NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY



NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY

DEPARTMENT OF PETROLEUM ENGINEERING

AND APPLIED GEOPHYSICS

Contact during exam:

Name: Harald Asheim

Tel.: 73594959

Exam results are due in week 51, 2010

EXAM IN COURSE TPG4245 PRODUCTION WELLS

Wednesday December 1, 2010

Time: 0900 - 1300

Permitted aids:

C: Specified printed and handwritten material allowed. Certain, simple calculator allowed.

Specified aids: A list of formulas is enclosed.

Problem 1 Gas Well

The following data are given for Lerchendahlfeltet:

Initial Pressure 197.9 bar

Reservoir Temperature 61 C

Gas gravity 0.58

Diameter production pipeline 174.6 mm

Length production pipeline 2040 m

Reservoir depth 1850

Height of reservoir layer 51 m

Drainage Area pr. well 1.3 • 105 m2

Standard Temperature 15 C

Standard Pressure 1 atm

Well Diameter 300 mm

Gas z-factor at reservoir conditions 0.86

Gas viscosity at reservoir conditions 0.0168 cP

Formation factor at reservoir conditions: 0.0066

Interfacial tension of water-gas 60 dyn / cm

1. December 2010 these measurements were made in well-35.2 K

|Production |Bottom well pressure |Temperature at tubing head |

|(Sm3/d) |(bar) |(C) |

|0 |153.7 |10 |

|0.96 · 106 |149.0 |35 |

|1.27 · 106 |146.8 |37 |

|1.68 · 106 |143.2 |40 |

a) Estimate the inflowcharacteristics

b) Estimate the pressure at the christmas tree when production is 1.5 .106 Sm3 /

After 2 years of production the reservoir pressure is expected to have fallen to 140 bar. Water production is assumed equal to 2% of the gas stream by the downhole conditions

c) Estimate the bottom hole pressure at the production: 0.5 .106 Sm3 / d,

d) Estimate the pressure at the production tree with production 0.5. 106 Sm3 / d

e) Can the pressure drop from bottom to top be reduced by selecting different diameter of the production pipe? Investigate and explain your recommendation

Problem 2 Inflow Control

A reservoir consists of two zones, as outlined in the figure below. Oil properties are equal n both zones:

Density at reservoir conditions: 766 kg/m3

Formation Factor: 1.5 m3/Sm3

Viscosity 1.2 cP

Pressure and productivity indices are measured / estimated:

 

| |Length |Spes. prod. ind. |Reservoir pressure |

|Sone 1 |200 m |1 m3/d/bar/m |210 bar |

| | | | |

|Sone 2 |800 m |3 m3/d/bar/m |200 bar |

:

The reservoir is planned produced with a single well as illustrated. The production target is 1000 Sm3 / d, from Zone 1 and 3000 Sm3 / d from Zone 2, a total of 4,000 Sm3 / d. If necessary we will use orifice-based inflow control to achieve the desired balance between production zones and preferably smooth flow along each zone.

 Sand may accumulate where the flow speed in the well pipe is less than 0.5 m / s. There is a danger of erosion if the flow speed is greater than 3 m / s. Therefore, we consider various pipe diameters in Zone 1 and Zone 2 (but equal diameter in each zone).

a) Select the pipe diameter for well in Zone 1 and Zone 2, so that we avoid the (counteract) erosion and limit the accumulation of sand

b) Where along the well pipe may sand accumulate when the pipe dimensions are as designed above. Compare this with the well pipe with the same diameter through both zones (also designed to avoid (prevent) erosion and sand accumulation limit).

c) Estimate the sand face pressure and pressure along the well pipe, when the well is producing as expected (1000 Sm3 / d, from Zone 1 and 3000 Sm3 / d from Zone 2; evenly flow within zones)

d) Design orifice based inflow control to achieve the production targets specified. (You can assume one ICD for each pipe section of 12m, and 4 orifices in each. ICD)

e) Alternatively, the well may be drilled and completed from the opposite direction, so that the flow direction is from Zone 2 to Zone 1, the opposite of what was assumed above. Consider the effects of this option on sand accumulation and productivity. (We select new pipe diameters in Zone 2 and Zone 1, to prevent erosion and accumulation of sand, as before)

[pic]

Figure: Simplified reservoir geometry and wellbore

Formulae 2010

Fluid properties (SI, pressure in bar):

Density, gas saturated oil: [pic]

Formation factor saturated oil,: [pic]

Above saturation pressure: [pic]

Gas density : [pic]

Formation factor, gas: [pic]

Gas solubility: [pic]

Viscosity due to dissolved gas:[pic] , [pic]: viscosity of gas free oil;

[pic] ; [pic]

Under saturated oil: [pic]

Single phase flow in reservoir and well

Inflow characteristics: [pic]

Exponential decline: [pic]

Flow in pipe: [pic]

Friction factor correlation: [pic]

Reynolds number: [pic]

For circular pipes: wetted perimeter: S = πd ; x-section : A = πd2/4

Pressure drop through orifices: [pic]

Vertical wells, radial inflow

Pseudo stationary PI: [pic]

Pseudo stationary flow distribution: [pic]

Transient well pressure [pic]

Skin pressure loss [pic]

Skin due to partly completion :

[pic]

Skin due to inclination ( relative to vertical well)

[pic] ….. for : θ < 75o

Horizontal wells, stationary flow:

Long wells, in the middle of reservoir layer: [pic]

Shorter well [pic]

Skin pressure loss: [pic]

Skin due to location within the reservoir layer:

[pic] [pic] for b > 5 rw

Skin due to inclined well through the layer: [pic]

Skin, due to round well in anisotropic reservoir [pic]

Inflow with pressure loss along the well: [pic]

Anisotropy

Scaling rules for anisotropic permeability: [pic] [pic]

Equivalent well bore length: [pic]

Equivalent angle: [pic] evt: [pic]

Deviation from linear PI

Forcheimer’s equation: [pic]

Forcheimer, radial inflow:[pic]

Vogel’s: [pic]

Linear extrapolation, relatied to Vogel: [pic]

Segregated flow

Stationary crest: [pic]

Stationary cone: [pic]

Pseudo stationary, critical rate [pic]

Flow in inclined layer: [pic]

- αw : stable interface inclination [pic]

Two phase flow in pipes

Rising/sinking velocity for small bubbles/drops: [pic]

K = 1.53 for bubbles. K = 2.75-3.1 for drops

Rise velocity for Dumitrescu bubbles: [pic]

Velocities: [pic] [pic]

Drift flux relation: [pic]

Usually Co= 1—1.4

Stationary liquid fraction: [pic]

Flux fraction: [pic]

Volume averaged density: [pic]

Flow averaged density: [pic]

Pipe flow relation: [pic]

fo : 1-phase friction factor correlation,

for 2-phase Reynolds number: [pic]

Slip multiplier: [pic]

Critical velocity : [pic]

Superficial velocity, at given total velocity: [pic]

Kinematic wave velocity: [pic]

Unit conversions

1 cp = 10-3 Pas 1 bar = 105Pa

1 Darcy = 0.9869 ( 10-12 m2 1 dyn/cm = 10-3 N/m

Physical constants, definitions

Standard temperature :288 K Standard pressure: 1.01 bar

General gas constant :8314 Mole weight air : 28.97 kg/kmole

Acceleration of gravity :9.81 … m/s2

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