Geertsma’s Model for Porosity/Transit-Time Relationship in Excel Formulas

Geertsma’s model is a porosity-transit time relationship that is used to estimate the porosity of a rock formation from the transit time of acoustic waves through the formation. The model is based on the assumption that the pore space of a rock is made up of a network of interconnected capillaries. The capillaries are assumed to be cylindrical in shape and to have a uniform radius. The model relates the transit time of acoustic waves through the formation to the porosity of the rock and the radius of the capillaries.

The model is useful because it provides a way to estimate the porosity of a rock formation without having to measure it directly. This can be important in situations where direct measurements are difficult or impossible to obtain. However, it is important to note that the model is based on several assumptions that may not always be valid. For example, the model assumes that the capillaries are cylindrical in shape and have a uniform radius, which may not be true in all cases. Additionally, the model assumes that the pore space of the rock is made up of a network of interconnected capillaries, which may not be true for all rock formations.

Basic Theory:

Geertsma’s model establishes a relationship between porosity (φ) and transit time (𝒯) through the
following equation:

φ = a · T^b

Where:

• φ is the porosity,
• T is the transit time,
• a and b are constants.

Procedures:

1. Determine Constants (a and b): Conduct laboratory measurements or refer to literature to
   find appropriate values for a and b.
2. Collect Transit Time Data: Gather transit time data from well logs or seismic surveys.
3. Apply Geertsma’s Model in Excel:
   • Create a table with columns for transit time (T), porosity (φ), and constants a and b.
   • Use the formula φ = a · T^b to calculate porosity for each transit time.
4. Scenario:
   • Assume a = 0.0005 and b = 2.
   • Generate a set of transit times ranging from 50 to 150 milliseconds.
5. Excel Implementation:
   • Input the constants and transit times into an Excel table.
   • Use the formula φ = a · T^b to calculate porosity for each transit time.
6. MATLAB Comparison:
   • Write a MATLAB script implementing Geertsma’s model with the provided constants and transit times.
   • Compare the results obtained in Excel and MATLAB.

Example:

Let’s consider a scenario with the following parameters:

• a = 0.0005
• b = 2
• Transit times (T): 50, 75, 100, 125, and 150 milliseconds.

Table:

Excel Calculation:

Perform the calculations in the table to obtain porosity values.

MATLAB Script:

a = 0.0005;
b = 2;
transit_times = [50, 75, 100, 125, 150];
porosity_matlab = a .* transit_times.^b;