Exercise 2.1 Radial flow

A well is producing 670 Sm3/d in a cylindrical drainage volume.

You may use some of the following data:

-outer radius 150 m

-wellradius 0.1 m

-layer thickness50 m

-formation volume factor1.5 m3/Sm3

-porosity20%

-permeability1000 mD (0.987 m2)

-bottomhole pressure195 bar

-viscosity reservoir oil 2 cP

Estimate and illustrate as function of distance from the well:

a)Rate, at stationary flow

b)Rate, at pseudostationary flow

c)Pressure, at stationary flow

d)Pressure, at pseudostationary flow

2.2: PI relationship

Cylindrical reservoir geometry is outlined below. The flow will then be radial straight towards the well, such that the area A only depends on the distance from the well: A=hS=h2r.

a. Expression productivity index by the relationship:

b. Estimate the PI based on average reservoir pressure:

Exercise 2.3

The following data is known about a vertical well:

Viscosity: 1cP

Gas/oil ratio : 40 Sm3/Sm3

Oil gravity : 0.8

Gas gravity: 0.6

Formation volume factor: 1.2 m3/Sm3

Payzone thickness: 50 m

Compressibility factor: 3*10-8 Pa-1

Wellbore radius: 0.1 m

Distance to outer boundary: 300 m

Outer boundary condition: closed boundary

Inner boundary condition: completed over whole layer

Initial reservoir pressure : 200 bar

Production test at 2 different rates gives the following result:

Time (min) / 0 / 1 / 2 / 10 / 20 / 30 / 60 / 120
Rate: 1000Sm3/d / Brønntrykk
(bar) / 200 / 198.3 / 198.1 / 197.8 / 197.6 / 197.5 / 197.4 / 197.2
Rate: 2000Sm3/d / Well pressure
(bar) / 200 / 196.6 / 196.3 / 195.6 / 195.3 / 195.1 / _ / _

a)Estimate the productivity index by fitting a straight line through the measured data

b)Examine if the reported data have been measured under transient or pseudo stationary conditions

c)Evaluate the productivity index, by the transient pressure response relation

d)How long production time is necessary to reach pseudo stationary conditions

Exercise 2.4

For radial wells we have assumed cylindrical flow and derived the following productivity index

Will this formula be applicable for the drainage geometries illustrated below?