Examples of Numerical Simulation

As examples of numerical simulation of petrophysical properties of rocks, the following formations were used: (a) Mesozoic terrigenous and carbonate reservoir rocks and shales in the East Pre-Caucasus oil-and gas-bearing province and in the adjacent offshore areas of the Middle Caspian Basin, and (b) Neogenic sandstones in the Apsheron oil- and gas-bearing region and in the adjacent offshore areas of the South Caspian Basin.

The method and software for numerical simulation of petrophysical properties of rocks can be applied to any geologic and stratigraphic attributes independent of the age and post-sedimentary changes of the rocks.

A. The Numerical Simulation of Reservoir

Properties of Mesozoic Sandstones

Model Input. Geological age: 140-190 my; dynamic deformation: 1.8-2.2 tectonic-stratigraphic units (dimensionless); depth of burial:

2.0-2.5 km; formation temperature: 85-95°C; rate of sedimentation: 100-200 m/my; quartz content: 60-80%; degree of cementation: 1218%; Trask sorting coefficient: 3-4; initial porosity before compaction: 0.35-0.45; initial permeability before compaction: 1,000-2,000 mD;

and density of rock matrix: 2.6-2.7 g/cm . Model Output: 1. Simulation of porosity

Statistical Distribution

Range in Porosity,

Fraction Minimum

Maximum

Frequency

Relative Frequency

Cumulative

Relative Frequency

0.118

0.130

34

0.113

0.113

0.130

0.142

106

0.354

0.467

0.142

0.154

109

0.363

0.830

0.154

0.167

43

0.143

0.973

0.167

0.179

6

0.020

0.993

0.179

0.191

2

0.007

1.000

Porosity distribution: mean = 0.144; minimum = 0.118; maximum = 0.191; standard deviation = 0.0117; and variance = 8.13%.

2. Simulation of permeability

Statistical Distribution

Range in Permeability,

Statistical Distribution

Range in Permeability,

Minimum

Maximum

Frequency

Relative Frequency

Cumulative Relative Frequency

11.422

18.402

25

0.083

0.083

18.402

25.382

138

0.460

0.543

25.382

32.362

105

0.350

0.893

32.362

39.342

27

0.090

0.983

39.342

46.322

3

0.010

0.993

46.322

53.302

2

0.007

1.000

Permeability distribution: mean = 25.39 mD; minimum = 11.42 mD; maximum = 53.30 mD; standard deviation = 5.84 mD; and variance = 22.99%.

3. Simulation of density

Statistical Distribution

Range in Bulk Density, g/cm3 Cumulative

--Relative Relative

Minimum Maximum Frequency Frequency Frequency

2.267 2.301 100 0.333 0.793

Bulk density distribution: mean = 2.270 g/cm ; minimum = 2.166

g/cm ; maximum = 2.368 g/cm ; standard deviation = 0.0378 g/cm ; and variance = 1.67%.

B. The Numerical Simulation of the Mesozoic Carbonate Rock Properties

Model Input. Geological age: 140-190 my; dynamic deformation: 1.8-2.2 tectonic-stratigraphic units; depth of burial: 2.0-2.5 km; formation temperature: 85-95°C; homogeneity of rocks: 0.7-0.9; initial porosity before compaction: 0.35-0.45; and density of rock matrix: 2.67-2.75 g/cm3.

Model Output

1. Simulation of porosity

Statistical Distribution

Range in Porosity,

Fraction Cumulative

--Relative Relative

Minimum Maximum Frequency Frequency Frequency

Porosity distribution: mean = 0.132; minimum = 0.109; maximum = 0.165; standard deviation = 0.01092; and variance = 8.25%.

2. Simulation of density

Statistical Distribution

Range in Bulk Density,

Statistical Distribution

Range in Bulk Density,

g/cm3

Minimum

Maximum

Frequency

Relative Frequency

Cumulative

Relative Frequency

2.296

2.322

9

0.030

0.030

2.322

2.348

27

0.090

0.120

2.348

2.375

79

0.263

0.383

2.375

2.401

85

0.283

0.667

2.401

2.427

65

0.217

0.883

2.427

2.453

35

0.117

1.000

Density distribution: mean = 2.385 g/cm ; minimum = 2.296 g/cm ;

maximum = 2.453 g/cm ; standard deviation = 0.0326 g/cm ; and variance = 1.37%.

C. The Numerical Simulation of the Mesozoic Shale Properties

Model Input. Geological age: 140-190 my; dynamic deformation: 1.8-2.2 tectonic-stratigraphic units; depth of burial: 2.0-2.5 km; formation temperature: 85-95°C; rate of sedimentation: 100-200 m/ my; content of smectites: 30-40%; degree of cementation: 10-12%; Trask sorting coefficient: 3-4; initial porosity before compaction: 0.450.55; and density of rock matrix: 2.6-2.7 g/cm .

Model Output

1. Simulation of porosity

Statistical Distribution

Range in Porosity,

Fraction

Cumulative

Relative

Relative

Minimum Maximum

Frequency Frequency

Frequency

0.097 0.118 0.118 0.138

21 0.070 70 0.233

0.070 0.303

0.130 0.159 102 0.340 0.643

Porosity distribution: mean = 0.151; minimum = 0.097; maximum = 0.222; standard deviation = 0.0226; and variance = 14.97%.

2. Simulation of density

Statistical Distribution

Range in Bulk Density,

Statistical Distribution

Range in Bulk Density,

g/cm3

Minimum

Maximum

Frequency

Relative Frequency

Cumulative Relative Frequency

2.082

2.139

11

0.037

0.037

2.139

2.195

43

0.143

0.180

2.195

2.252

103

0.343

0.523

2.252

2.309

95

0.317

0.840

2.309

2.365

36

0.120

0.960

2.365

2.422

12

0.040

1.000

Density distribution: mean = 2.251 g/cm ; minimum = 2.082 g/cm ;

maximum = 2.422 g/cm ; standard deviation = 0.06197 g/cm ; and variance = 2.75%.

D. The Numerical Simulation of Reservoir Properties of Neogene Sandstones

Model Input. Geological age: 10-12 my; dynamic deformation: 1.1-1.2 tectonic-stratigraphic units; depth of burial: 2.0-2.5 km; formation temperature: 85-95°C; rate of sedimentation: 500-800 m/ my; quartz content: 60-80%; degree of cementation: 10-15%; Trask sorting coefficient: 3-4; initial porosity before compaction: 0.35-0.45; initial permeability before compaction: 2,000-3,000 mD; and density of rock matrix: 2.6-2.7 g/cm3.

Model Output

1. Simulation of porosity

Statistical Distribution

Range in Porosity,

Fraction Cumulative

Range in Porosity,

Fraction Cumulative

Relative

Relative

Minimum

Maximum

Frequency

Frequency

Frequency

0.225

0.243

30

0.100

0.100

0.243

0.261

87

0.290

0.390

0.261

0.278

113

0.377

0.767

0.278

0.296

57

0.190

0.957

0.296

0.313

11

0.037

0.993

0.313

0.331

2

0.007

1.000

Porosity distribution: mean = 0.266; minimum = 0.225; maximum = 0.331; standard deviation = 0.0176; and variance = 6.61%.

2. Simulation of permeability

Statistical Distribution

Range in Permeability,

Statistical Distribution

Range in Permeability,

mD

Cumulative

Relative

Relative

Minimum

Maximum

Frequency

Frequency

Frequency

299.21

372.45

10

0.033

0.033

372.45

446.28

72

0.240

0.273

446.28

519.81

116

0.387

0.660

519.81

593.35

75

0.250

0.910

593.35

666.88

23

0.077

0.987

666.88

740.42

4

0.013

1.000

Permeability distribution: mean = 492.30 mD; minimum = 299.21 mD; maximum = 740.42 mD; standard deviation = 72.00 mD; and variance = 14.62%.

Mathematical Modeling of Geological Processes 379 3. Simulation of density

Statistical Distribution

Range in Bulk Density, g/cm3 Cumulative

--Relative Relative

Minimum Maximum Frequency Frequency Frequency

Density distribution: mean = 1.946 g/cm ; minimum = 1.792 g/cm ;

maximum = 2.074 g/cm ; standard deviation = 0.0509 g/cm ; and variance = 2.62%.

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