Bibliography

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List of equations assignment

Bibliography

1. Archie, G. E. (1942). The electrical resistivity log as an aid in determining some reservoir characteristics. Transactions of the AIME, 146(01), 54-62.
2. Asquith, G. & D. Krygowski, 2004, Basic Well Log Analysis, AAPG Methods in Exploration Series, No. 16, Second Edition, American Association of Petroleum Geologists (AAPG).
3. Atlas, D. (1974). Log review I. Dresser Atlas Division, Dresser Industries.
4. Clavier, C., Hoyle, W., & Meunier, D. (1971). Quantitative interpretation of thermal neutron decay time logs: part I. Fundamentals and techniques. Journal of Petroleum Technology, 23(06), 743-755.
5. Coates, G. R., & Dumanoir, J. L. (1973, January). A new approach to improved log-derived permeability. In SPWLA 14th Annual Logging Symposium. Society of Petrophysicists and Well-Log Analysts.
6. Dewan, J. T. (1983). Essentials of modern open-hole log interpretation. PennWell Books.
7. Fertl, W. H. (1975, January). Shaly sand analysis in development wells. In SPWLA 16th Annual Logging Symposium. Society of Petrophysicists and Well-Log Analysts.
8. Larionov, V. V. (1969). Borehole radiometry. Nedra, Moscow, 127.
9. Raymer, L. L., Hunt, E. R., & Gardner, J. S. (1980, January). An improved sonic transit time-to-porosity transform. In SPWLA 21st annual logging symposium. Society of Petrophysicists and Well-Log Analysts.
10. Schlumberger, A. (1975). guide to Wellsite interpretation of the Gulf Coast. Schlumberger Well Services, Houston.
11. Simandoux, P. (1963). Dielectric measurements on porous media, application to the measurements of water saturation: study of behavior of argillaceous formations. Revue de l’Institut Francais du Petrol, 18(supplementary issue), 93-215.
12. Stieber, S. J. (1970, January). Pulsed Neutron Capture Log Evaluation-Louisiana Gulf Coast. In Fall Meeting of the Society of Petroleum Engineers of AIME. Society of Petroleum Engineers.
13. Timur, A. (1968, January). An investigation of permeability, porosity, and residual water saturation relationships. In SPWLA 9th annual logging symposium. Society of Petrophysicists and Well-Log Analysts.
14. Wyllie, M. R. J., & Rose, W. D. (1950). Some theoretical considerations related to the quantitative evaluation of the physical characteristics of reservoir rock from electrical log data. Journal of Petroleum Technology, 2(04), 105-118.
15. Wyllie, M. R. J., Gregory, A. R., & Gardner, G. H. F. (1958). An experimental investigation of factors affecting elastic wave velocities in porous media. Geophysics, 23(3), 459-493.

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Calculate Gas Reserves (Gf)

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List of equations assignment

Gas Reserves

Where:
• Gf= volumetric recoverable gas reserves in standard cubic feet (SCF)
• 43,560= area of 1 acre, in square feet
• A= drainage area in acres
• h= reservoir thickness in feet
• ɸ= porosity, decimal fraction
• Sh= hydrocarbon saturation (1.0 - Sw), decimal fraction
• RF= recovery factor
• Bbgi= gas volume factor (in SCF/cu ft)

Calculate Volumetric Producible Gas Reserves (Gf)
A: Acres		h: pies
ɸ: Decimal		Sh: Decimal
Bgi: SCF /cubic ft		FR: Decimal

Gas Volume Factor (Bgi)

Where:
• TSC= temperature (°F) at standard conditions
• PSC= PSC= surface pressure (psi) at standard conditions
• P= reservoir pressure (psi)
• Z=gas compressibility factor
• Tf= formation temperature (°F)
• Bgi = calculated by the ratio of surface and formation pressures

Calculate Gas Volume Factor (Bgi)
Tsc: °F		Psc: psi
P: psi		Z:
Tf: °F

Other way to calculate producible gas reserves is by replacing the gas volume factor for a pressure ratio:

Where:
• Gf= volumetric recoverable gas reserves in standard cubic feet (SCF)
• 43,560= area of 1 acre, in square feet
• A= drainage area in acres
• h= reservoir thickness in feet
• ɸ= porosity, decimal fraction
• Sh= hydrocarbon saturation (1.0 - Sw), decimal fraction
• RF= recovery factor
• Pf1= surface pressure (psi) (atmospheric, approximately 15 psi)
• Pf2= reservoir pressure (psi)

Calculate Volumetric Producible Gas Reserves (Gf)
A: Acres		h: ft
ɸ: Decimal		Sh: Decimal
Pf2/Pf1: SCF / cubic ft		FR: Decimal

This pressure ratio is calculated the following way:

Pf2/Pf1 = (0.43 * Depth) / 15

Where:
• 0.43 = average pressure gradient (psi/ft) and depth is in feet.

Calculate Gas Volume Factor (Bgi) - Pressures
Depth: ft

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Calculate Oil Reserves (Nf)

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List of equations assignment

Oil Reserves

Where:
• Nf= volumetric recoverable oil reserves in stock-tank barrels (STB)
• 7758= barrels per acre-foot
• A= drainage area in acres
• h= reservoir thickness in feet
• ɸ= porosity (decimal fraction)
• Sh= hydrocarbon saturation (1-Sw) (decimal fraction)
• RF= recovery factor
• Boi= oil volume factor, or reservoir barrels per stock-tank barrel

Calculate Volumetric Producible Oil Reserves (Nf)
A: Acres		h: ft
ɸ: Decimal		Sh: Decimal
FR: Decimal		Boi: Bbls/STB

Oil Volume Factor (Boi)

Where:
• Boi= oil volume factor, or reservoir barrels per stock-tank barrel
• GOR= gas-oil ratio

Calculate Oil Volume Factor (Boi)- GOR
GOR: SCF / STB

Gas-Oil Ratio (GOR)

GOR (Oil-Gas Ratio) = (Gas in cubic feet) / (Oil in barrels)

Calculate Gas-Oil Ratio (GOR)
Gas: cubic ft		Oil: Bbls

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Calculate Water Saturation - Flushed Zone Sxo

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List of equations assignment

Water Saturation (Sw) - Flushed Zone Sxo

There are diverse equation for water saturation calculation in the flushed zone. Here are some of the equations proposed by different authors:

1) First Equation

Where:
• Sxo= water saturation of the flushed zone
• Sw= water saturation of the uninvaded zone

Calculate Water Saturation (Sw) - Flushed Zone (Sxo)
Sw: Decimal

2) Second equation

Where:
• Sxo= water saturation of the flushed zone
• Rmf= resistivity of the mud filtrate at formation temperature
• Rxo= shallow resistivity from a very shallow reading device such as lateolog-8, microspherically focused log, or microlaterolog
• F= Formation Factor

Calculate Water Saturation (Sw)- Flushed Zone (Sxo) - Formation Factor (F)
F:		Rmf: ohm-m
Rxo: ohm-m

3) Third equation- Archie

Where:
• Sxo= water saturation of the flushed zone
• Rmf= resistivity of the mud filtrate at formation temperature
• Rxo= shallow resistivity from a very shallow reading device such as lateolog-8, microspherically focused log, or microlaterolog
• ɸ = porosity
• a= tortuosity factor
• m= cementation exponent
• n= saturation exponent

Calculate Water Saturation (Sw)- Archie- Flushed Zone (Sxo)
a:		Rmf: ohm-m
Rxo: ohm-m		ɸ: Decimal
m:		n:

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Calculate Total Water Saturation Swt (shale corrected)

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List of equations assignment

Total Water Saturation (Swt)- Shale Corrected

There is another equation for the calculation of total (shale-corrected) water saturation. This uses parameters like water resistivity, apparent water resistivity, besides of a constant "b" that depends on water saturation and bound-water resistivity. The equation is the following:

Where:
• Swt= total (shale corrected) water saturation
• Rw= resistivity of formation water at formation temperature
• Rwa= apparent water resistivity
• b= constant

Calculate Total Water Saturation (Swt) - Shale Corrected
b:		Rw: ohm-m
Rwa: ohm-m

Constant b

Constant b depends of water saturation, bound-water resistivity, and the resistivity of a bound-water formation. The equation to calculate it, is expressed the following way:

Where:
• Swb= bound-water saturation
• Rw= resistivity of formation water at formation temperature
• Rb= bound-water resistivity
• b= constant

Calculate Constant b
Swb: Decimal		Rw: ohm-m
Rb: ohm-m

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Calculate Water Saturation Sw (Simandoux, 1963)

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List of equations assignment

Water Saturation (Sw)- Simandoux (1963)

Another well known equation to calculate water saturation is Simandoux's equation (1963). This uses the same parameters used in other equations from other authors (e.g. Schlumberger, Ferlt, etc.), like shale volume, porosity, water resistivity, true formation resistivity, and shale/clay resistivity. The equation expression is the following:

Where:
• Sw= water saturation of the uninvaded zone
• Rt= true formation resistivity (i.e., deep induction or deep laterolog corrected for invasion)
• Rw= resistivity of formation water at formation temperature
• ɸ = porosity
• Vshale= shale volume
• Rshale= shale/clay resistivity value in a formation

Calculate Water Saturation (Sw) - Simandoux (1963)
Rw: ohm-m		ɸ: Decimal
Vsh: Decimal		Rsh: ohm-m
Rt: ohm-m

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Calculate Water Saturation Sw (Schlumberger, 1975)

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List of equations assignment

Water Saturation (Sw)- Schlumberger (1975)

Schlumberger (1975) also proposed an equation to calculate water saturation, and the parameters included in that expression are very similar to the ones used in Ferlt's equation (1975), but adding a different parameter: a shale/clay resistivity value. The similar parameters are shale volume, porosity, water resistivity, and true formation resistivity. The equation is the following:

Where:
• Sw= water saturation of the uninvaded zone
• Rt= true formation resistivity (i.e., deep induction or deep laterolog corrected for invasion)
• Rw= resistivity of formation water at formation temperature
• ɸ = porosity
• Vshale= shale volume
• Rshale= shale/clay resistivity value in a formation

Calculate Water Saturation (Sw) - Schlumberger (1975)
Vsh: Decimal		Rsh: ohm-m
ɸ: Decimal		Rw: ohm-m
Rt: ohm-m

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Calculate Water Saturation Sw (Ferlt, 1975)

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List of equations assignment

Water Saturation (Sw) - Ferlt (1975)

Among the equations for the calculation of water saturation, we find Ferlt's equation (1975). This one includes the values of porosity, water resistivity, true formation resistivity, shale volume, and a constant "a", which its value is known for certain zones. The equation is the following:

Where:
• Sw= water saturation of the uninvaded zone
• Rt= true formation resistivity (i.e., deep induction or deep laterolog corrected for invasion)
• Rw= resistivity of formation water at formation temperature
• ɸ = porosity
• Vshale= shale volume
• a= 0.25 at the Golf Coast
• a= 0.35 at the Rocky Mountains

Calculate Water Saturation (Sw) - Ferlt (1975)
ɸ: Decimal		Rw: ohm-m
Rt: ohm-m		a:
Vsh: Decimal

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Calculate Water Saturation Sw (Dewan, 1983)- Dispersed Shale Model

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List of equations assignment

Water Saturation (Sw)- Dewan (1983) - Dispersed Clay Model

Dewan (1983) also created an equation for the calculation of water saturation for dispersed clay models. This equation includes values such as water and true formation resistivities, sonic derived porosity, and a constant "q" that depends on the density and sonic derived porosity. The expression is the following:

Where:
• Sw= water saturation of the uninvaded zone
• Rt= true formation resistivity (i.e., deep induction or deep laterolog corrected for invasion)
• Rw= resistivity of formation water at formation temperature
• ɸs= sonic porosity
• q= intergranular space filled with clay

Calculate Water Saturation (Sw) - Dispersed Clay Model- Dewan (1983)
Rw: ohm-m		ɸs: Decimal
Rt: ohm-m		q:

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Constant q (intergranular space filled with clay)

Constant q is related to the intergranular space filled with clay, and this depends on the values of density and sonic porosity. The equation to calculate it, is the following:

Where:
• ɸD= density porosity
• ɸs= sonic porosity
• q= intergranular space filled with clay

Calculate Constant q
ɸs: Decimal		ɸd: Decimal

Calculate Compensated Water Saturation Sw - (Dewan, 1983)

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List of equations assignment

Water Saturation (Sw) - Compensated Water Saturation Equation - Dewan (1983)

Dewan (1983) proposed an equation for the calculation of compensated water saturation, and this takes into account certain rock and fluid properties such as water resistivity, formation resistivity, and sonic derived porosity. The expression is the following:

Where:
• Sw= water saturation of the uninvaded zone
• Rt= true formation resistivity (i.e., deep induction or deep laterolog corrected for invasion)
• Rw= resistivity of formation water at formation temperature
• ɸs= sonic porosity

Calculate Water Saturation (Sw) - Compensated - Dewan (1983)
Rw: ohm-m		Rt: ohm-m
ɸs: Decimal

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