Inflow Performance Relationship

Introduction

Subsurface production of hydrocarbon has to do with the movement of fluid from the

reservoir through the wellbore to the wellhead. This fluid movement is divided into

two as depicted in Fig. 9.1.

The flow of fluids (hydrocarbons) from the reservoir rock to the wellbore is

termed the inflow. The inflow performance represents fluid production behavior of

a well’s flowing pressure and production rate. This differs from one well to another

especially in heterogeneous reservoirs. The Inflow Performance Relationship (IPR)

for a well is the relationship between the flow rate of the well (q), average reservoir

pressure (Pe) and the flowing pressure of the well (Pwf). In single phase flow, this

relationship is a straight line but when gas is moving in the reservoir, at a pressure

below the bubble point, this is not a linear relationship.

A well starts flowing if the flowing pressure exceeds the backpressure that the

producing fluid exerts on the formation as it moves through the production system.

When this condition holds, the well attains its absolute flow potential.

The backpressure or bottomhole pressure has the following components:

• Hydrostatic pressure of the producing fluid column

• Friction pressure caused by fluid movement through the tubing, wellhead and

surface equipment

• Kinetic or potential losses due to diameter restrictions, pipe bends or elevation

changes.

The IPR is often required for estimating well capacity, designing well comple￾tion, designing tubing string, optimizing well production, nodal analysis calcula￾tions, and designing artificial lift.

Factors Affecting IPR

Factors influencing the shape of the IPR are the pressure drop, viscosity, formation

volume factor, skin and relative permeability across the reservoir.

There are several existing empirical correlations developed for IPR. This are:

9.3 Straight Line IPR Model

When the flow rate is plotted against the pressure drop, it gives a straight line from

the origin with slope as the productivity index as shown in the figure below.

Steps for Construction of Straight Line IPR

Step 1: Obtain a stabilize flow test data

Step 2: Determine the well productivity

Step 3: Assume different pressure value to zero in a tabular form

Step 4: Calculate the rate corresponding to the assume pressure

Step 5: Make a plot of rate versus pressure

9.4 Wiggins’s Method IPR Model

Wiggins (1993) developed the following generalized empirical three phase IPR

similar to Vogel’s correlation based on his developed analytical model in 1991:

For Oil

Klins and Majcher IPR Model

Based on Vogel’s work, Klins and Majcher (1992) developed the following IPR that

takes into account the change in bubble-point pressure and reservoir pressure.

Standing’s Method

The model developed by Standing (1970) to predict future inflow performance

relationship of a well as a function of reservoir pressure was an extension of Vogel’s

model (1968).

Vogel’s Method

Undersaturated Oil Reservoir

An undersaturated reservoir is a system whose pressure is greater than the bubble

point pressure of the reservoir fluid. For the fact that the pressure of the reservoir is

greater than the bubble point pressure does not mean that as production increases for

a period of time, the pressure will not go below the bubble point pressure. Hence,

careful evaluation will lead to a right decision and vice versa.

Since the reservoirs are tested regularly, it means that the stabilized test can be

conducted below or above the bubble point pressure. Thus, for:

Case: pressure above bubble point

From stabilized test data point, the productivity index is:

Vogel IPR Model for Saturated Oil Reservoirs

This is a reservoir whose pressure is below the bubble point pressure of the fluid. In

this case, we calculate the maximum oil flow rate from the stabilized test and then

generate the IPR model. Mathematically

Fetkovich’s Model

According to Tarek (2010), the model developed by Fetkovich in 1973 for under￾saturated and saturated region, was an expansion of Muskat and Evinger (1942)

model derived from pseudosteady-state flow equation to observe the IPR nonlinear

flow behavior.

9.8.1 Undersaturated Fetkovich IPR Model

Saturated Fetkovich IPR Model

Cheng Horizontal IPR Model

Cheng (1990) presented a form of Vogel’s equation for horizontal wells that is based

on the results of a numerical simulator. The proposed expression has the following

form