2. DRILLING ENGINEERING
Vahid Salimi

3. Textbook Applied Drilling Engineering, by :Adam T. Bourgoyne Jr.,
Martin E. Chenevert,
Keith K. Millheim
F.S. Young Jr.,.

4. Contents: pore pressure and fracture pressure drilling hydraulics
casing design
under balanced drilling
directional drilling

5. pore pressure and fracture pressure
Chapter 1
pore pressure and fracture pressure

6. HP (psi) = 0.052 x ρf (ppg) x D (ft)
Hydrostatic Pressure
Hydrostatic pressure is defined as the pressure exerted by a column of fluid.
The pressure is a function of the average fluid density and the vertical height or depth of the fluid column.
Mathematically, hydrostatic pressure is expressed as:
HP (psi) = x ρf (ppg) x D (ft)
where:
HP = hydrostatic pressure
ρf = average fluid density
D = true vertical depth or height of the column

7. Hydrostatic Pressure(cont’d)
Hydrostatic pressures can easily be converted to equivalent mud weights and pressure gradients.
Hydrostatic pressure gradient is given by:
HG = HP / D … (psi/ft)

8. Example
Calculate the hydrostatic pressure for the following wells:
a. mud weight = 9 ppg, hole depth = ft MD (measured depth), 9900 ft TVD (true vertical depth)
b. mud gradient = psi / ft, hole depth = ft MD (measured depth), 9900 ft TVD (true vertical depth)
solution a.
HP (psi) = x ρf (ppg) x D (ft) = x 9 x 9900 = 4632 psi b.
Hydrostatic pressure = fluid gradient (psi / ft) x depth (ft) psi
= (psi /ft) x 9900(ft) = 4633 psi

9. Mud Weight (MW) should be kept heavy enough so that hydrostatic head of mud column is higher than formation pressure at any depth. Usually 150 psi
Need to know formation pressure in order to determine MW
Pf = MW D
Pf Formation Pressure, psi
MW Mud Weight, ppg
D True Vertical Depth, ft
150 Safety, psi

10. Example
You are drilling with 7.9 ppg oil base mud. If the formation pressure is predicted 5,000 psi at 9,000 ft true vertical depth, what is the required MW in order to have 150 psi overpressure ?
5, = MW 9,000
MW = 11 ppg

11. OVERBURDEN PRESSURE σov = 0.052 x ρb x D
The overburden pressure is defined as the pressure exerted by the total weight of overlying
formations above the point of interest.
The total weight is the combined weight of both the formation solids (rock matrix) and formation fluids in the pore space.
The overburden pressure can therefore be expressed as the hydrostatic pressure exerted by all materials overlying the depth of interest:
σov = x ρb x D
where
σov = overburden pressure (psi)
ρb = formation bulk density (ppg)
D = true vertical depth (ft)

12. OVERBURDEN PRESSURE(cont’d)
Overburden gradient under field conditions of varying lithological and pore fluid density is given by:
σovg= 0.433[(1 – φ)ρma +(φxρf)]
where
σovg= overburden gradient, psi/ft
φ= porosity expressed as a fraction
ρf= formation fluid density
ρma= matrix density

13. matrix and fluid densities
Substance Density (gm/cc)
Sandstone
Limestone
Dolomite
Anhydrite
Halite
Gypsum
Clay
Freshwater
Seawater
Oil
Gas
To convert densities from gm/cc to gradients in psi/ft use:
Gradient (psi/ft) = x (gm /cc)
To convert from psi/ft to ppg, use:
Density (ppg) = gradient (psi/ft) / 0.052

14. Pore pressure
The magnitude of pressure in the pore of formation known as the pore pressure
Pore pressure
= formation pressure
=formation fluid pressure
=reservoir pressure
=pressure in fluid contained in the pore spaces of the rock

15. Example
Determine the pore pressure of a normally pressured formation in the Gulf of Mexico at 9,000’ depth.
Solution
p = psi/ft * 9,000 ft = 4,185 psig

16. Homework: Pore Pressure Profiles
The following pore pressure information has been supplied for the well you are about to drill.
a. Plot the following pore pressure/depth information on a P-Z diagram :

17. b. Calculate the pore pressure gradients in the formations from surface; to 8000ft; to 8500ft; and to 9500ft. Plot the overburden gradient (1 psi/ft) on the above plot.
Determine the mud weight required to drill the hole section: down to 8000ft; down to 8500ft; and down to 9500ft.
Assume that 200 psi overbalance on the formation pore pressure is required.

18. c. If the mudweight used to drill down to 8000ft were used to drill into the formation pressures at 8500ft what would be the over/underbalance on the formation pore pressure at this depth?

19. d. Assuming that the correct mudweight is used for drilling at 8500ft but that the fluid level in the annulus dropped to 500 ft below drillfloor, due to inadequate hole fill up during tripping. What would be the effect on bottom hole pressure at 8500ft ?

20. e. What type of fluid is contained in the formations below 8500ft.

21. Normal Pore Pressure =0.433 psi/ft for fresh water
Pressure of a column of water extending from the formation to the surface
The magnitude of normal pore pressure varies with the concentration of dissolved salts, type of fluid, gases present and temperature gradient.
=0.433 psi/ft for fresh water
=0.465 psi/ft for seawater

22. Subnormal Formation Pressure
Subnormal pore pressure is defined as any formation pressure that is less than the corresponding fluid hydrostatic pressure at a given depth.
Subnormal formation pressure can cause lost circulation of water as the drilling fluid.

23. ABNORMAL PORE PRESSURE
Abnormal pore pressure is defined as any pore pressure that is greater than the hydrostatic pressure of the formation water occupying the pore space.
Abnormal pressure is sometimes called overpressure or geopressure.
Abnormal pressure can be thought of as being made up
of a normal hydrostatic component plus an extra amount of pressure.
This excess pressure is the reason why surface control equipment (e.g. BOPs) are required when drilling oil and gas wells.

24. ABNORMAL PORE PRESSURE(cont’d)
Abnormal formation pressure can cause a kick with water as the drilling fluid.

25. Normal and Abnormal Pore Pressure
Normal Pressure Gradients
West Texas: psi/ft
Gulf Coast: psi/ft
Abnormal Pressure Gradients
Depth, ft
Normal pore pressure is defined as the formation fluid pressure that is equal to the hydrostatic pressure of the formation fluids. Abnormally pressured formation have a pressure gradient greater than normal pressure. Normal pressure varies from location to location. We must be able to predict formation pressure to adequately design our wellbore, as well as for safety.
10,000’
Pore Pressure, psig

26. Pore Pressure vs. Depth Normal Abormal Depth, ft
5,000
10,000
15,000
20,000
0.433 psi/ft lb/gal
0.465 psi/ft lb/gal
Depth, ft
Normal
Abormal
This is a typical plot of pore pressure vs. depth. Pressure is usually plotted in equivalent density on the horizontal axis and depth is plotted on the vertical axis, increasing downward. Normally pressure plots as a vertical line.
Pore Pressure Equivalent, lb/gal
{ Density of mud required to control this pore pressure }

27. Fracture Gradient Pore Pressure Gradient
Here we have a plot of pore pressure and fracture pressure vs. depth.

29. Transition zone
The upper portion of the region of abnormal pressure is called the transition zone

30. Causes Of Abnormal Pore Pressure
Compaction Effects
Diagenetic Effects
Differentional Density Effects
Fluid Migration Effects

31. Diagenetic Effects
With increasing pressure and temperature, sediments undergo a process of chemical and physical changes collectively known as diagenesis.
Diagenesis is the alteration of sediments and their constituent minerals during post depositional compaction.
Diagenetic processes include the formation of new minerals, recrystallisation and lithification.
Diagenesis may result in volume changes and water generation which if occurring in a seabed environment may lead to both abnormal or sub-normal pore pressure.

32. Clay Diagenesis Clay Diagenesis (Conversion of Smectite to Illite)
If the water released in this process cannot escape during compaction, then the pore fluid will support an increased portion of the overburden and will thus be abnormally pressured.
Diagenesis of Sulphate Formations
Anhydrite (CaSO4) is diagenetically formed from the dehydration of gypsum (CaSO4.2H2O).
During the process large volumes of water are released and this is accompanied by a 30-40% reduction in formation volume

33. HIGH PRESSURE NORMAL PRESSURE 7. Abnormal Pressure
661. Drilling Engineering

36. Homework

37. When crossing faults it is possible to go from normal pressure to abnormally high pressure in a short interval.
7. Abnormal Pressure
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38. Well “A” found only Normal Pressure ...
7. Abnormal Pressure
661. Drilling Engineering

39. Methods of estimating pore pressure
Direct measurement
It is possible only when the formation has been drilled
It is expensive
Indirect measurement
The main parameter is the variation of porosity with depth (porosity dependent parameter)
If pore pressure is normal, porosity-dependent parameter (x) have an easily recognized trend because of the decreased porosity with increased depth of burial and compaction.
A departure from the normal pressure trend signals a probable transition zone.
Detection of the depth at which this departure occurs is critical because casing must be set in the well before excessively pressured permeable zones can be drilled safely.

40. Prediction and Detection of Abnormal Pressure Zones
1. Before drilling
Shallow seismic surveys
Deep seismic surveys
Comparison with nearby wells
7. Abnormal Pressure
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41. Prediction and Detection of Abnormal Pressure Zones
2. While drilling
Drilling rate, gas in mud, etc. etc.
D - Exponent
DC - Exponent
MWD - LWD
Density of shale (cuttings)
7. Abnormal Pressure
661. Drilling Engineering

42. Prediction and Detection of Abnormal Pressure Zones
3. After drilling
Resistivity log
Conductivity log
Sonic log
Density log
7. Abnormal Pressure
661. Drilling Engineering

43. Compaction Theory of Abnormal Pressure
During deposition, sediments are compacted by the overburden load and are subjected to greater temperatures with increasing burial depth.
Porosity is reduced as water is forced out.
Hydrostatic equilibrium within the compacted layers is retained as long as the expelled water is free to escape
If water cannot escape, abnormal pressures occur

46. Compaction Theory
In Porous formation the overburden stress is supported by rock matrix stress and pore pressure
Bulk Density = ρm (1-Ф) + ρf Ф
The average porosity in sediments ,generally decreases with increasing depth - due to the increasing overburden
This results in an increasing bulk density with increasing depth, and increasing rock strength
Average Porosity Ф = ρm - ρb / ρm – ρf
Plot Ф Vs. Depth on similog graph.

49. Example
Calculate the overburden stress at a depth of 7,200 ft in the Santa Barbara Channel.
Assume
φo = 0.37
ρma = 2.6 gm/cc
kφ = ft-1
ρf = gm/cc

50. Solution

53. Homeworks

54. Homeworks (cont’d)

55. Homeworks (cont’d)

56. Pore pressure prediction methods
Measure the porosity indicator (e.g.density) in normally pressured, clean shales to establish a normal trend line.
When the indicator suggests porosity values that are higher than the trend, then abnormal pressures are suspected to be present.
The magnitude of the deviation from the normal trend line is used to quantify the abnormal pressure.

58. Equivalent Matrix Stress Method

60. Example
Estimate the pore pressure at 10,200’ if the equivalent depth is 9,100’. The normal pore pressure gradient is psi/ft. The overburden gradient is 1.0 psi/ft.
ASSUME:
At 9,100’, pne = * 9,100 = 3,940 psig
At 9,100’, σobe = 1.00 * 9,100 = 9,100 psig
At 10,200’, σob = 1.00*10,200 = 10,200 psig

61. Solution

62. Approach 2: Empirical correlation
More accurate
Need numerous data
Uses (Xo-Xn) or (Xo/Xn) to predict the magnitude of the abnormal pressure

63. Prediction of pore pressure by seismic data

66. Homework

73. Pore pressure indications while drilling
Drilling rate (ROP)
gas in mud
Pit level
Flowline temperature

74. Rate Of Penetration(ROP)
Drill bits break the rock by a combination of several processes including: Compression (weight-on-bit), shearing (rpm) and sometimes jetting action of the drilling fluid.
The speed of drilling is described as the rate of penetration (ROP) and is measured in ft/hr.
The rate of penetration is affected by numerous parameters namely:
Weight On Bit (WOB)
Revolutions Per Minute (RPM)
bit type
bit wear
hydraulic efficiency
degree of overbalance
drilling fluid properties
hydrostatic pressure and
hole size
Formation properties

75. TABLE 2.8 -
Note, that many factors can influence the drilling rate, and some of these factors are outside the control of the operator.

76. Effect of bit weight and hydraulics on penetration rate
Drilling rate increases more or less linearly with increasing bit weight.
A significant deviation from this trend may be caused by poor bottom hole cleaning
Inadequate hydraulics or excessive imbedding of the bit teeth in the rock

77. The chip hold down effect
Effect of Differential Pressure on Drilling Rate
Differential pressure is the difference between wellbore pressure and pore fluid pressure
Decrease can be due to:
The chip hold down effect
The effect of wellbore pressure on rock strength

78. If all parameters affecting ROP are held constant whilst drilling a uniform shale sequence then ROP should decrease with depth. This is due to the natural increased compaction with depth reflecting a decrease in porosity and increased shale density and increased shale (compressive) strength.
When entering an abnormally pressured shale, the drill bit sees a shale section which is undercompacted. The increased porosity and decreased density of the undercompacted section results in the formation becoming more ‘drillable’ as there is less rock matrix to remove. Consequently ROP increases, assuming all drilling parameters were kept constant.

79. Drilling underbalanced can further increase the drilling rate.

80. Drilling Rate as a Pore Pressure Predictor
Penetration rate depends on a number of different parameters.
R = K(P1)a1 (P2)a2 (P3)a3… (Pn)an

81. Modified d-exponent

82. Or, in its most used form:
The D Exponent basically attempts to correct the ROP for changes in RPM, weight on bit and hole size.
The D exponent increases linearly with depth, reflecting increased rock strength with depth. For abnormally pressured shales, the D exponent deviates from the normal trend and actually decreases with depth.

83. dc-exponent Mud weight also affects R An adjustment to d may be made:
dc = d (rn /rc)
where
dc = exponent corrected for mud density
rn = normal pore pressure gradient
rc = effective mud density in use

84. d-exponent
The d-exponent normalizes R for any variations in W, db and N
Under normal compaction, R should decrease with depth. This would cause d to increase with depth.
Any deviation from the trend could be caused by abnormal pressure.

85. Example While drilling in a Gulf Coast shale, R = 50 ft/hr
W = 20,000 lbf
N = 100 RPM
ECD = 10.1 ppg (Equivalent Circulating Density)
db = 8.5 in
Calculate d and dc

86. Solution

90. Example

92. solution

97. Ratio Method
The ratio method is much simpler and does not require values of overburden. To calculate pore pressure, use the following formula:

98. Homework
Using the Eaton Method, calculate the pore pressure at depth ft given:
dcn (from normal trend) = 1.5 d-units
dco (from new trend) = 1.1 d-units
Overburden gradient = 19 ppg
Normal pore pressure in area = 9 ppg

99. Fracture Pressure

101. Prediction of Fracture Gradients
Well Planning
Theoretical Fracture Gradient Determination
Hubbert & Willis
Matthews & Kelly
Ben Eaton
Comparison of Results
Experimental Frac. Grad. Determination
Leak-off Tests
This lesson will cover methods, both theoretical and experimental, to estimate fracture pressures
Fracture Gradients

102. In-Situ Earth Stresses

104. Example

106. Fracture Gradient Determination
2. Matthews & Kelly:
where Ki = matrix stress coefficient
s = vertical matrix stress, psi
Matthews & Kelly assumed an overburden gradient of 1 psi/ft. They also realize that fracture pressure is a not only a function of pore pressure, but also the matrix stress. They also developed the concept of the matrix stress coefficient.
Fracture Gradients

107. Example
A Texas Gulf Coast well has a pore pressure gradient of psi/ft. Well depth = 11,000 ft.
Calculate the fracture gradient in units of lb/gal using Matthews & Kelly method
Summarize the results in tabular form, showing answers, in units of lb/gal and also in psi/ft.
We use an example to compare the three methods.
Fracture Gradients

108. Example
2. Matthews & Kelly
In this case P and D are known, may be calculated, and is determined graphically.
(i) First, determine the pore pressure gradient.
Matthews & Kelly
Fracture Gradients

109. Example - Matthews and Kelly
(ii) Next, calculate the matrix stress.
S = P + s
s = S - P
= 1.00 * D * D
= * D
= * 11,000
s = 2,915 psi
Fracture Gradients

110. Example - Matthews and Kelly
(iii) Now determine the depth, , where, under normally pressured conditions, the rock matrix stress, s would be 2,915 psi.
Sn = Pn + sn n = “normal”
1.00 * Di = * Di + 2,915
Di * ( ) = 2,915

111. Example - Matthews and Kelly
(iv) Find Ki from the plot on the right, for
For a south Texas Gulf Coast well,
Di = 5,449 ft
Ki = 0.685
Fracture Gradients

112. Example - Matthews and Kelly
(v) Now calculate F:

113. Leak off Test
A test carried out to the point where the formation leaks off

114. Here are typical results of a leak-off test.
Fracture Gradients

115. Experimental Determination of Fracture Gradient
Example:
In a leak-off test below the casing seat at 4,000 ft, leak-off was found to occur when the standpipe pressure was 1,000 psi. MW = 9 lb/gal.
What is the fracture gradient?

116. Solution Leak-off pressure = PS + DPHYD = 1,000 + 0.052 * 9 * 4,000
= 2,872 psi
Fracture gradient = psi/ft
EMW = ?
13.8 lb/gal

117. Homework
While performing a leak off test the surface pressure at leak off was 940 psi. The casing shoe was at a true vertical depth of 5010 ft and a mud weight of 10.2 ppg was used to conduct the test.
Calculate: the maximum allowable mud weight at this depth .

118. Homework
A leakoff test was carried out just below a 13 3/8" casing shoe at 7000 ft. TVD using 9.0 ppg mud. The results of the tests are shown below.
What is the maximum allowable mud weight for the 12 1/4" hole section ?
BBLS PUMPED SURFACE PRESSURE
(psi)

119. Equivalent Circulating Density (ECD)
When the drilling fluid is circulating through the drillstring, the borehole pressure at the bottom of the annulus will be greater than the hydrostatic pressure of the mud.
The extra pressure is due to the frictional pressure required to pump the fluid up the annulus. This frictional pressure must be added to the pressure due to the hydrostatic pressure from the column of mud to get a true representation of the pressure acting against the formation a the bottom of the well.
An equivalent circulating density (ECD) can then be calculated from the sum of the hydrostatic and frictional pressure divided by the true vertical depth of the well.

120. Homework
If the circulating pressure losses in the annulus of the above well is 300 psi when drilling at 7500ft with 9.5ppg mud, what would be the ECD of the mud at 7500ft.