Copyright 2003, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the SPE European Formation Damage Confer-ence to be held in The Hague, The Netherlands 13-14 May 2003. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any posi-tion of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for com-mercial purposes without the written consent of the Society of Petroleum Engineers is prohib-ited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.

Abstract Compressive wellbore failure is a major contributor to sanding problems and casing collapse in many oil and gas fields. This type of failure occurs when the wellbore pressure exceeds the rock strength, typically in unconsolidated and weakly-cemented rocks or in consolidated rocks where stimulation programs may have removed or weakened the rock cement. The complex interrelationships between the physical factors that act on the wellbore to result in this type of failure makes the dynamic modeling of wellbore stability challenging. Most of the available models for predicting sanding and well col-lapse use openhole logs with very little success. The dynamic mechanical properties obtained from logs are typically too optimistic and hence require calibration to static measure-ments on selected core samples. It is, however, important to address issues relating to the representativeness and the rela-tive volumes of investigation of the core data. The associated uncertainties of the core and wireline log measurement scales and conditions must be considered for an effective model. This paper presents a systematic core-to-log integration tech-nique that enables the static mechanical rock properties meas-ured on rock samples to be used in the effective calibration of dynamic wireline data for mechanical log analysis. Relation-ships are developed between static and dynamic mechanical rock properties. Three different field examples are presented that demonstrate that rock strength, optimum drawdown and compressive fail-ure are related to reservoir rock quality and can be predicted by rock typing or flow units in sandstones. This work dem-onstrates that the flow units concept in combination with the mechanical logs may be used effectively as predictive tools for identifying weak zones that are prone to mechanical collapse and therefore should be avoided during completions. Some of the applications and benefits of the methodology shown in this paper include:

1. The validated model can be used to determine the

maximum drawdown for the onset of sanding. 2. The combined use of flow units and mechanical

properties can help avoid zones that are prone to me-chanical collapse.

3. Unwarranted sand control operations like gravel packing can be avoided, thereby optimizing field productivity and hence profitability.

Introduction Wellbore failure resulting in sanding and sand control is a very critical challenge in oil and gas production. It is critical to address this problem because some of the problems associated with sanding are: (1) high pressure drop due to sand fill in perforations; (2) erosion of down-hole and surface tubulars resulting in loss of well control; (3) separation and handling of sand in produced fluid and (4) subsidence and casing collapse. The following subsurface conditions may favor wellbore failure: (1) unconsolidated formations; (2) water break-through in weak to intermediate strength formations; (3) reservoir pres-sure depletion in relatively strong formations and (4) abnor-mally high lateral tectonics. One of the methods typically used to prevent excessive sand production in poorly consolidated reservoir rocks is gravel packing. Gravel packing is expensive and can cost up to 1 million dollars for high-pressure offshore wells. It restricts the wellbore and makes for workovers diffi-cult and expensive. It limits production from the wellbore due to high-pressure drawdown. Another method that is typically used including moderate to high permeability reservoirs (for formation damage remedia-tion and sand control) is frac-pack. This entails the placement of short, wide, highly conductive propped fractures. This method is very effective for removing formation damage when acidizing fails, and for sand control when gravel pack or other sand exclusion methods fail. Frac-pack is better than a conventional gravel pack because the reduction in pressure drawdown results in less potential for sanding. Despite the additional cost of the frac pack to the initial completion, a subsequent workover to clean out pro-duced sand and installation of a gravel pack is more expensive and sometimes impossible. Therefore, a reliable method to cost effectively predicts the need to gravel pack is the key to improving productivity, cost effectively. Many factors respon-sible for sanding problems must be understood. In addition to

SPE 82236

Calibrated Wireline Mechanical Rock Properties Model for Predicting and Preventing Wellbore Collapse and Sanding. Henry A. Ohen, SPE, Integrated Reservoir Solutions, Core Laboratories

2 SPE 82236

the intrinsic compressive strength of the rock, the conditions necessary for the sand to form stable arches around perfora-tions must be understood. Formation strength is controlled by mineralogical and textural attributes of the reservoir rock as well as the state of the con-fining stress. The type and proportion of fluid being produced is also a contributing factor. In field operations, it is typically observed that as the water-oil ratio increases, the amount of sand produced from an unconsolidated formation also in-creases. It can be concluded, therefore, that increased water production weakens the strength of the rock. Previously pub-lished laboratory work1 indicates that when the wetting phase saturation of two different fluids present in the formation is at or near irreducible, cohesive forces between grains help sus-tain a stable arch even after some sanding has occurred. Sev-eral papers have been published2-5 showing a correlation be-tween rock strength and dynamic elastic constant determined from sonic velocity and density measurements. Although there are other techniques available6, the most widely used log analysis technique for estimating formation strength was pre-sented over a decade ago4. This method is based on dynamic elastic properties, analysis of induced stress, and the theory of rock failure. The uniaxial strain model is typically used in the industry for sand control prediction and wellbore stability analysis. Mini-mum stress is predicted using the overburden and pore pres-sures along with Poissons Ratio. It has been shown7 that Pois-sons Ratio (PR) can effectively be determined from sonic and lithology logs that indicate the clay content of the reservoir rock. PR can also be derived from core measurements at simu-lated reservoir conditions. Apart from the issue of scale, the major limitation of core measurement is that PR is not typi-cally measured in non-productive horizons, whereas sonic logs are continued through the entire interval. For effective cali-bration, core measurement should also be performed in non-productive zones. Literature8-10 abounds with studies that indi-cate the need to establish criteria for core-sonic log integration. Review of Models for Sanding and Wellbore Failure Stein and Hilchie2 developed a model that relates potential for sanding to the shear strength of the formation. This model is limited in several ways including the fact that the effect of pressure depletion and increased water production is not in-cluded. The work reported in reference 3 is an empirical corre-lation based on log data only. It gave the threshold for sand as a ratio between shear modulus and bulk modulus as 8X1011. This also has the same drawback as the Stein and Hills model. The model reported in reference 4 is an improvement as it uses the Mohrs circle technique to relate failure to near-wellbore stresses. This method is typically referred to as the dry model because it is shown to be applicable only to cases of no water production. Critical review of literature indicates that the more effective model for sand prediction is one form of the Mohrs circle method or the other. Therefore to model the effect of water cut on the sand prediction models, it is neces-sary to understand the behavior of the rock with increased water saturation. It is believed that higher water cut requires higher shear strength11. Results of laboratory studies12 show that cohesive strength increases with increasing wetting phase

saturation up to 80%, above which there is a rapid decrease in cohesive strength. A previous study4 shows that cohesive strength can be related to the product of unixial compressive strength and bulk modulus. A particular study13 on Gulf Coast gas wells indicates that cohesive strength can be correlated to clay volume and bulk modulus. The cohesive strength depends on reservoir pressure, because as the reservoir depletes the shear stress increases. It may increase to the point that the formation will fail in shear. Therefore, any model used to pre-dict sanding in the life of a reservoir must be cognizant of res-ervoir pressure depletion to ensure that it stays within the fail-ure envelope. The point to be made here is that there is no model presented so far that can be used in all cases to predict onset of sanding. The efficacy of any method depends greatly on the type, amount and quality of pertinent data used. Sanding and well-bore failure are related to: (1) mechanical rock properties, (2) permeability and porosity, (3) lithological composition of the rock and clay content and (4) fluid saturation and capillarity. All these data must be obtained through the integration of wireline logs, with actual measurement on core samples to be used in any model of choice. Theoretical Basis We have used the Mohr-Coulomb analytical method with sys-tematic calibration of the input data. We have employed the dependency of rock mechanical properties on rock types in the form of hydraulic (Flow) units14. The input parameters into the model can be classified as (1) Mechanical Rock Properties and rock types (2) Reservoir pressure and fluid saturation, and (3) In-situ Stress Conditions Mechanical Rock Properties and Rock Types The mechanical properties of the rock that must be determined accurately through core-log integration include: (a) Poissons Ratio, (b) Youngs Bulk and Shear moduli and (c) Poroelastic or Biot constant ().

Poissons Ratio Poissons Ratio ( ) is the ratio of the lateral strain to longitu-dinal strain when a longitudinal stress is applied. Poissons Ratio for a homogeneous, isotropic and elastic rock is given as:

=1

25.0 2

2

DTCDTSDTCDTS

PR------------------------ (1)

Shear Modulus or Modulus of Rigidity

Shear Modulus (G) is the ratio of the shear strain to the ap-plied shear stress, which for a homogeneous, isotropic and elastic rock is given as:

221038.1

DTSXG B= -------------------------------- (2)

SPE 82236 3

Youngs Modulus The Youngs Modulus (E) is the ratio of tensile (or compres-sive) strength to tensile (or compressive) strain, which for a homogeneous, isotropic and elastic rock is given as:

)1(2 PRGE += ------------------------------------- (3)

Bulk Modulus Bulk Modulus (Kb) represents the ratio of the change in for-mation volume to the change in the average of the three prin-ciple stresses. For a homogeneous, isotropic and elastic rock it is given as:

= 22 341348.1

DTSDTCK Bb --------------- (4) Hydraulic (Flow) Units Only limited core measurements are typically performed for the calibration of mechanical rock properties. It is therefore necessary to find a systematic way of extrapolating these ex-pensive core measurements to formations or zones where they are not available. The concept of hydraulic units is used in this regard. A Hydraulic Unit is a zone that is continuous over a defined volume of the reservoir. It has similar average reservoir rock properties, which affect fluid flow in zones with similar bed-ding characteristics14. It has also been defined as the volume of the total reservoir rock within which geological and petro-physical properties that affect fluid flow are internally consis-tent and predictably different from properties of other rock volumes. It is therefore logical that Hydraulic Units Zona-tion can be used to identify zones of similar mechanical rock properties and infer potential for failure. In this paper we have used the procedures described previously to identify zones with similar mechanical rock properties so that, the Hydraulic Units Zonation can be used to infer failure.15, 16,17 In-situ Stresses The state of stress on an element of a reservoir rock with a borehole can be described by three orthogonal components: (1) vertical Stress (Z), (2) radial Stress (r) and (3) tangential Stress (). The components are given as follows:

)(2 21 += VZ --------------------------- (5)

WFP= 213 ---------------------------------- (6)

WFr P= ------------------------------------------------- (7) Where 1 and 1 are minimum and maximum horizontal stresses, respectively. The overburden stress, V , is typically calculated from density logs as follows:

D gdD0 ------------------------------------------------- (8)

With the assumption of uniaxial strain conditions, the two horizontal stresses are typically written in terms of the over-burden stress, reservoir pressure, Poissons Ratio, and Biot constant. Horizontal stresses are dependent on rock lithology and mineralogy through the dependency of Poissons Ratio. If we assume by definition that the two horizontal stresses are equal18, the horizontal stresses are as follow: For Medium to High Porosity Rocks The theoretical derivation in reference 7 was intended for the high porosity Texas Gulf Coast sandstone. In this case, the equation for the horizontal stress is given as:

)1

1(1

+== roH PP ----------------- (9)

For Low Porosity Rocks with Possible Micro Fractures The Anderson model was modified by Newberry et al19 for low porosity micro-fractured rock with the additional assump-tion that minifracture is formed perpendicular to the least prin-ciple stress, making =1 in the direction of least principle stress. This results in a transversely anisotropic model where:

)1

1(1

+== roH PP -------------- (10)

Biot Constant. Obviously, the Biot constant is critical in the analysis of the influence of pore pressure on rock deformation. It is therefore important to ensure it is obtained accurately. The Biot con-stant relates the extent of compressibility of the dry skeletal frame of a material like the rock relative to the rock material, which makes up the skeletal frame. The Biot Constrant is de-fined as:

)/(1 ssk KK= -------------------------------- (11) Prediction of rock failure and sanding must include the known value of Biot constant for accuracy. This constant has been typically obtained from empirical correlation. One of these models as proposed by Krief et al20 is shown below:

( )

=

111

3

---------------------------------- (12)

The Biot constant can be determined experimentally if we make the isotropic assumption. Hence, the influence of pore pressure on mechanical rock properties is dependent only on the isotropic component in the poroelastic model that relates stress, pore pressure, strain, and volume of fluid injected21. Hence:

Pr)/( Bp VV = -------------------------------- (13) One approach to determine Biot constant is described in refer-ence 20. Klimentos, et al have presented another approach,

4 SPE 82236

which is an experimental method based on laboratory acoustic measurements22. In this method, both the dynamic and static moduli of core samples are measured under vacuum. The vac-uum dry rock condition is necessary to represent the skeletal framework of the rock. The P- and S- waves thus measured are used to determine the bulk modulus of the dry skeletal framework of the rock. Mineralogical analysis on the rock is used to determine the bulk modulus of the rock matrix through individual mineral volume averages. The key to effective use of these experimental data is the abil-ity to correlate the experimental Biot constant to bulk modulus on a case-by-case basis by regression. Formation Failure Criteria (FFC) In order to determine the compressive failure condition, we have relied on the Coulomb criterion based on Mohrs circle. This criterion states that23: ( 0)tan 231 = UCS --------------------- (14) Where 1and 3 are major and minor effective stresses, re-spectively. Effective stress is given as a function of total stress as:

pTEff P = --------------------------------------- (15) Total or mean effective stress is estimated as:

3/)2( oHT P+= -------------------------------- (16) If we assume that both the minor and major effective stresses are equal, then the failure criteria is given as:

0)tan1( 2 = UCSEff ---------------------- (17) Finally failure criteria can be defined as:

0)tan1( 2 >= UCSFFC Eff ------------ (18) Angle of Internal Friction The angle of internal friction is very important to obtaining failure criteria and computation of critical drawdown pressure. The failure envelope from Mohrs circle analysis is controlled by two critical parameters: (1) initial shear strength and (2) angle of internal friction. It has been demonstrated that uncon-solidated rocks have lower angles of internal friction than con-solidated rocks, probably due to grain slippage. Experimental studies have shown that the angle of internal friction is related to porosity, as presented in reference number 4. Critical Wellbore Pressure Critical wellbore pressure, according to the Mohr-Coulomb failure criteria, is give as:

=

vv

vvP

Piryx

CW

115.01

cot*1

15.05.1

(19)

With the assumption that the two horizontal stresses are equal, we obtain:

=

vv

vvP

PirH

CW

115.01

cot*1

12/

--------- (20)

The maximum allowable drawdown pressure is then computed from the following equation:

)()( MaxPPMaxPW WR = ------------------------ (21) The initial shear strength, i, is typically used in critical pres-sure calculations and is obtained from empirical correlations between compressive strength and bulk modulus. The initial shear strength can be obtained from triaxial measurements on core samples and Mohrs circle analysis. As shown in the two examples presented later, several values of the initial shear strength were obtained from Mohrs circle analysis when cor-related to confining pressure, compressive strength of the rock, and bulk modulus. Examples of the application of the models The two-step calibration process described previously24 is recommended. Dipole sonic logs are often used to determine the compressional and shear wave velocities in reservoir rocks at frequencies between 10 kHz and 50 kHz and used to compute rock mechanical properties. Consequently, to be more useful, field dipole sonic logs should be calibrated to core-measured values. Therefore, there are two types of calibration needed for dipole sonic logs. The first calibration determines the direct correlation between sonic and dipole sonic velocities, which has a frequency-dependent dispersion effect. The second calibration compares dynamic values for mechanical rock properties to laboratory triaxial or uniaxial values. Mechanical Rock Properties Calibration Examples We present two examples to demonstrate the calibration of dynamic mechanical properties, corrected for ultrasonic-seismic frequency, to static triaxial mechanical properties.

Example A Figures 1, 2 and 3 demonstrate relationships between dy-namic and static mechanical properties from the Gulf of Mex-ico. The static Youngs Modulus varies from 0.09-0.36x106 psi, and the dynamic Youngs Modulus is about 18 times greater than the static Youngs Modulus. Both the dynamic bulk and shear modulus are an order of magnitude more than

SPE 82236 5

the static values. Figure 4 shows the compressive strength model defined by the static Youngs Modulus and clay vol-ume. Cohesive strength is defined by the bulk modulus, un-confined compressive strength, and clay volume as shown in Figure 5. All these equations make it possible to determine these mechanical rock properties as continuous curves. As shown in Figure 6, this example is a relatively weak forma-tion. The reason these rock samples are relatively weak can also be linked back to microscopic mineralogical attributes of the reservoir rock obtained on the samples shown in Table 1. The samples have low to moderate quartz content. Clay con-tent (detrital and authigenic) of the samples ranges from 21% to 57% of the whole rock as determined by XRD.

Hydraulic (Flow) Units Identification Example A The permeability and porosity were measured at 2000-psi stress condition and processed to determine the Reservoir Quality Index (RQI) for each plug. RQI embodies the varia-tion of the microscopic pore space attribute of the rock. Then, employing the Hydraulic Units (HU) Zonation technique, a transformation of RQI ranges into hydraulic units was per-formed. The porosity and permeability data from the key cored well were checked for random errors. The filtered per-meability and porosity data were then used as follows to ob-tain HU zonation: 1. Discrete values of flow zone indicators (FZI) were calcu-

lated from the available data using the following equation:

Z

RQIFZI = 2. Histogram of the discrete FZI was constructed to deter-

mine the number of observable populations based on the number of normal distributions.

3. Cluster analysis was performed using the numbers of units predicted from step # 2 to separate the samples into clusters.

4. Log-log plot of RQI versus porosity group z was made for the different cluster groups as shown in Figure 4.

Four hydraulic units were identified based on the data from the key cored well. The descriptive statistics (Table 2) of the FZI per hydraulic unit indicate that in each hydraulic unit, the difference between the mean and median values of the pa-rameters are minimal, which means that the rock properties can be averaged within these units with minimal errors.

Core-log Integration The logs were edited as necessary to remove spikes that are obvious errors rather than reflections of sand properties. The logs were checked for depth match relative to one another. For the results of integrated reservoir studies to be accurate, con-sistent, and comparable from well to well, multi-well log nor-malization was carried out on a logging run-specific basis for each well.

The porosity and permeability from core analysis, in digital form, for the wells were also loaded into the database and depth-shifted against the logs. Log porosity was interpreted from the density, neutron, and sonic logs. Core porosity was compared with log porosity to perform the depth match. Where available, core gamma and log gamma were also used to aid the depth-matching process. Cross plots of core porosity versus log-derived porosities for the key cored well were made to assess that match between the log and core porosities. The density porosity provided the best match with core porosity, and hence was used in the calculation that follows. The core and log data at same depths were extracted from sec-tions of the well and the core analysis (FZI) was put together with the corresponding depth-shifted, normalized and edited log attributes in order to train the logs in pattern recognition to recognize hydraulic units based on reservoir quality or to calculate flow zone indicator. The core-derived FZI was found, through a rank correction exercise, to co-relate with the edited and normalized GR and NMD (neutron minus density porosity) logs.

Neural Network Modeling Knowledge of log-rock relationships was used to train the neural network (NN) brain to learn the relationship between the core FZI and the selected log signatures. Then the network applied what it learned to generate FZI in the wells using the logs. Training examples were selected where the logs (GR and NMD) were fully resolved and the relationships between the logs are clearly seen. On achieving a satisfactory NN solution in the training well, that solution was taken to a confirmation well, which has the well sections where cores and logs were both present as in the key cored well. The NN model was ap-plied to each well individually to generate deterministic FZI in the other wells.

Example B Figures 7, 8 and 9 are relationships between dynamic and static mechanical properties for our second example from the Gulf of Mexico. The static Youngs Modulus varies from 0.21-1.44 x106 psi, and dynamic Youngs Modulus is about 5 times the static Youngs Modulus. This reservoir rock is of intermediate strength. Finally, the microscopic mineralogical attributes of the reservoir rock show why it is fairly strong. As shown in Table 3, the rock samples have moderate quartz con-tent. Clay contents (detrital and authigenic) of the samples range from 11% to 40% of the whole rock as determined by XRD. Figure 10 shows the compressive strength model defined by the static Youngs Modulus and clay volume for this reservoir rock. Cohesive strength is defined by the bulk modulus, un-confined compressive strength and clay volume in Figure 11. Again, all these equations make it possible to determine these mechanical rock properties as continuous curves. Results and Validation Figure 12 compares the failure criteria determined using dy-namic data to those using static data in example A. This figure also shows that the stable zones that add intervals that are less

6 SPE 82236

prone to failure correspond to the best hydraulic (flow) units. Figure 13 is a crossplot of the critical drawdown pressure de-termined from the dynamic models compared to the calibrated static model. Figure 14 compares the calculated compressive strength for the two methods. The well used in this example produced a lot of sand after completion, which resulted in cas-ing collapse. As shown, the dynamic model gives an erroneous impression that the interval that failed was stable when com-pared to the results of the calibrated static model, which indi-cates potential for collapse. A closer look at the zone of inter-est shows that although there are some strong intervals within the completed interval (approximately 9300ft and 9700ft), the laminated weak zones within and the weak zones above and below the interval caused the failure. This would have been avoided if the dynamic model were calibrated to laboratory measured static data as shown in figure 12. Two wells that failed due to different reasons are selected to demonstrate the importance of proper calibration in Example B. Figure 15 shows that well # 1 should have been selectively completed (in the 12650-12730 ft interval) to avoid the weak laminations. The perforations at 13343-13410 ft should have been avoided based on the calibrated model. Figure 15 also indicates that the dynamic model was not sufficient to make this decision. For the second well, shown in Figure 16, one can also see that the top two sets of perforations are in zones with a lot of red and few green laminations, hence it failed. The third set of perforations at the top are in stable zones but had casing collapse because of the weak formations above and below. The lower perforations have both red and green lami-nations but no record of sand failure had been recorded for this zone. Conclusions 1. The two-step calibration method when applied to dynamic

mechanical properties from wireline logs has the potential to predict sanding wellbore failure.

2. A properly calibrated Mohr-Coulomb failure criteria is an effective model to differentiate between stable and weak reservoir rock based on wireline log data.

3. The Hydraulic Units concept can be used in combination with mechanical logs as predictive tools to qualitatively determine potentially stable and weak zones in a well for effective completion strategy.

Recommendations The methodology and procedure detailed in this work should be used to determine a field-specific calibrated model for rock failure predictions in fields where sanding and potential rock failure is an issue. Nomenclature

PR = Poissons Ratio DTS = Shear Wave Travel Time DTC = Compressional Wave Travel Time PWF = Flowing Well Pressure UCS = Unconfined Compressive Strength P = Pressure FFC = Failure Criteria

PCW = Critical Wellbore Pressure FZI = Flow Zone Indicator HU = Hydraulic Units RQI = Reservoir Quality Index G = Shear Modulus B = Bulk Density E = Youngs Modulus Kb = Bulk Modulus z = Vertical Stress r = Radial Stress = Tangential Stress v = Overburden Stress H = Horizontal Stress

= Poissons Ratio Po = Overburden Pressure Pr = Reservoir Pressure = Biot Constant Ksk = Bulk Modulus of the Skeletal Frame Ks = Static Bulk Modulus = Angle of Internal Friction t = Total Stress PW = Drawdown Pressure

Acknowledgment The author would like to thank Core Laboratories for the per-mission granted to publish this manuscript. Additional thanks go to my collegues in Reservoir Technlogies Division of Core Laboratories and my dedicated assistant Mary Ann Cisneros for helping to put this paper together. Reference

1. Hall, C.D., Jr., and Harrisberger, W.H. Stability of Sand Arches: A Key to Sand Control, J. Pet. Tech. (july 1970), 821-829.

2. Stein, N and Hitchie, D. W: Estimating the Maximum Production Rate Possible from Friable Sanstones Without Using Sand Control, J. Pet. Tech. (Sept. 1972) 1157-1160; Trans., Aime, 253.

3. Tixier, M.P, Loveless, G. W, and Anderson, R. A., Esti-mation of Formation Strength Based on the Mechanical Properties Log, SPE Trans., 48, (1973)

4. Coates, G. R and Denoo, S.A. Mechanical Properties Pro-gram Using Borehole Analysis and Mohrs Circle, SPWLA 22nd Annual Logging Symposium, (June, 1981).

5. Barrow, D.C and Lasseigne, C. A, A Field Evaluation of the Mohrs Circle Technique for Predicting Sand Strength, SPE 13087 presented at the 59th Annual Technical Confer-ence and Exhibition held in Houston, Texas, September 16-19, 1984.

6. Nordgren, R. P. Strenght of Well Completions, 18th U.S. Sympossium on Rock Mechanics, Keystone, Co. (June, 1977).

7. Anderson, R.A, Ingram D.S. and Zanier A. M., Determin-ing Fracture Pressure Gradient from Well Logs, J. Pet. Tech., November 1973, 1269-1268.

8. Veatch, R. W. Jr. and Crowell, R.F.: Joint Re-seach/Operation Programs Accelerate Massive Hydraulic Fracturing Technology, JPT (Dec. 1982)1763-75.

9. Whitehead, W.S., Hunt, E.R., and Holditch, S.A.: Effects of Lithology and Reservoir Pressure on the In-Situ Stresses in the Waskom (Travis Peak) Field, Paper SPE 16403 pre-

SPE 82236 7

sented t the 1987 SPE/DOE Low Permeability Reservoir Sympossium, Denver, May 18-20

10. Holditch, S.A. et al.: The GRI Staged Fluid Experiment, SPEFE (Sept. 1988) 519-33

11. Ghalambor Ali et al: Predicting Sand Production in US Gulf Coast Gas Wells Producing Free Water, JPT (Dec. 1989) 1336-43;

12. Durrett, J.L. et al: Seeking a Solution to Sand Control, JPT (Dec. 1977) 1664-72

13. Weingarten, J.S. and Perkins, T.K. Prediction of Sand Production in Gas Wells: Methods and Gulf of Mexico Case Studies, SPE 24979 presented at the 87th Annual Technical Confenerec and Exhibition of SPE in Washing-ton D.C, October 4-7, 1992.

14. Amaefule J.O., Altunbay M., Tiab, D., Kersey, D.G., and Keelan, D.K.: "Enhanced Reservoir Description: Using Core and Log Data to Identify Hydraulic (Flow) units and predict permeability in uncored Intervals/Wells", paper SPE 26436, presented at the 68th Annual SPE conference and exhibition, Houston, Texas, October 3 - 6, 1993.

15. Rincone J.G, R. Delgado, H. Ohen, P. Enwere, A. Guerini, P. Mrquez,: Effective Petrophysical Fracture Characteri-zation Using the Flow Unit Concept-San Juan Reservoir, Orocual Field, Venezuela, SPE 63072.

16. Amaefule J.O., Altunbay M., Ohen, H, D.G., and Keelan, D.K A Hydraulic (Flow) Units-Based Approach for Pre-dicting Formation Damage in Uncored Interval/Wells Us-ing Core/Log Data, presented at the International Sympo-sium on Formation Damage Control, 9-10 February, 1994.

17. Ohen, A. H., Ajufo, A., and Curby, F.: A Hydraulic (Flow) Units Based Model for the Determination of Petro-physical Properties from NMR Relaxation Measurements, paper SPE 30626 presented at the 1995 SPE Annual Tech-

nical Conference and Exhibition held in Dallas, Texas, 22-25 October 1995.

18. Thiercelin, M.J., and Plumb, R.A, A Core-Based Predic-tion of Lithologic Stress Contrasts in East Texas Forma-tion, SPE 21847, presented at rge Rocky Mountain Re-gional Meeting and Low- Permeability Reservoirs Sympos-sium held in Denver, Colorado, April 15-17, 1991.

19. Newberry, B.M. Prediction of Vertical Hydraulic Fracture Migration Using Compressional and Shear Wave Slow-ness, paper SPE 13895 presented at the 1985 SPE Low-Permeability Gas Reservoir Sympossium. Denver, May 19-22.

20. Krief, M., et al. A Petrophysical Interpretation Using the Velocity of P and S Waves (Full-Wave form Sonic), The Log Analyst (November-December, 1990) 355.

21. Laurent Jerome et al, Pore-Pressure Influence in the Poroelastic Behavior of Rocks: Experimental Studies and Results, SP Formation Evaluation, June 1993, 117-122

22. Klimentos T. et al Experiemntal Determination of the Biot Constant: Application in Formation Evaluation (Sonic Porosity, Rock Strenght, Earth Stresses and sanding Predic-tions, SPE 30593, presented at the SPE Annual Technical Conference and Exhibition held in Dallas, USA, 22-25 October, 1995.

23. Svennekjaer, Manel Bratti, R. K; Rock Mechanics Appplied to Drilling An Operational Reviews, paper presented at the EUROC 98 held in Trandhein, Norway, 8-10 July, 1998.

24. Ohen, H. A., From Microscopic and Macroscopic Core Analysis Scale to Gigascopic Seismic Scale - Are we go-ing beyond the Realm of Reality?, presentation at the 26rd Annual SPE International Technical Conference and Exhi-bition in Abuja, Nigeria, August 5-7, 2002.

8 SPE 82236

Table 1: Mineralogy of the Rock in Example A

Table 3: Mineralogy of the Rock in Example B

Sample Depth (ft) Qtz Kspar Plag Cal Clay

101 8871.5 27 4 5 2 57 102 8875.0 40 6 9 3 37

103 8877.6 45 5 9 2 32 104 8886.8 61 6 11 3 18

105 8893.5 55 6 9 1 26

106 8898.8 44 6 9 19 17 107 8903.7 55 7 12 0.6 22

108 8910.1 46 6 11 0.4 31

109 8917.5 48 7 12 0.7 28 110 8923.1 53 7 10 1 25

111 8929.5 19 3 5 0.5 64

112 9537.5 23 2 8 9 55 113 9544.4 55 2 7 8 24

114 9547.2 51 1 5 16 23

115 9549.5 51 3 7 6 26 116 9551.2 48 2 6 17 20

117 9553.8 52 3 8 3 28

118 9558.3 46 2 10 2 36 119 9560.1 42 3 9 2 38

120 9565.8 50 2 10 9 25

121 9571.2 42 3 10 7 32 122 9575.5 39 2 10 6 38

123 8746R 44 5 9 1 36

124 8737 53 5 10 6 21

125 9209 45 6 11 0.5 33

Table 2: Descriptive Statistics of the Flow Units HU_1 HU_2 HU_3 HU_4 Mean 0.4702 0.1552 0.0824 0.0454 Standard Error 0.0617 0.0077 0.0029 0.0015 Median 0.4201 0.1501 0.0851 0.0433 Standard Deviation 0.2047 0.0230 0.0149 0.0073 Sample Variance 0.0419 0.0005 0.0002 0.0001 Kurtosis 0.2141 -0.1674 -1.1358 -1.2439 Skewness 1.0917 0.7606 -0.0072 0.3839 Range 0.6053 0.0673 0.0483 0.0221 Minimum 0.2554 0.1309 0.0596 0.0349 Maximum 0.8607 0.1982 0.1079 0.0571 Sum 5.1721 1.3968 2.1434 1.1343 Count 11 9 26 25

Depth Quartz K-Feldspar Plagioclase Calcite Fe-Dolomite Total Clay

(feet)

12723.4 41 4 15 1 1 36 12732.4 42 7 19 2 0 29 12741.4 44 6 27 8 1 14 12743.5 51 3 25 5 0 16 12752.5 53 5 20 11 0 10 12755.9 46 6 27 2 0 18 12765.6 44 6 16 1 0 32 12774.4 40 5 12 1 0 40 12777.6 52 5 22 5 0 16 13203.5 55 0 21 0 0 23 13208.0 57 0 25 1 0 17 13218.9 60 0 25 0 0 11 13221.0 55 0 30 0 0 15 13221.5 59 0 26 0 0 14 13225.6 55 0 25 3 0 17 13243.4 53 0 21 1 0 23

13252.5 49 0 19 1 0 29

SPE 82236 9

Figure 1: Static Young's Modulus (unconfined ) from Dynamic Bulk Modulus - Example A

ES = 0.0158ED2.7399

R2 = 0.8473

0.000.200.400.600.801.001.201.401.60

0 1 2 3 4 5 6

Dynamic Young Modulus (Mpsi)

Stat

ic Y

oung

Mod

ulus

(M

psi)

Figure 2: Static Bulk Modulus (unconfined ) from Dynamic Bulk Modulus - Example A

KS = 0.0209KD2.4192

R2 = 0.7943

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4 5

Dynamic Bulk Modulus (Mpsi)

Stat

ic B

ulk

Mod

ulus

(Mps

i)

Figure 3: Static Shear Modulus (unconfined ) from Dynamic Bulk Modulus- Example A

S = 0.2039S - 0.1165R2 = 0.8715

0.000.050.100.150.200.250.300.350.40

0 0.5 1 1.5 2 2.5

Dynamic Shear Modulus (Mpsi)

Stat

ic S

hear

Mod

ulus

(M

psi)

10 SPE 82236

Figure 4: Compressive Strength at Different Net Confining Stress- Example A

1000

10000

100000

1000 10000 100000

Measured Compressive Strength, PSI

Cal

cula

ted

Com

pres

sive

St

reng

th, P

SI EXP(exp(/39853)(5.7318ES0.04313+2.2344VCL-

Figure 5: Cohensive Strength at Different Net Confining Stress- Example A

0

200

400

600

800

1000

0 200 400 600 800 1000

Measured Cohensive Strength, PSI

Cal

cula

ted

Coh

ensi

ve

Stre

ngth

, PSI

=EXP(3.564(KSxCS)0.0533+1.464VCL-0.0944))

Figure 6: Flow Units Donation for Example A

0.001

0.01

0.1

1

0.1 1

Porosity Group

RQ

I HU_4

HU_3

HU_2

HU_1

SPE 82236 11

Figure 7 Static Bulk Modulus from Dynamic Bulk Modulus at Different Net Confining Stress

0.00

0.50

1.00

1.50

2.00

0 0.5 1 1.5 2

Measured Bulk Modulus, Mpsi

Cal

cula

ted

Bul

k M

odul

us,

Mps

i

KS=0.21831KD(EXP((/4508.4)2.42584))

Figure 8: Static Shear Modulus from Dynamic Shear Modulus at Different Net Confining Stress

0.00

0.50

1.00

1.50

2.00

0 0.5 1 1.5 2

Measured Shear Modulus, Mpsi

Cal

cula

ted

Shea

r M

odul

us, M

psi S=0.1675D(EXP((/4717.5)0.25083))

Figure 9: Static Young's Modulus from Dynamic Young's Modulus at different Net Confining Stress

0.00

0.50

1.00

1.50

2.00

0 0.5 1 1.5 2

Measured Young's Modulus, Mpsi

Cal

cula

ted

Youn

g M

odul

us,

Mps

i

ES=0.1675ED(EXP((/4637.2)0.185))

12 SPE 82236

Figure 10: Compressive Strength at Different Net Confining Stress- Example B

1,000.00

10,000.00

100,000.00

1000 10000 100000

Measured Compressive Strength, PSI

Cal

cula

ted

Com

pres

sive

St

reng

th, P

SI

EXP(exp(/36662)(45.5ES0.00944-36.272VCL-

Figure 11: Cohensive Strength at Different Net Confining Stress- Example B

0

200

400

600

800

1000

0 200 400 600 800 1000

Measured Cohensive Strength, PSI

Cal

cula

ted

Coh

ensi

ve

Stre

ngth

, PSI

=EXP(3.6378(KSxCS)0.0227+2.0469VCL-0.07321))

SPE 82236 13

FIG.12

14 SPE 82236

Fig. 14: Dynamic Versus Static Compressive Strength

Fig. 13: Comparison of Dynamic to Static Drawdown Pressures

SPE 82236 15

FIG. 15

16 SPE 82236

Fig. 15a: Comparison of Dynamic to Static Drawdown Pressures

Fig. 15b: Dynamic Versus Static Compressive Strength

SPE 82236 17

FIG. 16

18 SPE 82236

Fig. 16b: Dynamic Versus Static Compressive Strength

Fig. 16a: Comparison of Dynamic to Static Drawdown Pressures