Inflow performance relationship

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1. What is IPR and uses of IPR?

IPR stands for Inflow Performance Relationship. The relation between the flow rate (q) and the flowing bottom-hole pressure (Pwf) states the inflow performance relationship. For a gas well to flow there must be a pressure differential from the reservoir to the well bore and the fluid characteristics and changes with time. There is a linear relationship between the reservoirs producing at the pressures above the bubble point pressure, this is the pressure when Pwf is greater or equal to bubble point pressure.

Inflow Performance Relations

The linear form of an IPR represents the Productivity Index (PI), which is the inverse of the slope of IPR. The gas reservoir is deliberately evaluated using the well inflow performance relationship (IPR). Gas well IPR also depends on the flow conditions, that is, transient, steady state or pseudo state flows which are determined by reservoir boundary conditions.

Uses of IPR:

  1. It is special type of measurement property which is used to measure life and productivity of reservoir.
  2. Inflow performance relationship is useful as a tool monitor well performance and predicts the simulation and artificial lift requirements of a number of wells.
  3. In order to check or correct the size of a well to an accurate value IPR of a well must be known.

2. List three main factors affecting IPR?

The three important factors affecting IPR are:

  1. Pressure inside the reservoir.
  2. Nature of reservoir fluids.
  3. Types of rocks.

3. Explain inflow and outflow performance?

Inflow performance of a reservoir is defined as the functional relationship between the flowing bottom-hole and the resulting flow rate. It is the rate at which fluid will flow towards the wellbore and depends on the viscosity of the fluid, the permeability of the rock, and the driving force. For a gas well to flow there must be a pressure difference from reservoir to the well-bore at the reservoir depth. If the well-bore pressure is equal to the reservoir pressure there can be no inflow. If the well-bore pressure is zero , the inflow would be a maximum possible i.e the Absolute Open Flow (AOF).

For intermediate well-bore pressures, the inflow will vary. For each reservoir, there will be unique relationship between the inflow rate and wellbore pressure. For a heterogeneous reservoir, the inflow performance might differ from one well to another. The performance is commonly defined in term of a plot of surface production rate (stb/d) versus flowing bottom hole pressure (pwf in psi). Several models are available for determining the different types of Inflow performance Relation; they are Straight line flow, Vogel's method, Future IPR flows, The Fetkovich method and many more.

Outflow Performance involves fluid flow through flow through the production tubular, the wellhead and the surface flow line. In general the fluid flow involves the pressure difference across each segment of the fluid flow. Calculating the pressure drop at each segment is serious problem as it involves the simultaneous flow of oil, gas and water(multiphase flow), which implies the pressure drop dependent on many variables in which some of them are inter-related.

Due to this, it is very difficult to find an analytical solution. Instead, empirical formulas and mathematical models have been developed and used for predicting the pressure drop in multiphase flow. In order to obtain the realistic results, it is therefore important to define the input parameters carefully, through close co-operation with production engineers and to check the results of the Vertical Flow Performance which is also called as the Outflow Performance.

4. State and explain Darcy's Equation?

Darcy's Law states the fundamental law of fluid motion in the porous media. It is used to describe the flow of fluid particles, which includes oil, water & gas, through petroleum reservoirs. It also governs the flow of the particles through the porous media and describes the relationship between the flow rate, pressure drop and fluid resistance.

The mathematical expression developed by Henry Darcy in 1865 states that the fluid travelling in a the velocity of a homogeneous fluid in a porous medium is proportional to the pressure gradient and inversely proportional to the fluid viscosity.

For a horizontal linear system, this relationship is:


Are the elevations at the top and bottom of the porous material or porous medium.

Gives the length of the sand filter and is given by the equation ?l = z1 - z2 p1,p2 Is the pressure due to the water flow, measured by manometers above and below the sand filter.

H1,H2 Represents the hydraulic head at the inlet and outlet of the tank and expressed as the sum of pressure head and elevation head.

By a series of experiments, Darcy established that, for the same sand, the discharge Q is:

  • proportional to the cross-sectional area A: Q ~ A;
  • Proportional to the difference in the height of the water: Q ~ (H2 - H1); notice that because H2 < H1, the head drop H2 - H1 < 0.
  • Inversely proportional to the flow length through the porous material: Q ~ 1/?l.

Darcy published the results of his experiment, and its law in 1856, opening the era of the groundwater hydrology. The same conclusions can be drawn no matter if the flow is vertical, horizontal, or in any other direction

Different porous media models to illustrate Darcy's experiment

n is the apparent velocity in centimeters per second and is equal to q/A, where q is the volumetric flow rate in cubic centimeters per second and A is total cross-sectional area of the rock in square centimeters. In other words, A includes the area of the rock material as well as the area of the pore channels. The fluid viscosity, µ, is expressed in centipoises units, and the pressure gradient, dp/dx, is in atmospheres per centimeter, taken in the same direction as nand q. The proportionality constant, k, is the permeability of the rock expressed in Darcy units. The negative sign is because the pressure gradient is negative in the direction of flow.

  • Laminar (viscous) flow
  • Steady-state flow
  • Incompressible fluids
  • Homogeneous formation

For turbulent flow, which occurs at higher velocities, the pressure gradient increases at a greater rate than does the flow rate and a special modification of Darcy's equation is needed. When turbulent flow exists, the application of Darcy's equation can result in serious errors


  • Standard Handbook of Petroleum and Natural Gas Engineering (2nd Edition) Edited by: Lyons, William C.; Plisga, Gary J. © 2005 Elsevier
  • Natural Gas Engineering Handbook By: Guo, Boyun; Ghalambor, Ali © 2005 Gulf Publishing Company
  • Gas Well Deliquification (2nd Edition) By: Lea, James F.; Nickens, Henry V.; Wells, Mike R. © 2008 Elsevier