permeability 0.1.1

A python package for calculating permeability

permeability

A Python package for calculating permeability of porous media using the seepage distance method, derived from the Darcy's law-based formula, with capillary pressure correction via the Young-Laplace equation:

$$ K = \frac{L^2 \cdot \mu \cdot \phi}{2 \cdot t \cdot \Delta P} $$

$$ t = \frac{\mu \cdot \phi \cdot L^2}{2 \cdot K \cdot \Delta P} $$

$$ z(t) = \sqrt{\frac{2 \cdot K \cdot \Delta P \cdot t}{\mu \cdot \phi}} $$

$$ p_c = \frac{2 \cdot \gamma \cdot \cos(\theta)}{r} $$

Capillary-Corrected Forms

When capillary pressure $p_c$ is considered, $\Delta P$ is replaced by $(\Delta P + p_c)$:

$$ K = \frac{L^2 \cdot \mu \cdot \phi}{2 \cdot t \cdot (\Delta P + p_c)} $$

$$ t = \frac{\mu \cdot \phi \cdot L^2}{2 \cdot K \cdot (\Delta P + p_c)} $$

$$ z(t) = \sqrt{\frac{2 \cdot K \cdot (\Delta P + p_c) \cdot t}{\mu \cdot \phi}} $$

$$ \Delta P = \frac{\mu \cdot \phi \cdot L^2}{2 \cdot K \cdot t} $$

$$ \Delta P = \frac{\mu \cdot \phi \cdot L^2}{2 \cdot K \cdot t} - p_c $$

Symbol	Meaning	Unit
$K$	Permeability	m²
$L$	Sample thickness along flow direction	m
$\mu$	Dynamic viscosity of fluid	Pa·s
$\phi$	Porosity of porous medium	dimensionless
$t$	Time for fluid to fully penetrate sample	s
$\Delta P$	Constant pressure difference across sample	Pa
$z$	Infiltration front position	m
$p_c$	Capillary pressure	Pa
$\gamma$	Surface tension of the liquid	N/m
$\theta$	Contact angle (wetting angle)	Degrees
$r$	Equivalent pore radius	m

This package also provides an MCP server that exposes these calculations as tools for AI assistants like Claude.

---

Installation

Using pip

pip install permeability

Using uv (recommended)

uv add permeability

---

Quick Start

Calculate Permeability from Experimental Data

from permeability.permeability import Seepage

# Experimental parameters
K = Seepage.calculate_permeability(
    L=0.003,   # Sample thickness: 3 mm
    mu=0.192,  # Fluid viscosity: 0.192 Pa·s
    phi=0.445, # Porosity: 0.445
    t=100,     # Penetration time: 100 s
    dP=1e4     # Pressure difference: 10,000 Pa
)
print(f"Permeability: {K:.3e} m²")  # ~3.84e-13 m²

Predict Infiltration Time

t = Seepage.calculate_infiltration_time(
    L=0.003,
    mu=0.192,
    phi=0.445,
    K=3.8448e-13,
    dP=1e4
)
print(f"Infiltration time: {t:.2f} s")  # ~100.00 s

Calculate Infiltration Front Position

# Single time point
z = Seepage.calculate_infiltration_front_position(
    K=1.284e-13,
    mu=0.192,
    phi=0.642,
    dP=1e5,
    t=120
)
print(f"Front position: {z:.4f} m")  # ~0.0050 m

# Multiple time points (for graphing)
import numpy as np
z_array = Seepage.calculate_infiltration_front_position_with_multiple_time(
    K=1.284e-13,
    mu=0.192,
    phi=0.642,
    dP=1e5,
    t=np.array([0, 30, 120])
)
print(f"Front positions: {z_array}")  # [0.0, 0.0025, 0.005]

Calculate Capillary Pressure

from permeability.permeability.Capillary import calculate_capillary_pressure

# Capillary pressure via Young-Laplace equation
p_c = calculate_capillary_pressure(
    gamma=0.072,  # Surface tension of water: 0.072 N/m
    theta=30,     # Contact angle: 30 degrees
    r=1e-6        # Pore radius: 1 µm
)
print(f"Capillary pressure: {p_c:.2f} Pa")  # ~124.71 Pa

Permeability with Capillary Correction

# Calculate permeability considering capillary pressure
K_corrected = Seepage.calculate_permeability(
    L=0.003,
    mu=0.192,
    phi=0.445,
    t=100,
    dP=1e4,
    p_c=124.71  # Capillary pressure (Pa)
)
print(f"Corrected permeability: {K_corrected:.3e} m²")

Calculate Pressure Difference

# Calculate the pressure difference applied across the sample
dP = Seepage.calculate_pressure_difference(
    L=0.003,
    mu=0.192,
    phi=0.445,
    K=3.8448e-13,
    t=100
)
print(f"Pressure difference: {dP:.2f} Pa")  # ~10000.00 Pa

# With capillary correction
dP_corrected = Seepage.calculate_pressure_difference(
    L=0.003,
    mu=0.192,
    phi=0.445,
    K=3.8448e-13,
    t=100,
    p_c=124.71  # Capillary pressure (Pa)
)
print(f"Corrected pressure difference: {dP_corrected:.2f} Pa")

Unit Conversion

from permeability.utils.UnitConverter import darcy2m2, m22darcy

# Convert m² to Darcy
darcy = m22darcy(m2K=3.8448e-13)
print(f"Permeability: {darcy:.3f} Darcy")  # ~0.390 Darcy

# Convert Darcy to m²
m2 = darcy2m2(darcyK=0.3896)
print(f"Permeability: {m2:.3e} m²")  # ~3.845e-13 m²

---

MCP Server

The package includes a Model Context Protocol (MCP) server that exposes permeability calculations as AI-accessible tools. After installing the package, start the server with:

Starting the Server

Once installed, simply run:

# Default port 8000
permeability_mcp

# Custom port
permeability_mcp --port 8080

The server starts via HTTP/SSE transport (http://localhost:8000 by default).

If you prefer to try it without installing, you can also use:

uvx --from permeability permeability_mcp

Configuration for AI Assistants

For Claude Desktop, add to your claude_desktop_config.json:

{
  "mcpServers": {
    "permeability": {
      "command": "permeability_mcp",
      "args": ["--port", "8080"]
    }
  }
}

For Cline (VS Code extension), add to your MCP settings:

{
  "mcpServers": {
    "permeability": {
      "command": "permeability_mcp",
      "args": ["--port", "8080"]
    }
  }
}

Available Tools

Once the MCP server is running, AI assistants can call:

Tool	Description
calculate_permeability_by_seepage_distance	Calculate $K$ (optionally with capillary correction via $p_c$)
calculate_infiltration_time	Calculate $t$ (optionally with capillary correction via $p_c$)
calculate_infiltration_front_position	Calculate $z(t)$ (optionally with capillary correction via $p_c$)
calculate_infiltration_front_position4multiple_times	Calculate $z(t)$ for multiple time points (optionally with capillary correction via $p_c$)
calculate_capillary_pressure	Calculate $p_c = 2\gamma\cos(\theta),/,r$ (Young-Laplace equation)
calculate_pressure_difference	Calculate $\Delta P$ (optionally with capillary correction via $p_c$)
darcy_to_m2_converter	Convert Darcy to m²
m2_to_darcy_converter	Convert m² to Darcy

Each tool accepts the same parameters as the Python API.

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API Reference

Seepage.calculate_permeability(L, mu, phi, t, dP, p_c=None)

Calculate permeability from seepage distance experiment data. When $p_c$ is provided, the capillary-corrected form is used.

$$ K = \frac{L^2 \cdot \mu \cdot \phi}{2 \cdot t \cdot \Delta P} \qquad\text{or}\qquad K = \frac{L^2 \cdot \mu \cdot \phi}{2 \cdot t \cdot (\Delta P + p_c)} $$

Parameter	Type	Description
L	float	Sample length/thickness along flow direction (m)
mu	float	Dynamic viscosity of fluid (Pa·s)
phi	float	Porosity of porous medium ($0 < \phi \le 1$)
t	float	Total time for fluid to fully penetrate sample (s)
dP	float	Constant pressure difference across sample (Pa)
p_c	float, optional	Capillary pressure for correction (Pa)

Returns: float — Permeability $K$ (m²)

---

Seepage.calculate_infiltration_time(L, mu, phi, K, dP, p_c=None)

Predict the time required for fluid to fully penetrate a sample. When $p_c$ is provided, the capillary-corrected form is used.

$$ t = \frac{\mu \cdot \phi \cdot L^2}{2 \cdot K \cdot \Delta P} \qquad\text{or}\qquad t = \frac{\mu \cdot \phi \cdot L^2}{2 \cdot K \cdot (\Delta P + p_c)} $$

Parameter	Type	Description
L	float	Sample length/thickness along flow direction (m)
mu	float	Dynamic viscosity of fluid (Pa·s)
phi	float	Porosity of porous medium ($0 < \phi \le 1$)
K	float	Permeability (m²)
dP	float	Constant pressure difference across sample (Pa)
p_c	float, optional	Capillary pressure for correction (Pa)

Returns: float — Infiltration time $t$ (s)

---

Seepage.calculate_infiltration_front_position(K, mu, phi, dP, t, p_c=None)

Calculate the infiltration front position at a given time. When $p_c$ is provided, the capillary-corrected form is used.

$$ z(t) = \sqrt{\frac{2 \cdot K \cdot \Delta P \cdot t}{\mu \cdot \phi}} \qquad\text{or}\qquad z(t) = \sqrt{\frac{2 \cdot K \cdot (\Delta P + p_c) \cdot t}{\mu \cdot \phi}} $$

Parameter	Type	Description
K	float	Permeability (m²)
mu	float	Dynamic viscosity of fluid (Pa·s)
phi	float	Porosity of porous medium ($0 < \phi \le 1$)
dP	float	Constant pressure difference across sample (Pa)
t	float	Time elapsed (s)
p_c	float, optional	Capillary pressure for correction (Pa)

Returns: float — Infiltration front position $z$ (m)

---

Seepage.calculate_infiltration_front_position_with_multiple_time(K, mu, phi, dP, t, p_c=None)

Calculate the infiltration front position at multiple time points (useful for plotting). When $p_c$ is provided, the capillary-corrected form is used.

$$ z(t) = \sqrt{\frac{2 \cdot K \cdot \Delta P \cdot t}{\mu \cdot \phi}} \qquad\text{or}\qquad z(t) = \sqrt{\frac{2 \cdot K \cdot (\Delta P + p_c) \cdot t}{\mu \cdot \phi}} $$

Parameter	Type	Description
K	float	Permeability (m²)
mu	float	Dynamic viscosity of fluid (Pa·s)
phi	float	Porosity of porous medium ($0 < \phi \le 1$)
dP	float	Constant pressure difference across sample (Pa)
t	numpy.ndarray	Array of time values (s)
p_c	float, optional	Capillary pressure for correction (Pa)

Returns: numpy.ndarray — Array of infiltration front positions $z$ (m)

---

Seepage.calculate_pressure_difference(L, mu, phi, K, t, p_c=None)

Calculate the pressure difference across a sample. When $p_c$ is provided, the capillary-corrected form is used.

$$ \Delta P = \frac{\mu \cdot \phi \cdot L^2}{2 \cdot K \cdot t} \qquad\text{or}\qquad \Delta P = \frac{\mu \cdot \phi \cdot L^2}{2 \cdot K \cdot t} - p_c $$

Parameter	Type	Description
L	float	Sample length/thickness along flow direction (m)
mu	float	Dynamic viscosity of fluid (Pa·s)
phi	float	Porosity of porous medium ($0 < \phi \le 1$)
K	float	Permeability (m²)
t	float	Total time for fluid to fully penetrate sample (s)
p_c	float, optional	Capillary pressure for correction (Pa)

Returns: float — Pressure difference $\Delta P$ (Pa)

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calculate_capillary_pressure(gamma, theta, r)

Calculate capillary pressure using the Young-Laplace equation.

$$ p_c = \frac{2 \cdot \gamma \cdot \cos(\theta)}{r} $$

Parameter	Type	Description
gamma	float	Surface tension of the liquid (N/m)
theta	float	Contact angle / wetting angle (Degrees)
r	float	Equivalent pore radius (m)

Returns: float — Capillary pressure $p_c$ (Pa)

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darcy2m2(darcyK)

Convert permeability from Darcy to m².

Parameter	Type	Description
darcyK	float	Permeability in Darcy

Returns: float — Permeability in m²

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m22darcy(m2K)

Convert permeability from m² to Darcy.

Parameter	Type	Description
m2K	float	Permeability in m²

Returns: float — Permeability in Darcy

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Development

Setup

git clone https://github.com/1Vewton/permeability.git
cd permeability
uv sync

Running Tests

uv run pytest

Code Style

uv run flake8

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License

This project is licensed under the GNU General Public License v3.0. See the LICENSE file for details.