lorenz_from_flow_fractions
Calculate the Lorenz coefficient to quantify vertical conformance by analyzing flow and permeability-thickness fractions from production data.
Instructions
Calculate Lorenz coefficient from flow and permeability fractions.
LORENZ FROM PRODUCTION DATA - Computes Lorenz coefficient from layer-by-layer flow and permeability data. Essential for analyzing actual production data and quantifying vertical conformance from measured production allocation.
Parameters:
flow_frac (list, required): Flow fractions from each layer (0-1). Must sum to 1.0. Length must match perm_frac. Example: [0.1, 0.2, 0.3, 0.4].
perm_frac (list, required): Permeability-thickness fractions (kh fractions) for each layer (0-1). Must sum to 1.0. Length must match flow_frac. Example: [0.05, 0.15, 0.25, 0.55].
Input Data Sources:
PLT (Production Logging Tool): Flow rate per layer from production logs
Tracer Tests: Flow allocation from tracer response
Production Allocation: Flow rates from well test analysis
Core Data: Permeability and thickness from core analysis
Log Data: Permeability from well logs, thickness from formation tops
Lorenz Coefficient Calculation: Constructs Lorenz curve from data:
Sort layers by kh fraction (ascending)
Calculate cumulative kh fraction (x-axis)
Calculate cumulative flow fraction (y-axis)
Calculate area between curve and diagonal (45° line)
L = 2 × area (normalized to 0-1)
Interpretation:
L < 0.3: High conformance (flow matches capacity)
L = 0.3-0.6: Moderate conformance (some flow imbalance)
L ≥ 0.6: Poor conformance (severe flow imbalance)
Applications:
Production Allocation Analysis: Quantify vertical conformance from PLT data
PLT Interpretation: Convert PLT flow rates to heterogeneity measure
Tracer Test Analysis: Evaluate sweep efficiency from tracer response
Vertical Conformance Evaluation: Assess waterflood performance
History Matching: Match simulation to measured production allocation
Performance Diagnosis: Identify layers with poor conformance
Returns: Dictionary with:
lorenz_coefficient (float): Lorenz coefficient (0-1)
number_of_layers (int): Number of layers analyzed
method (str): "Lorenz from flow and permeability fractions"
interpretation (str): Conformance level guidance
inputs (dict): Echo of input parameters
Common Mistakes:
Flow fractions don't sum to 1.0 (must normalize)
Perm fractions don't sum to 1.0 (must normalize)
Length mismatch between flow_frac and perm_frac
Using weight fractions instead of flow fractions
Not sorting layers correctly (must sort by kh)
Using wrong kh calculation (must be k × h, not just k)
Example Usage:
{
"flow_frac": [0.1, 0.2, 0.3, 0.4],
"perm_frac": [0.05, 0.15, 0.25, 0.55]
}Result: L ≈ 0.4-0.5 (moderate conformance - high-k layers produce more than their capacity fraction, low-k layers produce less).
Note: This is the most direct way to calculate Lorenz from actual production data. Always ensure fractions sum to 1.0 and layers are correctly matched. High L indicates poor vertical conformance (flow imbalance).
Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| request | Yes |
Output Schema
| Name | Required | Description | Default |
|---|---|---|---|
No arguments | |||