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Module C -1: Stresses Around a Borehole - I

Module C -1: Stresses Around a Borehole - I. Argentina SPE 2005 Course on Earth Stresses and Drilling Rock Mechanics Maurice B. Dusseault University of Waterloo and Geomec a.s. Common Borehole Stability Symbols. s 1 , s 2 , s 3 : Major, intermediate, minor stress

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Module C -1: Stresses Around a Borehole - I

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  1. Module C -1: Stresses Around a Borehole - I Argentina SPE 2005 Course on Earth Stresses and Drilling Rock Mechanics Maurice B. Dusseault University of Waterloo and Geomec a.s

  2. Common Borehole Stability Symbols • s1,s2,s3: Major, intermediate, minor stress • Sv, Sh, SH: Total earth stresses, or Sv, Shmin, SHMAX, or sv, shmin, sHMAX • sr, sq: Radial, tangential, borehole stresses • sr, sq, sv, shmin, sHMAX, etc…: Effective stresses • r, ri: Radial direction, borehole diameter • po, p(r): Initial pressure, p in radial direction • MW, pw: Mudweight, pressure in borehole • E, n: Young’s modulus, Poisson’s ratio • f, r, g: Porosity, density, unit weight • k: Permeability • These are the most common symbols we use

  3. Terminology and Symbols Problems • Often, the terminology and symbols used are confusing and irritating • This complexity arises because: • The area of stresses and rock mechanics is somewhat complex by nature • The terminology came from a discipline other than classical petroleum engineering • There is still some inconsistency in symbology, such as Sh, Sh, Shmin, sh, all for shmin … • We will try to be consistent • Please spend the time to understand • Physical principles are the most important

  4. Other Conundrums • How do we express stresses? • As absolute stresses? As stress gradients? As equivalent density of the overburden? As equivalent mud weights? • e.g. PF = 18 ppg means 18 pounds per US Gallon is the fracture pressure at some (unspecified) depth (fracture gradient = (3/z). • e.g. shmin gradient is 21 kPa/m (or 21 MPa/km) • e.g. The minimum stress is 2.16 density units • e.g. shmin is 66 MPa (at z = 3.14 km depth) • All of these are the same! (or could be) • Which method is used usually depends who you are talking to! (Drillers like MW…)

  5. The Basic Symbols, 2-D Borehole • Far-field stresses are natural earth stresses and pressures, genera-ted by gravity, tectonics… • Borehole stresses are generated by creation of an opening in a natural stress field • Far-field stresses: scale: 100’s of metres • Borehole stresses scale: 20-30  ri (i.e. local- to small-scale) sHMAX Far-field stress shmin po s‛q s‛r ri q r pw Borehole stress

  6. Important to Remember… • sq is the tangential stress, also called the hoop stress, you will see it repeatedly referred to in these terms • sq lies parallel (tangential) to the wall trace • The magnitude of sq is affected by: • In situ stresses • MW and cake efficiency • Temperature and rock behavior • It is the most critical aspect of the stress condition around a borehole… • High sq values lead to rock failure • Lower sq values usually imply stability

  7. Borehole Stability Analysis Concept • First, we need stresses around the borehole… • In situ stresses are vital • Δp, ΔT, chemistry affect these stresses • Mud cake efficiency • In some cases, rock properties are also needed • Then, we must compare the maximum shear stress with the rock strength… • We need to know the rock strength • We need to know if the rock has been weakened by poor mud chemistry and behavior • If matrix stress exceeds strength, we say the rock has yielded (or “failed”)

  8. Plotting Stresses Around a Borehole Far-field stresses smax s sq smin Vertical borehole smax smin sr pw = 0 radius Vertical borehole • Usually, we plot , r values along one or the other of the principal stress directions

  9. Stresses Around a Borehole • One Dimensional Case: • A borehole induces a stress concentration • Two- and three-dimensional cases are more complicated (discussion deferred) • Stress “lost” must be redistributed to the borehole flanks (i.e.: s concentration) Initial stress (F/A) (F/A = stress) F F F F (2F/A) High sq near the borehole, but low sr! F = force, A = Area, F/A = stress

  10. Stress Redistribution • Around the borehole, a “stress arch” is generated to redistribute earth stresses Everyone carries an equal load (theoretical socialism) In reality, some carry more load than others (higher ‛ near the borehole wall) Far away (~5D): ~no effect elastic rocks have rigidity (stiffness) “lost” s “elastic” rocks resistribute the “lost” stress D These guys may “yield” if they are overstressed

  11. Stresses “Arch” Around Borehole • The pore pressure in the hole is less than the total stresses • Thus, the excess stress must be carried by rock near the hole • If the stresses now exceed strength, the borehole wall can yield • However, “yield” is not “collapse”! A borehole with yielded rock can still be stable… shmin circular opening, pw sHMAX

  12. Arching of Stresses load arches lintels stress arching

  13. Shear Stresses • Shear stress is the cause of shear failure • The maximum shear stress at a point is half the difference of 1 and 3 • max = (‛1 - ‛3)/2, or (‛ - ‛r)/2 in the figure s sq Vertical borehole smax smin sr pw = 0 radius Vertical borehole

  14. Assumptions: • The simplest stress calculation approach is the Linear Elastic rock behavior model • This behavior model is very instructive • It leads to (relatively) simple equations Symbols used Far-field stress smax sq smin sr q ri r Known as the “Kirsch” Equations pw = 0

  15. Comments • Note that the equations are written in terms of effective stresses (sq, sr, ‛min…), with no pore pressure in the hole • Far-field effective stresses are the earth stresses, and they have fixed directions • sq, sr can be calculated for any specific point (r, q) around the borehole, for r  ri • Later, one may introduce more complexity: T, p(r), non-elastic behavior, and so on… • These require software for calculations; various commercial programs are available

  16. Calculations with In Situ Stresses • For a vertical borehole, the least critical condition is when ‛hmin = ‛HMAX = ‛h • ‛]max in this case = 2· ‛h if pw = po • However, we can still get rock yield! • However, in most cases, especially in tectonic regions and near faults… • The stresses are not the same! • This means that the shear stresses are larger around the borehole after it is drilled • This means that rock yield is more likely! • Borehole stability issues are more severe • Lost circulation more critical

  17. What is a Linear Elastic Model? Stress-strain plot σ‛ – stress (σ‛1 – σ‛3) E = Ds/De = Young’s modulus εa – axial strain • The simplest rock behavior model we use… • Strains are reversible, no yield (failure) occurs • Linear relationship between stress & strain • Rock properties are the same in all directions σ‛a = σ‛1 σ‛r= σ‛3 σ‛a

  18. Lessons from the Elastic Model - I • Even in an isotropic stress field (e.g. shminsHMAX for a vertical hole in the GoM), shear stress concentration exists around the hole • This can lead to rock yield. How to counteract? • We can partly counteract with mud weight • E.g.: if pw = shmin = sHMAX = sh (i.e.: MW = sh/z) • If the filter cake is perfect (no Dp near hole) • In practice, this is not done: if MW = sh/z, we are at fracture pressure & drilling is slower! • Higher MW reduces the magnitude of the shear stress, which reduces the risk of rock yield, but increases LC risk, slows drlg…

  19. Lessons from the Elastic Model - II • Fracture breakdown pressure is calculated to be Pbreakdown = 3σ’hmin - σ’HMAX + po • In practice, this is not used for design • Fracture propagation is Ppropagation = shmin, also taken to be PF (fracture pressure) for planning of MW programs • This is often taken to be MW]max • MW is usually maintained to be less than shmin • In practice, it is often possible to use some methods to “strengthen” the borehole • This allows drilling somewhat “overbalanced”, when pw > σhmin, (this must be done carefully!)

  20. Borehole Stresses if shmin sHMAX σ σ HMAX HMAX σ σ hmin hmin • Here, we plot the tangential stress, s‛q • Higher stress difference is serious! It gives rise to highers‛q values. Rupture?? σHMAX σHMAX Calculated from Kirsch equations, along principal stress directions σhmin 3.2·σ 2·σhmin σhmin hmin pw pw 2σhmin 1.6·σ hmin ( = 1.4) ( = 1.0) Far-field stresses, shmin, sHMAX, are: shmin – po, sHMAX – po wellbore pressure pw assumed to be equal to po Sing06.021

  21. High sHMAX - shmin Cases (Tectonic) = 3.0) ( = 2.0) ( σ σ HMAX HMAX σ σ hmin hmin • It gets worse in tectonic cases! • When shmin- sHMAX is large, the borehole wall in the sHMAX direction is in tension! Induced fractures can be generated during pw surges σ σ HMAX HMAX σ sq ~ 8σ hmin σ pw sq ~ 5σ hmin hmin pw hmin σ hmin Sing06.022 *Note: here, borehole pressure, pw, is assumed = po

  22. Plot of the Tangential Stresses • Here, σθstressesat the wall (ri) are plotted as a function of θ • Note the symmetry +90° σθ(ri) σHMAX rw θ 0 σHMAX -90° Refer to paper by Grandi for details

  23. Borehole Wall Stresses (@r = ri) • Now, introduce effective stresses: e.g. symbols  for total, s for effective • Maximum stress at the borehole wall: σq]max = 3·σHMAX - σhmin – po (total stresses) sq]max = 3·σ’HMAX - σ’hmin (effective stresses) • Minimum stress at the borehole wall: σq]min = 3·σhmin - σHMAX - po (total stresses) s’q]min = 3·σ’hmin - σ’HMAX (effective stresses) • For a general 3-D solution for inclined wellbores: use a software solution (big equations!)

  24. Preliminary Comments… s radius • Creation of a borehole:  high tangential stresses (sq), low radial stresses (sr) • The larger sHMAX - shmin, the higher sq is (in the direction of shmin), the lower sq is (in the direction of sHMAX) • Radial effective stress (sr) is low near the borehole wall, zero right at the wall sq pw = 0 sr

  25. More Preliminary Comments… • If both stresses are equal (sh) and MW = po: at borehole wall: sq = 2sh, and sr = 0 • If sHMAX – shmin is large, sq is increased, and sr doesn’t change too much • This greatly increases the shear stresses • These shear stresses are responsible for failure of the rock, breakouts, sloughing… • How do we control this? • High effective mud weights reduce this • Mud cooling shrinks rock, reduces stresses • Avoid shale swelling, promote shale shrinkage

  26. Mud Weight Effect (equal s case) sq Assume sHMAX =shmin= s sr pw = 0 s s s radius radius radius Here, we assume for simplicity that we have “perfect” mud cake, and that the pore pressure in the rock is zero sq sr pw = 0.3s sq sr pw = 0.8s

  27. Let’s Include Pore Pressures… s Mud pressure - pw sq Assume sHMAX =shmin= s sr Pore pressure - po pw = 0.6s perfect cake radius Positive support force = pw – po is applied in the case of a perfect mud cake: this is a strong stabilizing force because it increases confining stress, this will be discussed later, when we introduce rock strength Much of what we do in mud chemistry and MW management is to try and keep a positive support force right at the wall. This acts like a liner in a tunnel, keeping the rock from deteriorating and reducing the shear stresses. If it is lost by poor cake…, deterioration can be expected, especially in shale.

  28. Filter Cake Efficiency • The better the filter cake, the better the support pressure on the borehole wall • Support pressure = pw - pi • If there is poor filter cake, support pressure on a shale may be almost zero! • This support pressure is a true effective stress that is acting in a radial outward direction, holding rock in place! • In WBM in shales, the support pressure tends to decay with time! • Soon after increase in MW – good stability • After some time (days, weeks), sloughing can start again because support p decays

  29. Horizontal vs. Vertical Wellbore? • σv = 0.9 psi/ft, σh = 0.6 psi/ft, p = 0.4 psi/ft Vertical Hole In non-tectonic systems (shmin ~ sHMAX) vertical holes are subjected to lower shear stresses; they are generally more stable than horizontal holes sq = 0.4 psi/ft 0.2 0.2 Stress State Horizontal Hole sv = 0.5 psi/ft 0.5 sq = 0.1 psi/ft, top, bottom 0.2 sh = 0.2 psi/ft sq = 1.3 psi/ft, sides sh = 0.2 psi/ft

  30. Tectonic Stress Conditions Vertical well 0.1 2.7 2.7 0.1 This orientation is the best one for this case, showing the importance of knowing the in situ stresses sv = 0.5 psi/ft Horizontal well aligned with minimum stress, hmin 2.5 shmin = 0.3 psi/ft 0.5 0.5 Horizontal well aligned with minimum stress, HMAX 1.2 2.5 sHMAX = 1.0 psi/ft 0.4 0.4 Vertical effective stress = 0.5 psi/ft Min. horizontal effective stress = 0.3 psi/ft 1.2 Max. horizontal effective stress = 1.0 psi/ft

  31. TABLE 1 Stress at borehole wall (σ’θ) in a tectonically active area (Compressive stresses are +ve; Tensile stresses are -ve) Depth of investigation is 5,000 ft Maximum Stress Minimum Stress (σθ]MAX) (σθ]min) Hole No. Configuration Gradient Magnitude Gradient Magnitude ( psi/ft) ( psi) ( psi/ft) ( psi) 1 Vertical 2.7 13,500 -0.1 -500 Parallel to 2 minimum 2.5 12,500 0.5 2,500 horizontal stress Parallel to 3 maximum 1.2 6,000 0.45 2,000 horizontal stress

  32. 3-Dimensional Borehole Stresses Borehole radial, axial & tangential stresses, sr, sa, sq F Y F, Y are dip and dip direction (wrt x) of the borehole axis x, y, z are coordinates oriented parallel to s1, s2, s3 s1, s2, s3are the principal total stress magnitudes po is the pore pressure x Effective stresses: s1 = s1 - po s2 = s2 - po s3 = s3 - po s2 y s1 po s3 Almost always, principle stresses can be taken as  and  to the earth’s surface z

  33. What About the Axial Stress?? • Axial stress, sa, acts parallel to the hole wall,  to sr, sq • Usually ignored in borehole stability • However, if sa is very large compared to sr & sq, it can also cause yield • More sophisticated analysis req’d • Almost always, using the hole angle and azimuth, we do the following: • Determine maximum and minimum stresses in the plane of the hole • Carry out a 2-D stability analysis sr, sa, sq

  34. The Best Well Orientation • In a relaxed (non-tectonic) basin, sv > shmin ~ sHMAX, vertical wells are the most stable • In a tectonic basin, an estimate of the stresses is essential; for example: • If sHMAX > sv > shmin, we still have to know the specific values to decide the best trajectory • If sHMAX = 0.7, sv = 0.5, shmin = 0.4 psi/ft, a horizontal well parallel to sHMAX is the best • If sHMAX = 0.7, sv = 0.6, shmin = 0.4 psi/ft, a well parallel to shmin is likely the best • Careful Rock Mechanics analysis is best • +0ther factors: fissility, fractures…

  35. Stresses and Drilling sv sHMAX ~ sv >> shmin To increase hole stability, the best orientation is that which minimizes the principal stress difference normal to the axis 60-90° cone sHMAX shmin sv Favored hole orientation sv Drill within a 60°cone (±30°) from the most favored direction sHMAX sHMAX shmin shmin sHMAX >> sv > shmin sv >> sHMAX > shmin

  36. “Showing” the Best Trajectory sv sHMAX • This is a polar plot of “ease of drilling” • Related to magnitude of shear stress on wall • This is based in situ stress knowledge • In this example, a horizontal well, W to E, seems to be “easiest” • A horizontal well N to S is the worst (all other factors being equal) shmin

  37. Typical Troublesome Hole (GoM) 14 14 ¾” ¾” x 17 x 17 ½” ½” 17 17 ½” ½” x 20 x 20 ” ” 16 16 ” ” Liner Liner 13 3/8 13 3/8 ” ” 16.00 15.00 14.00 Pore pressure PP MWmin Lade 13.00 shmin Sh Stress, pressure in ppg sv Sv 12.00 Planned Casing Planned Csg Actual Casing Actual Csg 11.00 Drill MW Drill MW MW to Keep Hole Open MW to keep hole open 10.00 9.00 8.00 Depth in feet 3000’ 4000’ 5000’ 6000’ 7000’ 8000’ 9000’ 4960 Stuck Pipe: no rotation, no circulation Increase MW to get out of hole Losing 300 bbl.hr (ballooning?) Pack-off Hole tight with pumps off

  38. The Plan … The Reality • Hole planned from offset wells (sv, shmin, log correlations to strength data, po…) • Jagged line is a prediction of MW to sustain reasonable borehole stability • Brown line: chosen MW program from stability calculation (using “Lade” criterion) • Red line was the actual mud weight needed to cope with a series of problems • The casings were set higher than expected and an extra string was eventually needed

  39. How do We Sustain Stability? • MW control (up or down) • Mud properties control (reduce ECD) • Trip and connection policy (speed, surge…) • Inhibitive WBM: minimize chemical effects • OBM: eliminate chemical effects • Air or foam UB drilling (shallow, strong rx) • Use fn-gr LCM, gilsonite in fractured shale • Cool the drilling mud to reduce sq, reducing the chances of rock failure • When all else fails, sidetrack, set casing

  40. Well Design and Cost Optimization High Risk      Low Risk Actual (Likely) Well Costs Well Design Costs • High risks are mainly related to low MW, rapid drilling, increased well blowout risks… Low cost if successful. • Low risks are mainly associated with slow drilling and high MW, but drillings time is long… Generally costly… • In between, there is a level of acceptable risks with a lower cost factor

  41. Borehole Cost Optimization • Affected by drilling speed, casing string costs, cleaning problems, cost of drilling mud, risks, trip problems… • Optimizing this in “real time” is the challenging task of the Drilling Engineer Lost circulation Safe 1.0 The shape of the cost curve changes, depending on the stresses and where we are in the hole! “Ballooning” Fluid influx 0.8 Shear failure sloughing Stress to Strength ratio 0.6 Mud Weight

  42. Borehole Stability and Hydraulics • Borehole management is not only stresses, rock strength, MW and mud properties! • It is also dependent on hydraulics: • Pumping strategy and cleaning capabilities • Gel strength, viscosity, mud density • BHA design, ECD, even tripping policy Hydraulics Rock mechanics

  43. How do We Predict RM Stability? • We need to know the rock stresses in situ • Vertical, horizontal usually, sv, shmin • Pore pressures (especially overpressure cases) • We need to know the rock strength • Lab testing of core • Correlations to geophysical log data bases • Testing of drill chips (penetrometers, sonic…) • Then, we make predictions of stability MW • This is an indicator only! • Careful monitoring on the active well • Improvement of our “calibrations”, ECD…

  44. Lessons Learned • Stress concentrations arise naturally when a hole is drilled • The tangential stress sq is critical • Affected by stress, tectonics, rock behavior… • Borehole cake and mud support are critical • We can calculate stresses, but rock parameters are (E, n, Y, Co, To…) needed • We can reduce the effects of high sq • MW, lower T, better cake, OBM… • We can use log data and correlations to predict the MW for stability

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