Geomechanical modeling-workflow and Applications

This work aimed to present a detailed workflow for building a geomechanical model. For a case study, the workflow is then applied to a horizontal well X. The first step in building a geomechanical model is gathering data regarding well information (tubing, casing, deviation...), geological information (type of fault, permeability, reservoir radius, skin...), logs data (density, resistivity, sonic, caliper...), in-situ test data (leak-off test, formation test,...) and core data (tensile strength test, fracture toughness test, tri-axial test...). The second step is to build the geomechanical model using data analysis so that information about state of stress (vertical and principal horizontal stresses, pore pressure, concentration stress around wellbore) and rock mechanical properties (unconfined compressive strength, tensile strength, fracture toughness, Young modulus, Poisson ratio) can be determined. Moreover, the differences in data analysis for vertical and horizontal wells were also mentioned in this work. Furthermore, it is evident that the more data we get, the more accurately a geomechanical model can be built. However, in reality, not all necessary data can be obtained, so this work also explained how to draw the most information from available data so that we can minimize the number of assumptions and uncertainties. An accurate geomechanical model is very essential for others works such as well bore stability or performance prediction of a well stimulation technique. The case study of this work presented the geomechanical modeling for the well X. The paper then presented the application of geomechanical modeling for the Evaluation of High Energy Gas Fracturing performance as well as for Sand Control analysis.


INTRODUCTION
Geomechanics in petroleum industry deals with issues in geosciences related to rock mechanics.Geomechanics is used to predict important parameters such as in-situ stresses (vertical and principal horizontal stresses, pore pressure, concentration stress around wellbore) and rock mechanical properties (unconfined compressive strength, tensile strength, fracture toughness, Young modulus, Poisson ratio).In case of necessary, geological information (type of fault, permeability, reservoir radius, skin…) can also be included in geomechanics study.
Geomechanical evaluation is useful for the study of wellbore stability as well as for predicting the performance of reservoir stimulation works (for example, hydraulic fracturing/high energy gas fracturing).As these works demand considerably high in financial support and in time, having an accurate geomechanical model is therefore essentially important in petroleum industry.
Building a geomechanical model requires different scales data collection: from large scale, such as world stress map project [1], [2], reservoir/regional scale (stress map, type of fault…), to well scale, such as logs data (density, resistivity, sonic, caliper…), and to core scale, such as core test (tensile strength test, fracture toughness test, tri-axial test…).Multiple scales data collection is necessary because stress magnitudes and orientation are frequently not homogeneous on a reservoir scale, and can be substantially modified by presence of faults as well as lithological changes and contrast in rock mechanical properties [3], [4].In some faultcontrolled reservoirs, local stress reorientations of up to 90 o relative to the regional trend have been reported [5], [6].In such cases, inference of local in situ stress orientations from regional scale maps would inevitably lead to an incorrect pre-drilling prediction.Regarding local stresses, they vary in function of depth and type of rocks, as well as type of fault and type of pore pressure (normal or abnormal), so core test data is also needed to calibrate the geomechanical model.
In this paper, we present a detailed workflow to build and calibrate geomechanical models.We also discuss some essential differences in geomechanical models of horizontal and vertical wells.As we explained in the previous paragraph, the accurate level of a geomechanical model depends on the available data.In reality, not all necessary data can be obtained, so we also explain in this paper how to draw the most information from available data so that we can minimize the number of assumptions and uncertainties.Subsequently, the workflow is applied to a horizontal well X.Then, the gemechanical model freshly built is used to predict the well stimulation's performance using High Energy Gas Fracturing.Another application is to study the Sand Control.

GENERAL WORKFLOW IN BUILDING A GEOMECHANICAL MODEL
The general workflow in building a geomechanical model consists of two main steps: 1) Data acquisitions & Analysis; 2) Geomechanical modelling.This workflow can be viewed in Figure 1.
In data acquisition step, we must collect as many data as possible because the more data is available, the less uncertainties and assumptions we have to make, hence the more accurate the geomechanical model is.However, in reality not all necessary data can be obtained, so we must know how to draw the most information from available data.Therefore, we present in Table 1 different possible ways to determine in-situ stresses and rock mechanical properties, so that the user can decide which way to follow depending on the available data.Let us take the Fracture toughness for example.The most accurate information should be the core test data.However, the core collection as well as the test cost considerably high and pose difficulties in operation.Hence in many case we do not have the core test data for fracture toughness.In this case, if we have Young modulus of the rock or sonic logs, empirical correlations can be used to determine fracture toughness (KIC -MPa.m -1/2 ) according to Whittaker et al.And in case we do not have any of above information, the fracture toughness can still be deduced from type of rock if we have this kind of information.Certainly the value determined in this way will be the least accurate.Hence, in order to have an accurate geomechanical model, it is always better to have in-situ updated information, such as core test, formation test and logs data.The well X schematic is presented in Figure 2 which shows that the horizontal length is about 1818 ft.The data acquisition is summarized in Table 2.It is worthy noted that the Table 2 summarized only the available information that was useful for geomechanical modeling.

Data analysis & Geomechanical parameter determination
We can remark that some critical test data are missing, such as the test for pore pressure (XPT), for minimum & maximum horizontal stresses (LOT, XLOT, Minifrac, Caliper), and for rock mechanical properties (Core tests).Moreover, the density log is missing so the determination of vertical stress will be less accurate.
One more important remark is that the well is horizontal, so the stress must be calculated using TVD.Unfortunately the MD versus TVD is not available, so we had to use these following assumptions: -The well is perfectly vertical until MD 2036 ft (Figure 2) -From MD 2036 ft to MD 2635 ft, the well is curved in circle with an arc length of 2635-2036 = 599 ft, the angle is 90 o , so the radius is 599 ft / (π/2) = 381 ft -From MD 2635 ft to 4853 ft the well is perfectly horizontal The vertical stress σv was calculated from assumption on type of rock (limestone).The density of limestone in this region was about 2.5 g/cc.
The pore pressure (Po) was calculated using resistivity log basing on Eaton's method: The hydrostatic pressure Phydrostatic was about 0.46 psi/ft.
The subscripts n and log refer to the normal and measured values of resistivity (R).The exponents shown in the Equation 5are typical values that are often changed for different regions so that the predictions better match pore pressures inferred from other data.In our case we do not have other data so we assumed the exponent factor to be 1.2 as given by Eaton method.The normal values of R is determined using trend-line method.However, the major problem with all trend-line methods is that the user must pick the correct normal compaction trend.Sometimes there are too few data to define the Normal Compaction Trendline (NCT), sometimes the data are too noisy to draw a correct NCT, which is our case.Hence, in order to determine NCT, one of the possibilities is to use the Equation 6given by Zhang [10]: where R0 is the resistivity in the mudline; b is the slope of logarithmic resistivity normal compaction trendline; Z is the TVD below the mudline.We do not have Formation test data so we could not calibrate the pore pressure model, hence we assumed b to be equal to 0.000034 [10].It should be noted that the pore pressure in the formation near the wellbore is affected by drilling induced stresses.Therefore, in order to obtain the formation pore pressure the deep resistivity is needed for the pore pressure calculation.In our case, the resistivity log is available but we do not have the R0 (resistivity in the mudline).Hence, we make assumption that the pore pressure is equal to the hydrostatic pressure (assumed to be about 0.46 psi/ft).
The minimum horizontal stress was calculated according to Equation 7[4]: 7] where σ T is tectonic stress which was taken to be 0; v is Poisson ratio which was taken to be 0.3 for limestone.The Equation 7 is applied only to Normal fault, which is our case.For other types of fault, we can find suitable empirical equations in [4].
The maximum horizontal stress might be calculated from Shmin, pore pressure, combined with Drilling-Induced Tensile Fracture or with Wellbore failure analysis (Breakout), but this is not possible in our case due to lack of data.In this case, we determined the maximum horizontal stress using Anderson's theory: At each depth, the range of possible values of Shmin and SHmax are established by (i) Anderson faulting theory (which defines the relative stress magnitude), (ii) the fact that the least principal stress must always exceed the pore pressure (to avoid hydraulic fracturing) and (iii) the difference between the minimum and maximum principal stress which cannot exceed the strength of the crust (which depends on depth and pore pressure).An example of Anderson's graph for normal fault is given in Figure 3.
Due to lack of core test data, the fracture toughness mode I was taken to be 0.99 MPa.m - 1/2 (900 psi.in -1/2 ).This value was the test result for limestone taken from paper of Schimdt [11].
The tensile strength was calculated from Fracture Toughness mode I using empirical correlation of Whittaker et al.We now calculate the minimum horizontal pressure Shmin using Equation 7of Zoback [4] in which σ T (tectonic stress) was assumed to be 0 and v (Poisson ratio) was assumed to be 0.3 for limestone.For cross check, the Shmin is also determined from Anderson's graph for normal fault (Figure 3).The minimum horizontal stress is determined to be about 1672 psi at 2417 ft TVD (this is the depth where mechanical well simulation is intended to be done).In the same manner, the maximum horizontal stress is determined to be about 2000 psi at 2417 ft TVD.At this depth, the fracture toughness mode I for limestone was taken to be 0.99 MPa.m -1/2 (900 psi.in -1/2 ) [11].Hence, the tensile strength is about 7.78 MPa.
The concentration stress around the wellbore is calculated for a horizontal well.We need to do an axis transformation.Then, the tangential stress at the borehole wall varies between the maximum value σθ,max = 3σH − σh − pw and the minimum value σθ,min = 3σh − σH -pw [3].We remark that the maximum and minimum values of concentration stress for deviated wellbore are different from the values for a vertical wellbore [4], which are : the maximum value σθ,max = 3σH − σh -2.pw and the minimum value σθ,min = 3σh − σH -2.pw.This is a very important point to be taken into account for deviated and horizontal wells.These equations show that for the same values of pore pressure and maximum and minimum principal horizontal stresses, a horizontal well sustains higher concentration stress than vertical well.Another difference between deviated and vertical wells is the direction for perforation and/or for mechanical well stimulation (fracturing).For vertical well, it is well known that the perforation direction should be the one of maximum principal horizontal stress.However, it is not the same for horizontal well where the perforation direction should be determined in function of the type of fault and of the direction of the well.The same remark was mentioned in the literature for the geometry development of fractures induced by hydraulic fracturing.These discussion points are out of scope in this paper so we mention here only the remarks.

APPLICATION OF GEOMECHANICAL MODEL FOR PREDICTION OF HIGH ENERGY GAS FRACTURING PERFORMANCE
The geomechanical model built was then used to predict the High Energy Gas Fracturing performance for the well X.The HEGF is a well-stimulation method based on solidpropellant, capable of generating multiple fractures in the reservoir rock when the proper energy-time profile is applied to the wellbore.Such multiple fractures networks have a high probability of intersecting natural fractures and therefore increase the permeability of the near wellbore region.However, the HEGF job cost considerably high and therefore its performance must be evaluated before realizing.
For a rectilinear fracture, the minimum pressure required to extend the fracture is: [Equation 9] With KIC is fracture toughness, σ is the minimum value of concentration stress around wellbore and XL is the fracture length.
According to Stoller [12], the fracture volume and fracture width are: With v is Poisson ratio, E is Young modulus, Kn and Mn are empirical constants depending on the number of fractures, H is fracture height (assumed to be the reservoir thickness).From the geomechanical model determined for the well X in the previous section, we determined the fracture length after a HEGF job.The result of fracture length presented in Table 3 showed good accordance with litterature results [13].
Table 3. Prediction results of High Energy Gas Fracturing performance

APPLICATION OF GEOMECHANICAL MODEL FOR SAND CONTROL
Another application of this geomechanical model is to study the Sand Control.The sand production in reservoirs is mainly driven by: 1) Depletion-induced stress path causing changes mainly in horizontal stresses; 2) Failure of mainly sandstones apart from interbedded nondepleting shales; 3) Perforation failure; and 4) Shear failure due to high flowrate.
Sand production can causes serious problems to the production (e.g.erosion of downhole and surface equipment, accumulation of sand in downhole and surface equipment, formation collapse), hence the best safeguard is to integrate the sand production risk assessment in the field development planning study, so different sand control scenarios can be prepared.The TWC can be related to UCS by empirical correlations.For example: for moderate to very strong sandstones: TWC = 80.8765 x UCS 0.58 [Equation 13] and for very unconsolidated sandstones: TWC = 37.5 x UCS 0.6346  [Equation 14] We can calculate the Critical Drawdown Pressure as following: CDP is the maximum drawdown to be in the free sand production.If the drawdown is higher than CDP, sand will be produced.

And the Critical Bottomhole Flowing
Pressure is: 20] For the case study, we analyse the sand production prediction for a well Y with below geomechanical parameters (Table 4).For equations 13 & 14 to estimate the TWC, the UCS must be known.Normally, the UCS can be determined from sonic log according to the following equation: UCS = 838825*e -0.057Dt [14] [Equation 21] With Dt is the Compressional Wave Transit Time (μs/ft).
However in reality many times the sonic log is not available.For the well Y, we estimate the value of UCS for limestone to be ranged from 8000 to 10000 psi.The UCS sensitivity analysis is presented in Figure 7.We remark that: -Sand-free drawdown at initial reservoir pressure 8000 psi -Can be produced sand-free with a constant drawdown of 5000 psi until the reservoir depletes to 6000 psi -For reservoir pressure under 6000 psi, we can still have sand-free production but the drawdown must be adjusted -No sand-free production for reservoir pressure under 2300 psi which should lead to well abandonment The well trajectory sensitivity analysis is presented in Figure 8.We remark that sand-free production zone becomes smaller when the well becomes more deviated.

CONCLUSIONS
This paper presented: 1) General workflow for building a geomechanical model; 2) Detailed data acquisition with different kinds of data; 3) Detailed data analysis with different ways to determine geomechanical parameters so that in case of data missing the geomechanical model can still be built.Hence, the number of assumptions and uncertainties can be reduced; 4) Application of geomechanical modeling in HEGF study and Sand Control analysis.

Figure 2 .
Figure 2. Schematic of the well X MPa and KIC in MPa.m -1/2 Young modulus & Poisson ratio were calculated from Fracture Toughness mode I using empirical correlation of Whittaker et al. [7]: KIC = 0.336 + 0.026.E with E is GPa and KIC is MPa.m -1/2 .

Figure 3 .
Figure 3. Variation of stress magnitudes with depth in normal faulting stress regimes for hydrostatic conditions [4]

Figure 4 .
Figure 4. Fracture geometry.We can see clearly that the geomechanical modeling is heavily involved in these steps.The

Figure 5 .
Figure 5. Rock failure occurs when stress exceeds strength

Table 1 .
Building a geomechanical model using different kinds of data.

Table 2 .
Available data useful for geomechanical modeling of the well X.

Table 4 .
Geomechanical model of the well Y