. Serious problems might occur when coupling degree between different modules is not strong enough and it neglects or underestimates the effect of different physics on each other. For instance, for a mechanically-sensitive reservoir, implementing a one-way or even a simple two-way coupling approach might lead to significant errors in the results. Examples are unconsolidated rocks such as shallower reservoirs or oil sands or shale gas reserves and fractured reservoirs. I fully acknowledge this fact that we still have a long way to understand the detailed physics of fluid flow/heat transfer and geomechanics interaction for different reasons such as the science being young and research being costly and expensive but there is no excuse for ignoring what we already know.
Naturally, for a modeler coming from one discipline, it is a common tendency to underestimate the influences or complexities of other disciplines and ‘take it easy’ when it comes to ‘them’. Flipping through the literature, many examples may be found, e.g., reservoir engineers who see geomechanics as one of the ‘add ons’ of their reservoir modeling softwares and also geomechanics specialist with similar mentality about fluid flow modeling. We may even encounter experts from other disciplines (like mathematicians) who, without a solid understanding of any of these physics, still insist on doing all different parts of the job themselves assuming the story is just about solving some equations or using a software package. Occasionally, a similar attitude may even be observed in some software developing companies. Of course, in this diverse world of science, nobody can or expected to master every branch of science and coupled geomechanical modeling, as an inter-disciplinary practice, is not an exception and it, definitely, needs the collective knowledge of a diverse team of experts or let’s call it ‘expertise coupling’ in addition to coupling of different physics for its success.
To be continued.
In less than two weeks, at URTec 2015 in San Antonio, I will be presenting two papers on geomechanics of the Duvernay Formation based on the Canadian Discovery’s study on this play. The papers provide comprehensive information on different geomechanical components, workflows and results of the study.
The first paper (to be presented on Monday, July 20) discusses some of our interesting observations based on detailed reviews of drilling experience for several wells that confirm the existence of different regional drilling patterns in the play. The paper demonstrates how using in-situ stresses, wellbore stability analysis, and core descriptions can help with explaining the reasons behind these differences, a major one being the potential influence of existing carbonate reefs on the geomechanical response of the play.
The second paper (to be presented on Tuesday, July 21) reviews the integrated workflows developed and implemented to combine core description and geomechanical, geochemical, and petrophysical data to identify and characterize different fracture fabrics. The paper also shows how integrating these data can provide a reliable methodology for characterizing rock fraccability and brittleness. Such a methodology may be a strong base for using log and seismic data for fracture characterization through quantitative interpretation.
In case you are also attending the conference, it would be great to have you there for the presentations and hear your questions, comments, and suggestions. I may also be found at the CDL booth in the exhibit area for most of the conference time. The abstracts for the papers are given below.
A Regional Review of Geomechanical Drilling Experience and Problems in the Duvernay Formation in Alberta
Mehrdad Soltanzadeh, Amy Fox, Sarah Hawkes, David Hume
The Duvernay Formation has been an attractive unconventional play for several producers during the last few years, and the number of drilled wells in this play has been increasing rapidly. Nevertheless, drilling in this formation is usually considered a challenging practice due to the extremely high stresses and pore pressures that can be encountered. Drilling in the Duvernay and its overlying formation, the Ireton, has shown a wide variety of drilling incidents such as sloughing, tight spots, bridges and lost circulation. This paper summarizes the results of a comprehensive regional review of drilling experience for 43 Duvernay wells. In this review, the details of drilling experience for these wells were documented using a graphical approach that captures important information on the details of drilling incidents including depths and dates, along with information on mud weights and well trajectory. As an initial part of a broader regional geomechanical study of the Duvernay, these data were statistically analyzed to identify the stratigraphic and spatial variation of drilling patterns throughout the study area. The results revealed significant differences between drilling patterns in the three major active areas of the play including south (Willesden Green and Edson), central (Kaybob), and the northwest regions. In general, wells in the central region can be drilled with lower mud weights than other regions, and experience fewer drilling problems. Because pore pressure in the Duvernay Formation in this area is as high as in the other two regions, the difference in drilling experience was attributed to considerable differences in in situ stress, which appears to be related to the presence of Leduc reefs. These stress differences were confirmed by modelling and distribution of fractures in the study area.
Application of Mechanical and Mineralogical Rock Properties to Identify Fracture Fabrics in the Devonian Duvernay Formation in Alberta
Mehrdad Soltanzadeh, Graham Davies, Amy Fox, David Hume, Nasir Rahim
Mechanical rock properties, along with in situ stresses and pore pressure, play critical roles in forming fractures in reservoir rocks. As part of a regional geomechanical analysis of the Duvernay resource play, several Duvernay cores were analyzed in detail, including the identification of different types of natural and induced fractures. The observed natural fractures include uncategorized natural fractures and polished slip faces (PSF) with rare presence of cleavage. Coring-induced fractures included petal and petal-centreline fractures and bed parallel parting (BPP). Comparison of the presence of the different fracture fabrics with mechanical and mineralogical properties of the rock revealed strong correlations between rock properties and fracture types. Such correlations may be efficiently implemented for characterization of fracture fabrics in the rock using wireline logs or seismic surveys. The observed natural and induced fractures in the cores have also been utilized to revisit and verify the concept of rock brittleness. The analyses show that, as a result of high clay content and overpressuring, the conventional mineralogical and mechanical brittleness indices do not adequately describe the variability of the Duvernay Formation stratigraphic units. Alternative indices developed for this study (i.e., plane-strain Young’s modulus and clay-based brittleness index) seem to be able to represent the mechanical behaviour of rock much more precisely. This study suggests that using natural and induced fracture fabrics observed on image logs and in cores, along with mineralogical and mechanical rock properties, is a more practical approach to assist with identifying sweet spots in unconventional plays.
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
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.
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.
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.
It would be a great feeling to hold a borehole in the palm of your hand, turn it around, look at the propagated fractures around it, and ask yourself: “ok, why don’t these two fracture wings propagate in the same plane?” This was my experience when I was playing with the glass blocks with deviated boreholes drilled in them at Geoconvention this year. The fractured blocks were the results of photoelasticity tests performed at University of Alberta trying to simulate fracture initiation and propagation induced by drilling. The results show how different stress states can lead to formation of different types of fractures such as bi-wing, en echelon, bottomhole, and petal (see Jia et al., 2015 for more details). As can be observed in the figures here, the method proves to be an excellent mean for teaching geomechanics, a discipline that severely suffers from the lack of tangible educational resources.