Reservoir Engineering Formula Guide

Reservoir formulas answer different questions at different scales. Darcy and radial-flow relationships connect pressure drop to rock, fluid, and geometry. Productivity index summarizes a well's rate per unit drawdown. Vogel provides an empirical curved inflow relation for solution-gas-drive oil behavior. Material balance reconciles reservoir-wide production and injection with fluid and rock expansion.

A common failure is to choose an equation because its inputs are available rather than because its assumptions describe the reservoir. The workflow below starts with the physical question, identifies pressure and rate conditions, and then uses a simple equation as a transparent baseline before escalating to transient analysis, nodal analysis, or simulation.

Steady-state radial flow assumes a maintained outer pressure, while pseudosteady flow represents a bounded drainage volume after pressure disturbance reaches the boundaries. Transient flow uses time-dependent pressure propagation. These descriptions concern reservoir pressure behavior and should not be confused with choosing a linear or Vogel-shaped IPR.

Record the boundary model, drainage dimensions, net thickness, permeability, viscosity, formation volume factor, wellbore radius, and skin basis with an analytical rate. The logarithmic radius term means geometry errors may be less dominant than permeability or skin, but they are still part of the model definition.

Straight-line PI is rate divided by average reservoir pressure minus flowing bottomhole pressure. A PI calculated from one test is most useful when compared with later tests collected on a consistent pressure, rate, completion, and fluid basis. A decline can indicate pressure depletion, mobility change, skin growth, liquid loading, scale, or test inconsistency.

Extrapolating a constant PI to zero flowing pressure can overstate deliverability when pressure crosses bubble point or multiphase flow develops. Outflow performance, facilities, artificial lift, sand, water, gas handling, and drawdown limits also constrain the achievable operating rate.

Vogel's normalized equation relates rate to the ratio of flowing pressure and average reservoir pressure for solution-gas-drive oil wells. The original relationship was developed from simulation behavior and is not a universal law for every oil, completion, pressure state, or drive mechanism.

For an undersaturated reservoir with flowing pressure below bubble point, a composite IPR can use a linear segment above bubble point and a curved segment below it. Calibrating the curve to a representative test point is generally more defensible than assuming an arbitrary absolute open-flow rate.

Material balance requires a consistent pressure history, cumulative production and injection, PVT properties, rock and connate-water compressibility, and any aquifer model. It estimates connected in-place volumes under the chosen tank assumptions; it does not by itself locate bypassed oil or describe spatial pressure variation.

Plotting diagnostic terms and checking straight-line behavior can reveal inconsistent data or a missing drive mechanism. A numerical answer without a pressure history and residual review is much weaker than a transparent model that shows which expansion and influx terms dominate.