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.

Multi-well production aggregation methods, drilling schedule impact on field profiles, and schedule-based cumulative production forecasting

Complete theory and equations for classical 2D hydraulic fracture geometry models including PKN, KGD, and Radial (penny-shaped) with Carter leakoff and fluid efficiency

Theory and equations for proppant settling velocity, wall effects, hindered settling, power-law fluid corrections, and transport ratio calculations in hydraulic fractures

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

p/z method for volumetric gas reservoirs, modified p/z for geopressured reservoirs, and OGIP estimation techniques

Havlena-Odeh straight-line method for oil reservoir analysis, OOIP estimation, gas cap ratio determination, and Campbell plot interpretation

Theory and application of aquifer models for water influx calculation: Pot, Schilthuis steady-state, Fetkovich pseudo-steady-state, and Van Everdingen-Hurst unsteady-state

Calculation of underground withdrawal F, expansion terms Eo, Eg, Efw, effective compressibility, and two-phase formation volume factor Bt

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.

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

Theory and equations for critical and subcritical choke flow including Gilbert-type correlations, Sachdeva, Ashford-Pierce, and single-phase choke models

Theory and equations for pipeline pressure drop and flow capacity including Weymouth, Panhandle A/B, Darcy-Weisbach, and two-phase correlations

Gas hydrate formation conditions, Hammerschmidt equation for temperature depression, and thermodynamic inhibitor calculations for methanol and MEG

CO2 corrosion prediction using the de Waard-Milliams model, NACE severity classification, and erosional velocity calculations per API RP 14E

Theory and equations for ESP pump performance including head-capacity curves, total dynamic head, staging calculations, brake horsepower, and best efficiency point analysis

Theory and equations for gas interference in ESP systems including free gas volume at pump intake, void fraction calculations, gas separator efficiency, and Turpin-Dunbar correction factors

Theory and equations for correcting ESP pump performance curves for viscous fluid effects, including Turpin and Stepanoff correction factor methods for head, efficiency, and flow rate derating

Theory and equations for ESP motor horsepower selection, amperage calculations, load factor analysis, cable voltage drop, cable size selection, and power loss estimation

Theory and calculations for gas lift valve operation including dome pressure, opening and closing pressures, spread, and gas throughput

Pump displacement calculation, fillage analysis, volumetric efficiency, effective stroke length, and pump intake pressure for sucker rod pumping

Sucker rod string design including rod weight, stretch calculations, polished rod loads, stress analysis, and API 11L dynamic factors

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.

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

Theory and equations for the Peng-Robinson cubic equation of state including mixing rules, alpha functions, and volume translation

Theory and methods for PT flash calculations, Rachford-Rice equation, stability analysis, and K-value estimation

Theory and construction of phase envelopes showing bubble point and dew point curves, cricondentherm, and cricondenbar

Methods for estimating critical properties, splitting heavy fractions, and lumping components for equation of state modeling

Viscosity prediction methods for compositional EoS modeling including Lee-Gonzalez-Eakin, Lorentz-Bray-Clark, and Pedersen models

Common probability distributions used in petroleum engineering Monte Carlo simulation including normal, lognormal, triangular, uniform, PERT, and truncated distributions

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