chpt3_4

57

Chapter 3

CAPILLARY PRESSURE AND RELATIVE PERMEABILITY BEHAVIOR OF THE J1 AND J2 RESERVOIRS AT

BULLWINKLE

Capillary pressure and relative permeability behavior of unconsolidated sands are

documented (Honarpour et al., 1986; Reynolds, 2000). Reynolds (2000) observed

capillary pressure behavior of deepwater turbidites and described differences present in

six facies. Honarpour et al. (1986) discussed several models for estimating relative

permeability between end-point measurements and documented empirical exponents used

by other workers to describe flow behavior associated with unconsolidated sands. Kikani

and Smith (1996) stated that Corey’s (1954) relative permeability model was used in

reservoir simulation to mimic production behavior for the unconsolidated J-sands at

Bullwinkle.

In this chapter, capillary pressure and relative permeability behavior of

unconsolidated sands of the J1 and J2 reservoirs at Bullwinkle are characterized and

modeled. Mercury injection data, collected using whole-core samples, are used to

evaluate in-situ fluid capillary behavior. End-point relative permeability and saturation

data from whole core samples, constrain the movement of fluids at these end-points.

Between these end-point values, Corey’s (1954) two-phase model is used to simulate the

relative permeability characteristics. Finally, core analysis, log-based petrophysical data

(Comisky, 2002), and capillary data from another deepwater field are combined to define

the hydraulic properties of six different Flow Units present in the J1 and J2 sands.

58

Characterization of The Hydraulic Behavior Present in Three Flow Units Using Whole Core Data Capillary Pressure Behavior

Capillary pressure experiments were performed on sixteen whole-core plug

samples, by Shell Oil Co., from three Flow Units sampled by the 65-1-ST and A-32-BP

wells in the J1 and J2 sands (Figs. 3-1, 3-2, Tables 3-1, 3-2). Capillary pressure

measurements were obtained by mercury injection tests using a methodology similar to

that described by Purcell (1949) (Figs. 3-3, 3-4, 3-5, Tables 3-3, 3-4, 3-5). Comisky

(2002) described six Flow Units for the J1 and J2 sands (analogous to facies) that were

interpreted from well log and core data.

Fifteen of the sixteen whole-core samples have mercury-air capillary entry

pressures between 7 and 9 psi, irreducible air saturation (wetting phase) of 1% to 10%,

and transition pressures (transition zone) that range from 13 psi to 285 psi (Figs. 3-3, 3-4,

3-5, Tables 3-3, 3-4, 3-5). The sixteenth sample, #3 from Flow Unit 2 in the 65-1-ST

(Figure 3-4), has higher entry pressure (41 psi) and a lower porosity than other samples

(Tables 3-1, 3-2).

The capillary behavior of the fifteen samples is similar to that documented by

Reynolds (2000) for the Mars Field (Mississippi Canyon Block 807), a deepwater

reservoir located in the Gulf of Mexico. He documented capillary pressure for six facies,

each having equal entry and transition pressures while recording different irreducible

wetting phase saturations. The saturation differences were attributed to differences in

grain size and clay content, where smaller grain sizes and higher clay content result in

higher irreducible wetting phase saturations.

59

A-32-BP PenetrationC.I. = 100’

RB

RAPermeabilityBarriers

BLK 64 BLK 65

1 MileBLK 108 BLK 109

13000

12500

12000

1200

0

1150

0

110 0

0

FlowUnit 2

Flow Unit 3

Flow Unit 5

Flow Unit 6

Flow Unit 2

Flow Unit 3

Figure 3-1: J1-sand Flow Unit map overlain by structure contours. Whole core samples were obtained from the A-32-BP well located in reservoir B (RB). The A-32-BP whole core was extracted from hydrocarbon bearing sands in the J1-RB (11,931 ft. to 11,975 ft., SSTVD) and J2-RB (Figure 3-2) reservoirs. The Flow Unit interpretation was performed by Comisky (2002).

60

A-32-BP Penetration65-1-ST Penetration

RA

RB

1 Mile

PermeabilityBarriersBLK 64 BLK 65

BLK 108 BLK 109

C.I. = 100’

12500

1200

0

1150011000

13000

12500Flow Unit 1

Flow Unit 2

Flow Unit 4

Flow Unit 6

Figure 3-2: J2-sand Flow Unit map overlain by structure contours. Two whole cores were obtained from the J2-sand, the A-32-BP (#1) in reservoir B (RB), and the 65-1-ST1 (#2) in reservoir A (RA). The A-32-BP whole core was extracted from hydrocarbon bearing sands in the J1-RB (Figure 3-1) and the J2-RB (11,987 ft. to 12,065 ft. SSTVD). The 65-1-ST whole core (12,420 ft. to 12,480, SSTVD) was extracted from the water leg of the J2-RA. The Flow Unit interpretation was performed by Comisky (2002).

61

1

10

100

1000

10000

0.0 0.2 0.4 0.6 0.8 1.0

Sample 35Sample 36Sample 43Sample 53ASample 54Sample 55Sample 60

1.0 0.8 0.6 0.4 0.2 0.0Mercury and Gas Saturation

0.0 0.2 0.4 0.6 0.8 1.0Water Saturation

Oil-W

ater Capillary Pressure (psi)

100

10.0

1.0

0.1

Mer

cury

-Air

Cap

illar

y Pr

essu

re (p

si)

Gas

-Oil

Cap

illar

y Pr

essu

re (p

si)

100

10.0

1.0

0.1

Figure 3-3: A-32-BP capillary pressure data for J2 sand whole core plug samples (Shell Petrophysical Services, 1990). Data shown are from core plug samples 35 (core depth = 12868.5 ft., SSTVD = 11992.6 ft.), 36 (core depth = 12869.0 ft., SSTVD = 11993.0 ft.), 43 (core depth = 12872.8 ft., SSTVD = 11996.3 ft.), 53A (core depth = 12901.8, SSTVD = 12021.4 ft.), 54 (core depth = 12907.5 ft., SSTVD = 12026.3 ft.), 55 (core depth = 12924.8 ft., SSTVD = 12040.6 ft.), 60 (core depth = 12952.6 ft., SSTVD = 12064.7 ft.). Samples are from Flow Unit #1 (Comisky, 2002). Sample properties are found in Tables 3-1 and 3-2. Data for sample 53A is shown in Table 3-3.

62

1

10

100

1000

10000

0.0 0.2 0.4 0.6 0.8 1.0

Sample 1Sample 2Sample 3Sample 6Sample 4

0.0 0.2 0.4 0.6 0.8 1.0

1.0 0.8 0.6 0.4 0.2 0.0

Water Saturation

Mercury and Gas Saturation

Mer

cury

-Air

Cap

illar

y Pr

essu

re (p

si)

Gas

-Oil

Cap

illar

y Pr

essu

re (p

si)

100

10.0

1.0

0.1

Oil-W


100

10.0

1.0

0.1

Figure 3-4: 65-1-ST capillary pressure data (Shell Petrophysical Services, 1987). Data shown are from whole core samples 1 (core depth = 13086.8 ft., SSTVD = 12468.8 ft.), 2 (core depth = 13089.5 ft., SSTVD = 12471.5 ft.), 3 (core depth = 13095.5 ft., SSTVD = 12477.5 ft.), 6 (core depth = 13101.5, SSTVD = 12483.5 ft.), and 4 (core depth = 13108.4, SSTVD = 12490.4 ft.) from the J2-RA aquifer. Samples are from Flow Unit #2 (Comisky, 2002). Sample properties are found in Tables 3-1 and 3-2. Data for sample 2 is shown in Table 3-4.

63

1

10

100

1000

10000

0.0 0.2 0.4 0.6 0.8 1.0

Sample 13Sample 14Sample 20Sample 30

1.0 0.8 0.6 0.4 0.2 0.0Mercury and Gas Saturation

0.0 0.2 0.4 0.6 0.8 1.0Water Saturation

Oil-W


100

10.0

1.0

0.1

Mer

cury

-Air

Cap

illar

y Pr

essu

re (p

si)

Gas

-Oil

Cap

illar

y Pr

essu

re (p

si)

100

10.0

1.0

0.1

Figure 3-5: A-32-BP capillary pressure data for J1 sand whole core plug samples (Shell Petrophysical Services, 1990). Data shown are from whole core plug samples 13 (core depth = 12808.2 ft., SSTVD = 11938.5 ft.), 14 (core depth = 12813.2 ft., SSTVD = 11942.8 ft.), 20 (core depth = 12819.2 ft., SSTVD = 11947.9 ft.), and 30 (core depth = 12845.7 ft. SSTVD = 11973.2 ft.). Samples are from Flow Unit #3 (Comisky, 2002). Sample properties are found in Tables 3-1 and 3-2. Data from sample 20 is shown in Table 3-5.

64

Table 3-1: Atmospheric properties of whole core samples used for mercury injection test (Shell Petrophysical Services, 1987, 1990). Flow Units determined by Comisky (2002).

Whole Core Sample Flow

Unit Sand Core Depth(ft.)

SSTVD (ft.) Porosity

A-32-BP 13 3 J1 12808.2 11938.5 0.347 A-32-BP 14 3 J1 12813.2 11942.8 0.388 A-32-BP 20 3 J1 12819.2 11947.9 0.396 A-32-BP 30 3 J1 12845.7 11973.2 0.369 A-32-BP 35 1 J2 12868.5 11992.6 0.367 A-32-BP 36 1 J2 12869.0 11993.0 0.342 A-32-BP 43 1 J2 12872.8 11996.3 0.383 A-32-BP 53A 1 J2 12901.8 12021.4 0.382 A-32-BP 54 1 J2 12907.5 12026.3 0.340 A-32-BP 55 1 J2 12924.8 12040.6 0.373 A-32-BP 60 1 J2 12952.6 12064.7 0.382 65-1-ST 1 2 J2 13086.8 12468.8 0.427 65-1-ST 2 2 J2 13089.5 12471.5 0.47 65-1-ST 3 2 J2 13095.5 12477.5 0.328 65-1-ST 6 2 J2 13101.5 12483.5 0.399 65-1-ST 4 2 J2 13108.4 12490.4 0.399

Table 3-2: Stressed properties of whole core samples used for mercury injection test (Shell Petrophysical Services, 1987, 1990). Flow Units determined by Comisky (2002).

Whole Core Sample Flow Unit Sand

Vertical Effective

Stress (psi) Porosity

Air Permeability

(mD) A-32-BP 13 3 J1 2100 0.296 1196 A-32-BP 14 3 J1 2100 0.310 1866 A-32-BP 20 3 J1 2100 0.324 1997 A-32-BP 30 3 J1 2100 0.293 1097 A-32-BP 35 1 J2 2100 0.295 1728 A-32-BP 36 1 J2 2100 0.282 1150 A-32-BP 43 1 J2 2100 0.320 1945 A-32-BP 53A 1 J2 2100 0.322 1602 A-32-BP 54 1 J2 2100 0.295 496 A-32-BP 55 1 J2 2100 0.323 1724 A-32-BP 60 1 J2 2100 0.334 1347 65-1-ST 1 2 J2 2000 0.306 - 65-1-ST 2 2 J2 2000 0.347 - 65-1-ST 3 2 J2 2000 0.261 - 65-1-ST 6 2 J2 2000 0.32 - 65-1-ST 4 2 J2 2100 0.332 -

65

Table 3-3: Mercury-air (Shell Petrophysical Services, 1990), calculated oil-water and gas-oil capillary pressure data for sample 53A (A-32-BP, J2 sand). Data is from Flow Unit 1 (Comisky, 2002).

Mercury-air Capillary Pressure - Pcma

(psi) SHg

Oil-water Capillary Pressure - Pcow

(psi) Sw

Gas-oil Capillary Pressure - Pcgo

(psi) Sg

7.0 0.004 0.245 0.996 0.147 0.004 8.0 0.377 0.280 0.624 0.168 0.377 9.0 0.543 0.315 0.458 0.189 0.543

11.0 0.642 0.385 0.358 0.231 0.642 13.0 0.693 0.455 0.307 0.273 0.693 15.0 0.717 0.525 0.283 0.315 0.717 17.0 0.734 0.595 0.266 0.357 0.734 21.0 0.762 0.735 0.239 0.441 0.762 26.0 0.783 0.910 0.217 0.546 0.783 31.0 0.799 1.085 0.201 0.651 0.799 41.0 0.823 1.435 0.177 0.861 0.823 51.0 0.835 1.785 0.165 1.0712 0.835 76.0 0.856 2.661 0.144 1.596 0.856

101.0 0.868 3.536 0.132 2.121 0.868 131.0 0.875 4.586 0.125 2.752 0.875 161.0 0.882 5.636 0.118 3.382 0.882 201.0 0.887 7.037 0.113 4.222 0.887 251.0 0.891 8.787 0.109 5.272 0.891 301.0 0.895 10.537 0.105 6.322 0.895 401.0 0.900 14.038 0.101 8.423 0.900 601.0 0.907 21.040 0.093 12.624 0.907 801.0 0.912 28.041 0.088 16.825 0.912 1001.0 0.917 35.043 0.083 21.026 0.917 1501.0 0.922 52.546 0.078 31.528 0.922 2001.0 0.924 70.050 0.076 42.030 0.924

66

Table 3-4: Mercury-air (Shell Petrophysical Services, 1987), calculated oil-water and gas-oil capillary pressure data for sample 2 (65-1-ST, J2 sand). Data is from Flow Unit 2 (Comisky, 2002).


(psi) SHg


(psi) Sw


(psi) Sg

6.0 0.276 0.210 0.724 0.126 0.276 7.0 0.385 0.245 0.615 0.147 0.385 8.0 0.512 0.280 0.488 0.168 0.512 9.0 0.574 0.315 0.426 0.189 0.574

10.0 0.620 0.350 0.380 0.210 0.620 11.0 0.645 0.385 0.355 0.231 0.645 13.0 0.695 0.455 0.305 0.273 0.695 15.0 0.723 0.525 0.277 0.315 0.723 17.0 0.745 0.595 0.255 0.357 0.745 21.0 0.778 0.735 0.222 0.441 0.778 26.0 0.805 0.910 0.195 0.546 0.805 31.0 0.824 1.085 0.176 0.651 0.824 41.0 0.850 1.435 0.150 0.861 0.850 51.0 0.868 1.785 0.132 1.071 0.868 76.0 0.894 2.661 0.106 1.596 0.894

101.0 0.908 3.536 0.092 2.121 0.908 131.0 0.920 4.586 0.080 2.752 0.920 161.0 0.928 5.636 0.072 3.382 0.928 201.0 0.935 7.037 0.065 4.222 0.935 251.0 0.941 8.787 0.059 5.272 0.941 301.0 0.946 10.537 0.054 6.322 0.946 401.0 0.954 14.038 0.046 8.423 0.954 601.0 0.963 21.040 0.037 12.62 0.963 801.0 0.968 28.041 0.032 16.825 0.968 1001.0 0.972 35.043 0.028 21.026 0.972 1501.0 0.978 52.546 0.022 31.528 0.978 2001.0 0.980 70.050 0.020 42.030 0.980

67

Table 3-5: Mercury-air (Shell Petrophysical Services, 1990), calculated oil-water and gas-oil capillary pressure data for sample 20 (A-32-BP, J1 sand). Data is from Flow Unit 3 (Comisky, 2002).


(psi) SHg


(psi) Sw


(psi) Sg

6.0 0.036 0.210 0.964 0.126 0.036 7.0 0.418 0.245 0.582 0.147 0.418 8.0 0.587 0.280 0.413 0.168 0.587 9.0 0.658 0.315 0.342 0.189 0.658

10.0 0.703 0.350 0.297 0.210 0.703 11.0 0.733 0.385 0.267 0.231 0.733 13.0 0.771 0.455 0.229 0.273 0.771 15.0 0.794 0.525 0.206 0.315 0.794 17.0 0.810 0.595 0.191 0.357 0.810 21.0 0.829 0.735 0.171 0.441 0.829 26.0 0.846 0.910 0.154 0.546 0.846 31.0 0.858 1.085 0.142 0.651 0.858 41.0 0.873 1.435 0.127 0.861 0.873 51.0 0.883 1.785 0.117 1.071 0.883 76.0 0.897 2.661 0.103 1.596 0.897

101.0 0.906 3.536 0.094 2.121 0.906 131.0 0.911 4.586 0.089 2.752 0.911 161.0 0.917 5.636 0.083 3.382 0.917 201.0 0.922 7.037 0.078 4.222 0.922 251.0 0.925 8.787 0.075 5.272 0.925 301.0 0.928 10.537 0.072 6.322 0.928 401.0 0.932 14.038 0.068 8.423 0.932 601.0 0.940 21.040 0.060 12.624 0.940 801.0 0.944 28.041 0.056 16.825 0.944 1001.0 0.949 35.043 0.051 21.026 0.949 1501.0 0.954 52.546 0.046 31.528 0.954 2001.0 0.959 70.050 0.041 42.030 0.959

68

Amyx et al. (1960) also showed capillary behavior of equal-entry and transition pressures

for sandstones having permeabilities of 200 mD and higher. Comisky (2002) documents

mean permeabilities for each Flow Unit that range from 460 mD to 2250 mD.

Oil-water Capillary Pressure

Mercury injection test data are converted from laboratory mercury-air conditions

to reservoir oil-water conditions using Purcell’s (1949) relation (Figs. 3-3, 3-4, 3-5,

Tables 3-3, 3-4, 3-5),

=

)cos()cos(

mama

owowmaow PcPc

θσθσ

. (3-1)

Pcow is the oil-water capillary pressure and Pcma is the mercury-air capillary pressure.

The oil-water interfacial tension (σow) is 15 dynes/cm based on a reservoir

temperature of 165oF (Livingston, 1938) (Table 3-6). We assume the water phase wets

the grains completely and set the oil-water contact angle (θow) to zero (Schlowalter, 1976)

(Table 3-6). The reported mercury-air interfacial tension (σma) is 484 dynes/cm and

contact angle is (θma) 130o (Shell Petrophysical Services, 1987) (Table 3-6). Oil-water

capillary pressure is calculated as 3.5% of the mercury-air capillary pressure (Figs. 3-3,

3-4, 3-5, Tables 3-3, 3-4, 3-5).

Fifteen samples have oil-water entry pressures ranging from 0.20 to 0.25 psi and

transition zone pressures from 0.5 to 10.0 psi. These same samples display the same

irreducible saturations (1% to 10%) as observed in the mercury-air data, as expected.

The sixteenth sample, #3, has a calculated oil-water entry pressure of 1.44 psi.

69

Table 3-6: Two-phase interfacial tension and contact angles.

Fluid Interaction

Interfacial Tension

(Dynes/cm)

Contact Angle

(Degrees) Mercury-Air 484 130 Oil-Water 15 0 Gas-Water 25 - Gas-Oil 10 -

70

Gas-oil Capillary Pressure

The spreading coefficient (S) relates gas-oil capillary pressure to oil-water

capillary pressure (Kalaydjian et al., 1995) through interfacial tensions. The spreading

coefficient is the balance of the three interfacial tensions,

)( goowgwS σσσ +−= , (3-2)

acting on the gas/oil/water contact and is zero when the liquid phases are in the presence

of a common vapor phase (Kalaydjian et al., 1995). We assume the spreading coefficient

is zero for this system and calculate the gas-oil interfacial tension (σgo = 10 dynes/cm)

using a gas-water interfacial tension (σgw) of 25 dynes/cm (Hough et al., 1951) and

Equation 3-2 (Table 3-6).

Gas-oil capillary pressure (Pcgo) is calculated from a simplified version of

Purcell’s (1949) relation (Amyx et al., 1960; Firoozabadi et al., 1988),

=

ow

goowgo PcPc

σσ

. (3-3)

Equation 3-1 reduces to Equation 3-3 by assuming that the gas-oil contact angle is equal

to the oil-water contact angle.

The ratio of the gas-oil to oil-water interfacial tension is 60%, which constrains

the calculated values of gas-oil capillary pressure (Figs. 3-3, 3-4, 3-5, Tables 3-3, 3-4, 3-

5). Fifteen samples have oil-water entry pressures ranging from 0.12 to 0.15 psi and

transition zone pressures from 0.3 to 6.0 psi. These same samples display irreducible

saturations ranging from 1% to 10%, as observed in the mercury-air and oil-water data.

The sixteenth sample, #3, has a calculated gas-oil entry pressure of 0.86 psi.

71

Relative Permeability Behavior

In the absence of experimental three-phase relative permeability data, two-phase

relative permeability behavior is characterized from end-point saturation and

permeability data. Later, this two-phase relative permeability behavior is used to

calculate three-phase oil relative permeability in the presence of oil, water and gas using

Stone’s Model II (1973).

End-point saturation (Swirr, Sor) and permeability (ko, kw) data were obtained

from 11 whole core samples (Tables 3-7, 3-8) using a procedure outlined by Thomas et

al. (1979). Measurements were conducted on stressed samples (Figs. 3-6, 3-7, Table 3-8)

using a laboratory brine (Table 3-7) and oil (ρo = 0.86 gm/cc).

Residual oil saturation (Sor) decreases with increasing irreducible water

saturation (Swirr) (Figure 3-6, Tables 3-7, 3-8). This trend had been observed by other

workers in high permeability sandstone cores (Wardlaw et al., 1979; Maldal et al., 1999).

Maldal et al. (1999) stated that higher oil saturation could result in larger initial oil

volumes being snapped off in the waterflood displacement process resulting in higher

Sor. Maldal et al. (1999) also observed that Sor is dependent on the waterflood rate,

where lower rates result in lower Sor (higher oil recovery).

End-point oil and water relative permeability are calculated (Figure 3-7, Tables 3-

8, 3-9) from:

brine

orow k

kk = (3-4)

and

72

brine

wrw k

kk = . (3-5)

ko is the effective permeability to oil flow in the presence of Swirr, kw is the effective

permeability associated with brine in the presence of Sor, kbrine is the permeability

associated with brine, krow is the oil relative permeability, and krw is the brine relative

permeability.

Calculated end-point relative permeabilities, from measured data, are related to

end-point saturations. Eleven samples have end-point krow values that range from 0.6 to

1.1 for Swirr values between 0.38 and 0.19 (Figure 3-7, Tables 3-8, 3-9). Sample 3

records higher krow (1.35), higher Swirr (0.718), and significantly lower permeability (2.6

mD) than the other samples (permeability range from 450 to 1656 mD) (Table 3-8). We

average krow (0.866) of the core data, neglecting the anomalous sample 3, because no

apparent trend is evident. End-point krw values range from 0.49 to 0.19, which

correspond to Sor values of 0.18 to 0.32 (Figure 3-7, Table 3-8, 3-9). Here, sample 3

records a lower krw (0.07) and Sor (0.14), which is expected because 71.8% of the pore

volume is filled by irreducible water. These end-point krw values increase linearly with

increasing Sor (Figure 3-7).

Calculated relative permeability greater than 1.0 is not uncommon. Other

workers report this behavior associated with water and brine in low permeability sands

(Jones and Owens, 1980; Ward and Morrow, 1987). Theoretically, this result is counter-

intuitive. Relative permeability is referenced to a specific permeability measured at

100% saturation and should be equal to or less than 1.0. The phenomenon is attributed to

hydration, plugging, and bound water (Jones and Owens, 1980).

73

0.10

0.15

0.20

0.25

0.30

0.35

0.0 0.2 0.4 0.6 0.8

Irreducible Water Saturation (Swirr)

Res

idua

l Oil

Satu

ratio

n (S

or) Flow unit 1 (J2: A-32-BP)

Flow unit 2 (J2: 65-1-ST)Flow unit 3 (J1: A-32-BP)

Sample 3

Figure 3-6: Residual oil saturation (Sor) versus irreducible water saturation (Swirr) from end-point relative permeability core data (Table 3-8) (Shell Petrophysical Services, 1987, 1990). The data show a decrease in Sor for higher values of Swirr. Samples were measured at near-insitu stress conditions (Table 3-8). Sample 3 records lower permeability (2.6 mD) than the other samples (460 to 1656 mD).

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0.0 0.2 0.4 0.6 0.8 1.0Sw

Rel

ativ

e Pe

rmea

bilit

y

krow (Unit 1)krw (Unit 1)krow (Unit 2)krw (Unit 2)krow (Unit 3)krw (Unit 3)

Sample 3

Sample 3

Figure 3-7: Calculated end point relative permeabilities for Flow Units 1, 2, and 3 (Tables 3-8, 3-9). Data shows that krw decreases as Sw increases, where Sw = 1-Sor. krow values show no trend. Sample 3 records lower permeability (2.6 mD) than the other samples (460 to 1656 mD).

74

Table 3-7: End-point relative permeability test sample data at atmospheric conditions (Atm.) and stressed conditions (Stress) (Shell Petrophysical Services, 1987, 1990).

Whole Core Sample Sand Flow

UnitCore

Depth (ft.) SSTVD

(ft.) Atm.

Porosity Stress (psi)

Stress Porosity

Stress Permeability

(mD)

NaCl (ppm)

A-32-BP 18 J1 3 12813'7" 11943.1 0.375 200 0.344 1540 210000 A-32-BP 34 J1 3 12849'0" 11976.1 0.333 200 0.311 1005 210000 A-32-BP 50 J2 1 12884'10" 12006.7 0.385 200 0.352 2265 210000 A-32-BP 57 J2 1 12938'6" 12052.5 0.382 200 0.363 2035 210000 65-1-ST 1 J2 2 13086'11" 12468.8 0.401 2000 0.325 1160 220000 65-1-ST 2 J2 2 13089'8" 12471.6 0.435 2000 0.340 1060 220000 65-1-ST 3 J2 2 13095'6" 12477.5 0.317 2000 0.256 3 220000 65-1-ST 4 J2 2 13108'4" 12490.3 0.385 2000 0.328 1050 220000 65-1-ST 6 J2 2 13101'6.5" 12483.5 0.384 2000 0.317 450 220000 65-1-ST 10 J2 2 13092'5" 12474.5 - 2200 0.306 1150 230000 65-1-ST 14 J2 2 13107'8" 12489.6 - 2200 0.329 1592 230000

Table 3-8: End-point relative permeability data from stressed whole core samples (Shell

Petrophysical Services, 1987, 1990).

Whole Core Sample Sand Flow

Unit Stress (psi) kbrine

Pcow (psi) ko Swirr kw Sor

A-32-BP 18 J1 3 2100 1136 16.0 1213 0.189 558 0.292 A-32-BP 34 J1 3 2100 776 17.0 638 0.206 328 0.316 A-32-BP 50 J2 1 2100 1536 9.4 1295 0.216 610 0.240 A-32-BP 57 J2 1 2100 1656 8.2 1250 0.192 542 0.260 65-1-ST 1 J2 2 2000 1160 36.0 1190 0.228 440 0.175 65-1-ST 2 J2 2 2000 1060 48.0 920 0.238 370 0.183 65-1-ST 3 J2 2 2000 2.6 205.0 3.5 0.718 0.2 0.139 65-1-ST 4 J2 2 2000 1050 46.0 930 0.221 340 0.186 65-1-ST 6 J2 2 2200 450 94.0 470 0.346 85 0.181 65-1-ST 10 J2 2 2200 1150 43.6 730 0.218 373 0.264 65-1-ST 14 J2 2 2200 1592 37.2 1265 0.297 378 0.251

75

Comparison of Mercury Injection Data with End-Point Saturation Data

Estimation of the wetting phase saturation using mercury injection test data

results in lower values than observed in other determination methods (Longeron et al.,

1995). Measured end-point water saturations are 10% to 25% greater than determined by

mercury injection (Figure 3-8, Tables 3-3, 3-4, 3-5, 3-7, 3-8). Amyx et al. (1960)

displayed comparisons of water-air and mercury-air capillary pressure measurements that

show similar behavior. The deviation of wetting phase saturation, observed here, is most

likely due to use of different fluids (mercury-air and oil-water) in the two experimental

methods. Here, we interpret that air does not effectively replicate the wetting

characteristics of water for these samples.

Corey’s Two-Phase Relative Permeability Model

Two-phase relative permeability is simulated for the range of saturations present

between constrained end-point values. Corey’s (1954) model is used for this purpose

based on its simplicity and limited input data requirements (Swirr and Sor). The model is

derived from capillary pressure concepts and is widely accepted to be fairly accurate for

consolidated porous media experiencing drainage (Honarpour et al., 1986). The model

has also been proposed for unconsolidated sands using different empirical exponents

(Honarpour et al., 1986).

Corey’s equations for wetting and non-wetting relative permeability between

constrained end-points is as follows:

btrw Swak )( *= , (3-6)

And

76

0.1

1.0

10.0

100.0

0.0 0.2 0.4 0.6 0.8 1.0Sw

Oil-

wat

er C

apill

ary

Pres

sure

(psi

)

0

1

10

100Sample 53AFlow Unit 1

(a)

0.1

1.0

10.0

100.0

0.0 0.2 0.4 0.6 0.8 1.0Sw

Oil-

wat

er C

apill

ary

Pres

sure

(psi

)

0.1

1

10

100Sample 2Flow Unit 2

(b)

0.1

1.0

10.0

100.0

0.0 0.2 0.4 0.6 0.8 1.0Sw

Oil-

wat

er C

apill

ary

Pres

sure

(psi

)

0.1

1

10

100Sample 20Flow Unit 3

(c)

Figure 3-8: Comparison of mercury injection test data with end-point relative permeability data. Converted oil-water capillary pressure curves are for samples (a) 53A, (b) 2, and (c) 20 (Tables 3-4, 3-5, 3-6). End-point relative permeability data are for (a) samples 50, 57, (b) samples 1, 2, 4, 6, 10, 14, and (c) samples 18, 34 (Table 3-8). Saturations differences are due to different wetting phase characteristics of the fluids used in the two experiments (mercury-air, and oil-water).

77

))(1()1( *2* drnwt SwSwck −−= . (3-7)

krwt and krnwt are the wetting and non-wetting phase relative permeabilities, respectively.

a, b, c, d are empirical constants. Sw* is the effective wetting phase saturation, defined

as:

)1()(*

SorSwirrSwirSwtSw−−

−= . (3-8)

Swt and Swir are the wetting phase saturation and the respective irreducible saturation.

Corey coefficients (a and c) constrain relative permeability at end-point

saturations (Swirr and Sor). Sw* collapses to 1.0 when the wetting phase saturation is

equal to one minus the irreducible non-wetting phase saturation (ie. Sw = 1-Sor). Sw* is

0.0 when the wetting phase is equal to the irreducible wetting phase (ie. Sw = Swirr).

Thus, a is equal to krwt when Sw* is 1.0 and b is equal to krnwt when Sw* is 0.0.

Relative permeability, between constrained end-points, is controlled by the Corey

exponents b and d. Oil-water Corey exponents of 3.0 and 3.5 have been proposed for

unconsolidated sands (Honarpour et al., 1986). Lower exponent values result in a more

concave relative permeability curve (lower relative permeability, thus more

heterogeneous sand), while higher exponent values result in a less concave curve (more

homogeneous sand). These exponents are reservoir, if not sand, specific and are adjusted

based on simulation results.

Corey’s Model: Oil-Water Relative Permeability

Oil-water relative permeability is modeled using endpoint saturation

measurements (Figure 3-7, Table 3-10). For each sampled Flow Unit, the measured end-

78

point saturations and relative permeabilities are averaged and then modeled (Figs. 3-9, 3-

10, 3-11, Table 3-11). We assume the wetting phase is water and non-wetting phase is

oil and use oil-water Corey exponents (b=2.5, d=3.0) reported by Kikani and Smith

(1996) for the Bullwinkle J-sands. The Corey coefficients (a and c) are constrained by

the average end-point relative permeability values (Table 3-10).

Modeled oil-water relative permeability values, for the range of saturations

between constrained end-points, form a concave shape (Figs. 3-9, 3-10, 3-11, 3-12). For

each Flow Unit, average krow values are constrained at Swirr (Table 3-10) and decrease to

0.0 at Sor and modeled krw is 0.0 at Swirr and increase to krw at Sor (Tables 3-10, 3-11).

krow, in Flow Unit 3, is higher at Swirr (krow = 0.95) and distributed over a smaller range

of saturations (∆Sw = 0.499) than Flow Units 1 (∆Sw = 0.546) and 2 (∆Sw = 0.535), thus

krow decreases to Sor faster (Figure 3-12, Table 3-11). Similarly, krw, in Unit 3, is higher

(krw = 0.46) at Sor and decreases to Swirr over a smaller range of saturations (∆Sw =

0.499) (Figure 3-12, Table 3-11).

Corey’s Model: Gas-Oil Relative Permeability

Corey’s model (1954) (Equations 3-6 through 3-8) is used to simulate gas-oil

relative permeability (Figure 3-13, Tables 3-10, 3-12) using the average Swirr and Sor

values from the oil-water system. The wetting phase saturation (Sliq) is the sum of Swirr

and oil saturation (So) and the non-wetting phase saturation is gas (Sg). We use gas-oil

Corey exponents (b=4.0 and d=1.5) reported by Kikani and Smith (1996). Endpoint

relative permeability data for a gas-oil system were not collected, but krog should equal

krow at Sg equal to zero. The Corey gas exponent (c)is set to 1.0.

79

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0Sw

Rel

ativ

e Pe

rmea

bilit

y

0.0

0.2

0.4

0.6

0.8

1.00.0000 0.2000 0.4000 0.6000 0.8000 1.0000

krwkrowkrow @ Swirrkrw @ Sor

Figure 3-9: Modeled oil-water relative permeability for Flow Unit 1 (A-32-BP, J2 sand) (Table 3-12). Model is based on average end-point saturations and relative permeabilities from samples 50 and 57 (Tables 3-8, 3-9, 3-10), and oil-water Corey exponents from Kikani and Smith (1996).

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0Sw

Rel

ativ

e Pe

rmea

bilit

y

0

0

0

1

1

1

0.0000 0.2000 0.4000 0.6000 0.8000 1.0000


Figure 3-10: Modeled oil-water relative permeability for Flow Unit 2 (65-1-ST, J2 sand) (Table 3-12). Model is based on average end-point saturations and relative permeabilities from samples 1, 2, 4, 6, 10, and 14 (Tables 3-8, 3-9, 3-10), and oil-water Corey exponents from Kikani and Smith (1996).

80

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0Sw

Rel

ativ

e Pe

rmea

bilit

y

0

0

0

1

1

1

0 0 0 1 1 1


Figure 3-11: Modeled oil-water relative permeability for Flow Unit 3 (A-32-BP, J1 sand) (Table 3-12). Model is based on average end-point saturations and relative permeabilities from samples 18, 34 (Tables 3-8, 3-9, 3-10), and oil-water Corey exponents from Kikani and Smith (1996).

81

0.0

0.2

0.4

0.6

0.8

1.0

0.00 0.25 0.50 0.75 1.00Sw

Oil-

Wat

er R

elat

ive

Perm

eabi

lity krw (Flow

Unit 1)

krow (FlowUnit 1)

krw (FlowUnit 2)

krow (FlowUnit 2)

krw (FlowUnit 3)

krow (FlowUnit 3)

Figure 3-12: Comparison of modeled oil-water relative permeability curves for Flow Units 1, 2, and 3 (Table 3-12). Model is based on average end-point saturations and relative permeabilities for each Flow Unit (Table 3-10), and oil-water Corey exponents from Kikani and Smith (1996).

0.0

0.2

0.4

0.6

0.8

1.0

0.00 0.25 0.50 0.75 1.00Sg

Gas

-Oil

Rel

ativ

e Pe

rmea

bilit

y krg (FlowUnit 1)

krog (FlowUnit 1)

krg (FlowUnit 2)

krog (FlowUnit 2)

krg (FlowUnit 3)

krog (FlowUnit 3)

Figure 3-13: Modeled gas-oil relative permeability curves for Flow Units 1, 2, and 3 (Table 3-13). Model is based on average end-point saturations for each Flow Unit (Table 3-10), and gas-oil Corey exponents from Kikani and Smith (1996).

82

Table 3-9: Calculated end-point relative permeability values.

Whole Core Sample Sand Flow Unit krow @ Swirr krw @ Sor

A-32-BP 18 J1 3 1.07 0.49 A-32-BP 34 J1 3 0.82 0.42 A-32-BP 50 J2 1 0.84 0.40 A-32-BP 57 J2 1 0.75 0.33 65-1-ST 1 J2 2 1.03 0.38 65-1-ST 2 J2 2 0.87 0.35 65-1-ST 3 J2 2 1.35 0.07 65-1-ST 4 J2 2 0.89 0.32 65-1-ST 6 J2 2 1.04 0.19 65-1-ST 10 J2 2 0.63 0.32 65-1-ST 14 J2 2 0.79 0.24

Table 3-10: Average oil-water end-point saturation and relative permeabilities from whole core data for Flow Units 1, 2 and 3. End-point relative permeabilities are equal to the Corey coefficients a and

c.

Whole Core Sand Flow

Unit Swirr krow (a) Sor krw

(c) A-32-BP J2 1 0.204 0.800 0.250 0.360 65-1-ST J2 2 0.258 0.849 0.207 0.300 A-32-BP J1 3 0.197 0.950 0.304 0.460

83

Table 3-11: Modeled oil-water relative permeability for Flow Units 1, 2, and 3 from whole core data.

Flow Unit 1 (A-32-BP, J2 sand)

Flow Unit 2 (65-1-ST, J2 sand) Flow Unit 3

(A-32-BP, J1 sand) Sw krw krow Sw krw krow Sw krw krow

0.2040 0.0000 0.8000 0.2580 0.0000 0.8490 0.1970 0.0000 0.9500 0.2500 0.0002 0.6688 0.3000 0.0001 0.7197 0.2500 0.0006 0.7561 0.3000 0.0020 0.5357 0.3500 0.0015 0.5750 0.3000 0.0040 0.5867 0.3500 0.0069 0.4128 0.4000 0.0056 0.4415 0.3500 0.0133 0.4330 0.4000 0.0167 0.3028 0.4500 0.0139 0.3220 0.4000 0.0310 0.2990 0.4500 0.0330 0.2081 0.5000 0.0278 0.2196 0.4500 0.0600 0.1886 0.5000 0.0575 0.1310 0.5500 0.0488 0.1366 0.5000 0.1030 0.1045 0.5500 0.0919 0.0727 0.6000 0.0784 0.0744 0.5500 0.1628 0.0471 0.6000 0.1377 0.0331 0.6500 0.1180 0.0328 0.6000 0.2423 0.0146 0.6500 0.1967 0.0106 0.7000 0.1692 0.0097 0.6500 0.3442 0.0017 0.7000 0.2704 0.0014 0.7500 0.2333 0.0010 0.6960 0.4600 0.0000 0.7500 0.3600 0.0000 0.7930 0.3000 0.0000

Table 3-12: Modeled gas-oil relative permeability for Flow Units 1, 2, and 3 from whole core data.

Flow Unit 1 (A-32-BP, J2 sand)

Flow Unit 2 (65-1-ST, J2 sand) Flow Unit 3

(A-32-BP, J1 sand) Sg krg krog Sg krg krog Sg krg krog

0.0000 0.0000 0.8000 0.0000 0.0000 0.8490 0.0000 0.0000 0.9500 0.0500 0.0011 0.5448 0.0500 0.0012 0.5734 0.0500 0.0015 0.6227 0.1000 0.0088 0.3561 0.1000 0.0093 0.3711 0.1000 0.0114 0.3883 0.1500 0.0289 0.2213 0.1500 0.0306 0.2277 0.1500 0.0375 0.2273 0.2000 0.0665 0.1290 0.2000 0.0705 0.1305 0.2000 0.0861 0.1225 0.2500 0.1260 0.0691 0.2500 0.1335 0.0684 0.2500 0.1625 0.0589 0.3000 0.2107 0.0329 0.3000 0.2229 0.0316 0.3000 0.2704 0.0240 0.3500 0.3227 0.0133 0.3500 0.3410 0.0121 0.3500 0.4117 0.0076 0.4000 0.4627 0.0041 0.4000 0.4881 0.0034 0.4000 0.5858 0.0015 0.4500 0.6295 0.0008 0.4500 0.6627 0.0005 0.4500 0.7882 0.0001 0.5000 0.8185 0.0000 0.5000 0.8588 0.0000 0.4990 1.0000 0.0000 0.5460 1.0000 0.0000 0.5350 1.0000 0.0000 0.8030 1.0000 0.0000 0.7960 1.0000 0.0000 0.7420 1.0000 0.0000

84

Differences in the gas-oil relative permeability concave behavior, for the three

Flow Units, are due to different residual Sliq (Sg = 1-Sliq) (Figure 3-13, Table 3-12).

Flow Unit 3 has the highest residual Sliq (0.499) followed by Flow Units 2 (0.535) and 1

(0.545) (Table 3-12). The end-point values of krg are 1.0 at the residual Sliq and decrease

to zero at Sg equal to 0.0, while krog is equal to the end-point value of krow at Sg equal 0.0

and decrease to 0.0 at the residual Sliq.

Predictability of Relative Permeability: A Comparison Using Other Models

Many workers have proposed predictive models of two-phase oil-water and gas-

oil relative permeability. Relative permeability behavior have also been modeled using

Brooks & Corey’s (1964) model and a neural network model (Silpngarmlers et al., 1996)

to highlight differences in model behavior (Figure 3-14). Curves modeled using Brooks

& Corey’s (1964) model are constrained using oil-water capillary pressure data (Sample

53A), end-point saturations, and relative permeability (Table 3-13). Neural network

curves are based on rock (permeability, porosity, irreducible water saturation, residual oil

saturation) and fluid properties (viscosity, density) (Table 3-14).

The predicted relative permeability behaviors from the three models are different.

Both the Brooks & Corey’s and neural network models predict higher water relative

permeabilities (krw) and lower oil relative permeabilities (krow) for the range of saturations

between end-points. Both Corey’s (1954) and Brooks & Corey’s (1964) models are

constrained by end-point data, while the neural network model is not. The three sets of

relative permeability curves will result in significantly different simulated saturation

behavior. Specifically, Corey’s model will predict the least water flow for increases in

85

0.0

0.2

0.4

0.6

0.8

1.0

0.00 0.25 0.50 0.75 1.00Sw

Rel

ativ

e Pe

rmea

bilit

y

krw (ANN)

krow (ANN)

krw (Corey)

krow (Corey)

krw (Brooks& Corey)

krow (Brooks& Corey)

Figure 3-14: A comparison of modeled oil-water relative permeability using Corey’s (1954), Brooks & Corey’s (1964), and a neural network (Silpngarmlers et al., 1996) two-phase models (Tables 3-11, 3-13, 3-14). The comparisons are based on whole core (A-32-BP) end-point saturation data and average fluid properties from Flow Unit 1.

86

Table 3-13: Modeled oil-water relative permeability using Brooks and Corey’s two-phase model (1964). Model inputs are oil-water capillary pressure (Sample 53A) and average whole core endpoint

data for Flow Units 1.

Sw krw krow 0.204 0.0000 0.8162 0.217 0.0006 0.7267 0.239 0.0018 0.6000 0.266 0.0053 0.4565 0.283 0.0102 0.3652 0.307 0.0215 0.2594 0.358 0.0513 0.1434 0.458 0.1458 0.0389 0.624 0.2693 0.0078 0.750 0.3600 0.0000

Table 3-14: Modeled oil-water relative permeability using a neural network two-phase model

(Silpngarmlers et al., 1996). Values are based on average rock and fluid properties for Flow Units 1.

Sw krw krow 0.160 0.0000 0.6770 0.200 0.0070 0.6110 0.250 0.0270 0.5230 0.300 0.0570 0.4330 0.350 0.1013 0.3440 0.400 0.1585 0.2610 0.450 0.2280 0.1880 0.500 0.3075 0.1250 0.550 0.3938 0.0760 0.600 0.4833 0.0380 0.650 0.5724 0.0140 0.700 0.6582 0.0020 0.747 0.7339 0.0000

87

water saturation followed by Brooks & Corey’s (1964) and the neural network curves,

respectively. Corey’s (1954) model is used here because of its proven effectiveness by

Kikani and Smith (1996) on the Bullwinkle J-sands.

Conclusions

Capillary pressure and relative permeability behavior observed in J1 and J2 sand

core data are consistent with homogeneous type sands having low irreducible water

saturation and residual oil saturation.

Capillary pressure behavior is consistent with documented behavior of

unconsolidated sands in other deepwater reservoirs. Entry and transition pressures show

little deviation for all but one sample, while the irreducible wetting phase saturation

varies from 1% to 10%. Wetting phase saturation differences have been attributed to

differences in grain size and clay content, data that are not available here.

Experimental end-point data highlight trends for rock and fluid properties. End-

point saturations indicate that Sor increases with decreasing Swirr, a phenomenon

observed and explained by other workers (Maldal et al., 1999). Swirr data are 10 to 25%

greater than determined from mercury injection test data, suggesting that air does not

replicate the wetting phase characteristics of water. End-point krw values linearly increase

with increasing Sor, while no trend is evident for end-point krow.

Modeled two-phase relative permeability behavior, between constrained end-

points, is a function of the end-point saturations, end-point relative permeabilities, and

empirical constants. Corey’s (1954) model collapses to the end-point relative

permeability values (Corey coefficients) at end-point saturations. Between these

constrained end-points the Corey exponents control the value of relative permeability.

88

Modeling Hydraulic Behavior of the Six Flow Units

The hydraulic behavior of J1 and J2 sands are modeled for six different Flow

Units defined by Comisky (2002). The behavior is interpreted from the limited core data,

described previously, and log-derived petrophysical properties. Specifically,

petrophysically based end-point water and oil saturations are used to model this behavior.

Constraining End-point Water and Oil Saturations of the Six Flow Units

Log-derived initial water saturation values (Swi) are interpreted to be the

irreducible water saturation (Swirr) based on the calculated capillary pressures at each

well. The oil-water capillary pressure is calculated (O’Conner, 2000),

gHPc owow )( ρρ −= , (3-10)

for wells of height H above the free water level (Figs. 3-1, 3-2, Tables 3-15 through 3-

20), where g is the acceleration due to gravity, ρw is the density of brine (1.16 gm/cm3)

(Comisky, 2002), and ρo is the average density of oil (0.72 gm/cm3) (Chapter 2). Data

from 18 wells show that Pcow range from 13.5 psi (well A-4-BP, J1 sand) to 249.6 psi

(well A-33, J2 sand) in the J1 and J2 sands (Tables 3-15 through 3-20). These capillary

pressures are greater than the interpreted transition zone pressures (0.5 to 10.0 psi) from

core data, thus log-based Swi values are interpreted to approximate Swirr.

An empirical relation of the whole-core end-point saturation data, described in the

previous section, is used to approximate the residual oil saturation (Sor) for the six Flow

Units. Whole core Sor and Swirr are empirically related using a linear least-squares

regression (Figure 3-6, Table 3-8):

2890.02256.0 +−= SwirrSor . (3-9)

89

Then, Sor is calculated for each Flow Unit by substituting the log-based Swi values

(Comisky, 2002) in Equation 3-9 (Table 3-21). The calculated Sor values range from

0.23 to 0.26 for values of Swi between 0.25 and 0.14 (Table 3-21).

Modeling Capillary Pressure in the Six Flow Units

Capillary pressure curves are modeled for six Flow Units (Figs. 3-15 through 3-

22, Tables 3-23 through 3-28). Average log-based Swi values (Table 3-21) define the

irreducible water saturation for each Flow Unit. The oil-water capillary pressure (Pcow)

for each Flow Unit is modeled with an entry pressure of 0.2 psi and transition pressures

from 0.5 to 10.0 psi as implied by the whole core data (Figs. 3-3, 3-4, 3-5). The gas-oil

capillary pressure (Pcgo) is calculated as described previously (Equation 3-3).

The capillary pressure curves are used to establish the initial oil, water, and gas

saturations present above the original oil-water contact (OOWC) in the J1 and J2 sand

reservoirs (Figs. 3-15 through 3-22, Tables 3-23 through 3-28). The Swirr values in each

capillary curve specify the initial saturation differences for each Flow Unit. Further,

these curves predict the transition of saturations (transition zone) from a fluid contact

(100% Sw or Sliq) to Swirr at in-situ equilibrium conditions. The transition of water is

75.8 ft. above the OOWC and for oil is 26.9 ft. above the OGOC.

90

0.1

1.0

10.0

100.0

1000.0

0.0 0.2 0.4 0.6 0.8 1.0Saturation (Sw and Sg)

Cap

illar

y Pr

essu

re (p

si)

0

1

10

100

1000Syn Pcow (Sw)Syn Pcgo (Sg)Pcow (Sw)

Figure 3-15: Modeled oil-water and gas-oil capillary pressure curves for Flow Unit 1 (Table 3-21). Triangles represent oil-water capillary pressures associated with wells in Flow Unit 1 located in the J1 sand (A-32-BP, A-38, A-4-BP) (Table 3-14).

0.1

1.0

10.0

100.0

1000.0


Cap

illar

y Pr

essu

re (p

si)

0

1

10

100

1000Pcow (Sw)Syn Pcow (Sw)Syn Pcgo (Sg)

Figure 3-16: Modeled oil-water and gas-oil capillary pressure curves for Flow Unit 2 (Table 3-22). Triangles represent oil-water capillary pressures associated with the 65-1 well in Flow Unit 2 (J1 and J2 sands) (Table 3-15).

91

0.1

1.0

10.0

100.0

1000.0


Cap

illar

y Pr

essu

re (p

si)

0

1

10

100

1000Pcow (Sw)Syn Pcow (Sw)

Syn Pcgo (Sg)

Figure 3-17: Modeled oil-water and gas-oil capillary pressure curves for Flow Unit 3 (Table 3-23). Triangles represent oil-water capillary pressures associated with wells in Flow Unit 3 located in the J1 sand (109-1ST, A-32-BP, A-38, A-4-BP) (Table 3-16).

0.1

1.0

10.0

100.0

1000.0


Cap

illar

y Pr

essu

re (p

si)

0

1

10

100


Figure 3-18: Modeled oil-water and gas-oil capillary pressure curves for Flow Unit 4 (Table 3-24). Triangles represent oil-water capillary pressures associated with wells in Flow Unit 4 located in the J2 sand (109-1, A-1, A-2-BP, A-34, A-35, A-37, A-3-BP, A-5-BP) (Table 3-17).

92

0.1

1.0

10.0

100.0

1000.0


Cap

illar

y Pr

essu

re (p

si)

0

1

10

100


Figure 3-19: Modeled oil-water and gas-oil capillary pressure curves for Flow Unit 5 (Table 3-25). Triangles represent oil-water capillary pressures associated with wells in Flow Unit 5 located in the J1 sand (A-1, A-11-BP, A-35, A-37, A-3-BP, A-41) (Table 3-18).

0.1

1.0

10.0

100.0

1000.0


Cap

illar

y Pr

essu

re (p

si)

0

1

10

100


Figure 3-20: Modeled oil-water and gas-oil capillary pressure curves for Flow Unit 6 (Table 3-26). Triangles represent oil-water capillary pressures associated with wells in Flow Unit 6 located in the J2 sand (109-1ST, A-11-BP) and both J1 and J2 sands (A-33) (Table 3-19).

93

0.1

1.0

10.0

100.0

1000.0

0.0 0.2 0.4 0.6 0.8 1.0Sw

Oil-

Wat

er C

apill

ary

Pres

sure

(psi

)

0.1

1

10

100

1000Flow Unit 1Flow Unit 2Flow Unit 3Flow Unit 4Flow Unit 5Flow Unit 6

Figure 3-21: Comparison of modeled oil-water capillary pressure (Pcow) curves for the six Flow Units (Tables 3-21 through 3-26).

0.1

1.0

10.0

100.0

0.0 0.2 0.4 0.6 0.8 1.0Sg

Gas

-Oil

Cap

illar

y Pr

essu

re (p

si)

0

1

10

100Flow Unit 1Flow Unit 2Flow Unit 3Flow Unit 4Flow Unit 5Flow Unit 6

Figure 3-22: Comparison of modeled gas-oil capillary pressure (Pcgo) curves for six Flow Units (Tables 3-21 through 3-26).

94

Table 3-15: Rock properties for wells in Flow Unit 1. Water saturation values are from Comisky (2002).

Flow Unit Sand Well SSTVD (ft)

Pcow (psi) Swi

1 J2 A-32-BP 12022 74.87 0.16 1 J2 A-38 12218 37.53 0.14 1 J2 A-4-BP 12337 14.86 0.18

Table 3-16: Rock properties for wells in Flow Unit 2. Water saturation values are from Comisky

(2002).


Pcow (psi) Swi

2 J1 65-1-ST 12361 - 1.00 2 J2 65-1-ST 12454 - 1.00 2 J1 65-1 12120 38.10 0.19 2 J2 65-1 12185 43.82 0.20 2 J2 A-36 12621 - 1.00


(2002).


Pcow (psi) Swi

3 J1 109-1ST 11315 191.47 0.10 3 J1 A-32-BP 11931 74.11 0.23 3 J1 A-38 12122 37.72 0.21 3 J1 A-4-BP 12249 13.53 0.22


(2002).


Pcow (psi) Swi

4 J2 109-1 12028 73.73 0.11 4 J2 A-1 11677 140.60 0.08 4 J2 A-2-BP 11928 92.78 0.18 4 J2 A-34 11817 113.93 0.12 4 J2 A-35 11419 189.76 0.11 4 J2 A-37 11573 160.42 0.18 4 J2 A-3-BP 11467 180.61 0.19 4 J2 A-5-BP 12119 56.39 0.14

95

Table 3-19: Rock properties for wells in Flow Unit 5. Water saturation values are from Comisky (2002).


Pcow (psi) Swi

5 J1 A-1 11562 144.41 0.14 5 J1 A-11-BP 11498 156.61 0.14 5 J1 A-35 11297 194.90 0.20 5 J1 A-37 11455 164.80 0.22 5 J1 A-3-BP 11363 182.33 0.16 5 J1 A-41 11373 180.42 0.13


(2002).


Pcow (psi) Swi

6 J2 109-1ST 12185 43.82 0.21 6 J2 A-11-BP 11493 175.66 0.20 6 J1 A-33 11017 248.25 0.35 6 J2 A-33 11105 249.58 0.25

Table 3-21: Average porosity and initial water saturation (Comisky, 2002) with estimated residual oil

saturation.

Flow Unit Sand Φ Swi Sor 1 J2 0.33 0.160 0.253 2 J1 & J2 0.31 0.200 0.244 3 J1 0.32 0.190 0.246 4 J2 0.32 0.140 0.257 5 J1 0.33 0.170 0.251 6 J1 & J2 0.28 0.250 0.233

96

Modeling Relative Permeability in Six Flow Units

Oil-water and gas-oil relative permeability are modeled for six Flow Units using

Corey’s two-phase model (1954) (Figs. 3-23 through 3-36, Tables 3-23 through 3-28).

Model inputs for each Flow Unit are the log-based Swi values and empirically related Sor

values (Table 3-21). The Corey exponents reported by Kikani and Smith (1996) are used.

The Corey water coefficient (a), which is equal to the end-point water relative

permeability (krw), is related to Sor using a linear least square regression fit to a cross-plot

of whole core Sor and end-point krw (Figure 3-37, Tables 3-10, 3-22):

0472.0658.1 −= Sora . (3-11)

The Corey oil coefficient (c = 0.866) is an average of calculated end-point oil relative

permeability (krow) values from whole core data (Table 3-10). The end-point values of

krog are set equal to endpoint krow and endpoint krw is set at 1.0.

The modeled relative permeability behavior, for the six Flow Units, is similar due

to small differences in residual oil saturations (Figs. 3-23 through 3-36). These small

differences are due to a lack of whole core data. Therefore, the two-phase relative

permeability behavior is considered an unconstrained property. Additionally, this two-

phase behavior is used to predict three-phase relative permeability behavior using Stone’s

Model II (1973).

97

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0Sw

Rel

ativ

e Pe

rmea

bilit

y

krwkrow

Figure 3-23: Modeled oil-water relative permeability curves for Flow Unit 1 (Table 3-21). The thick line is the relative permeability of water in the presence of oil (krw) and the thin line is the relative permeability of oil in the presence of water (krow). The average initial water saturation (Swi), based on log data, is 0.160 and the estimated residual oil saturation (Sor) is 0.253 (Table 3-13).

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0Sg

Rel

ativ

e Pe

rmea

bilit

y

krgkrog

Figure 3-24: Modeled gas-oil relative permeability curves for Flow Unit 1 (Table 3-21). The thick line is the relative permeability of gas in the presence of liquid (oil and water) (krg) and the thin line is the relative permeability of oil in the presence of gas and irreducible water (krog). The average initial water saturation (Swi), based on log data, is 0.160 and the estimated residual oil saturation (Sor) is 0.253 (Table 3-13).

98

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0Sw

Rel

ativ

e Pe

rmea

bilit

y

krwkrow


0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0Sg

Rel

ativ

e Pe

rmea

bilit

y

krgkrog


99

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0Sw

Rel

ativ

e Pe

rmea

bilit

y

krwkrow

Figure 3-27: Modeled oil-water relative permeability curves for Flow Unit 3 (Table 3-23). The thick line is the relative permeability of water in the presence of oil (krw) and the thin line is the relative permeability of oil in the presence of water (krow). The average initial water saturation (Swi), based on log data, is 0.190 and the estimated residual oil saturation (Sor) is 0.246 (Table3-13).

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0Sg

Rel

ativ

e Pe

rmea

bilit

y

krgkrog


100

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0Sw

Rel

ativ

e Pe

rmea

bilit

y

krwkrow


0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0Sg

Rel

ativ

e Pe

rmea

bilit

y

krgkrog


101

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0Sw

Rel

ativ

e Pe

rmea

bilit

y

krwkrow


0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0Sg

Rel

ativ

e Pe

rmea

bilit

y

krgkrog


102

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0Sw

Rel

ativ

e Pe

rmea

bilit

y

krwkrow


0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0Sg

Rel

ativ

e Pe

rmea

bilit

y

krgkrog


103

0.0

0.2

0.4

0.6

0.8

1.0

0.00 0.25 0.50 0.75 1.00Sw

Oil-

Wat

er R

elat

ive

Perm

eabi

lity krw (Unit 1)

krow (Unit 1)krw (Unit 2)krow (Unit 2)krw (Unit 3)krow (Unit 3)krw (Unit 4)

krow (Unit 4)krw (Unit 5)krow (Unit 5)krw (Unit 6)krow (Unit 6)

Figure 3-35: Comparison of modeled oil-water relative permeability curves for six Flow Units (Tables 3-21 through 3-26).

0.0

0.2

0.4

0.6

0.8

1.0

0.00 0.25 0.50 0.75 1.00Sg

Gas

-Oil

Rel

ativ

e Pe

rmea

bilit

y krg (Unit 1)krog (Unit 1)krg (Unit 2)krog (Unit 2)krg (Unit 3)krog (Unit 3)krg (Unit 4)krog (Unit 4)krg (Unit 5)krog (Unit 5)krg (Unit 6)krog (Unit 6)

Figure 3-36: Comparison of modeled gas-oil relative permeability curves for six Flow Units (Tables 3-21through 3-26).

104

0.25

0.30

0.35

0.40

0.45

0.50

0.20 0.23 0.26 0.29 0.32

Residual Oil Saturation (Sor)

Cor

ey C

oeffi

cien

t (a)

Figure 3-37: Corey coefficient a versus average residual oil saturation from core data (Tables 3-10). Trend line is a linear least squares fit to the data. The value of a is equal to end-point krw at Sor and is used to determine a for each of the six Flow Units.

105

Table 3-22: Oil-water Corey coefficient a and c values used to model oil-water relative permeability for the six Flow Units described by Comisky (2002). Values of a are linearly related to Sor and c is

an average value derived from core data (Tables 3-10, 3-11)

Flow Unit Sand Sor a c 1 J2 0.253 0.372 0.866 2 J1 & J2 0.244 0.357 0.866 3 J1 0.246 0.361 0.866 4 J2 0.257 0.379 0.866 5 J1 0.251 0.369 0.866 6 J1 & J2 0.233 0.339 0.866

106

Table 3-23: Modeled oil-water and gas-oil relative permeability and capillary pressure for Flow Unit 1 (J2 sand).

Oil-water Gas-oil Sw krw k row Pcow (psi) Sg krg krog Pcgo (psi)

0.160 0.0000 0.8490 20.000 0.000 0.0000 0.8490 0.1333 0.200 0.0001 0.7363 2.4000 0.050 0.0009 0.5946 0.1400 0.250 0.0013 0.6030 1.1000 0.100 0.0071 0.4022 0.1467 0.300 0.0051 0.4786 0.7500 0.150 0.0234 0.2608 0.1533 0.350 0.0126 0.3652 0.5400 0.200 0.0539 0.1604 0.1600 0.400 0.0254 0.2650 0.4100 0.253 0.1060 0.0890 0.1670 0.450 0.0449 0.1801 0.3400 0.300 0.1719 0.0485 0.1733 0.500 0.0723 0.1119 0.3000 0.350 0.2643 0.0226 0.1800 0.550 0.1092 0.0612 0.2900 0.400 0.3809 0.0087 0.1867 0.600 0.1568 0.0273 0.2800 0.450 0.5214 0.0025 0.1933 0.650 0.2165 0.0084 0.2700 0.500 0.6841 0.0004 0.2000 0.700 0.2898 0.0010 0.2600 0.550 0.8640 0.0000 0.2267 0.747 0.3723 0.0000 0.2510 0.587 1.0000 0.0000 0.2550

0.840 1.0000 0.0000 13.333 Table 3-24: Modeled oil-water and gas-oil relative permeability and capillary pressure for Flow Unit

2 (J1 and J2 sands).

Oil-water Gas-oil Sw krw krow Pcow (psi) Sg krg krog Pcgo (psi)

0.200 0.0000 0.8490 20.000 0.000 0.0000 0.8490 0.1333 0.250 0.0003 0.7015 1.6000 0.050 0.0011 0.5824 0.1400 0.300 0.0021 0.5632 0.8500 0.100 0.0083 0.3841 0.1467 0.350 0.0070 0.4356 0.5600 0.150 0.0274 0.2414 0.1533 0.400 0.0166 0.3211 0.4300 0.200 0.0631 0.1427 0.1600 0.450 0.0325 0.2223 0.3500 0.244 0.1116 0.0842 0.1670 0.500 0.0561 0.1415 0.3000 0.300 0.2002 0.0382 0.1733 0.550 0.0891 0.0799 0.2900 0.350 0.3069 0.0160 0.1800 0.600 0.1331 0.0375 0.2800 0.400 0.4407 0.0053 0.1867 0.650 0.1895 0.0127 0.2700 0.450 0.6005 0.0011 0.1933 0.700 0.2599 0.0020 0.2600 0.500 0.7829 0.0001 0.2000 0.756 0.3574 0.0000 0.2490 0.556 1.0000 0.0000 0.2375

0.800 1.0000 0.0000 13.333

107



0.190 0.0000 0.8490 20.000 0.000 0.0000 0.8490 0.1333 0.250 0.0004 0.6755 1.4000 0.050 0.0010 0.5857 0.1400 0.300 0.0027 0.5409 0.7900 0.100 0.0080 0.3889 0.1467 0.350 0.0082 0.4170 0.5500 0.150 0.0262 0.2465 0.1533 0.400 0.0186 0.3062 0.4100 0.200 0.0606 0.1473 0.1600 0.450 0.0353 0.2111 0.3400 0.246 0.1097 0.0858 0.1670 0.500 0.0599 0.1336 0.3000 0.300 0.1923 0.0408 0.1733 0.550 0.0938 0.0749 0.2900 0.350 0.2951 0.0176 0.1800 0.600 0.1386 0.0348 0.2800 0.400 0.4241 0.0061 0.1867 0.650 0.1957 0.0115 0.2700 0.450 0.5787 0.0014 0.1933 0.700 0.2667 0.0017 0.2600 0.500 0.7559 0.0001 0.2000 0.754 0.3607 0.0000 0.2490 0.564 1.0000 0.0000 0.2275

0.810 1.0000 0.0000 13.333 Table 3-26: Modeled oil-water and gas-oil relative permeability and capillary pressure for Flow Unit

4 (J2 sand).


0.140 0.0000 0.8490 20.000 0.000 0.0000 0.8490 0.1333 0.200 0.0004 0.6863 2.0000 0.050 0.0008 0.6005 0.1400 0.250 0.0023 0.5594 1.0000 0.100 0.0065 0.4111 0.1467 0.300 0.0071 0.4416 0.7000 0.150 0.0216 0.2704 0.1533 0.350 0.0160 0.3348 0.5000 0.200 0.0499 0.1694 0.1600 0.400 0.0304 0.2412 0.3900 0.257 0.1027 0.0920 0.1670 0.450 0.0515 0.1625 0.3400 0.300 0.1594 0.0541 0.1733 0.500 0.0806 0.0999 0.3000 0.350 0.2453 0.0263 0.1800 0.550 0.1191 0.0538 0.2900 0.400 0.3541 0.0109 0.1867 0.600 0.1682 0.0235 0.2800 0.450 0.4857 0.0035 0.1933 0.650 0.2292 0.0069 0.2700 0.500 0.6390 0.0007 0.2000 0.700 0.3035 0.0007 0.2600 0.550 0.8103 0.0001 0.2267 0.743 0.3789 0.0000 0.2520 0.603 1.0000 0.0000 0.2605

0.860 1.0000 0.0000 13.333

108



0.170 0.0000 0.8490 20.000 0.000 0.0000 0.8490 0.1333 0.200 0.0001 0.7628 2.5000 0.050 0.0009 0.5916 0.1400 0.250 0.0010 0.6261 1.2000 0.100 0.0074 0.3977 0.1467 0.300 0.0042 0.4984 0.8000 0.150 0.0243 0.2559 0.1533 0.350 0.0111 0.3815 0.5500 0.200 0.0561 0.1559 0.1600 0.400 0.0231 0.2778 0.4100 0.251 0.1078 0.0874 0.1670 0.450 0.0417 0.1896 0.3400 0.300 0.1787 0.0458 0.1733 0.500 0.0683 0.1185 0.3000 0.350 0.2745 0.0208 0.1800 0.550 0.1043 0.0653 0.2900 0.400 0.3952 0.0078 0.1867 0.600 0.1511 0.0295 0.2800 0.450 0.5405 0.0021 0.1933 0.650 0.2102 0.0093 0.2700 0.500 0.7081 0.0003 0.2000 0.700 0.2830 0.0012 0.2600 0.579 1.0000 0.0000 0.2500 0.749 0.3690 0.0000 0.2500 0.830 1.0000 0.0000 13.333

Table 3-28: Modeled oil-water and gas-oil relative permeability and capillary pressure for Flow Unit

6 (J1 and J2 sand).


0.250 0.0000 0.8490 20.0000 0.000 0.0000 0.8490 0.1333 0.300 0.0003 0.6907 3.0000 0.050 0.0013 0.5652 0.1400 0.350 0.0025 0.5432 1.2000 0.100 0.0103 0.3593 0.1467 0.400 0.0083 0.4084 0.6300 0.150 0.0338 0.2156 0.1533 0.450 0.0196 0.2895 0.4700 0.200 0.0778 0.1200 0.1600 0.500 0.0383 0.1896 0.3600 0.233 0.1204 0.0773 0.1640 0.550 0.0663 0.1112 0.3200 0.300 0.2452 0.0264 0.1733 0.600 0.1052 0.0552 0.2900 0.350 0.3742 0.0092 0.1800 0.650 0.1571 0.0206 0.2700 0.400 0.5342 0.0022 0.1933 0.700 0.2236 0.0042 0.2600 0.450 0.7223 0.0002 0.2133 0.767 0.3391 0.0000 0.2470 0.517 1.0000 0.0000 0.2550

0.750 1.0000 0.0000 13.3333

109

Conclusions

Capillary pressure and relative permeability are modeled to establish initial fluid

saturations and multiphase fluid behavior for reservoir simulation of the J1 and J2 sand

reservoirs.

The capillary and relative permeability behavior of the J1 and J2 sand reservoirs

are characterized. Mercury injection data mimic behavior observed in other deepwater

turbidite sands. End-point permeability and saturation data document decreases in Sor

that correspond to increases in Swirr and decreases in krw. These characteristics are

incorporated into the model using empirical relationships.

Modeled capillary pressure behavior of the six Flow Units mimics whole core

data and compare to data documented at Mars. Capillary differences exit in the wetting

phase irreducible saturation only. The resultant curves are used in reservoir simulation to

establish the initial saturation conditions above the OOWC for each of the six Flow

Units.

Modeled two-phase relative permeability approximates the multiphase flow

characteristics of six Flow Units in the J1 and J2 sands. Empirical correlations between

end-point saturations and the water end-point relative permeability are based on limited

whole core data. Corey’s (1954) two-phase model is used to predict the relative

permeability between these constrained end-point values. These two-phase relative

permeability curves are used to predict three-phase relative permeability using Stone’s

Model II (1973).

110

Chapter 4

ROCK COMPACTION EFFECTS ON POROSITY AND PERMEABILITY OF THE UNCONSOLIDATED J-SANDS

AT BULLWINKLE Reservoir sands in unconsolidated systems are highly compressible (Merle et al.,

1976; Yale et al., 1993; Ostermeier, 1993, 1996, 2001; Davies and Davies, 1999;

Flemings et al., 2001). The compressibility versus effective stress for the Bullwinkle J2

sand has been documented (Flemings et al., 2001). Ostermeier (1993, 1996, 2001)

documented porosity and permeability effects due to changes in compressibility for

increases in vertical effective stress of unconsolidated turbidite sands from the Gulf of

Mexico. Kikani and Smith (1996) reported non-linear compaction effects on porosity

and permeability, for the J-sands at Bullwinkle. These effects correspond to non-linear

compressibility behavior documented by Ostermeier (1993, 1996, 2001). Davies and

Davies (1999) described stress-dependent permeability as a function of rock type for

unconsolidated turbidites (from a Plio-Pleistocene deepwater field in the Gulf of Mexico

and the Pliocene Wilmington Field in California) and addressed implications for

production associated with the observed behavior.

In this chapter, stress dependent porosity and permeability behavior of the J1 and

J2 sands at Bullwinkle are characterized and modeled. A Fetkovich (1971) material

balance model, constrained by historical production and pressure data, is used to calculate

pore compressibility behavior. The inferred compressibility behavior is consistent with

uniaxial deformation data. This model of pore compressibility is used to calculate the

reduction in porosity due to increases in vertical effective stress during production.

111

Permeability reductions corresponding to changes in porosity are grain size dependent

and empirically modeled based on deformation data.

Whole Core Data

Uniaxial deformation experiments were run on whole core samples, by Shell Oil

Co., located in three different Flow Units, described by Comisky (2002), in the J1 and J2

sand (Chapter 3: Figs. 3-1, 3-2). Three experiments were run on 65-1-ST samples

(Tables 4-1, 4-2, 4-3) and seven on the A-32-BP (Tables 4-4 through 4-10) using a

protocol outlined by Ostermeier (1996). The 65-1-ST samples are from Flow Unit 2

(Tables 4-1, 4-2, 4-3) in the J2 sand, while samples from the A-32-BP are from separate

Flow Units in the J1 and J2 sands (3 and 1, respectively) (Tables 4-4 through 4-10)

(Comisky, 2002).

Initial In-situ Vertical Effective Stress

Vertical effective stress (σv ) can be approximated as,

pvv PS −=σ , (4-1)

where Sv is the overburden stress and Pp is the pore pressure. The overburden stress (Sv)

is calculated from the bulk density log. Lupa et al. (2002) approximated it as a linear

function of depth over the J-sand interval;

.)(*88.0 ftzft

psiSv

= . (4-2)

In the J-sands prior to production, the vertical effective stress (σv) increases by 1515 psi

from 1050 psi at the crest to 2565 psi at the base of the J2 sand (Figure 4-1).

112

10000

10500

11000

11500

12000

12500

13000

13500

7000 8000 9000 10000 11000 12000

Pressure (psi)

SSTV

D (f

t.)OverburdenStress

Oil Pressure

WaterPressure

GasPressure

Crest J2-RB

Crest J2-RA

σv=2565 psiJ2 sand base

σv=1050 psi

Figure 4-1: Pressure vs. depth in the J2 sand at initial conditions. Pressures are based on a measured reference pressure of 8550 psi at 12070 ft., SSTVD and the assumption that the system is at steady state (no potential gradients). Overburden stress (Sv) calculation is from Equation 4-2. Brine, oil, and water densities are assumed to be constant and 1.16 gm/cc, 0.75 gm/cc, 0.34 gm/cc, respectively (see Chapter 2). Values use to construct this plot are in Table 4-11.

113

Table 4-1: Deformation data from the 65-1-ST whole core, sample 10 (13092.3 ft., measured depth; 12486.3 ft., SSTVD) located in the J2 sand (Shell Petrophysical Services, 1987). Pore compressibility

values (cp) are calculated from Equation 4-3. Sample is from Flow Unit #2 (Comisky, 2002). Bold values are close to the initial in-situ vertical effective stress (2309.8 psi).

σv (psi) Φ k

(mD) cp

(10-6 psi-1) 200 0.3214 1293 80.0 750 0.3118 1268 42.9 1250 0.3072 1184 34.8 1750 0.3035 1153 27.3 2200 0.3009 1142 33.3 2700 0.2974 1099 22.0 3200 0.2951 1034 22.1 3700 0.2928 987 24.1 4700 0.2878 926 25.9 5700 0.2825 824 37.5 6700 0.2749 703 43.1 7700 0.2663 529 43.0 8700 0.2579 391 40.8 9700 0.2501 296 -



σv (psi) Φ k

(mD) cp

(10-6 psi-1) 200 0.3713 1528 68.5 750 0.3625 1344 63.2 1250 0.3552 1241 56.8 1750 0.3487 1123 59.7 2200 0.3426 1022 69.3 2700 0.3348 937 63.8 3200 0.3277 814 71.7 3700 0.3198 701 42.3 4700 0.3106 526 59.3 5700 0.2979 340 29.2 6700 0.2918 239 35.8 7700 0.2844 152 26.5 8700 0.279 114 34.3 9700 0.2721 84.6 -

114



σv (psi) Φ k

(mD) cp

(10-6 psi-1) 200 0.3102 30.9 51.0 750 0.3042 21.8 35.9 1250 0.3004 19.4 34.3 1750 0.2968 16.8 39.4 2200 0.2931 14.9 32.8 2700 0.2897 14.5 28.2 3200 0.2868 12.2 34.2 3700 0.2833 10.7 54.7 4700 0.2722 7.18 78.2 5700 0.2567 3.14 74.4 6700 0.2425 1.89 57.7 7700 0.2319 1.12 52.8 8700 0.2225 0.751 53.8 9700 0.2132 0.673 -

Table 4-4: Deformation data from the A-32-BP whole core, sample 16 (12823.4 ft., measured depth; 11943.0 ft., SSTVD) located in the J1 sand (Shell Petrophysical Services, 1990). Pore compressibility


σv (psi) Φ k

(mD) cp

(10-6 psi-1) 200 0.3174 3296 53.3 2000 0.2966 2420 34.0 3000 0.2895 2039 59.8 4000 0.2772 1708 37.4 5000 0.2697 1384 59.4 6000 0.258 957 52.8 7000 0.2479 659 71.3 8000 0.2346 390 25.1 9000 0.2301 308 -

115



σv (psi) Φ k

(mD) cp

(10-6 psi-1) 200 0.3544 4533 67.3 2000 0.3267 2611 46.8 3000 0.3164 1996 48.1 4000 0.306 1495 73.9 5000 0.2903 929 70.4 6000 0.2758 561 42.6 7000 0.2673 405 60.2 8000 0.2555 250 49.4 9000 0.2461 154 -



σv (psi) Φ k

(mD) cp

(10-6 psi-1) 200 0.3358 4166 68.7 2000 0.3082 2583 49.2 3000 0.2977 2037 34.0 4000 0.2906 1697 61.6 5000 0.2779 1188 68.8 6000 0.2641 770 49.4 7000 0.2545 572 43.7 8000 0.2462 399 41.5 9000 0.2385 263 -



σv (psi) Φ k

(mD) cp

(10-6 psi-1) 200 0.3203 1137 36.0 2000 0.3062 913 31.5 3000 0.2995 818 20.0 4000 0.2953 696 46.1 4500 0.2905 612 64.0 5000 0.2839 497 -

116



σv (psi) Φ k

(mD) cp

(10-6 psi-1) 200 0.3501 3341 40.3 2000 0.3336 2372 27.0 3000 0.3276 2279 20.9 3500 0.3253 1988 31.9 4000 0.3218 1776 40.3 4500 0.3174 1526 38.8 5000 0.3132 1300 -



σv (psi) Φ k

(mD) cp

(10-6 psi-1) 200 0.3426 3136 60.4 2000 0.3181 2095 64.1 3000 0.3042 1717 45.4 3500 0.2994 1556 42.9 4000 0.2949 1428 43.3 4500 0.2904 1264 47.6 5000 0.2855 1149 -



σv (psi) Φ k

(mD) cp

(10-6 psi-1) 200 0.3585 3589 42.0 2000 0.3411 2716 34.7 3000 0.3333 2353 39.6 3500 0.3289 2109 50.7 4000 0.3233 1906 61.2 4500 0.3166 1508 81.3 5000 0.3078 1142 -

117

Table 4-11: Pressure versus depth in the J2 sand at initial conditions. Pressures are based on a measure value of 8550 psi at 12070 ft, SSTVD and the assumption that th esystem is at steady state.

Overburden stress (Sv) is calculated from Eq. 4-2. Brine, oil, and water densities are assumed constant at 1.16 gm/cc, 0.75 gm/cc, and 0.34 gm/cc, respectively.

Depth SSTVD

(ft.)

Sv (psi)

Oil Phase Pressure

(psi)

Water Phase Pressure

(psi)

Gas Phase Pressure

(psi)

Minimum σv

(psi) 10500 9091 8040 - - 1050 10600 9187 8072 - - 1115 10700 9283 8105 - - 1178 10800 9380 8137 - - 1242 10900 9476 8170 - - 1306 11000 9573 8202 - - 1371 11100 9670 8235 - - 1435 11200 9766 8267 - - 1499 11300 9863 8300 - - 1563 11400 9960 8332 - - 1628 11500 10057 8365 - - 1578 11600 10154 8397 - - 1661 11700 10251 8430 - - 1743 11800 10349 8462 - 8523 1826 11900 10446 8495 - 8537 1909 12000 10543 8527 - 8552 1991 12100 10641 8560 - 8567 2074 12200 10738 8592 - 8581 2157 12300 10836 8625 - - 2211 12400 10934 8657 8655 - 2279 12500 11032 - 8705 - 2326 12600 11130 - 8755 - 2374 12700 11228 - 8806 - 2422 12800 11326 - 8856 - 2470 12900 11424 - 8906 - 2518 13000 11522 - 8956 - 2566

118

Pore Compressibility

Pore compressibility (cp) is defined as (Flemings et al., 2001) (derivation in

Appendix C),

( ) vv

p

pp

VV

cσσ ∂Φ∂

Φ−Φ−=

∂∂

−=111 , (4-3)

where Vp is the pore volume and Φ is the porosity. The cp of the whole core samples is

calculated from deformation data (Figs 4-2, 4-3, Tables 4-1 through 4-10). In two of the

three samples, from the 65-1-ST well, cp increases with increasing vertical effective stress

over the range of stresses present during production (Figure 4-2, Tables 4-1, 4-2, 4-3). In

the A-32-BP, all seven samples record this same behavior (Figure 4-3, Tables 4-4

through 4-10). In sample 14, from the 65-1-ST, cp decreases with increasing stress, in

contrast to the other samples.

Ostermeier (1993, 1996, 2001) examined the compressibility for four different

deepwater Gulf of Mexico turbidite reservoirs and showed similar behavior. In

deformation experiments, Ostermeier (1993, 1996, 2001) showed that compressibility

often increased (strain softening) and then decreased (strain hardening) with increasing

vertical effective stress. Ostermeier (2001) suggested that at initial conditions ductile

grains were load-supporting. With increased effective stress, the yield strength of these

grains was reached and the compressibility increased.

Compaction Effects On Permeability

Permeability decreases with increasing stress (Figs. 4-4, 4-5, Tables 4-1 through

4-10). The J1 samples, from the A-32-BP, record higher permeability than samples from

the J2 in the A-32-BP and 65-1-ST (Figure 4-6). In the J1 sand, permeability measured

119

0

20

40

60

80

100

0 2000 4000 6000 8000

σv (psi)

c p (1

0-6 p

si-1

) #10 (J2)

#14 (J2)

#22 (J2)

σv

(initial)σv

(12/99)

Figure 4-2: Pore compressibility (cp) vs. vertical effective stress (σv) for 65-1-ST whole core samples (Tables 4-1, 4-2, 4-3). These samples are from the J2 sand. The initial in-situ vertical effective stress (σvi) is approximately 2319 psi (range = 2309 psi to 2329 psi) and in Dec., 1999 σv is 4800 psi (Appendix A: Figure A.14).

0

20

40

60

80

100

0 2000 4000 6000 8000σv (psi)

c p (1

0-6 p

si-1

)

#16 (J1)

#19 (J1)

#21 (J1)

#33 (J2)

#46 (J2)

#51 (J2)

#56 (J2)

σv

(initial)

σv

(12/99)

Figure 4-3: Pore compressibility (cp) vs. vertical effective stress (σv) for A-32-BP whole core samples (Tables 4-4 through 4-10). These samples were extracted from both the J1 and J2 sand. The σvi is approximately 2014 psi (range = 1979 psi to 2050 psi) and in Dec., 1999 σv is 4500 psi (Appendix A: Figure A.14).

120

0

1000

2000

3000

4000

5000

0.20 0.25 0.30 0.35 0.40Φ

k (m

D)

#10 (J2)#14 (J2)#22 (J2)

Figure 4-4: Permeability (k) vs. porosity (Φ) data for the 65-1-ST whole core samples (Tables 4-1, 4-2, 4-3).

0

1000

2000

3000

4000

5000

0.20 0.25 0.30 0.35 0.40Φ

k (m

D)

#16 (J1)#19 (J1)#21 (J1)#33 (J2)#46 (J2)#51 (J2)#56 (J2)

Figure 4-5: Permeability (k) vs. porosity (Φ) data for the A-32-BP whole core samples (Tables 4-4 through 4-10).

121

on stressed samples (2000 psi) ranged from 2611 mD to 2420 mD with a mean value of

2538 mD (Tables 4-4, 4-5, 4-6). Permeability measured on stressed samples (2000 psi)

in the J2 sand range from 2716 mD to 913 mD with a mean value of 2024 mD (Tables 4-

7, 4-8, 4-9, 4-10). The 65-1-ST samples (samples 10, 14), stressed at 2200 psi, record

permeabilities ranging from 1142 mD to 1022 mD with a mean value of 1082 mD

(Tables 4-1, 4-2).

Permeabilities at a given porosity are lower for finer grained samples (Figure 4-6,

Table 4-12). For example, the minimum and maximum median grain sizes in the A-32-

BP well (J2 sand) are 135 µm and 174 µm, respectively, and the average of these median

values is 152 µm (Figure 4-6). In contrast at the 65-1-ST well (J2 sand) the average

median grain size is 121 µm with a range of 54 µm to 166 µm (Figure 4-6). No grain

size data were collected in the J1 sand.

Davies and Davies (1999) described compaction as stress-related physical

changes due to grain slippage, grain rotation, ductile changes in grain shape, and grain

fracturing. These compaction processes results in a decrease in pore volume (lower

porosity) and decrease in pore throat radius (lower permeability). In the J1 and J2 sands,

it is assumed that compaction is due to grain slippage and rotation.

The observed cp behavior may be explained by Ostermeier’s (2001) hypothesis,

presented earlier, or by physical changes in the matrix material. The early time cp

behavior may be explained by grains that are initially slightly cemented (friable sand).

For a certain increase in effective stress, the cementing material may break or crack,

breaking the bond between grains. For further increases in vertical effective stress the

grains slip, rotate and reorient. This grain slippage and rotation corresponds to increases

122

0

1000

2000

3000

4000

5000

0.20 0.25 0.30 0.35 0.40Φ

k (m

D)

65-1-ST (J2): Flow Unit #2 - Dm = 121 umA-32-BP (J1): Flow Unit #3 - ?A-32-BP (J2): Flow Unit #1 - Dm = 152 um

Figure 4-6: Permeability (k) vs. porosity (Φ) data for the A-32-BP and 65-1-ST samples. The data are separated by Flow Unit (Tables 4-1 through 4-10). Differences correspond to grain size (Table 4-12) and in-situ permeability. Data are shown separately in Figures 4-4 and 4-5. Dm is the median grain size as reported by core analyses.

0

1000

2000

3000

4000

5000

0.20 0.25 0.30 0.35 0.40Φ

k (m

D)

fine upper - Dm = 200 umfine lower - Dm = 150 umvery-fine upper - Dm = 100 um65-1-ST (J2) - Dm = 121 umA-32-BP (J1) - ?A-32-BP (J2) - Dm = 152 um

Figure 4-7: Permeability-porosity relationships using the Carman-Kozeny model (Table 4-13). Deformation data is from the 65-1-ST and A-32-BP samples (Tables 4-1 through 4-10). Dm is the median grain size of whole core samples. Modeled permeability-porosity relationships are for grain sizes of Dm=100 µm (very-fine upper), Dm=150 µm (fine lower), and Dm=200 µm (fine-upper) (Table 4-13).

123

Table 4-12: Average rock properties from whole core samples for sampled Flow Units 1, 2, and 3 (Table 4-1 through 4-10). Average properties are at approximate intial in-situ σv (A-32-BP = 2000

psi, 65-1-ST = 2200 psi).

Whole Core

Flow Unit Sand k (mD) Φ

Dm (µm)

A-32-BP 1 J2 2024 0.311 152 65-1-ST 2 J2 1082 0.325 121 A-32-BP 3 J1 2538 0.322 -

Table 4-13: Permeability-porosity relations for three different grain sizes (Dm) using the Carman-Kozeny model.

Φ k

(mD) Dm = 200 µm

k (mD)

Dm = 150 µm

k (mD)

Dm = 100 µm 0.20 639.6 359.8 159.9 0.22 895.6 503.8 223.9 0.24 1224.7 688.9 306.2 0.26 1642.4 923.9 410.6 0.28 2166.9 1218.9 541.7 0.30 2819.7 1586.1 704.9 0.32 3626.3 2039.8 906.6 0.34 4617.2 2597.2 1154.3 0.36 5828.8 3278.7 1457.2 0.38 7304.6 4108.9 1826.2

124

in cp with increasing vertical effective stress. Then, at higher vertical effective stresses

the grains may orient themselves such that slippage and rotation can no longer occur.

With further increases in stress, cp decreases rapidly because the matrix material has

compacted.

Relating Permeability to Porosity Using The Carman-Kozeny Model

The coupled porosity (Φ) -permeability behavior is simulated with the Carman-

Kozeny (CK) model (Figure 4-7, Table 4-13), where permeability (k) is defined as,

2

32

)1(**72 Φ−ΤΦ

=Dm

k . (4-4)

T is the flow tortuosity, Dm is grain diameter, and the constant 72.0 (dimensionless) is

related to pore geometry (Panda et al., 1994). Grain size diameters of 100 µm (very-fine

upper), 150 µm (fine lower), and 200 µm (fine upper) are modeled (Figure 4-7, Table 4-

13). The Bullwinkle data (Figure 4-7, Table 4-13) could be simulated with a tortuosity

factor (T) equal to 11.0.

Pore Compressibility Behavior Derived From A Material Balance Model

Fetkovich’s (1971) approach is used to model the pore compressibility behavior

in the J1 and J2 sands. Fetkovich’s (1971) approach is a time-incremental approach that

solves for the pressure in the reservoir and at the mid point in the aquifer (Figure 4-8). It

is a box model with constant rock and fluid properties. The change in pressure at each

time step is a function of fluid injected and produced and changes in pore

compressibility.

125

Model Geometry and Rock and Fluid Property Inputs

It is assumed that the J1, J2, J3, J4 and the Rocky reservoirs are connected by a

common aquifer (Figure 4-9) based on the observation that there is pressure

communication between them (Holman and Robertson, 1994). Reservoir and aquifer

volumes for these sands are listed in Table 4-14. These volumes are constrained by

seismic and log data (Swanston, 2001; Comisky, 2002).

The entire J1, J2, J3, J4, and Rocky sand system is modeled as a single

rectangular system of width (b), height (h), reservoir length (l), and aquifer length (L)

(Figure 4-8). The total volume of the aquifer is set equal to the mapped value of

1.154X109 barrels, while the hydrocarbon volume is set equal to the combined J1 and J2

mapped value of 2.134X108 barrels (Table 4-15). Only the oil present in the J1 and J2 is

considered for the material balance model. Hydrocarbons in the Rocky, J3 and J4 sands

are ignored.

The height, h, was set equal to the average sand thickness of the J2 sand, 45 ft.

The width, b, is set equal to the length of the J2 oil-water contact, 10,000 ft. The aquifer

and reservoir lengths (L and l, respectively) are calculated based on the assumption that

the total volume is fixed by the mapped volumes (Tables 4-14, 4-15).

Values of porosity and water saturation (Swi) are averaged from the six Flow

Units present in the J1 and J2 sands (Comisky, 2002) (Table 4-15) (Chapter 3: Figs. 3-1,

3-2). The permeability in the aquifer is specified at 1060 mD based on the permeability

of Flow Unit 2, which is located in the aquifer of both sands (Comisky, 2002) (Table 4-

15).

126

ReservoirAquifer

PresPaq

Wp

NpWinj

lL

b

h

Figure 4-8: Schematic of Fetkovick material balance model. Dimensions are reservoir length (l), aquifer length (L), reservoir and aquifer width (b) and thickness (h). Dimensions shown are not to scale. Actual model dimensions are found in Table 4-15. Constant rock and fluid properties are based on rock and fluid samples. Np is the produced volume of oil, Wp is the produced volume of water, and Winj is the injected volume of water. Paq is the average aquifer pressure and Pres is the aquifer-reservoir interface pressure.

J1+J2

J3Rocky

J4

Figure 4-9: J-sand and Rocky sand connectivity model. The J1 and J2 are interpreted to be connected in the hydrocarbon column while the J3, J4, and Rocky sands are interpreted to connect to the J2 sand in the aquifer.

127

Table 4-14: Reservoir and aquifer volumes for J-sands and Rocky (Swanston, 2001). Fluid volumes are based on seismic limits and average sand thickness as recorded by well logs. Equivalent aquifer

volume is used for sizing of the aquifer for material balance calculations.

Sand Estimated Oil Volume (MRB)

Estimated Free Gas Volume (MRB)

Estimated Aquifer Volume (MRB)

Equivalent Aquifer Volume (MRB)

J1 53,743 0 94,855 94,855 J2 159,576 0 300,576 300,576 J3 20,759 10,560 194,056 225,375 J4 24,546 0 332,668 357,214

Rocky 20,450 5,016 151,411 176,877 Total 279,074 15,576 1,073,566 1,154,897

Table 4-15: Input properties for Fetkovich material balance model (Figure 4-9).

Width of reservoir and aquifer – b (ft) 10,000 Average height (J1+J2) of sand – h (ft) 45 Length of reservoir – l (ft) 10,150 Length of aquifer - L (ft) 45,000 Average porosity - Φ 0.32 Average Initial oil saturation in reservoir – Soi 0.82 Average Initial water saturation in reservoir – Swi 0.18 Average Oil formation volume factor – Boi (res Bbl/STB) 1.55 Brine formation volume factor – Bw (res. Bbl/STB) 1.0002 Oil compressibility – co (psi-1) 1.00E-05 Water compressibility – cw (psi-1) 3.00E-06 Estimated brine viscosity - µw (cp) 0.5 Average permeability in the aquifer – kw (mD) 1060 Initial pressure at 12,070 ft. datum - Pi (psi) 8550 J1 and J2 Reservoir oil volume - OOIP (MRB) 213,448 J1, J2, J3, J4, and Rocky water volume – OWIP (MRB) 1,154,051

128

Constant fluid properties are specified. Hydrocarbon properties (µo, Boi, co) are

taken from a mid-dip location (12,070 ft., SSTVD) based on the J-RB equation of state

fluid model developed in Chapter 2 (Table 4-15). Correlations for aquifer properties of

viscosity (µw) (McCain, 1988), formation volume factor (Bwi) (McCain, 1988), and

compressibility (cw) (Osif, 1984) are based on a reservoir temperature of 165oF, a brine

density of 1.16 gm/cc (Comisky, 2002) and average aquifer pressure of 8750 psi at

12,700 ft., SSTVD (Table 4-15).

The Fetkovich Model – Cumulative and Incremental Models

The Fetkovich (1971) model is used to calculate the average and instantaneous

system behavior of the J1 and J2 sands. The average behavior is calculated using a

cumulative model (as presented by Fetkovich, 1971), which references the initial

condition at each time step and calculates pressure based on an average change in system

conditions. This cumulative model is modified to calculate the instantaneous behavior

using an incremental model that assumes the system is at hydrostatic equilibrium at each

time step. The instantaneous behavior is calculated using the same set of equations, but

the initial aquifer pressure (Piaq) and reservoir pressure (Pires) are set to the pressures

calculated in the previous time step, the volume of oil produced is subtracted from the

original oil in place (N), and the volume of water influx (We(n)) is calculated at each time-

step.

Both the cumulative and incremental approaches suffer limitations. The

cumulative approach calculates only the average compressibility that must be present to

achieve the pressure between any two points in time. Thus, the change in compressibility

at each incremental change in effective stress cannot be captured. In contrast, the

129

incremental approach calculates the instantaneous compressibility. However, it violates a

basic assumption of the Fetkovich (1971) model: namely that there are no potential

gradients at the start of each timestep.

The average aquifer pressure (Paq(n)) for each time-step (n) is calculated,

( )injnaqi

iaqnaq WWeWeiP

PP −∑

−= )()( , (4-5)

Where Winj is the water injected, and

615.5***** iaqtw PcLhb

WeiΦ

= (4-6)

is the maximum encroachable water. The constant 5.615 converts cubic feet to reservoir

barrels. The total compressibility, ctw, in the aquifer is the sum of the water

compressibility (cw) and pore compressibility. The mobile volume of water influencing

the reservoir per time-step (We(n)) is calculated,

−

−−=

∆

−−

−

ntWeiqwi

nresnresnaq

in e

PPP

PWeiWe 1

22)()1(

)1()( , (4-7)

where ∆tn is the time-step size (calendar month). The maximum water flow rate into the

reservoir (qwi), otherwise known as the productivity index (P.I.),

( )

−=

3

***03127.1

LPhbk

Eqw

iaqwwi

µ, (4-8)

is a function of permeability (kw), viscosity of brine (µw), and aquifer length (L), where

the constant 1.127X10-3 converts millidarcy-feet per centipoise to reservoir barrels per

day. The aquifer-reservoir interface pressure (Pres(n)), for a time-step, is based on the

undersaturated oil material balance equation,

130

( )

( ) 2/1**

**** )1()(

−+−

−+∑+−−=

∆−

−

ntWeiqwi

iaqoe

oeiresnnres

ePWeiBoicNpcN

BoicNpcNPWeBwiWpBoiNpP .

(4-9)

Np and Wp are the total monthly volumes of oil and water produced, respectively. The

initial oil and water formation volume factors are Boi and Bwi, respectively. The total

compressibility in the reservoir (ce) is the sum of the pore compressibility and

compressibility of saturation weighted oil (co) and water; ce = cp + Soi*co + Swi*cw. The

original oil in place (N) is calculated from:

BoiSoilhbN

*615.5**** Φ= , (4-10)

where Soi is the average initial oil saturation in the reservoir.

Model Results

The average and instantaneous pore compressibility behavior is calculated from

both the cumulative and incremental models that successfully match the observed

pressures (Figs. 4-10, 4-11, 4-12). A striking observation is that in order to match the

pressure in the reservoir, an increase in compressibility with time is necessary for both

models (Figure 4-10). Modeled pore compressibility is calculated to be 10 X 10-6 psi-1 at

the in-situ initial vertical effective stress (2062 psi at 12070 ft., SSTVD) for both models.

The average cp behavior increases to 120 X 10-6 psi-1 for a 2450 psi increase in stress in

the reservoir, while the instantaneous cp behavior increases to 150 X 10-6 psi-1 for the

same increase in stress (Figure 4-10, Tables 4-16, 4-17).

131

0

40

80

120

160

1500 2000 2500 3000 3500 4000 4500 5000

σv (psi)

cp (1

0-6 p

si-1

)

AverageInstantaneousSample 56

1989

1991

1994

1996

0

40

80

120

160

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

Date

c p(1

0-6ps

i-1)

Average

Instantaneous

Sample 56

σv (ksi)

Figure 4-10: Calculated average (Table 4-16) and instantaneous (Table 4-17) pore compressibility (cp) vs. vertical effective stress (σv) and time for a material balance match of historical reservoir pressure (Figs. 4-11, 4-12). Deformation data is from whole core sample 56 from the A-32-BP whole core (Table 4-10). The initial average in-situ vertical effective stress is 2062 psi at 12070 ft., SSTVD. All compressibility values are calculated for a depth of 12070 ft., SSTVD.

132

6000

7000

8000

9000

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

Date

Pres

sure

(psi

)

1612

2612

3612

4612

Modeled Reservoir Pressure

Modeled Aquifer Pressure

Historical Reservoir Pressure

v (psi)

Figure 4-11: Modeled reservoir and aquifer pressures using the Fetkovich (1971) cumulative (average) material balance model (Table 4-18). Pressure match is based on the calculated average pore compressibility behavior shown in Figure 4-10 (Table 4-16). Pressure and stress values are referenced to a 12,070 ft., SSTVD datum depth. Observed pressure data is found in Appendix A.

6000

7000

8000

9000

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

Date

Pres

sure

(psi

)

1612

2612

3612

4612

Modeled Reservoir Pressure

Modeled Aquifer Pressure

Historical Reservoir Pressure

v (psi)

Figure 4-12: Modeled reservoir and aquifer pressures using the Fetkovich (1971) incremental (instantaneous) material balance model (Table 4-19). Pressure match is based on the calculated instantaneous pore compressibility behavior shown in Figure 4-10 (Table 4-17). Pressure and stress values are referenced to a 12,070 ft., SSTVD datum depth. Observed pressure data is found in Appendix A.

133

Table 4-16: Derived average cp values using the cumulative Fetkovich material balance model. Values were calculated for a match in reservoir pressure (Figure 4-10, 4-11).

cp (10-6 psi-1)

Average σv (psi)

Average Reservoir Pressure (psi)

10.0 1562 9050 10.0 1662 8950 10.0 1762 8850 10.0 1862 8750 10.0 1962 8650 10.0 2062 8550 10.0 2162 8450 11.3 2262 8350 12.6 2362 8250 14.0 2462 8150 15.3 2562 8050 16.6 2662 7950 18.0 2762 7850 19.3 2862 7750 20.0 2962 7650 22.2 3062 7550 26.8 3162 7450 31.3 3262 7350 35.9 3362 7250 40.4 3462 7150 45.0 3562 7050 54.4 3662 6950 63.8 3762 6850 73.2 3862 6750 82.6 3962 6650 85.0 4062 6550 92.0 4162 6450 101.3 4262 6350 110.6 4362 6250 120.0 4462 6150 132.0 4562 6050 144.0 4662 5950 150.0 4762 5850 152.2 4862 5750 156.6 4962 5650 161.1 5062 5550 165.5 5162 5450

134

Table 4-17: Derived cp values using the incremental Fetkovich material balance model. Values were calculated for a match in reservoir pressure (Figure 4-10, 4-12).

cp (10-6 psi-1)

Average σv (psi)

Average Reservoir Pressure (psi)

10.0 1562 9050 10.0 1662 8950 10.0 1762 8850 10.0 1862 8750 10.0 1962 8650 10.0 2062 8550 10.0 2162 8450 14.5 2262 8350 19.0 2362 8250 23.6 2462 8150 28.1 2562 8050 32.6 2662 7950 37.2 2762 7850 41.7 2862 7750 44.0 2962 7650 51.8 3062 7550 67.4 3162 7450 83.0 3262 7350 98.7 3362 7250 114.3 3462 7150 130.0 3562 7050 134.7 3662 6950 139.4 3762 6850 144.1 3862 6750 148.8 3962 6650 150.0 4062 6550 150.0 4162 6450 150.0 4262 6350 150.0 4362 6250 150.0 4462 6150 150.0 4562 6050 150.0 4662 5950 150.0 4762 5850 150.0 4862 5750 150.0 4962 5650 150.0 5062 5550 150.0 5162 5450

135

Table 4-18: Modeled reservoir and aquifer pressure for calculated average pore compressibility results (Table 4-16). Initial pressure is 8550 psi, which is referenced to 12,070 ft. SSTVD datum.

Date Reservoir Pressure

(psi)

Aquifer Pressure

(psi) Date

Reservoir Pressure

(psi)

Aquifer Pressure

(psi) Date

Reservoir Pressure

(psi)

Aquifer Pressure

(psi) Jul-89 8547 8550 Nov-92 6981 7403 Mar-96 6283 6824

Aug-89 8514 8547 Dec-92 7030 7352 Apr-96 6280 6800 Sep-89 8481 8540 Jan-93 7043 7314 May-96 6274 6778 Oct-89 8446 8530 Feb-93 6945 7351 Jun-96 6272 6756 Nov-89 8413 8516 Mar-93 6854 7302 Jul-96 6271 6735 Dec-89 8394 8501 Apr-93 6779 7234 Aug-96 6265 6715 Jan-90 8361 8485 May-93 6697 7156 Sep-96 6265 6695 Feb-90 8327 8466 Jun-93 6622 7257 Oct-96 6263 6677 Mar-90 8309 8446 Jul-93 6858 7190 Nov-96 6263 6658 Apr-90 8233 8422 Aug-93 6766 7123 Dec-96 6269 6641 May-90 8191 8394 Sep-93 6663 7054 Jan-97 6270 6626 Jun-90 8140 8363 Oct-93 6807 6996 Feb-97 6271 6611 Jul-90 8110 8330 Nov-93 6890 7199 Mar-97 6267 6596

Aug-90 8077 8298 Dec-93 6793 7156 Apr-97 6263 6582 Sep-90 8067 8267 Jan-94 6699 7115 May-97 6266 6568 Oct-90 8020 8237 Feb-94 6635 7070 Jun-97 6269 6744 Nov-90 7946 8202 Mar-94 6562 7022 Jul-97 6384 6695 Dec-90 7920 8164 Apr-94 6501 6962 Oct-97 6402 6684 Jan-91 7858 8129 May-94 6439 6912 Nov-97 6411 6673 Feb-91 7805 8088 Jun-94 6386 6854 Dec-97 6415 6662 Mar-91 7855 8053 Jul-94 6332 6800 Jan-98 6412 6653 Apr-91 7930 8031 Aug-94 6511 6755 Feb-98 6418 6644 May-91 7967 8020 Sep-94 6446 6957 Mar-98 6417 6635 Jun-91 7987 8014 Oct-94 6399 6909 Apr-98 6415 6626 Jul-91 7997 8011 Nov-94 6357 6861 May-98 6411 6618

Aug-91 7828 7997 Dec-94 6312 6816 Jun-98 6415 6610 Sep-91 7676 8018 Jan-95 6321 6777 Jul-98 6420 6602 Oct-91 7577 7969 Feb-95 6283 6735 Aug-98 6420 6595 Nov-91 7481 7907 Mar-95 6396 6700 Sep-98 6427 6589 Dec-91 7439 7955 Apr-95 6347 6891 Oct-98 6427 6582 Jan-92 7461 7897 May-95 6316 6857 Nov-98 6430 6576 Feb-92 7371 7833 Jun-95 6486 6833 Dec-98 6434 6570 Mar-92 7272 7762 Jul-95 6444 6811 Jan-99 6436 6566 Apr-92 7186 7679 Aug-95 6408 6788 Feb-99 6438 6560 May-92 7240 7678 Sep-95 6373 6766 Mar-99 6438 6556 Jun-92 7149 7616 Oct-95 6346 6747 Apr-99 6437 6551 Jul-92 7061 7602 Nov-95 6319 6726 May-99 6436 6547

Aug-92 7028 7529 Dec-95 6295 6899 Jun-99 6430 6542 Sep-92 6988 7452 Jan-96 6288 6874 Jul-99 6427 6538 Oct-92 6894 7384 Feb-96 6289 6848 Aug-99 6424 6533

Sep-99 6421 6529

136

Table 4-19: Modeled reservoir and aquifer pressure for calculated incremental pore compressibility results (Table 4-17). Initial pressure is 8550 psi, which is referenced to 12,070 ft. SSTVD datum.

Date Reservoir Pressure

(psi)

Aquifer Pressure

(psi) Date

Reservoir Pressure

(psi)

Aquifer Pressure

(psi) Date

Reservoir Pressure

(psi)

Aquifer Pressure

(psi) Jul-89 8547 8550 Nov-92 7024 7581 Mar-96 6289 6855

Aug-89 8514 8547 Dec-92 6996 7559 Apr-96 6290 6844 Sep-89 8481 8540 Jan-93 6961 7537 May-96 6287 6834 Oct-89 8446 8530 Feb-93 6939 7510 Jun-96 6290 6823 Nov-89 8413 8516 Mar-93 6907 7486 Jul-96 6295 6813 Dec-89 8394 8501 Apr-93 6881 7471 Aug-96 6295 6803 Jan-90 8362 8485 May-93 6853 7463 Sep-96 6303 6793 Feb-90 8327 8466 Jun-93 6830 7446 Oct-96 6309 6784 Mar-90 8309 8446 Jul-93 6806 7432 Nov-96 6317 6775 Apr-90 8233 8422 Aug-93 6778 7427 Dec-96 6334 6766 May-90 8192 8394 Sep-93 6745 7419 Jan-97 6342 6759 Jun-90 8140 8363 Oct-93 6712 7408 Feb-97 6352 6751 Jul-90 8111 8330 Nov-93 6678 7389 Mar-97 6354 6743

Aug-90 8077 8298 Dec-93 6645 7367 Apr-97 6357 6736 Sep-90 8067 8267 Jan-94 6607 7344 May-97 6368 6729 Oct-90 7996 8236 Feb-94 6590 7317 Jun-97 6381 6722 Nov-90 7931 8198 Mar-94 6562 7293 Jul-97 6489 6706 Dec-90 7876 8158 Apr-94 6542 7277 Oct-97 6501 6702 Jan-91 7825 8119 May-94 6521 7254 Nov-97 6504 6698 Feb-91 7784 8076 Jun-94 6505 7236 Dec-97 6500 6694 Mar-91 7832 8040 Jul-94 6490 7214 Jan-98 6491 6690 Apr-91 7903 8016 Aug-94 6474 7193 Feb-98 6493 6687 May-91 7942 8009 Sep-94 6464 7180 Mar-98 6488 6683 Jun-91 7965 8005 Oct-94 6444 7168 Apr-98 6483 6679 Jul-91 7979 8002 Nov-94 6429 7154 May-98 6476 6675

Aug-91 7830 7994 Dec-94 6412 7138 Jun-98 6480 6671 Sep-91 7647 7974 Jan-95 6390 7124 Jul-98 6487 6668 Oct-91 7502 7943 Feb-95 6383 7107 Aug-98 6488 6664 Nov-91 7408 7907 Mar-95 6368 7091 Sep-98 6497 6661 Dec-91 7337 7867 Apr-95 6362 7072 Oct-98 6498 6658 Jan-92 7268 7829 May-95 6348 7052 Nov-98 6503 6655 Feb-92 7239 7792 Jun-95 6346 7028 Dec-98 6511 6652 Mar-92 7212 7759 Jul-95 6334 7007 Jan-99 6514 6650 Apr-92 7187 7733 Aug-95 6325 6987 Feb-99 6517 6647 May-92 7157 7703 Sep-95 6316 6965 Mar-99 6518 6645 Jun-92 7131 7669 Oct-95 6311 6942 Apr-99 6518 6642 Jul-92 7103 7654 Nov-95 6305 6920 May-99 6518 6640

Aug-92 7091 7637 Dec-95 6300 6898 Jun-99 6512 6637 Sep-92 7080 7622 Jan-96 6291 6878 Jul-99 6509 6635 Oct-92 7049 7603 Feb-96 6293 6866 Aug-99 6508 6632

Sep-99 6506 6630

137

Comparison of Deformation and Material Balance cp Behavior Pore compressibility as observed in deformation experiments and material

balance models increase with increases in vertical effective stress (Figure 4-10). The

pore compressibility values from whole core sample #56 (Table 4-10) are higher than

both modeled average and instantaneous cp values at the in-situ vertical effective stress

(2064 psi). At the maximum stress historically encountered in the reservoir (4500 psi)

the core cp is lower. Both whole core data and the modeled results are of the same order

of magnitude and have similar shape to cp behavior reported by Ostermeier (1993, 1996,

2001).

Parameter Sensitivity Analysis Using the Instantaneous cp Behavior

Additional pressure support is required after 1992 to approximate the historical

pressure behavior. Using a constant compressibility (cp = 10 X10-6 psi-1) the simulated

pressure response is too low after 1992 (Figure 4-13). It is interpreted that an increase in

pore compressibility, as observed in core data, is required for pressure support.

The modeled pressure response, for the instantaneous pore compressibility

behavior (Table 4-17), is sensitive to the permeability of the rock in the aquifer (Figure 4-

15). The simulated pressure response for the high permeability case (k = 1500 mD) show

lower pressure differences between the aquifer and reservoir than for the low

permeability case (k = 500 mD) (Figure 4-14). This is an expected result because high

permeability sands equilibrate faster.

The effect of the cross-sectional flow area (b * h) on simulated pressure is

evaluated using the instantaneous pore compressibility behavior (Table 4-17). Two

sensitivity cases are presented, where the system width (b), reservoir length (l), and

138

2000

3000

4000

5000

6000

7000

8000

9000

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

Date

Pres

sure

(psi

)

1612

2612

3612

4612

5612

6612

7612

8612

Modeled Reservoir PressureModeled Aquifer PressureHistorical Reservoir Pressure

v (psi)

Figure 4-13: Modeled reservoir pressures using the Fetkovich (1971) incremental material balance model with a constant pore compressibility of 10 X10-6 psi-1 in the reservoir and aquifer. Pressure and stress values are referenced to a 12,070 ft., SSTVD datum depth. Observed pressure data is found in Appendix A.

139

5000

6000

7000

8000

9000

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

Date

Pres

sure

(psi

)

1612

2612

3612

4612

5612

Modeled res. pres.Modeled aquifer pres.Historical res. pres.

v (psi)k = 500 mD

5000

6000

7000

8000

9000

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

Date

Pres

sure

(psi

)

1612

2612

3612

4612

5612

Modeled res. pres.Modeled aquifer presHistorical res. pres.

v (psi)

k = 1500 mD

Figure 4-14: Modeled reservoir pressures using the Fetkovich (1971) incremental material balance model with permeabilities in the aquifer of 500 mD and 1500 mD. Results are compared with the reference permeability case (1060 mD) in Figure 4-12. Pressure match is based on the calculated instantaneous pore compressibility behavior shown in Figure 4-10 (Table 4-17). Pressure and stress values are referenced to a 12,070 ft., SSTVD datum depth. Observed pressure data is found in Appendix A.

140

5000

6000

7000

8000

9000

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

Date

Pres

sure

(psi

)

1612

2612

3612

4612

5612


v (psi)b=5,000 ft.

5000

6000

7000

8000

9000

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

Date

Pres

sure

(psi

)

1612

2612

3612

4612

5612


v (psi)

b=15,000 ft.

Figure 4-15: Modeled reservoir pressures using the Fetkovich (1971) incremental material balance model with widths (b) of 5000 ft. (L=90,000 ft., l=20,300 ft.) and 15000 ft. (L=6767 ft., l=30,000 ft.). Results are compared with the reference case (b = 10,000 ft., L=45,000 ft, l=10,150 ft.) in Figure 4-12. Pressure match is based on the calculated instantaneous pore compressibility behavior shown in Figure 4-10 (Table 4-17). Pressure and stress values are referenced to a 12,070 ft., SSTVD datum depth. Observed pressure data is found in Appendix A.

141

aquifer length (L) are varied (h is constant), such that the reservoir and aquifer volumes

are honored (Table 4-15). A decrease in the cross-sectional flow area (b = 5000 ft.)

results in lower reservoir pressures at early time, followed by a late time pressure

rebound (Figure 4-15, top). In the small cross-sectional flow area case the aquifer is

further away from the reservoir, requiring greater time for higher pressures in the aquifer

to reach the reservoir. This explains the modeled late time pressure rebound. A large

cross-sectional flow area (b = 15,000 ft) results in reservoir and aquifer pressures that are

nearly equal with time (Figure 4-15, bottom). The increase in cross-sectional flow area

places the aquifer closer to the reservoir, which allows the system to equilibrate faster.

The modeled pressure response, associated with the instantaneous pore

compressibility behavior, is sensitive to the size of the aquifer volume. The simulated

reservoir and aquifer pressures through time are lower for an aquifer having half the

reference volume (641,139 MRB, L=25,000 ft.) than for an aquifer that is twice the

reference volume (2,564,560 MRB, L=100,000) (Figure 4-16). For the small aquifer

case, both simulated pressures (aquifer and reservoir) drop below the historical reservoir

pressure. This suggests either the aquifer must be larger or cp must increase (Figure 4-

16, top). For the larger aquifer, the simulated reservoir pressure approximates the

historical data through 1997 and is too high thereafter (Figure 4-16, bottom). The

pressure rebound that follows results from a higher pressure in the aquifer. This suggests

either cp must decrease, or the permeability in the aquifer must be greater than assumed.

142

5000

6000

7000

8000

9000

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

Date

Pres

sure

(psi

)

1612

2612

3612

4612

5612

Modeled res. pres.

Modeled aquifer pres.Historical res. pres.

v (psi)

L=25,000 ft.

5000

6000

7000

8000

9000

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

Date

Pres

sure

(psi

)

1612

2612

3612

4612

5612


v (psi)

L=100,000 ft.

Figure 4-16: Modeled reservoir pressures using the Fetkovich (1971) incremental material balance model with aquifer volumes of 641,139 MRB (L=25,000 ft.) and 2,564,560 MRB (L=100,000 ft.). Results are compared with the reference case (L=45,000 ft.) in Figure 4-12. Pressure match is based on the calculated instantaneous pore compressibility behavior shown in Figure 4-10 (Table 4-17). Pressure and stress values are referenced to a 12,070 ft., SSTVD datum depth. Observed pressure data is found in Appendix A.

143

Model of Compaction Effects

For the purposes of reservoir simulation (Chapter 5), the modeled instantaneous

pore compressibility (cp) behavior (Figure 4-10, Table 4-17) is assumed to be equal for

all six Flow Units. This cp behavior is simulated through the use of a lookup table of

porosity and permeability reduction multipliers (PVMULT and TAMULT, respectively),

which are referenced to grid block pressure. This compaction model is constructed based

on an assumed initial porosity (Φref = 32%) and reference vertical effective stress (σref =

2062 psi) at 12,070 ft., SSTVD.

The data clearly suggests the reduction of bulk volume due to pore collapse.

However, the simulation equations assume constant bulk volume. To simulate the loss of

volume associated with pore volume reduction, the volume loss is modeled as an increase

in the volume of the solid grains (Figure 4-17). A mathematical comparison of the

calculation of pore compressibility for geomechanics and simulation is,

( ) ( ) 0=∆−∆−∆=∆−∆−∆simulationgpbcsgeomechanigpb VVVVVV , (4-11)

where ∆Vg (change in grain volume) in geo-mechanics is assumed to be zero and ∆Vb

(change in bulk volume) in simulation is zero. From this, it is assumed that,

( ) ( )simulationpcsgeomechanip VV ∆=∆ . (4-12)

thus,

( ) ( )simulationgcsgeomechanib VV ∆−=∆ . (4-13)

An additional assumption in using the simulation compaction model is that changes in

bulk volume have little influence on saturation changes and multiphase flow behavior.

144

InitialCondition Compaction

Geo-Mechanics

Simulation

V = V + Vbi pi gi V = V + Vbf pf gi

V = V + Vbi pi gi V = V + Vbi pf gf

∆vgi = 0

∆vbi = 0

Figure 4-17: Unconsolidated sands, such as are present at Bullwinkle, undergo a bulk volume reduction during pressure decrease as grains reorganize their packing structure. The change in solid volume is small (top). The reservoir simulation model assumes bulk volume is conserved (bottom). To simulate the effect of pore volume loss, the solid grains are assumed to increase in volume, by the same amount that the pore volume decreases. The terms are: Vbi = initial bulk volume, Vbf = compacted bulk volume, Vpi = initial pore volume, Vpf = compacted pore volume, Vgi = initial grain volume, Vgf = compacted (enlarged) grain volume. Green represents the oil filled pore volume, blue is the initial water saturation, and orange circles are the grains.

145

Porosity Reduction

The change in porosity due to an incremental change in vertical effective stress is

calculated,

( )( ) effpc σ∆Φ−Φ−=∆Φ 1 , (4-14)

for the range of stresses present during production (Table 4-17). The fractional change in

porosity (porosity reduction multiplier) is calculated,

ref

newPVMULTΦΦ

= , (4-15)

based on calculated porosity values (Φnew) for these stresses and the reference porosity

(Φref = 0.32) (Figs. 4-18, 4-19, Table 4-20).

Permeability Reduction

An empirical model is constructed based on the deformation data to relate

permeability to porosity,

Φ=

0.21

emk , (4-16)

to predict for the full range of porosity values present in the J1 and J2 sands (Figure 4-20,

Table 4-21). The empirical exponent 21.0 is an average value based on a least square

regression fit to each set of deformation data (Table 4-22). The empirical constant m is

proportional to the grain size diameter term (Dm) (Table 4-22) and is based on a least

squares regression fit to the deformation data using the curvature exponent of 21.0.

146

0.2

0.4

0.6

0.8

1.0

1.2

5000 6000 7000 8000 9000 10000Reservoir Pressure (psi)

Mul

tiplie

r

61216122612361246125612

Permeability Mult.Porosity Mult.

σv (psi)

1989

1991

1994

1996

Figure 4-18: Simulation multipliers of porosity (Φ) and permeability (k) (Tables 4-20, 4-23) versus reservoir pressure. The average initial in-situ reservoir pressure is 8550 psi (12,070 ft., SSTVD datum) and in Dec., 1999 is 6100 psi (Appendix A).

147

500

1000

1500

2000

1000 2000 3000 4000 5000 6000σv (psi)

k (m

D)

0.250

0.275

0.300

0.325461256126612761286129612

Reservoir Pressure (psi)

o =

32%

PermeabilityPorosity

1996

1994

1991

1989

Figure 4-19: Modeled porosity (Φ) and permeability (k) (Tables 4-20, 4-23) versus vertical effective stress (σv) calculated using the calculated incremental pore compressibility behavior. Values are calculated as a function ΦRef (32%) and reservoir pressure (8550 psi at a 12,070 ft., SSTVD datum). The porosity reduces to 28.2% by 1996. The permeability reduces to 819 mD by 1996 based on an initial in-situ permeability of 1825 mD.

148

Table 4-20: Reservoir compaction effects on porosity (Φ). Bold values represent the reference datum (12,070 ft., SSTVD) values.

Reservoir Pressure

(psi) Average σv

(psi) Φ Fractional

Change in Φ (PVMULT)

9050 1562 0.3211 1.0050 8950 1662 0.3209 1.0040 8850 1762 0.3207 1.0030 8750 1862 0.3204 1.0020 8650 1962 0.3202 1.0010 8550 2062 0.3200 1.0000 8450 2162 0.3198 0.9990 8350 2262 0.3196 0.9980 8250 2362 0.3193 0.9970 8150 2462 0.3191 0.9960 8050 2562 0.3189 0.9950 7950 2662 0.3186 0.9936 7850 2762 0.3182 0.9917 7750 2862 0.3177 0.9893 7650 2962 0.3171 0.9865 7550 3062 0.3164 0.9833 7450 3162 0.3155 0.9797 7350 3262 0.3146 0.9755 7250 3362 0.3135 0.9704 7150 3462 0.3121 0.9639 7050 3562 0.3103 0.9559 6950 3662 0.3082 0.9464 6850 3762 0.3057 0.9356 6750 3862 0.3030 0.9235 6650 3962 0.3001 0.9110 6550 4062 0.2972 0.8983 6450 4162 0.2942 0.8854 6350 4262 0.2911 0.8722 6250 4362 0.2880 0.8591 6150 4462 0.2849 0.8462 6050 4562 0.2819 0.8335 5950 4662 0.2788 0.8210 5850 4762 0.2758 0.8087 5750 4862 0.2728 0.7966 5650 4962 0.2698 0.7847 5550 5062 0.2669 0.7729 5450 5162 0.2640 0.7613

149

This empirical model is used to calculate the fractional change in permeability

(permeability reduction multiplier),

)(0.21 refnew

ref

new ekk

TAMULTΦ−Φ

== , (4-17)

for the range of stresses present during production (Figs. 4-18, 4-19, Table 4-23).

TAMULT is independent of permeability and the grain size related constant m. This

allows us to use the same set of multipliers in all six Flow Units present in the J1 and J2

sands regardless of permeability.

Porosity and Permeability Reduction Results

Porosity and permeability decrease non-linearly with increasing vertical effective

stress (Figure 4-19, Tables 4-20, 4-23). This is an expected result because they are

derived from the non-linear instantaneous pore compressibility behavior (Figure 4-10).

Further, this compaction behavior is nearly identical to compaction behavior documented

by Kikani and Smith (1996) for the Bullwinkle J-sands. Ostermeier (2001) documented

this compaction behavior for two deepwater turbidite sands.

Simulation of Compaction Behavior Using Compaction Regions

The compaction model developed here is a gross simplification of the initial

vertical effective stress behavior present in the J1 and J2 sands. The J1 and J2 sands span

a vertical distance of 2400 ft. that correspond to a range of in-situ vertical effective stress

of 1115.0 psi updip (10,600 ft., SSTVD) to 2565.0 psi downdip (13,000 ft., SSTVD).

The compaction model developed thus far is for a vertical effective stress of 2062 psi at a

12,070 ft., SSTVD, datum.

150

0

1000

2000

3000

4000

5000

0.20 0.25 0.30 0.35 0.40Φ

k (m

D)

m = 2.90m = 2.10m = 1.0665-1-ST (J2)A-32-BP (J1)A-32-BP (J2)

Figure 4-20: Permeability (k) vs. porosity (Φ) using an empirical model (Table 4-19) compared with deformation data (Tables 4-1 through 4-10). Modeled permeability-porosity relationships are fit with a least squares regression to the deformation data using curvature coefficient of 21.0 (Equation 4-16).

151

Table 4-21: Permeability-porosity model results for different “m” values.

Φ k

(mD) m = 2.90

k (mD)

m = 2.10

k (mD)

m = 1.06 0.20 193.4 140.0 70.7 0.22 294.3 213.1 107.6 0.24 448.0 324.4 163.7 0.26 681.8 493.7 249.2 0.28 1037.68 751. 4 379.3 0.30 1579.3 1143.6 577.2 0.32 2403.6 1740.5 878.5 0.34 3658.1 2649.0 1337.1 0.36 5567.6 4031.7 2035.0 0.37 6868.6 4973.8 2510.6

Table 4-22: Empirical constant m value and curvature exponents for the permeability-porosity

model.

Whole Core Sand m Curvature

A-32-BP J1 2.90 25.3 A-32-BP J2 2.10 22.3 65-1-ST J2 1.06 15.3

Average 21.0

152

Table 4-23: Reservoir compaction effects on permeability (k). Bold values represent the reference datum (12,070 ft., SSTVD) vertical effective stress (σv). k values calculated using Equation 4-16.

Reservoir Pressure

(psi) Average σv

(psi) Φ k (mD) Fractional

Change in k (TAMULT)

9050 1562 0.3211 1865 1.0231 8950 1662 0.3209 1857 1.0185 8850 1762 0.3207 1848 1.0138 8750 1862 0.3204 1840 1.0092 8650 1962 0.3202 1831 1.0046 8550 2062 0.3200 1825 1.0000 8450 2162 0.3198 1815 0.9954 8350 2262 0.3196 1806 0.9909 8250 2362 0.3193 1798 0.9864 8150 2462 0.3191 1790 0.9819 8050 2562 0.3189 1782 0.9774 7950 2662 0.3186 1770 0.9710 7850 2762 0.3182 1755 0.9626 7750 2862 0.3177 1736 0.9523 7650 2962 0.3171 1714 0.9402 7550 3062 0.3164 1689 0.9263 7450 3162 0.3155 1660 0.9108 7350 3262 0.3146 1628 0.8933 7250 3362 0.3135 1590 0.8725 7150 3462 0.3121 1543 0.8463 7050 3562 0.3103 1486 0.8152 6950 3662 0.3082 1421 0.7798 6850 3762 0.3057 1351 0.7410 6750 3862 0.3030 1275 0.6993 6650 3962 0.3001 1201 0.6587 6550 4062 0.2972 1129 0.6195 6450 4162 0.2942 1060 0.5816 6350 4262 0.2911 993 0.5450 6250 4362 0.2880 931 0.5107 6150 4462 0.2849 872 0.4788 6050 4562 0.2819 818 0.4490 5950 4662 0.2788 768 0.4213 5850 4762 0.2758 720 0.3954 5750 4862 0.2728 677 0.3713 5650 4962 0.2698 635 0.3488 5550 5062 0.2669 597 0.3278 5450 5162 0.2640 561 0.3082

153

Compaction behavior is non-linear (Figs. 4-18, 4-21; Tables 4-20, 4-23).

Modeled downdip initial vertical effective stress (1562 psi) is less than updip (2562 psi)

(Table 4-17). Updip of the reference location (12,070 ft.) the non-linear compaction

effects are experienced for less increase in vertical effective stress than downdip (Figure

4-22, Tables 4-20, 4-23). The implications of this modeled behavior are higher initial

vertical effective stress updip and lower downdip. Thus, at initial conditions the values

of porosity and permeability are decreased updip (compaction) and increased downdip

(decompaction). The initial values of porosity deviate from 0% to 1% and permeability

from 0% to 3% based on the compaction multipliers (Figure 4-22, Tables 4-20, 4-23).

To reduce these compaction and decompaction effects the reservoir is divided into

five reservoir pressure intervals of 200 psi (Figs. 4-23, 4-24, Table 4-24). The average

reservoir pressure of each interval is specified as the reference pressure. The porosity and

permeability multipliers are shifted, such that the reference pressure corresponds to a

multiplier of 1.0 (Tables 4-23, 4-24, 4-27). The porosity (PVMULT) and permeability

reduction multipliers (TAMULT) are set to 1.0 for the 200 psi interval to honor the initial

porosity and permeability input values (Tables 4-23, 4-24, 4-27).

Conclusions

The pore compressibility of the J1 and J2 sands at Bullwinkle increase with

increases in vertical effective stress. This observed behavior is documented by

deformation data from whole core samples and modeled results using a material balance

approach. Further, other workers have documented this type of behavior for deepwater

Gulf of Mexico turbidites.

154

0

40

80

120

160

1000 2000 3000 4000 5000

σv (psi)

c p (1

0-6 p

si-1

)

Model downdip

σv

Modelupdip

σv

Figure 4-21: Modeled incremental pore compressibility (cp) vs. vertical effective stress (σv) at initial conditions as established by the simulation model using a single compaction table (Table 4-17). Actual initial vertical effective stress in the J1 and J2 sands range updip to downdip, from 1050 psi to 2565 psi. The compaction model focuses on the time dependent compaction effects and does not account for the presence of initial vertical variation in stress state within a reservoir. Modeled values are referenced to a 12,070 ft., SSTVD, datum (Initial in-situ vertical effective stress = 2062 psi).

0.2

0.4

0.6

0.8

1.0

1.2

5000 6000 7000 8000 9000 10000Reservoir Pressure (psi)

Mul

tiplie

r

61216122612361246125612

Permeability Mult.Porosity Mult.

Updip Compaction

DowndipCompaction

σv (psi)

Figure 4-22: Simulation initialization effects on input maps of porosity (Φ) and permeability (k) using a single compaction table (Tables 4-20, 4-23). Updip reservoir pressure at 10,600 ft, SSTVD is 8072 psi. Downdip pressure is 8956 psi at 13,000 ft., SSTVD (Table 4-11).

155

5

4

2

3

1

Oil Producer

Water InjectorC.I. = 100’

RB

RAPermeabilityBarriers

BLK 64 BLK 65

1 MileBLK 108 BLK 109

12500

12000

1200

0

1150

0

1 100

0

Figure 4-23: J1 sand compaction table region map overlain by structure contours. The five regions are specified by 200 psi reservoir pressure intervals (Table 4-24). Black dots are production wells and white dots are injection wells. Reservoir pressures range from 8072 psi updip to 8956 psi downdip. Geologic barriers and connections are discussed in Chapter 5.

156

5

Oil ProducerWater Injector

RA

RB

1 Mile

PermeabilityBarriersBLK 64 BLK 65

BLK 108 BLK 109

C.I. = 100’

13000

12500

1200

0

12500

11000115001

42

3

Figure 4-24: J2 sand compaction region map overlain by structure contours. The five regions are specified by 200 psi reservoir pressure intervals (Table 4-24). Black dots are production wells and white dots are injection wells. Reservoir pressures range from 8072 psi updip to 8956 psi downdip. Geologic barriers and connections are discussed in Chapter 5.

157

Table 4-24: J1 and J2 sand compaction regions by fluid type. The oil phase pressure gradient is 0.325 psi/ft., gas phase pressure gradient is 0.146 psi/ft., and the water phase pressure gradient is

0.466 psi/ft.

Oil Phase - J1 and J2

CompactionRegion

Reservoir Pressure

Range (psi)

Depth Range (ft.)

Average Reservoir

Pressure (psi)

Average σv (psi)

Average Depth (ft.)

1 8000 to 8200 10525 to 11050 8100 1234 10790 2 8200 to 8400 11050 to 11600 8300 1579 11330 3 8400 to 8600 11600 to 12135 8500 1925 11865 4 8600 to 8800 12135 to OOWC 8700 2270 12405 5 8800 to 9000 - 8900 2432 12820

Gas Phase - J1-RA and J2-RA

CompactionRegion

Reservoir Pressure

Range (psi)

Depth Range (ft.)

Average Reservoir

Pressure (psi)

Average σv (psi)

Average Depth (ft.)

1 8000 to 8200 - 8100 1234 10790 2 8200 to 8400 - 8300 1579 11330 3 8400 to 8600 11000 to OGOC 8500 1925 11865 4 8600 to 8800 - 8700 2270 12405 5 8800 to 9000 - 8900 2432 12820

Water Phase - J1 and J2

CompactionRegion

Reservoir Pressure

Range (psi)

Depth Range (ft.)

Average Reservoir

Pressure (psi)

Average σv (psi)

Average Depth (ft.)

1 8000 to 8200 - 8100 1234 10790 2 8200 to 8400 - 8300 1579 11330 3 8400 to 8600 - 8500 1925 11865 4 8600 to 8800 OOWC to 12600 8700 2270 12405 5 8800 to 9000 12600 to 13030 8900 2432 12820

158

Table 4-25: Simulation model compaction region input tables for compaction regions 1 (8000 psi to 8200 psi) and 2 (8200 psi to 8400 psi). Reservoir compaction effects on porosity (Φ) and permeability

(k) are the same for each Flow Unit.

Compaction Region 1 Compaction Region 2 Reservoir Pressure

(psi)

σv (psi)

Reservoir Pressure

(psi)

σv (psi) PVMULT TAMULT

8200 1134 8400 1479 1.0000 1.0000 8100 1234 8300 1579 1.0000 1.0000 8000 1334 8200 1679 1.0000 1.0000 7900 1434 8100 1779 0.9980 0.9909 7800 1534 8000 1879 0.9970 0.9864 7700 1634 7900 1979 0.9960 0.9819 7600 1834 7800 2079 0.9950 0.9774 7500 1934 7700 2179 0.9936 0.9710 7400 2034 7600 2279 0.9917 0.9626 7300 2134 7500 2379 0.9893 0.9523 7200 2234 7400 2479 0.9865 0.9402 7100 2334 7300 2579 0.9833 0.9263 7000 2434 7200 2679 0.9797 0.9108 6900 2534 7100 2779 0.9755 0.8933 6800 2634 7000 2879 0.9704 0.8725 6700 2734 6900 2979 0.9639 0.8463 6600 2834 6800 3079 0.9559 0.8152 6500 2934 6700 3179 0.9464 0.7798 6400 3034 6600 3279 0.9356 0.7410 6300 3134 6500 3379 0.9235 0.6993 6200 3234 6400 3479 0.9110 0.6587 6100 3334 6300 3579 0.8983 0.6195 6000 3434 6200 3679 0.8854 0.5816 5900 3534 6100 3779 0.8722 0.5450 5800 3634 6000 3879 0.8591 0.5107 5700 3734 5900 3979 0.8462 0.4788 5600 3834 5800 4079 0.8335 0.4490 5500 3934 5700 4179 0.8210 0.4213 5400 4034 5600 4279 0.8087 0.3954 5300 4134 5500 4379 0.7966 0.3713 5200 4234 5400 4479 0.7847 0.3488 5100 4334 5300 4579 0.7729 0.3278 5000 4434 5200 4679 0.7613 0.3082

159

Table 4-26: Simulation model compaction region input tables for compaction regions 3 (8400 psi to 8600 psi) and 4 (8600 psi to 8800 psi). Reservoir compaction effects on porosity (Φ) and permeability

(k) are the same for each Flow Unit.

Compaction Region 3 Compaction Region 4 Reservoir Pressure

(psi)

σv (psi)

Reservoir Pressure

(psi)


8600 1825 8800 2170 1.0000 1.0000 8500 1925 8700 2270 1.0000 1.0000 8400 2025 8600 2370 1.0000 1.0000 8300 2125 8500 2470 0.9980 0.9909 8200 2225 8400 2570 0.9970 0.9864 8100 2325 8300 2670 0.9960 0.9819 8000 2425 8200 2770 0.9950 0.9774 7900 2525 8100 2870 0.9936 0.9710 7800 2625 8000 2970 0.9917 0.9626 7700 2725 7900 3070 0.9893 0.9523 7600 2825 7800 3170 0.9865 0.9402 7500 2925 7700 3270 0.9833 0.9263 7400 3025 7600 3370 0.9797 0.9108 7300 3125 7500 3470 0.9755 0.8933 7200 3225 7400 3570 0.9704 0.8725 7100 3325 7300 3670 0.9639 0.8463 7000 3425 7200 3770 0.9559 0.8152 6900 3525 7100 3870 0.9464 0.7798 6800 3625 7000 3970 0.9356 0.7410 6700 3725 6900 4070 0.9235 0.6993 6600 3825 6800 4170 0.9110 0.6587 6500 3925 6700 4270 0.8983 0.6195 6400 4025 6600 4370 0.8854 0.5816 6300 4125 6500 4470 0.8722 0.5450 6200 4225 6400 4570 0.8591 0.5107 6100 4325 6300 4670 0.8462 0.4788 6000 4425 6200 4770 0.8335 0.4490 5900 4525 6100 4870 0.8210 0.4213 5800 4625 6000 4970 0.8087 0.3954 5700 4725 5900 5070 0.7966 0.3713 5600 4825 5800 5170 0.7847 0.3488 5500 4925 5700 5270 0.7729 0.3278 5400 5025 5600 5370 0.7613 0.3082

160

Table 4-27: Simulation model compaction region input table for compaction region 5 (8800 psi to 9000 psi). Reservoir compaction effects on porosity (Φ) and permeability (k) are the same for each

Flow Unit.

Reservoir Pressure

(psi)


9000 2332 1.0000 1.0000 8900 2432 1.0000 1.0000 8800 2532 1.0000 1.0000 8700 2632 0.9980 0.9909 8600 2732 0.9970 0.9864 8500 2832 0.9960 0.9819 8400 2932 0.9950 0.9774 8300 3032 0.9936 0.9710 8200 3132 0.9917 0.9626 8100 3232 0.9893 0.9523 8000 3332 0.9865 0.9402 7900 3432 0.9833 0.9263 7800 3532 0.9797 0.9108 7700 3632 0.9755 0.8933 7600 3732 0.9704 0.8725 7500 3832 0.9639 0.8463 7400 3932 0.9559 0.8152 7300 4032 0.9464 0.7798 7200 4132 0.9356 0.7410 7100 4232 0.9235 0.6993 7000 4332 0.9110 0.6587 6900 4432 0.8983 0.6195 6800 4532 0.8854 0.5816 6700 4632 0.8722 0.5450 6600 4732 0.8591 0.5107 6500 4832 0.8462 0.4788 6400 4932 0.8335 0.4490 6300 5032 0.8210 0.4213 6200 5132 0.8087 0.3954 6100 5232 0.7966 0.3713 6000 5332 0.7847 0.3488 5900 5432 0.7729 0.3278 5800 5532 0.7613 0.3082

161

Permeability-porosity relationships are grain size dependent. Whole core

deformation data document that samples with larger grain sizes have higher

permeabilities for a specific porosity. This observation is supported with modeled

permeability-porosity relationships using the Carmen-Kozeny model.

Material balance derived pore compressibility is highly sensitive to the strength of

the aquifer. The Fetkovich material balance approach indicates that higher permeability

in the aquifer and higher cross-sectional flow area increases the flow potential of the

aquifer (strong aquifer). This additional aquifer strength reduces the need for pore

compressibility to match reservoir pressure.

The instantaneous pore compressibility behavior is used to model the compaction

effects on porosity and permeability for use in reservoir simulation. The compaction

behavior is assumed to be equal in all six Flow Units. The sands are partitioned into five

pressure (compaction) regions of 200 psi each and the compaction model is applied to

each of these regions to establish equal initial pore compressibility for all depth.

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