lorenz_to_beta
Convert Lorenz coefficient to Dykstra-Parsons beta parameter for reservoir heterogeneity quantification. Enables comparison of reservoirs using different metrics and conversion of literature data between these common measures.
Instructions
Convert Lorenz coefficient to Dykstra-Parsons beta parameter.
HETEROGENEITY QUANTIFICATION - Converts between two common measures of reservoir heterogeneity. Essential for comparing reservoirs using different heterogeneity metrics and for literature data conversion.
Parameters:
value (float, required): Lorenz coefficient (0-1). Must be 0 ≤ L ≤ 1. Typical: 0.2-0.7. Example: 0.5 for moderate heterogeneity.
Lorenz Coefficient (L):
Ranges from 0 (homogeneous) to 1 (completely heterogeneous)
Based on cumulative flow capacity vs cumulative storage capacity
Geometric interpretation: area between Lorenz curve and 45° line
L = 2 × area between curve and diagonal
Directly measurable from production data (PLT, tracer tests)
Dykstra-Parsons Beta (β):
Permeability variation coefficient (dimensionless, 0-1)
β = (k50 - k84.1) / k50
Based on log-normal permeability distribution
Requires permeability data (core, logs)
Common in literature and older studies
Conversion Relationship: Beta and Lorenz are related through log-normal distribution statistics. Higher Lorenz = higher Beta (both indicate more heterogeneity).
Typical Ranges:
L < 0.3 (homogeneous): β < 0.5
L = 0.3-0.6 (moderate): β = 0.5-0.7
L > 0.6 (heterogeneous): β > 0.7
Applications:
Waterflood Sweep Efficiency: Predict vertical sweep from heterogeneity
Vertical Conformance Analysis: Evaluate production allocation
Reservoir Characterization: Compare reservoirs using different metrics
Performance Prediction: Use beta in Dykstra-Parsons calculations
Literature Conversion: Convert published beta values to Lorenz
Returns: Dictionary with:
beta (float): Dykstra-Parsons beta coefficient (0-1)
lorenz_coefficient (float): Input Lorenz coefficient
method (str): "Lorenz to Dykstra-Parsons conversion"
interpretation (dict): Heterogeneity level guidance
inputs (dict): Echo of input parameters
Common Mistakes:
Lorenz coefficient outside valid range (must be 0-1)
Confusing Lorenz with other heterogeneity measures
Using beta from wrong distribution (must be log-normal)
Not understanding that conversion is approximate (depends on distribution)
Example Usage:
{
"value": 0.5
}Result: β ≈ 0.6-0.7 (moderate to high heterogeneity).
Note: Conversion assumes log-normal permeability distribution. For non-log-normal distributions, conversion may be less accurate. Always validate against actual permeability data when possible.
Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| request | Yes |
Output Schema
| Name | Required | Description | Default |
|---|---|---|---|
No arguments | |||