Gradientes De Fractura

Fracture Gradient Determination

Fracture Gradient Determination
• • • • • • Hubbert and Willis Matthews and Kelly Ben Eaton Christman Prentice Leak-Off Test (experimental)

Fracture Gradient Determination
• Read AWC Chapter 4 all

Well Planning
• Safe drilling practices require that the following be considered when planning a well:
– – – – – – Pore pressure determination Fracturegradient determination Casing setting depth Casing design H2S considerations Contingency planning

The Hubbert & Willis Equation
• Provides the basis of fracture theory and prediction used today. • Assumed elastic behavior. • Assumed effective stress exceeds the minimum by a factor of 3.

The Hubbert & Willis Equation
• If the overburden is maximum, the assumed horizontal stress is: • σH= 1/3(σob - pp) + pp • Equating fracture propagation pressure to minimum stress gives • pfp = 1/3(σob - pp) + pp

The Hubbert & Willis Equation
• pfp = 1/3(σob - 2pp) (minimum) • pfp = 1/2(σob - pp) (maximum)

Matthews and Kelly
• Developed the concept of variable ratio between the effective horizontal and vertical stresses, not a constant 1/3 as in H & W. • Stress ratios increaseaccording to the degree of compaction • σeH = KMKσev

Matthews and Kelly
• σeH = KMKσev • KMK = matrix stress coefficient • Including pore pressure • σH = KMK(σob - pp) + pp

Matthews and Kelly
• Equating fracture initiation pressure to the minimum in situ horizontal stress gives • pfi = KMK(σob - pp) + pp • and • gfi = KMK(gob - gp) + gp

Example 4.8
• Given: Table 4.4 (Offshore LA) •Estimate fracture initiation gradient at 8110’ and 15,050’ using Matthews and Kelly correlation

Example 4.8
For 8110’ gfi = 0.69(1 - .465) + .465 gfi = 0.834 psi/ft For the undercompacted interval at 15,050’, the equivalent depth is determined by: De = [15050-(.815*15050)]/.535 = 5204’

KMK = 0.61 KMK = 0.69

Example 4.8
• gfi = 0.61*(1-.815)+.815 = .928 psi/ft • Note: Overburden gradient wasassumed to be 1.0 psi/ft

Penebaker’s Gulf Coast
• gfi = Kp(gob - gp) + gp • where Kp is Penebaker’s effective stress ratio

Penebaker’s overburden gradient from Gulf Coast region

Depth where ∆t = 100 µsec/ft

Penebaker’s Effective Stress Ratio

Example 4.9
• Re-work Example 4.8 using Penebaker’s correlations where the travel time of 100 µsec/ft is at 10,000’

Example 4.9
•• • • • • At 8110’ gfi = 0.77(0.945 - 0.465) + 0.465 gfi = 0.835 psi/ft At 15050’ gfi = 0.94(0.984 - 0.815) + 0.815 gfi = 0.974 psi/ft

Eaton’s Gulf Coast Correlation
• Based on offshore LA in moderate water depths ⎛ µE ⎞ ⎟(g ob − g p ) + g p g fi = ⎜ ⎜1− µ ⎟ E ⎠ ⎝
Note the bracketed Poisson' s ratio term is an effective stress ratio

Mitchell’s approximation

Mitchell’s approximationMitchell’s approximation

Example 4.10

Example 4.10

Summary
• Note that all the methods take into consideration the pore pressure gradient. • As the pore pressure increases, so does the fracture gradient

Summary
• Hubbert and Willis apparently consider only the variation in pore pressure gradient. • Matthews and Kelly also consider the changes in rock matrix stress coefficientand the matrix stress

Summary
• Ben Eaton considers variation in pore pressure gradient, overburden stress, and Poisson’s ratio. • It is probably the most accurate of the three.

Summary
• The last two are quite similar and yield similar results. • None consider the effect of water depth.

Christman’s approach
• Christman took into consideration the effect of water depth onoverburden stress.

Example 4.11
• Estimate the fracture gradient for a formation located 1490’ BML. Water depth is 768’, air gap is 75’. • Repeat for water depth of 1500’

Example 4.11

Example 4.11

Christman
• Christman also noted that anomalously low fracture gradients seemed to be associated with formation having low bulk densities for the burial depth. He then developed the...