1

CHAPTER-2

PREDICTING FORMATION PRESSURES

Several methods of pressure prediction is available to the engineer. These

methods can be grouped logically as follows:

-areal analysis from seismic data,

-off-set well correlation log analysis, drilling parameter evaluation, production or

test data,

-real time evaluation as , a) qualitative, b) quantitative.

The real time analysis involves monitoring drilling and logging parameters

while the prospect well is drilled.

Origin of Abnormal Pressures

By definition, abnormal pressure is any geo-pressure that is different

from the established normal trend for the given area and depth. Pressure may

be less than normal, called sub-normal or greater than normal pressure which

has been termed geo-pressured, super pressured or simply abnormal pressure.

Sub-normal pressures present few direct well control problems. However,

subnormal pressures do cause many drilling and well planning problems. For

clarity, the term abnormal pressure will identify the pressures greater than

normal. Formation pressure is the presence of fluids in the pore spaces of the

rock matrix. These fluids are typically gas or salt water. The overburden stress

2

is created by the weight of the overlying rock matrix and the fluid filled pores.

The rock matrix stress is the overburden stress minus the formation pressure.

For general calculations the overburden stress gradient is often assumed to be

1.0 psi/ft with a density of 19.23 lb/gal, an average weight of fluid-filled rock.

Normal formation pressure is equal to the hydrostatic pressure of the

native formation fluids. In most cases, the fluids vary from fresh water with

density of 8.33 lb/gal (0.433 psi/ft) to salt water with density of 9.0 lb/gal

(0.465 psi/ft). However, some field reports indicate instances when the normal

formation fluid density was greater than 9.0 lb/gal. Regardless of the fluid

density, the normal pressure formation can be considered as an open hydraulic

system where pressure can easily be communicated throughout.

Formation pressures resulting from under compaction often cab be

approximated with some simple calculations. If it is assumed that compaction

does not occur below the barrier depth, the formation fluid below the barrier

must support overburden, rock matrix and the formation fluids. The pressure

can be calculated as:

P = 0.465 psi/ft (DB)+ 1.0 psi/ft (Di – DB)

DI = depth of interest below the barrier, ft

DB = depth of barrier, ft

P = formation pressure at Di , psi

3

Figure 1.1 Abnormal pore pressures are generated in the under-compacted

region because the shale matrix can’t support the overburden stress

Example 1-1:

A well is drilled to 15000 ft. The entrance into the abnormal pressures at

10000 ft is caused by under compaction. Calculate the expected formation

pressure at 15000 ft. Assume formation fluid and overburden stress gradients

are 0.465 psi/ft and 1.0 psi/ft respectively?

Solution:

The formation pressure at 15000 ft:

P = 0.465 psi/ft (DB)+ 1.0 psi/ft (Di – DB)

4

P = 0.465 psi/ft (10000)+ 1.0 psi/ft (15000 – 10000)

P = 9650 psi

P = (9650 / 0,052 x 15000)

P = 12.4 ppg

Log Analysis

Log analysis is a common procedure for pore pressure estimation in both

off-set wells and the actual well drilling. New measurement while drilling (MWD)

tools implement log analysis techniques in real time drilling mode.

The resistivity log was originally used for pressure detection. The log

response is based on the electrical resistivity of the total sample, which includes

the rock matrix and the fluid-filled porosity. If a zone is penetrated that has

abnormally high porosities ( at the same time high pressure) the resistivity of

the rock will be reduced due to the greater conductivity of water than rock

matrix. The expected response can be seen in Figure 1-2. This figure illustrates

several important points. Since the high formation pressures were originally

developed in shale sections and later equilized the sand zone pressures, only the

clean shale sections are used as plotting points. This excludes sand resistivities,

silty shale, lime and any other type of rock that may be encountered. As the

shale resistivities are selected and plotted, a normal trend line should develop

prior to entry into the pressured zone. An actual field case can be seen in Fig. 1-

5

2. The impermeable .shale section was entered at about 9,500 ft. Although this

section contained normal pressure from 9,500-9,800 ft, as evidenced by the

increasing resistivity of the normal trend, the reversal can be seen from 9,800-

10,900 ft. The mud weight was 9.0 lb/gal at 9.500 ft but was increased to

13.5 lb/gal at 10,900 ft.

6

Figure 1-2 Generalized shale resistivity plot

Hottman and Johnson developed a technique based on empirical

relationships whereby an estimate of formation pressures could be made by

noting the ratio between the observed and normal rock resistivities. As they

explained, the following steps arc necessary to estimate the formation pressure.

1. The normal trend is established by plotting the logarithm of shale resistivity

vs depth.

2. The top of the pressured interval is found by noting the depth at which the

plotted points diverge from the trend.

3. The pressure gradient at any depth is found as follows:

a) The ratio of the extrapolated normal shale resistivity to the observed shale

resistivity is determined.

b) The formation pressure corresponding to the calculated ratio is found from

Fig. 1-3.

7

Figure 1-3 Shale resistivity from the log

Figure 1-4 Emprical correlation of formation pressure gradient vs. a

ratio of normal to obseerved shale resistivity

8

Example 1-2:

Plot the data given below on a semi-log paper. Where does the entrance

into the abnormal pressure occur? Use Hottman and Johnson procedure to

compute formation pressure at each 1000 ft interval below the entrance into

pressures?

Resistivity,

ohm-m

Depth, ft Resistivity,

ohm-m

Depth, ft

0.54 4000 0.80 10400

0.64 4600 0.76 10700

0.60 5600 0.58 10900

0.70 6000 0.45 11000

0.76 6400 0.36 11100

0.60 7000 0.30 11300

0.70 7500 0.28 11600

0.74 8000 0.29 11900

0.76 8500 0.27 12300

0.82 9000 0.28 12500

0.90 9700 0.29 12700

0.84 10100 0.30 12900

Solution:

1- Plot the data. (Figure 1-5)

2- The estimated entrance into abnormal pressure occurs at 9700 ft.

3- Extrapolate the normal trend established between 8000 ft and 9700 ft.

9

Figure 1-5 Resitivity plot of example 1-2

4- The observed and extrapolated resistivities are at the bottom are 0.30 and

1.60 ohm-m.

5-Compute the ratio of Rnormal (Rn) and Robserved (Rob). R = Rn / Rob

10

R = 1.60 / 0.30

R = 5.333

6- From Fig. 1-4, the formation pressure associated with a ratio of 5.333 is 18

ppg.

Salinity Changes:

The Hottman and Johnson procedure, as well as the overlay techniques,

assume that formation resistivities are function or the following variables:

-lithology

-fluid content

-salinity

-temperature

-porosity

The procedures make the following assumptions with respect to these variables:

-lithology is shale,

-shale is water filled.

-water salinity is constant.

-temperature gradients are constant.

-porosity is the only variable affecting the pore pressure.

Foster and Whalen developed techniques for predicting formation

pressure in regions that have salinity variations. Their techniques have proved

11

successful and can be applied universally, although the complexity associated

with their use prevents wide acceptance. New computerized applications help

make the technique more useful. The Foster and Whalen method is based on a

formation factor, F, and its relationship to the shale resistivity and formation

water resistivity:

F=Ro / Rw

F = formation factor, dimensionless

Ro = shale resistivity, ohm-m,

Rw= formation water resistivity, ohm-m.

The shale resistivity, Ro is read directly from the log. The water

resistivity, Rw is computed from the mud filtrate resistivity, Rmf. The SP

deflection is computed from the shale base line. The formation pressures are

calculated from a plot of formation factors and the depth equivalent approach,

as previously presented. Example 1.3 will illustrate the procedures required to

calculate Rw and F.

Exampɬe 1-3:

Use the following data to calculate F and Rw. Assume that all the bed

thickness corrections are made.

Ro = 0.98 ohm-m

SP = -87 mv (deflection from shale base line)

Temp. = 190 F at 8000 ft

12

Depth of interest = 8000 ft

Rmf = 0.40 ohm-m at 90 F

NaCl=12000 ppm

Solution:

1-From Figure 1-6, a value of -87 mv yields 10.5 for the ratio.

2-The resistivity of the mud filtrate, Rmf, is 0.40 ohm-m at 90 F. It must be

converted to an equivalent value of Rmfe. (Fig. 1-8).

3- From Fig. 1-8, Rmfe = 0.195 ohm-m.

Figure 1-6 Rwe determination

13

4-Combining step 1 & 2.

SP = Rmfe / Rwe

10.5 = 0.98 / Rwe

Rwe = 0.0185 ohm-m

5- Fig. 1-7 is used to convert Rwe to Rw, or 0.028 ohm-m

F = Ro / Rw

F = 0.98 / 0.028

F = 35

Figure 1-7 Rwe conversion to Rw

14

Formation pressure calculations are made at defining the depth, in the

normal pressure region that has a formation factor of equivalent to the deeper

depth of interest. The upper depth is defined as the equivalent depth, De.

DG = 0.465 psi/ft (De) + (D - De) (1.0 psi/ft)

D = depth of interest, ft

De = equivalent depth, ft

G = formation pressure gradient, psi/ft at D

1.0 psi/ft = assumed overburden stress gradient

If the depths D and De are known, the formation pressure gradient, G, is

computed as

G = [ (1 psi/ft) D - 0.535 De ] / D

15

Figure 1-8 Temperature correction for Rw and Rmf

Example 1-4:

The following log data were taken from a well that is suspected to have

significant salinity variations in the formation fluids. Use Foster-Whalen method

16

to calculate formation pressures at each of the given depths. Assume that all

appropriate bed thickness corrections have been made to log values.

Logging Depths:

Depth, ft Rmf- ohm-m

10300 0.65 at 90 F

11400 0.89 at 80 F

Depth, ft Temp., F Robs, ohm-m SP Deflection,

mv

3900 114 0.76 -70

5400 135 0.76 -76

6900 162 0.84 -78

7700 170 0.96 -85

8900 191 0.99 -90

9700 201 1.23 -87

10300 211 1.02 -90

10700 218 0.93 -94

10850 221 0.73 -90

11400 239 1.30 -60

12000 250 1.70 -57

12600 261 2.08 -38

12800 270 1.03 -55

Solution:

The actual calculations will shown at a depth of 12800 ft.

1-The SP deflection from the shale baseline at 12800 ft is –55. From Fig. 1-6 a –

55 mv value at 270 F correlates as:

Rmf(e) / Rw(e) = 3.77

17

2-The resistivity of the mud filtrate (Rmf) at 12800 ft is 1.03. From Fig. 1-8,

this value is corrected from 90 F to the bottom hole temperature of 270 F.

3- The results from the above steps:

Rmf(e) / Rw(e) = 3.77

0.34 / Rw(e) = 3.77

Rw(e) = 0.090

4- Convert Rw(e) to Rw ( Fig. 1-8)

5- The formation factor, F is computed as :

F = Ro / Rw

F = 1.03 / 0.086

F = 12

18

Figure 1-9 Rwo,Ro, and F for Example 1.4

6-The values for Ro and Rw are plotted on Figure. 1-9.

7- A vertical line is constructed from the formation factor, F, at 12800 ft. (F =

12) until it intersects the normal trend line in the shallow sections. The points of

intersection are defined as the equivalent depth, or, 4800 ft.

19

8-The formation pressure at 12800 ft is computed as.

G = [ (1 psi/ft) D - 0.535 De ] / D

G = [ (1 psi/ft) 12800 - 0.535 . 4800 ] / 12800

G = 0.799 psi/ft

G = 0.799 / 0.052

G = 15.4 ppg

Example 1-5:

The following sonic log was taken from a well in Oklahama. Plot the data on

semi-log paper. Use Hottman and Johnson technique to calculate the formation

pressure at 11900 ft.

Travel Time,

sec/ft

Depth, ft Travel Time,

sec/ft

Depth, ft

190 3400 100 9800

160 5000 110 10000

140 6600 100 10200

120 7300 110 10400

122 7900 101 10600

105 8200 101 10800

110 8600 105 11100

99 9000 100 11400

99 9200 110 11600

98 9400 100 11900

100 9600 - -

Solution:

1-Plot the data on semi-log paper (Figure 1-10).

20

Figure 1-10 Sonic data plot

2-The divergence from the normal trend at 9500 ft denotes the entry into the

pressured zone.

3-At 12000 ft, the difference between the extrapolated normal trend and

observed value is 32 sec/ft.

21

4- Enter Figure 1-11 with a value of 32 sec/ft and read the formation pressure

as 17 ppg.

Figure 1-11 Emprical correlation of formation pressure gradients vs. a

difference

observed and normal travel times (Hottman & Johnson)

Bulk Density

When drilling in normally pressured zone bulk density of the drilled rock

should increase due to compaction, or porosity reduction. As high formation

pressures are encountered. the associated high porosities, will cause a deviation

in the expected bulk density trend. A typical plot of bulk densities is seen in Fig.

1-12. The transition from normal to abnormal pressures occurs at the depth

where divergence from the normal trend is observed. The resistivity plot shows

transition zones at 10,700 and 12,500 ft. The density log detected the lower

22

transition zone but was unable to define the upper transition zone due to the

lack of an established trend line.

Drilling Equations

Many mathematical models have been proposed in an effort to describe

the relationship of several drilling variables on penetration rate. Most depend on

the combination of several controllable variables and one combined formation

property.

Figure 1-12 Generalized shale density plot

23

Several of the models are designed for easy application in the field,

while others require computerization. When conscientiously applied, most

of the available models can accurately detect and quantify abnormal

formation pressures. An attempt to quantify differential pressure is the

basis of most drilling models. If this value is known, the formation pressure

can readily be calculated. Gamier and van Lingen showed that differential

pressure has a definite effect on penetration. In field studies, Benit and

Vidrine found evidence that the range in differential pressure of 0-500

psi has the greatest effect in reducing penetration. Perhaps the most

common model used by the industry is the de-exponent. The basis of the

model is found in Gingham's equation to define the drilling process:

(R / 60N) = a (12W / dB)b

R = bit penetration rate, ft/hr

N = rotary speed, rpm

W= bit weight, l000 lb

de = bit diameter, in.

b = bit weight exponent, dimensionless

a = formation drillability, constant, dimensionless

Jordan and Shirley modified Bingham's equation to the following form:

d = [ log (R / 60N) ] / [log (12W / 1000 dB)]

24

where; d replaces the b and a is assumed as unity. d depends more on

differential pressure than on operating parameters. In field applications

the d-exponent should respond to the effect of differential pressure.

Rehm and McClendon brought the equation to its final form by

realizing that mud weight increases would mask the difference between

normal and actual formation pressures. They proposed the normalization

ratio to account for the effect of mud weight increase:

dc = d (normal form. pressure ) / (actual mud weight)

dc = corrected d-exponent

d = original value,

normal form. pressure = ppg

actual mud weight = ppg

25

Figure 1-13 Typical d exponent plot

Example 1-6:

Geological and bit records from a control well were used with the de-

exponent principle to determine formation pressures. Compute the form.

pressures. Prepare a plot of formation pressure vs. depth.

Solution:

1-Calculate d-exponent;

d = [log (R / 60N)] / [log (12W / 1000 dB)] at 500 ft;

26

d = [log (95 / 60 (120))] / [log (12 (70) / 1000 (17.5))]

d= 1.425

2-The de-exponent is calculated as:

dc = d (9 /MW)

dc = 1.425 (9 / 9.2)

dc = 1.394

3-Plot dc-exponent.

Figure 1-14 dc exponent plot

27

4-The formation pressure is computed as;

FP = (9d / dc) -0.3

where; 0.3 represents the trip margin. At 16000 ft, the FP is equivalent to

15.7 ppg.

5-The formation pressure plot is also prepared (Figure 1-15).

Figure 1-15 Formation pressure plot