pyResToolbox MCP Server

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:

1. Sort layers by kh fraction (ascending)

2. Calculate cumulative kh fraction (x-axis)

3. Calculate cumulative flow fraction (y-axis)

4. Calculate area between curve and diagonal (45° line)

5. 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:

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).