Chapter 5 Gas Well Performance

8/9/2019 Chapter 5 Gas Well Performance

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NATURAL GAS ENGINEERING

CHAPTER 5 GAS WELL PERFORMANCE


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CONTENTS

5.1 Gas Well Performance

5.2 Static Bottom-hole Pressure(static BHP)

5.3 Flowing Bottom-hole Pressure(flowing BHP)


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LESSON LEARNING OUTCOME

At the end of the session, students should be able to:

Determine static bottom-hole pressure(static BHP) usingdifferent methods

Determine flowing bottom-hole pressure(flowing BHP) using

different methods


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Gas Well Performance

Figure (5.1) Gas Production Schematic


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Referring to Fig.(5.1), ability of a gas reservoir to produce

for a given set of reservoir conditions dependsdirectly on theflowing bottom-hole pressure,Pwf.

The ability of reservoir to deliver a certain quantity of gasdepends on

the inflow performance relationship (IPR)

flowingbottom-hole pressure (FBHP)

Flowing bottom-hole pressure dependson

Separator pressure

Configuration of the piping system


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These conditions can be expressed as:

(8.1)

(8.2)


7/417Figure (5.2) Deliverability test plot

The static or flowing pressure at the formation must beknownin order to predictthe productivity or absolute open flow

potential (AOF) of gas wells.

Preferred method is a bottom-hole pressure gauge (down-

hole pressure gauge).

However, Static BHP or Flowing BHP can be estimated from

wellhead data (gas specific gravity, well head pressure, well

head temperature, formation temperature, and well depth.)

Static and Flowing Bottom-Hole Pressures


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Basic Energy Equation

In the case of steady-state flow, energy balance can be

expressed as follows:

OR

(8.3)

(8.4)


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Figure (5.3) Flow in pipe (After Aziz.)


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Second term ( ) kinetic energy is neglected in pipeline flow

calculations. If no mechanical work is done on the gas (compression) or by

the gas (expansion through a turbine), the term wsis zero.

Reduced form of the mechanical energy equation may be

written as:

OR

cg

udu

2

(8.5)

(8.6)


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All equations now in use for gas flow and static head

calculationsare various forms of this Equation.The density of a gas ( ) at a point in a vertical pipe at

pressurepand temperature Tmay be calculated as:

(8.7)

g


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Fig.(5.4) Compressibility

factor for natural gases


13/4113Fig.(5.5) Moody Friction Factor Chart


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The velocity of gas flow ugat a cross section of a vertical pipe

is

(8.8)


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General vertical flow equation assuming a constant average

temperaturein the interval of interest is

(8.10)


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Sukker & Cornell, and Poettmann assumed gas deviation

factor varies only with pressure. But accurate in relatively

shallow wells.

A more realistic approach is that of Cullender & Smith.

They treated gas deviation factor as a function of both

temperature and pressure.


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StaticBottom-Hole Pressure

Average Temperature and Deviat ion Factor Method

The Equation is:

(8.20)

l ( )


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Example (1)

Calculate the static bottom-hole pressure of a gas well having a

depth of 5790 ft. The gas gravity is 0.60 and the pressure at the

wellhead is 2300 psia. The average temperature of the flow

string is 117oF.(Use Average Temperature & Deviation Factor

Method).

Solution


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First trial

Second trial


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Exercise 1

1. Calculate the static bottom-hole pressure of a gas

well having a depth of 8570 ft. The gas gravity is 0.63and the pressure at the wellhead is 2800 psia. The

average temperature of the flow string is 124oF.Use

average Temperature and Deviation Factor method.

=672 psia, =358 R

2. Calculate the static bottom-hole pressure of a gas

well having a depth of 9230 ft. The gas gravity is 0.66

and the pressure at the wellhead is 3100 psia. The

average temperature of the flow string is 119oF. .Use

average Temperature and Deviation Factor method.

=672 psia, =358 R


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Cullender and Smith Method

This is a more realistic approach that gas deviation factor is a

functionof both temperature and pressure.

Define

(8.25)

(8.26)

C ll d d S ith M th d


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Which, for the static case, reduces to

For the upper half,

For the lower half,

Static bottom-hole pressure at depth Z in the well is finally given by

WhereItsis evaluated atH= 0,ImsatZ/2 andIwsatZ.

(8.30)

(8.31)

(8.32)

(8.27)

(8.29)

C ll d d S ith M th d


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Cullender and Smith MethodCalculation procedure

First: to solve for an intermediate temperature and pressurecondition at the mid point of the vertical column;

Second: Repeat the calculations for bottom-holecondition.

-A value of Its is first calculated from Eqn 8.27 at surfaceconditions.

-Then, Imsis assumed(Its=Imsat first approximation) and pmsis

calculated for the mid point conditions.

-Using this value of Ims , a new value of Ims is computed.

-The new value of Imsis then used to recalculate pms.

-This procedure is repeated until successive calculations of pms

are within the desired accuracy (usually within 1 psi difference).



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-The Cullender and Smith method is the mostaccurate method for calculating bottom-hole

pressures.

-This method is generally applicable to shallow

and deep wells, sour gases, and digital

computations.


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E l ( )


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Example (2)

Solution

(a) Determine the value ofzat wellhead conditions and computeIts.


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(b) CalculateImsfor intermediate conditions at a depth of 5790/2or 2895 ft, assuming a straight line temperature gradient. As a

first approximation, assume

Ims =Its= 178Then, from Eqn 8.30,

(8.30)

(8.27)

(8.30)


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(c) CalculateIwsat bottom-hole conditions assuming, for the first

trial,Iws =Ims= 191. Then, from Eqn 8.31,

Since the two values of Pms are not equal, calculations arerepeated withPms=2477 psia.

This is a check of the pressure at 2895 ft.


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Repeating the calculation,

(d) Finally, using Eqn8.32,

QUIZZE i 2


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QUIZZExercise 2

1.Calculate static bottom-hole pressure using the following data

given:

Depth of the well=7900 ft.

Gas gravity = 0.65

Pressure at the wellhead = 2800 psia.

Temperature at well head=74oF

Average temperature of flow string=117F

Ppc=672psia

Tpc=358R

Take initial pressure 3100 psia for your trial and errorcalculation.

QUIZZ


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QUIZZ

Home Work(2)

1.Calculate static bottom-hole pressure by

using thefollowing data given in example 2.

Take tubing head pressure to be 3400 psia.Use Cullender and Smith method.

Flowing Bottom Hole Pressure


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FlowingBottom-Hole Pressure Flowing bottom-hole pressure of a gas well is the sum of the

flowing wellhead pressure, the pressure exerted by the weight

of the gas column, the kinetic energy change, and the energylosses resulting from friction.

As kinetic energy changeis very small, it is assumed zero.

For the situation of no heat loss from gas to surroundings

and no work performed by the system.

This equation is the basis for all methods of calculating

flowing bottom-hole pressures from wellheadobservations.

The only assumptions made so far are single-phasegas flow

and negligible kinetic energy change.

(8.33)

Average Temperature And Average


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Assumptions in the average temperature and average gasdeviation factor method are:

1. Steady-state flow

2. Single-phase gas flow, although it may be used for condensate

flow if proper adjustments are made in the flow rate, gas

gravity and Z-factor

3. Change in kinetic energy is smalland may be neglected

4. Constant temperatureat some average value

5. Constant gas deviation factor at some average value6. Constant friction factor over the length of the conduit

Average Temperature And Average

Gas Deviation Factor Method


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(8.40)

If Fanning friction factor is used, use thefollowing equation.

Moody friction factor = 4 * Fanning friction factor


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Equation8.39is to be applied when MoodyFriction factoris used.

Equation8.40is to be applied when Fanning

Friction factor is used.

Example (3)


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Example (3)

Calculate the flowing bottom hole pressureof a gas well from

the following surface measurements: Use Average temperature

and Deviation Factor method.

SolutionUsing Eqn 8.39,

First trial Guess P = 2500 psia


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First trial Guess,Pwf = 2500 psia

At 1.0 atm and 121.5oF.

Viscosity at average pressure:

The Reynolds number is given by


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The Reynold s number is given by

From the Moody friction factor chart, or by applying Jain Eqn

Then, Pwf= 2543 psia


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Second trial

There is no appreciable change in z for this trial; (first zvalue=0.825, and 0.825 again in second trial) ,so, first trial is

sufficiently accurate.


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Chapter 5 Gas Well Performance