## 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

 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

 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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