Home work 1 Due March 27, 2015

Please derive the Darcys equations in oil and gas field units, respectively, from the equation in Darcy units.

Please derive Eq.1.2.4 from Eq. 1.2.3

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Example 2.1 An incompressible fluid flows in a linear porous media with the following

properties:

Calculate:

(a) flow rate in bbl/day:

(b) apparent fluid velocity in ft/day; (c) actual fluid velocity in ft/ day.

Solution:

Calculate the cross-sectional area A:

A = (h) (width) = (20) (100) = 6000 ft2

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Homework 2 (Example 2.2) Assume that the porous media with the properties as given in the previous

example are tilted with a dip angle of 5 as shown in Figure 1.12. The incompressible fluid has a density of 42 lb/ft3. Resolve Example 1.1 using this additional information.

Example 1.1

An incompressible fluid flows in a linear porous media with the following properties:

Calculate:

(a) flow rate in bbl/day:

(b) apparent fluid velocity in ft/day; (c) actual fluid velocity in ft/ day.

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Example 2.3

Consider the linear system given in Example 1.1 and, assuming a slightly compressible liquid, calculate the flow rate at both ends of the linear system. The liquid has an average compressibility of 21 x 10-5 psi -1.

Solution : ..

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Home work 3 (Example 2.4) Due April 17, 2015

A natural gas with a specific gravity of 0.72 is flowing in linear porous media at 140F. The upstream and downstream pressures are 2100 psi and 1894.73 psi, respectively. The cross-sectional area is constant at 4500 ft2. The total length is 2500 ft with an absolute permeability of 60 md. Calculate the gas flow rate in scf/day (Psc = 14.7 psia, Tsc = 520oR).

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Home work 4 (Due April 17, 2015)

Please summary the steady state flow rate equations for each of the following cases different type of fluids and different reservoir geometries, such as,

(1) Linear flow of incompressible fluids,

(2) Linear flow of slightly compressible fluids,

(3) Linear flow of compressible fluids,

(4) Radial flow of incompressible fluids,

(5) Radial flow of slightly compressible fluids,

(6) Radial flow of compressible fluids.

Also explain each parameter and its unit used in the equations.

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Home work 5 (due April 17,2015)

Show that the radial form of Darcy's equation is the solution to Equation 1.2.65.

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Example 1.12 A well is producing at a constant flow rate of 300 SIB/day under unsteady-state flow conditions. The reservoir has the following rock and fluid properties (see Example 1.10):

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Calculate (1) p=? at t=0.1hrs

(2) p=? at t= 1 hrs

(3) p=? at t=10hrs

(4) ) p=? at t=50 hrs

Home work 6 Due April 24, 2015

Home work 7 (Example 1.13)

A gas well with a wellbore radius of 0.3 ft is producing at a constant flow rate of 2000 Mscf/ day under transient flow conditions. The initial reservoir pressure (shut-in pressure) is 4400 psi at 140F. The formation permeability and thickness are 65 md and 15 ft, respectively. 'The porosity is recorded as 15%. Example 1.7 documents the properties of the gas as well as values of m(p) as a function of pressures. The table is reproduced below for convenience:

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Assuming that the initial total isothermal compressibility is 3 x 10-4 psr", calculate the bottom-hole flowing pressure after 1.5 hours.

Home work 8 (Example 1.14)

A gas well is producing at a constant rate of 7454.2 Mscf/ day under transient flow conditions. The following- data is available:

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Calculate the bottom-hole flowing pressure after 4 hours by using: (a) the m(p) method; (b) thep2 method.

Home work 9 (Example 1.15)

The data of Example 1.13 is repeated below for convenience.

A gas well with a wellbore radius of 0.3 ft is producing at a constant flow rate of 2000 Mscf/day under transient flow conditions. The initial reservoir pressure (shut-in pressure) is 4400 psi at 140F. The formation permeability and thickness are 65 md and 15 ft, respectively. The porosity is recorded as 15%. The properties of the gas as well as values of m(p) as a function of pressures are tabulated below:

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Assuming that the initial total isothermal compressibility is 3 x 10-4 psi-1, calculate, the bottom-hole flowing pressure after 1.5 hours by using the p approximation method and compare it with the exact solution.

Home work 10 (Example 1.17)

An oil well is developed on the center of a 40 acre square-drilling pattern. The well is producing at a constant flow rate of 100 STB/ day under a serni-steady-state condition. The reservoir has the following properties:

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