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Generate Van Everdingen & Hurst aquifer influence functions.

CRITICAL AQUIFER MODELING TOOL - Creates dimensionless aquifer influence functions for AQUTAB keyword in ECLIPSE/Intersect. These functions quantify water influx from surrounding aquifers into hydrocarbon reservoirs.

Parameters:

• res (float or list, required): Dimensionless aquifer radius (ReD). Must be > 1.0. Can be scalar or list. Typical: 5-100. Example: 10.0. ReD = re/rw where re = aquifer outer radius, rw = reservoir radius.

• start (float, required): Minimum dimensionless time (tD_min). Must be > 0. Typical: 0.01-1.0. Example: 0.1.

• end (float, required): Maximum dimensionless time (tD_max). Must be > start. Typical: 10-1000. Example: 100.0.

• rows (int, required): Number of time points in table. Must be > 0. Typical: 20-100. Example: 50. More rows = smoother curves.

Background: Van Everdingen & Hurst (1949) developed analytical solutions for aquifer influx using diffusivity equation. These functions relate:

• Dimensionless time (tD) = (k × t) / (φ × μ × ct × rw²)

• Dimensionless pressure (pD) = aquifer response function

• Dimensionless radius (ReD) = aquifer geometry

Influence Function: The influence function pD(tD, ReD) represents the dimensionless pressure response at the reservoir-aquifer boundary. It depends on:

• Aquifer geometry (radial vs linear, finite vs infinite)

• Boundary conditions (constant rate vs constant pressure)

• Aquifer properties (permeability, porosity, compressibility)

Applications:

• Material Balance: Quantify aquifer support in material balance analysis

• Pressure Maintenance: Evaluate aquifer pressure support

• Water Influx: Calculate cumulative water influx over time

• History Matching: Match production history with aquifer model

• Production Forecasting: Predict future aquifer influx

Integration Method: Uses numerical integration (Gaussian quadrature) of diffusivity equation with high-resolution integration (M=8) for accuracy. The solution is computed at specified dimensionless time points.

Returns: Dictionary with:

• dimensionless_time (list): Dimensionless time values (tD)

• dimensionless_pressures (list): List of pD arrays (one per ReD)

• rows (int): Number of time points

• dimensionless_radii (list): ReD values used

• time_range (dict): Start and end dimensionless times

• note (str): Usage guidance for ECLIPSE

• inputs (dict): Echo of input parameters

Common Mistakes:

• ReD < 1.0 (aquifer radius must be > reservoir radius)

• tD_max < tD_min (end must be > start)

• Too few rows (<10) causing poor resolution

• Wrong dimensionless radius (must match aquifer geometry)

• Confusing dimensionless time with actual time

• Not accounting for aquifer compressibility

Example Usage:

Result: Table with 50 time points from tD=0.1 to tD=100.0 for ReD=10.0.

Note: AQUTAB keyword is ready for direct inclusion in ECLIPSE DATA file. The influence functions are dimensionless and must be scaled using reservoir and aquifer properties. For multiple aquifers, generate separate tables for each aquifer with different ReD values.