Wyllie time-average equation vs Gardner's equation vs RHG Equation for porosity

  • #1
getsrawal
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TL;DR Summary
Wyllie time-average equation vs Gardner's equation vs RHG Equation and what these equation are different from any other approach for calculating imbition method, ideal gas laws or mercury displacement method
If you were estimating porosity from velocity, which approach would you prefer to use among Wyllie time-average equation, Gardner's equation Or RHG Equation, when and why?

My answer is RHG equation as wylllie equation don't work for unconsolidate sand and give accurate results when it is saturated with brine solution. Garnder's equation mainly relates density with porosity not accounting with velocity and RHG equation is improved one. CAn you please help me with anything i'm missing here.

Are these three equation are different from any other approach like imbition method, ideal gas laws or mercury displacement method for calculating porosity?
 
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  • #2
Welcome to PF.

Would I be right in guessing that this question is about seismic velocity, in porous rocks, that are water saturated ?
 
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  • #3
Baluncore said:
Welcome to PF.

Would I be right in guessing that this question is about seismic velocity, in porous rocks, that are water saturated ?
yes it is about comparing results given by three equations. It is to discuss mainley what RPG equation have advantages over wyllie and Gardner's equation and what is appropriate method among three to measure porosity from velocity in different types of rocks.
 
  • #4
I am interested in the subject, but it is more than 40 years since I shot my last seismic survey.
Can you please post links to the equations.
 

What is the Wyllie Time-Average Equation and how is it used in porosity estimation?

The Wyllie Time-Average Equation is a formula used to estimate the porosity of a geological formation from acoustic travel times. It assumes that the travel time through a rock matrix and its pores are additive. The equation is often expressed as T = T_m * (1 - Φ) + T_f * Φ, where T is the total travel time, T_m is the travel time through the matrix, T_f is the travel time through the fluid in the pores, and Φ is the porosity. It is particularly useful in well logging for determining the porosity of a formation indirectly.

What is Gardner's Equation and how does it differ from the Wyllie Time-Average Equation?

Gardner's Equation is primarily used to estimate the bulk density of a rock from its acoustic velocity. The formula, ρ = α * V^β, where ρ is the bulk density, V is the P-wave velocity, and α and β are empirically derived constants, highlights a different aspect of rock properties compared to the Wyllie Time-Average Equation. Unlike the Wyllie equation, which is used to calculate porosity, Gardner's Equation is used to infer density, which can then be indirectly related to porosity.

What is the RHG Equation and its application in porosity calculations?

The RHG Equation, developed by Raymer, Hunt, and Gardner, is another approach to estimate porosity from sonic log data. It modifies the Wyllie Time-Average Equation by incorporating a more complex relationship between travel time and porosity. The equation is expressed as Φ = (T - T_m) / (T_f - T_m * C), where C is an empirical constant determined by rock type. This equation is particularly useful in more complex lithologies where the simple additive model of the Wyllie equation may not be sufficient.

How do the accuracies of these equations compare in different rock types?

The accuracy of each equation—Wyllie's, Gardner's, and RHG—varies depending on the rock type and the conditions of the formation. The Wyllie Time-Average Equation generally performs well in clean, consolidated sands but may be less accurate in shaly or carbonate rocks due to its simplistic assumptions. Gardner's Equation, being focused on density, is sensitive to variations in mineral composition and may not directly reflect porosity changes. The RHG Equation often provides better estimates in mixed or complex lithologies where the other two might fail to account for specific geological factors.

Which equation should be used for estimating porosity in a mixed lithology environment?

In a mixed lithology environment, the RHG Equation is often the preferred choice because it accounts for variations in rock properties more effectively than the Wyllie Time-Average or Gardner's Equations. Its formulation allows for adjustments based on empirical constants that can be tailored to specific rock types, providing more accurate porosity estimations where the rock properties vary significantly within the formation. However, it's crucial to calibrate any of these equations with core data or other independent porosity measurements to ensure accuracy.

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