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Petroleum Engineering Basic Course, TPG 4105 Production Engineering (Production/Well Technology and Processing)

LECTURE NOTES Jon Steinar Gudmundsson November 2008 INTRODUCTION (Petroleum Production Engineering)

- Flow and pressure in near wellbore formation - Flow and pressure in well/tubing - Wellhead and template conditions - Flowline, from template to platform or terminal - Processing subsea, platform or terminal

PRODUCTION WELLS Deliverability

- Analyze and then synthesize - Rate and pressure main parameters - Reservoir performance - Inflow performance - Outflow performance, tubing performance

Pressure Profile and Pressure States in Reservoirs

- Pressure profile from rw to re, from well radius to outer boundary

k = permeability φ = porosity c = compressibility h = reservoir thickness rw = well radius re = reservoir radius (radial system) e = exterior pw = pwf well flowing pressure pe = pressure at reservoir outer boundary pR = reservoir pressure (volume average)

- Steady-state (stasjonært tilstand), SS - Pseudosteady-state (pseudostasjonært tilstand), PSS

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- Transient state (ikke-stasjonært tilstand)

- Reservoir is almost like a flat pancake with properties k, φ, h and c. - Well has property s. - Well testing gives the groups kh (permeability thickness), representing the flow

capacity, while φch (porosity-compressibility thickness) give the storage capacity (of oil and/or gas)

- GOC is the gas-oil contact and WOC is the water-oil contact.

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- PSS arises when pressure profiles meet.

Darcy’s Law

drdpku

μ−=

q = uA A = 2πrh Integrating from r and p to rw and pwf, thereby cancelling the minus sign.

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

w

ooowf r

rkhBqpp ln

2πμ

ocs Bqq ..=

..cso V

VB =

u = Darcy velocity = filtering velocity (based on the whole area; that is, not only on the pore spaces)

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Superposition - The total pressure drop at any point in a reservoir is the sum of the pressure drops at

that point caused by the flow in each of the wells in the reservoir. - The diffusivity equation describes the pressure distribution in a reservoir with time

and distance. The solutions to the diffusivity equation are linear; therefore can the pressure values be added.

- The principle of superposition can also be used to take into account the presence of faults, by using imaginary wells.

Pressure in oil reservoir with cumulative time (cumulative production) - Usual pressure state PSS (when no injection of gas or water) - pR decreases with time, or with Np, cumulative production - pi is initial reservoir pressure

)( Ritpop ppcVBN −=

ooft cScc +=

thcA

Bqppt

ooiR φ−=

ct is total compressibility = Soco+cf where S stands for saturation, f stands for formation. If oil, gas and water are produced, the total compressibility is given by the expression

wwggooft cScScScc +++=

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Oil inflow performance

- PSS rate equation

⎥⎦

⎤⎢⎣

⎡+−⎟⎟

⎠

⎞⎜⎜⎝

⎛

−=

srrB

ppkhq

w

eoo

wfRo

4/3ln

)(2

μ

π

- Productivity index

)( wfRo ppPIq −=

⎥⎦

⎤⎢⎣

⎡+−⎟⎟

⎠

⎞⎜⎜⎝

⎛=

srrB

khPI

w

eoo 4/3ln

2

μ

π

- PSS pressure equation

⎥⎦

⎤⎢⎣

⎡+−⎟⎟

⎠

⎞⎜⎜⎝

⎛−= s

rr

khBqpp

w

eoooRwf 4/3ln

2πμ

The figure above shows the inflow performance of an oil well. At zero flow, the well flowing pressure is similar to the reservoir pressure. With increasing kh the oil flows more easily into the wellbore. The opposite applies to increasing skin, s.

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Skin factor - Damaged near wellbore formation, s >0 - Stimulated near wellbore formation, s<0 - Geometric skin or partial penetration skin, results from uneven flow path from

reservoir to perforations - Deposits (BaSO4, asphaltenes), s>0

Deliverability

- Reservoir performance - Inflow performance - Outflow performance

Imagine two nearby wells in a heterogeneous reservoir. One of the wells is fully penetrating while the other well is partially penetrating. The production tubing in the wells are identical. Therefore, the reservoir performance and the outflow performance of the two wells are the same, but the inflow performances are different; this due to geometric skin.

Gas inflow performance

- Rate equation from Darcy’s Law

∫ ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛=

e

wf

p

p gcs

cs

w

eg dp

zp

pTT

rrkhq

μπ

.

. 1

ln

2

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- Solution method, the pressure function, because gas viscosity and z-factor change with pressure

⎟⎟⎠

⎞⎜⎜⎝

⎛=

zppFgμ

)(

Integration numerically between pR and pwf

- Specific/limiting solutions

Low pressure, pressure function increases linearly with pressure such that 22"" wfR ppp −=Δ

High pressure, pressure function constant (same expression as for oil) wfR ppp −=Δ ""

Outflow performance

- Outflow performance, also called vertical lift performance - Pressure drop measured/calculated from wellhead to bottomhole (from pth to pwf) - Analytical equations and/or wellbore flow packages can be used for calculations - Each curve for each wellhead pressure (and, one production tubing design) - Production rate given by point where inflow and outflow curves meet.

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Reservoir temperature - Fourier’s Law, heat conduction (not convection) - Temperature gradient with depth (heat flux constant)

dxdTkAq −=

Pressure profiles in flowing wells

- Oil-only well - Gas-only well - Oil well with bubble point in wellbore

Hydrostatic pressure with depth

- Liquid-only

gLp ρ= - Gas-only (use average values of z and T). Solved by iteration.

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⎥⎦⎤

⎢⎣⎡= L

TRzgMpp o exp

In figures above, D used for depth. In equations, L used for depth/length.

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Well design - Casing cemented from wellhead to bottom - Casing perforated in oil producing formation(s) - Production tubing inside the casing (annulus between) - Packer at bottom of tubing to seal between casing and tubing - Production through perforations and up the tubing. - Downhole safety valve, typically at 200-400 m depth

Wellhead and manifold

- Two master valves (either fully open or fully closed) - One valve on top for logging operations (otherwise closed) - Wing valve on horizontal leg, used to open and closed well) - Choke valve after the wing valve (controls the well, flow and pressure) - All wells feed to manifold, and after that to process separator - Individual wells can be coupled from manifold and to test separator

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Artificial lift

- Downhole pumping - Gas lisft

Pumps - Volumetric (piston pump) - Dynamic (centrifugal)

o Rate depends on wheel diameter o Pressure depends on number of wheels

Ideal pump power (W) pqP Δ=

Real pump power (W)

η1pqP Δ=

where η is efficiency, typically 0.8 at design conditions. Characteristic curve of centrifugal pump. Usually given in “head” based on p=ρgh where h is the head (height of fluid column).

All pumps must have high enough suction pressure, otherwise the liquid will begin to “boil” upstream of the pump. This is expressed by NPSH (=Net Positive Suction Head), the head necessary to prevent boiling. In the oil industry where oil is to be pumped from a separator, the oil at the saturation point. Pumps must therefore be place well below the separator. Bubbles can be made; when these collapse, it is called cavitation, which “eats away” the metal in the pump.

With and without ESP (electrical submersible pump) pumping

- Pressure in tubing pt - Wellhead pressure pth (= WHP)

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With and without gas lift (GL)

- Pressure up the production tubing pt shown in left-hand-side drawing, where pth is tubing head pressure (=WHP).

- Pressure in the middle of the perforations, well flowing pressurepwf shown on righ-hand-side of drawing.

Downhole pump or compressor can increase the flowrate (Accelerate Recovery) and/lor increase the recoverable oil/gas (Increase Recovery).

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PROCESSING OF OIL AND GAS - On platforms - Subsea - Terminals - Surface Facilities, Jahn et al.

Block diagram, flow diagram and PID

- Block diagram, simple boxes with arrows between

- Flow diagram, shows what equipment used (same process as shown above)

- PID (Piping and Instrument Diagram) shows valves and instruments, also flow steam

number, with reference to tables with physical values - Flow diagram for Nyhamna and Kristin

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Kristin Prosess18.3 MSm³/sd210 bar

50°CPcric <105 barg

Kristin

GT Åsgard Transport

MeterScavenger, back-up

Fuel Gas

87 bar121°C

26°C

31°C

25°C

Meter TVP 0.965bar @ 30°CÅsgard C

26 bar

2 bar

20000 Sm3/sd67 bar70°C

30°C 30°C 30°C

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Compressors and compression - Characteristic curve

- Surge control

- Compressor power (ideal adiabatic compression)

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛

−=

−

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1

1

21

kk

pp

kkRT

MmP

kk

ppTT

1

1

212

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

v

p

CC

k =

Product specifications

- Oil TVP (true vapour pressure), RVP (Reid vapour pressure) BS&W (basic sediment & water) Temperature over pour point (wax) Salt content (NaCl etc.) Sulphur (H2S etc.)

- Water Oil content, < 40 ppm when discharged to sea (more stringent regulations on way) Particles, < 50 g/m3

- Gas Hydrocarbon (HC) dew point, 5-10 C under ambient Water dew point, 5 C under HC dew point Heating value, (GCV=gross calorific value) Wobbe index (WI=GCV/ γ )

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Non-HC gases (i.e. CO2, H2S etc.) Gas hydrates

- Formed when natural gas and liquid water are in contact above the equilibrium curve, typically below 20 C and above 50 bara.

- Water can be produced water and/or condensed water. - Typical composition, 15% wt. natural gas, 85% wt. water. - Volume ratio, 1 m3 hydrate contains 150-180 m3 natural gas. - Equilibrium curve depends on composition of gas and liquid water phase

Natural gas at reservoir conditions contains water vapour, according to diagram shown below (hand drawing of more accurate diagram from AGA). On production to the surface and along flowlines, the pressure and temperature (main effect) will decrease. Thereby reduces the “solubility” of water vapour in the natural gas and water condenses. This is the condensed water that combines with natural gas to form hydrate.

- Prevention of hydrate formation

Injection of antifreeze (glycol, e.g. MEG=monoetylenglycol) Thermal insulation for short distances (within field, from template to platform) Thermal insulation and electrical heating for medium long distances (DEH=direct electical heating) Cold flow for long distances (being developed)

- Hammerschmidts equation for antifreeze, lowers the “freezing” point (hydrate equilibrium curve)

-

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⎟⎠⎞

⎜⎝⎛−

=Δx

xMKT

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Table – Properties of inhibitors (antifreeze) used to prevent hydrate formation. M molicular weight , K empirical constant in Hammerschmidts equation and ρ density. ΔT is shifting of equilibrium curve and x is mass fraction antifreeze in aqueous phase. Inhibitor M (kg/kmol) K (-) ρ (kg/m3) MOH MEG DEG TEG NaCl

32 62 106 150 58

1297 1222 2425 3000 3000

800 1110 1120 - -

Temperature in pipes (and wells)

- Steady-state flow - Inlet T1, outlet T2, surroundings (e.g. sea) T (=constant) - Temperature decreases exponentially with distance

⎥⎥⎦

⎤

⎢⎢⎣

⎡−−+= L

mCdUTTTTp

πexp)( 12

- Insulated subsea pipelines, 1 < U < 2 (W/m2K) - Non-insulated subsea pipelines, 15 < U < 25 (W/m2K)

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Pressure drop in pipes (and wells) - Total pressure drop is wall friction + hydrostatic + acceleration -

agf pppp Δ+Δ+Δ=Δ

- Darcy-Weisbach equation for incompressible fluids (oil and/or water) for wall friction. Friction factor f from empirical experiments.

2

2u

dLfp f ρ=Δ

- Compressible fluids (gas), wall friction in horizontal pipe (not for vertical wellbore) -

( ) 0Lppln

fdpp

RTzmfMAd

21

222

1222

2

=+⎟⎟⎠

⎞⎜⎜⎝

⎛−−

For typical long gas pipelines from Norway to the Continent and Great Britain, the frictional pressure drop is on average 6 bar/100 km. It means that the natural logarithm term is quite small and can be ignored. Thereby, for example, the diameter can be found as the 5th root (note,A2 has d4).

- Friction factor Hydraulically smooth pipes, Blasius’ equation can be used for low Reynolds number, Re < 105.

25,0Re316,0

=f

μρud

=Re

Pipes with rough walls, Haaland’s equation is recommended for general use.

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠

⎞⎜⎝

⎛+⎟

⎠⎞

⎜⎝⎛−=

n11,1n

d75,3k

Re9,6log

n8,1

f1

n = 1 for liquids, n = 3 for gases

The table below shows how the friction factor in pipes depends on Reynolds number and on relative roughness, k/d. The table below gives typical roughness values for pipes.

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Material Average Absolut

Roughness (inch)

Average Absolut

Roughness (µm)

Internally plastic coated pipeline Honed bare carbon steel Electropolished bare 13Cr Cement lining Bare carbon steel Fiberglass lining Bare 13Cr

0.200×10-3 0.492×10-3 1.18×10-3 1.30×10-3 1.38×10-3 1.50×10-3 2.10×10-3

5.1 12.5 30.0 33.0 35.1 38.1 53.3

Separators and separasjon

- Gas-liquid (oil and water) and oil-water separation. - Horizontal and vertical separators based on gravitation - Figure of separator below, gas-liquid separator: Inlet (primary separation), tank

volume (secondary separation by gravitation) vortex preventer (liquid outlet), wire mesh (gas outlet), profiled plates in tank volume (drops coalesce)

Droplet mechanics

- TSV = terminal settling velocity, uD - General theoretical equation for drops

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G

GL

DD f

gduρρρ −

=34

fD is friction factor (drag coefficient) for drop

- Following is a simplification, giving room for using empirical data

G

GLsD ku

ρρρ −

=

ks is separation constant, empirical

- When Stokes Law applies, low Reynolds number, the exact solution of the general equation is

⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

G

GLD

gduμρρ

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2

When separation takes place in a hydrocyclon, for example, the gravitational constant g

can be replaced by (u2/r) where u is tangential velocity and r the hydrocyclon radius. Gas capacity of separators

- Vertical separator

( )zT

TppkAq cs

csG

GLsGcsG

1..

.... ⎟

⎠⎞

⎜⎝⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−=

ρρρ

API recommends for vertical separator

)/(11,0)/(05,0 smksm s << - Horizontal separator

58,0

6⎟⎠⎞

⎜⎝⎛−

=LkAq

G

GLsGG ρ

ρρ

API recommends for horizontal separator

smksm S /15,0/12,0 <<

NORSOK recommends ks = 0,137 m/s Gas density and standard conditions Real gas law znRTpV = Gas density

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( )zRT

pkgmolVn

=/

( )zRTpMmkg =3/ρ

( )kmolkgM / Standard conditions s.c. ..csnn =

....

....

cscs

cscsTRz

VpzRTpV

=

1.. =csz

zTT

ppVV

cs

cscs ⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

..

....

zTT

ppqq

cs

cscs ⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

..

....

Bg (=FVF gas) = zp

pTT

VV cs

cscs⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛= ..

....

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APPENDIX PVT (pressure-volume-temperature)

- Fasediagram

- Real gas law

znRTpV = - Specific density of gas (=gravity)

96,28γ

γ

=

=

gass

luft

gass

M

MM

- Pseudoreduced pressure and temperature (c=critical)

cr

cr

TTT

ppp

=

=

- Kay’s Rule (y is mole fraction)

∑

∑=

=

iicic

iicic

yTT

ypp

- Corresponding states - z-factor diagram (Standing-Katz diagram, figure from Rojey o.a. 1997)

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