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
1
-
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.
-
2
- PSS arises when pressure profiles meet.
Darcy’s Law
u=−
k dp
μ dr
q = uA
A = 2πrh
Integrating from r and p to rw and pwf, thereby cancelling the minus sign.
p = pwf +
μ o qo Bo ⎛ r ⎞
ln⎜ ⎟
2πkh ⎜⎝ rw ⎟⎠
q = qs.c. Bo
Bo =
V
Vs.c.
u = Darcy velocity = filtering velocity (based on the whole area; that is, not only on the
pore spaces)
3
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
N p Bo = V p ct ( pi − pR )
ct = c f + So co
pR = pi −
qo Bo
t
Aφct h
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
ct = c f + So co + S g cg + S wcw
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Oil inflow performance
- PSS rate equation
qo =
2πkh( pR − pwf )
⎡ ⎛ re ⎞
⎤
⎟⎟ − 3 / 4 + s ⎥
⎣ ⎝ rw ⎠
⎦
μ o Bo ⎢ln⎜⎜
-
Productivity index
qo = PI ( pR − pwf )
PI =
2πkh
⎡ ⎛ re ⎞
⎤
⎟⎟ − 3 / 4 + s ⎥
⎣ ⎝ rw ⎠
⎦
μ o Bo ⎢ln⎜⎜
-
PSS pressure equation
pwf = pR −
⎤
μ o qo Bo ⎡ ⎛ re ⎞
⎢ln⎜⎜ ⎟⎟ − 3 / 4 + s ⎥
2πkh ⎣ ⎝ rw ⎠
⎦
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
qg =
p
2πkh ⎛ Ts.c ⎞⎛ 1 ⎞ e ⎛⎜ p ⎞⎟
⎜
⎟
dp
⎜
⎟
⎛ re ⎞ ⎝ T ⎠⎜⎝ ps.c ⎟⎠ p∫wf ⎜⎝ μ g z ⎟⎠
ln⎜⎜ ⎟⎟
⎝ rw ⎠
6
-
Solution method, the pressure function, because gas viscosity and z-factor change with
pressure
⎛ p ⎞
⎟
F ( p) = ⎜
⎜μ z⎟
g
⎝
⎠
Integration numerically between pR and pwf
-
Specific/limiting solutions
Low pressure, pressure function increases linearly with pressure such that
2
" Δp" = pR2 − pwf
High pressure, pressure function constant (same expression as for oil)
" Δp" = pR − pwf
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)
q = − kA
dT
dx
Pressure profiles in flowing wells
- Oil-only well
- Gas-only well
- Oil well with bubble point in wellbore
Hydrostatic pressure with depth
- Liquid-only
p = ρgL
-
Gas-only (use average values of z and T). Solved by iteration.
8
⎡ gM
p = po exp ⎢
⎣ zRT
⎤
L⎥
⎦
In figures above, D used for depth. In equations, L used for depth/length.
9
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)
P = qΔp
Real pump power (W)
1
P = qΔp
η
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 righhand-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
-
13
6
Kristin Prosess
18.3 MSm³/sd
210 bar
Fuel Gas
Scavenger, back-up
Meter
50°C
Pcric <105 barg
31°C
Åsgard Transport
GT
25°C
26°C
30°C
30°C
30°C
Kristin
87 bar
121°C
20000 Sm3/sd
67 bar
70°C
26 bar
2 bar
Meter
TVP 0.965bar @ 30°C
Åsgard C
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Compressors and compression
- Characteristic curve
-
Surge control
-
Compressor power (ideal adiabatic compression)
k −1
⎡
⎤
m
⎛ k ⎞ ⎢⎛ p2 ⎞ k
P=
RT1 ⎜
⎟ ⎜⎜ ⎟⎟ − 1⎥⎥
M
⎝ k − 1 ⎠ ⎢⎝ p1 ⎠
⎢⎣
⎥⎦
⎛p ⎞
T2 = T1 ⎜⎜ 2 ⎟⎟
⎝ p1 ⎠
k=
k −1
k
Cp
Cv
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)
-
16
ΔT =
K⎛ x ⎞
⎜
⎟
M ⎝1− x ⎠
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
MOH
MEG
DEG
TEG
NaCl
M (kg/kmol)
32
62
106
150
58
K (-)
1297
1222
2425
3000
3000
ρ (kg/m3)
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
⎡ − Uπd ⎤
T2 = T + (T1 − T ) exp ⎢
L⎥
⎣⎢ mC p ⎥⎦
-
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
Δp = Δp f + Δp g + Δpa
-
Darcy-Weisbach equation for incompressible fluids (oil and/or water) for wall friction.
Friction factor f from empirical experiments.
f L 2
Δp f =
ρu
2d
-
Compressible fluids (gas), wall friction in horizontal pipe (not for vertical wellbore)
d A2 M
d ⎛ p 22 ⎞
2
2
−
−
p
p
ln⎜ ⎟ + L = 0
2
1
f ⎜⎝ p12 ⎟⎠
f m 2 z RT
(
)
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.
f =
0,316
Re 0, 25
Re =
ρud
μ
Pipes with rough walls, Haaland’s equation is recommended for general use.
⎡⎛ 6,9 ⎞ n ⎛ k ⎞1,11n ⎤
1,8
= − log ⎢⎜
⎟ ⎥
⎟ +⎜
n
f
⎢⎣⎝ Re ⎠ ⎝ 3,75d ⎠ ⎥⎦
1
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
Internally plastic coated pipeline
Honed bare carbon steel
Electropolished bare 13Cr
Cement lining
Bare carbon steel
Fiberglass lining
Bare 13Cr
Average
Absolut
Roughness
(inch)
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
Average
Absolut
Roughness
(µm)
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
19
4 gd
3 fD
uD =
-
fD is friction factor (drag coefficient) for drop
Following is a simplification, giving room for using empirical data
uD = ks
-
ρ L − ρG
ρG
ρ L − ρG
ρG
ks is separation constant, empirical
When Stokes Law applies, low Reynolds number, the exact solution of the general
equation is
uD =
gd 2 ⎛ ρ L − ρ G ⎞
⎟
⎜
18 ⎜⎝ μG ⎟⎠
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
p ⎞⎛ Ts.c. ⎞ 1
⎟⎟⎜
⎟
p
s
.
c
.
⎠⎝ T ⎠ z
⎝
⎛
(qG )s.c. = AG k s ρ L − ρG ⎜⎜
ρG
API recommends for vertical separator
0,05(m / s ) < k s < 0,11(m / s )
-
Horizontal separator
qG = AG k s
ρ L − ρG ⎛ L ⎞
⎜ ⎟
ρG ⎝ 6 ⎠
0 , 58
API recommends for horizontal separator
0,12m / s < k S < 0,15m / s
NORSOK recommends ks = 0,137 m/s
Gas density and standard conditions
Real gas law
pV = znRT
Gas density
20
n
(mol / kg ) = p
V
zRT
ρ (kg / m3 ) =
pM
zRT
M (kg / kmol )
Standard conditions s.c.
n = ns.c.
pV
p V
= s.c. s.c.
zRT zs.c. R Ts.c.
zs.c. = 1
⎛ p ⎞⎛ T ⎞
⎟⎟ z
V = Vs.c. ⎜⎜ s.c. ⎟⎟⎜⎜
p
T
⎝
⎠⎝ s.c. ⎠
⎛ p ⎞⎛ T ⎞
⎟⎟ z
q = qs.c. ⎜⎜ s.c. ⎟⎟⎜⎜
⎝ p ⎠⎝ Ts.c. ⎠
Bg (=FVF gas) =
⎛ T ⎞⎛ ps.c. ⎞
V
⎟⎜
⎟z
= ⎜⎜
Vs.c. ⎝ Ts.c. ⎟⎠⎜⎝ p ⎟⎠
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APPENDIX
PVT (pressure-volume-temperature)
- Fasediagram
- Real gas law
pV = znRT
- Specific density of gas (=gravity)
M
γ = gass
M luft
M gass = γ 28,96
- Pseudoreduced pressure and temperature (c=critical)
p
pr =
pc
T
Tc
- Kay’s Rule (y is mole fraction)
pc = ∑ pci yi
Tr =
i
Tc = ∑ Tci yi
i
-
Corresponding states
z-factor diagram (Standing-Katz diagram, figure from Rojey o.a. 1997)
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