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Reservoir Heterogeneity

Reservoir Heterogeneity
Reservoir Heterogeneity

How Can We Measure the Heterogeneity of a Reservoir Effectively?

In reservoir engineering, understanding how uniform—or not—your reservoir is can significantly impact management and extraction strategies. Here are two critical methods to determine this:

  • Lorenz coefficient
  • Dykstra-Parsons

Lorenz Coefficient: Developed by Schmalz and Rahme in 1950, this parameter quantifies the heterogeneity within a pay zone. It scales from zero (completely homogeneous) to one (highly heterogeneous), with classifications:

  • Zero: Completely homogeneous reservoir
  • 0 – 0.5: Low heterogeneity “relatively uniform properties”
  • 0.5 – 0.7: Moderate heterogeneity “some variation in properties”
  • 0.7-1: High heterogeneity “ significant variation in properties”

 

The following steps summarize the methodology of calculating Lorenz coefficient:

Step 1. Arrange all the available permeability values in a descending order.

Step 2. Calculate the cumulative permeability capacity Σkh and cumulative volume capacity ΣØh.

Step 3. Normalize both cumulative capacities such that each cumulative capacity ranges from 0 to 1.

Step 4. Plot the normalized cumulative permeability capacity versus the normalized cumulative volume capacity on a Cartesian scale.

Step 5. You can convert Lorenz coefficient to Dykstra-Parsons coefficient using the following correlation:

Example 1:

Dykstra-Parsons Coefficient: This statistical measure, introduced by Dykstra and Parsons in 1950, evaluates permeability variation. Steps include:

Step 1. Arrange the core samples in decreasing permeability sequence, i.e., descending order.

Step 2. For each sample, calculate the percentage of thickness with permeability greater than this sample.

Step 3. Using a log-probability graph paper, plot permeability values on the log scale and the % of thickness on the probability scale

Step 4. Draw the best straight line through the points.

Step 5. Read the corresponding permeability values at 84.1% and 50% of thickness. These two values are designated as k84.1 and k50.

Step 6. The following expression defines the Dykstra-Parsons permeability variation:

Example 2:

 

Conversion Between Two Coefficient:

The below figure shows the relation of the permeability variation V and Lorenz coefficient L for log-normal permeability distributions as proposed by Warren and Price (1961). This relationship can be expressed mathematically by the following two expressions:

 

In conclusion, mastering the Lorenz and Dykstra-Parsons coefficients is crucial for effectively managing reservoir heterogeneity

We have attached an excel sheet below

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