Theory & Background

Semi-analytical decline model for gas wells under boundary-dominated flow, derived from material balance principles

Complete theory and equations for classical Arps decline curves including exponential, hyperbolic, and harmonic models for production forecasting and EUR estimation.

Objective functions for evaluating decline curve model fit quality including SSE, log-space SSE, and weighted variants

Theory and equations for the Duong decline model designed for multi-fractured horizontal wells in shale and tight reservoirs with extended linear flow.

Aggregate production modeling for multi-well field development using parametric and discrete convolution approaches

Hybrid decline model combining hyperbolic and exponential decline with a terminal decline rate for realistic long-term production forecasting.

Theory and equations for the Ilk et al. Power Law Exponential decline model for tight gas and unconventional reservoirs, capturing transient-to-BDF transition.

Theory and equations for the Valkó-Lee Stretched Exponential decline model based on statistical physics, ideal for shale and unconventional reservoir analysis.

Empirical correlations for predicting the saturation pressure of crude oil from surface-measured fluid properties

McCain correlations for formation water density, formation volume factor, compressibility, viscosity, and solution gas-water ratio

Comprehensive correlations for natural gas compressibility factor, viscosity, density, formation volume factor, and pseudo-critical properties

Gas-oil interfacial tension correlations for wellbore hydraulics calculations

Empirical correlations for predicting isothermal compressibility of crude oil at saturated and undersaturated conditions

PVT correlations for oil formation volume factor including Standing, Vazquez-Beggs, Glasø, Al-Marhoun, Petrosky-Farshad, and Dindoruk-Christman methods.

Empirical correlations for predicting crude oil viscosity at dead, saturated, and undersaturated conditions

PVT correlations for solution gas-oil ratio including Standing, Vazquez-Beggs, Glasø, Al-Marhoun, Petrosky-Farshad, and Dindoruk-Christman methods.

Comprehensive correlation for predicting pressure drop and liquid holdup in multiphase flow through pipes at any inclination angle

Reynolds number, friction factor, and pressure drop calculations for single-phase liquid and gas flow in pipes

Hagedorn-Brown and Gray correlations for predicting pressure gradients in vertical and near-vertical wells

Method of images for modeling boundary effects including sealing faults, constant pressure boundaries, and combinations in well test analysis.

Definitions and equations for dimensionless pressure, time, radius, distance, and wellbore storage used in well test analysis and type curve matching.

Line source solution, Ei function, Stehfest numerical inversion, and wellbore storage/skin effects for infinite homogeneous reservoir well testing.

Analytical relative permeability models using power-law (Corey) and three-parameter (LET) formulations

Empirical relative permeability equations for consolidated rocks based on regression analysis of laboratory data

Comprehensive linear regression relative permeability equations for all rock types, wettability states, and fluid systems

Pore volume compressibility correlations for sandstone and limestone reservoirs

Numerical methods for interpolating, differentiating, and integrating tabular data using spline techniques

Utility functions for unit conversions, gravity transforms, and mathematical special functions used in petroleum engineering

Darcy and non-Darcy gas flow equations for vertical gas well performance and deliverability testing

Productivity index and drainage area correlations for horizontal and deviated wells

Dimensionless IPR curve for solution-gas drive wells producing below bubble point pressure

Productivity index calculations for vertical and horizontal wells under steady-state, pseudosteady-state, and transient flow conditions