6 Inflow control
When fluid flows in the well pipe, along the completed interval, the pressure falls. In
vertical wells th completed interval is usually relatively short, so that the pressure loss is
negligible. Dikken/1990 / proved that in long horizontal wells pressure losses become so
large that the lower parts of the completed interval, toe, becomes unproductive. Uneven
inflow could provide for early breakthrough of gas or water. The first patented equipment
to ensure smoother flow was Brekke and Sargeant/1992 / the Norwegian Hydro.
After 20 years of development it has become possible to complete wells with several
branches, Figure 6.1. Such wells are cost-effective. But to distribute the production along
the long intervals between different reservoirs can be challenging.
Figure 6.1 Smørbukk well Q-5 Y (Statoil 2009)
In this chapter we review the principles and equipment for flow control that is in
common use in 2011. There is considerable effort in development and new and improved
equipment. The basic principles are hopefully more durable, but it seems to be plenty of
challenges in the completion design, production monitoring, optimization and robustness.
6.1 Basic principles
Objectives: identify the interaction between flow and flow in the well
6.1.1 Flow from the reservoir to the well
The flow in the well will be zero where the completed interval begins (toe). At the end
(heel) the flow equals total production from the well. Along the completed interval, the
flow in the well pipe will increase as illustrated
Figure 6.2 Flow towards and flow along the completed interval
Inflow per unit length is usually called the inflow density: qL. Volume balance (continuity
relation) connects the inflow density to flow : Q along the well
qL 
Qi 1  Qi
x

x 0
dQ
dx
(6-1)
Darcy's law implies that the inflow density is proportional to the pressure difference
between reservoir and well. Proportionality factor: jL, is called specific productivity index
and can be understood as the productivity index per meter well
qL  jL  pR  pw x 
(6-2)
Productivity index is traditionally defined as the ratio between total production and
pressure drop from the reservoir to the well. Production is traditionally measured by
standard rate: qo, which can be converted to total downhole rate by multiplying by the
formation factor: Q = qoBo. Productivity index is derived preferably from Darcy's law by
assuming homogenous inflow along the well. Total production corresponds to the product
of flow density and completed the well length. The relationship between specific and
total productivity index is then
jL  J
Bo
Lw
(6-3)
The relation (6-3) assumes that the flow is perpendicular to the well. With pressure drop
along the well, this will not be quite correct, however, an acceptable approximation if the
flow resistance from the reservoir to the well is much larger than the flow resistance
along the well. Usually this will be the case.
6.1.2 Flow along the well
Pressure gradient along a horizontal well can be estimated with the common pipe flow
equation. Based on the flow, this

dpw

2
 8 f 2 5 Qx 
dx
 d
(6-4)
If the density is constant and the pressure is related to the reference height (hydraulic
potential), the (6-4) also apply to inclined and vertical wells.
6.1.3 Coupling between inflow and flow in the well
The flow velocity along the completed interval. Within the same reservoir, pressure at
the reference height is considered constant: dpR / dx = 0 By setting (6-1), (6-2) into (6-4),
we get the relationship between flow and flow
d 2Q

2
 j L 8 f 2 5 Q x 
2
dx
 d
(6-5)
In simple cases this can be handled analytically. We then multiply (6-5) with qL=dQ/dx
and applying the relationship:
2
2
dQ / dx d
and.
dQ
dx Q 2  1 3 dQ 3 dx
Q / dx  1 2 d dx dQ dx 
.
At the bottom of the well will flow to zero: Q (0) = 0 We obtain after integration
dQ
16 f
2
3
 qL xo   jL
Q x 
2 5
dx
3  d
(6-6)
Inflow density at the toe: qL(xo) is unknown. If the well is sufficiently long the inflow
density at the toe to zero, Dikken/1990 /. More generally, (6-6) may be integrated
numerically along the completed interval. By trial and error can we find the inflow density
at the toe so that the flow at the heel corresponds to total production. Figure 6.2 shows
the flow and pressure calculated for Scenario 1, Table 6.1
Figure 6.2: Pressure an inflow along the well
The figures show much greater flow density at the heel than the toe. The well pipe
deliberately chosen small so that the speed at 6 m / s at the heel. Larger pipe diameters
would provide less pressure drop along this and more even inflow from the reservoir.
Table 6.1: Scenario 1
Reservoir Pressure 200 bar
Specific productivity index: j = 0.1m3/d/bar,
Production Qt = 1000 m3 / d
Oil density 800 kg/m3.
Viscosity 1 cP
Inner diameter, production pipe: d = 50 mm
6.2 Homogeneous flow
In a homogeneous reservoir without pressure drop along the well, the inflow along the
completed interval will be homogeneous. If the pressure loss along the well is much
smaller than the pressure loss from the reservoir to the well, the inflow may be
approximately homogeneous. Below we shall examine where this is an acceptable
simplification.
With flow control homogeneous flow is often a goal. Press and rates estimated for
homogeneous flow therefore provides the necessary basis to select and dimension the
flow control valves.
6.2.1 Pressure in the well pipe and the sand face
With the constant influx density, the volume flow increase steadily along the completed
interval:
.
Qx  qL x
. By integrating (6-4) along the well pipe, we get the pressure drop
pw 
8

2
f 2 5 qL L3
3  d
(6-7)
From (6-2), we get the pressure drop from the reservoir to the sand face
p R  pw 
1
qL
jL
(6-8)
Figure 6.4 shows the pressure in the well wall and the well pipe calculated for Scenario
1, when production: Qt = 1000 Sm3 / d and the inflow homogeneous . Without flow
control, pressure in the well wall and the well pipe will be equal. The figure shows
negligible pressure difference between the well wall and the well pipe the first 300
meters. Further, the pressure in the well pipe to fall significantly below the pressure in
the well wall, thus violating the assumption of homogeneous flow
Figure 6.4 Pressure in the well wall and well, with homogeneous flow
6.2.2 Criterion for homogeneous flow
We will consider the inflow almost homogeneous if the difference in flow resistance
between the toe and heel:
,, is small compared to the average inflow
qL  jpw
density:
qL  Qt Lw
.
. This provides the criterion
  qL qL
,
With no flow at the beginning of the interval, ie starting from the toe, the criterion can be
developed as
 j
8

f 2 5 Qt L2
3  d
(6-9)
This makes it possible to examine whether the influx of a potential well is nearly
homogeneous. The difference is debatable, but the range:   0.05  0.1 , may seem
acceptable
6.3 Completion and equipment
6.3.1 Completion for inflow control
Figure 6.5 shows completions with inflow control. The influx from the reservoir enters
the annulus. Inflow from the annulus to the well pipe is through valves
Figure 6.5 Completion
Annular packers restricts the flow along the annulus and separate reservoir sections with
different properties. These annular packers have polymer seals that swell up when they
come into contact with oil.
Well pipe are screwed together by standard lengths (12 feet, 40 feet). All or some of
these are equipped with a sand screen and inflow control, Figure 6.6
Figure 6.6 Well tubular med sand screen and ICD (Reslink /2007/)
The sand screen can be made up of metal profiles, or fabrics woven from wire.
One problem is that holes may be in the screen if the local flow speed becomes large,
for example after gas breakthrough. Inflow Control can even out the inflow and thereby
reduce the risk of local erosion.
Inflow Control (ICD = "inflow Control Device") consists of valves with housing to protect
them. Control valves distribute the inflow as desirable. They should be mechanically
durable and also function according to intention also if the reservoir and fluid properties
differ from the expected, or change over time.
6.3.2 Static control valves
Figure 6.7 shows a photograph of a control, cut open. Part of the sand screen is seen to
the left. We see three nozzles inserted in the pipe wall. These are made of extra hard
material
Figure 6.7 Inflow control device (ICD) (ResLink /2007/)
Assuming that the velocity energy is dispersed after the nozzle, the pressure loss
becomes:
2
pc  0.5 vc
With distance Lc, between control units, the flow to each unit becomes: :
Qc  qL Lc
.
With nc nozzles, each with effective cross-sectional area: Ac, the valve characteristics
becomes
2
1  L 
pc    c  qL2
2  nc Ac 
(6-10)
Figure 6.8 illustrates friction pipes for inflow control. Small Reynolds number (Re <2500)
implies laminate flow, so that the friction factor is proportional to the viscosity: f=64/v2,
and pressure loss is proportional to the flow:
At high Reynolds number is the
p c ~ q L
friction factor is almost constant and the pressure loss is proportional to the squared
flow,
2
pc ~ qL
ie similar to nozzles.
Figure 6.8 Inflow control by friction pipes (Halliburton /2010/)
By adding the pressure drops due to wall friction and momentum loss, we obtain the
valve characteristic below. It is here assumed nf friction pipes, each of length: lf
 L
1  l
pc    f f  1  c
2  d
 n f A f
2
 2
 qL


(6-11)
Figure 6.9 shows the characteristics of nozzles (6-10) and friction pipes (6-11), for
"water" with density 1000 kg/m3, viscosity: 1cP; and "oil" with density 800 kg/m3 and
viscosity: 10 cP. Valve parameters are listed Table 6.2 below
Table 6.2 Parametres
Diameter Number Lengths Dictance between LCD’s
Nozzles
dc=3 mm nc= 3
…..
Lc = 12 m
Friction pipes df=5 mm nf= 6
lf=1m
Lc = 12 m
Figure 6.9 Comparison of valve characteristics
The figure shows that with our viscous oil, the characteristics of friction pipe ICD
becomes approximately linear. The flow through the nozzles will be unaffected by
viscosity, unless this is very large. Changing from oil to water, the flow through friction
pipes increases, while the flow through nozzle-based inflow control will decrease
somewhat.
6.3.3 Dynamic control valves
Valves with parts that change position without control from outside will be call dynamic.
The purpose may be to close after breakthrough of gas, or water. At present, dynamic
valve are applied on the pilot level. There is little reported experience with these.
Bernoulli valves
According to Bernoulli the pressure will decrease when the flow velocity increases. Such
pressure changes provide forces that can be used to open / close valves. Figure 6.10
illustrates the Bernoullivalve developed by Norsk Hydro and tried on the Troll field
Halvorsen & al /2012/
Figure 6.10 Cross section through Bernoulli valve
Figure 6.11 below are based on measurements provided in the patent application, Aakre
& Mathiesen/2008 /. Measurements up to flow "4" (units were not given) have been
adapted to the choke equation (6-10) and extrapolated further. This indicates choke
characteristics up to a limit. Above, the pressure difference may increase without
providing greater throughput
Figure 6.11 Comparison between Bernoulli valve and fixed choke
Buoyancy-controlled valve
There are valve prototypes with floats that raise in water but sink in oil, such that the
valve will block water.
Osmosis-controlled valve
Another concept is to allow the osmotic pressure to open and close the valve.
6.3.4 Steerable valves
These are valves that can be controlled from the surface. This provides flexibility to deal
with unforeseen developments. The reliability of such valve systems have in recent years
has been increasing compared to the systems were installed in the 90's. The valve, with
power supply and control systems, occupies space down hole. It therefore seems most
relevant to use a few controllable valves to control the production from the well branches.
For subsea wells, controllable valves may contribute to 2 to 5% of the total well cost,
significant, but hardly a deterrent.
Figure 6.1, at the beginning of the chapter illustrates a completion in which a controllable
valve (shown in yellow) to allocate production from two separate wells branches. Each
well branch is also equipped with passive inflow control to distribute the inflow and flow
along the completed intervals
Since the cost of drilling from the sea floor down to the reservoir is significant, the
drilling of several branches in the reservoir attractive. Often the availability of slots is
limited. With branched wells and inflow control separate reservoirs may be produced
from the same well slot.
6.4 Inflow performance with pressure drop along the well
Objectives: How the flow friction and flow control affects productivity
The inflow performance is as relationship between the well pressure and total production.
When the flow follows Darcy's law and the well pressure is constant, the inflow
performance becomes linear. When the pressure drops along the completed interval, it is
logical to consider the pressure at the heel, where the flow corresponds to the total
production and the well pressure provides tubing inlet pressure.
6.4.1 Without inflow control
Without flow control, the pressure at the heel may be computed from (6-2) and (6-6).
This gives the relationship between the well pressure and total production
pwt  pR 
1
jL
qL  xo   jL
2
16 f
Qt3
2 5
3  d
(6-12)
6.4.2 With flow control
With inflow control to achieve homogeneous flow , the pressure in the well pipe made (67). From this follows the flow characteristics
pwt  pR 
1
8

Qt  f 2 5 LwQt2
jL Lw
3  d
(6-13)
The linear contribution of (6-13) represents the pressure drop between the reservoir and
the wellbore wall, while the square represents the pressure drop along the well pipe.
Figure 6.13 below compares the inflow characteristics. The starting point is well Scenario
1
Figure 6.13 Inflow performances
Mathematically the inflow characteristics of (6-13) is similar to that based on
Forcheimer's equation. Based on measurements of flow characteristics alone, it will
therefore be difficult to distinguish between turbulent inflow and friction loss along the
well pipe.
6.5 Robustness
Objectives: Completions which also are efficient when conditions change
Before the well is put into production the knowledge of the reservoir is inadequate.
During production, the properties change. Completion should be robust for changes that
can reasonably be expected.
6.5.1 Optimal and robust selection of choke size
Given a completed interval as illustrated below, and provided production rate, we can
estimate choke sizes so that the inflow density is constant. The question then becomes
how these will work when the rate of change
Figur 6.14 Homogen innstrømning
With homogeneous flow, the sand face pressure is constant. The pressure difference
between the well wall and the well pipe is due to friction along the well pipe and must be
compensated by the pressure drop across the nozzles. If we at the toe assumes the same


pressure at sand face and in the pipe, then p x  pc x
Pressure loss along the well pipe can be expressed by (6-7) and pressure drop across the
nozzles at the (6-10). Combination of relations gives
0.5

Lc  0.75
 x
d c  x   1.31 d 2.5
nc f 0.5 

(6-14)
Figure 6.15 shows choke diametres that ensure homogeneous flow, calculated from for
Well Scenario 1. More interesting is that neither the reservoir pressure, productivity
index, density, or production rate are included in (6-14). The chokes will thus ensure
uniform flow even if these variables change
Figure 6.15 Optimal choke size
6.5.2 Robustness to gas breakthrough
Gas is less dense than the oil at reservoir conditions and much less viscous. From Darcy's
follow the flow density is proportional to the specific productivity index and the pressure


loss: qL  jL pR  pw . Productivity index is independent of density, but inversely
proportional to viscosity, so that the pressure loss from the reservoir to the wellbore wall
is proportional to and the viscosity ratio: pR  aqL , where
a=1/(jL
-10)
pc  bq , where b  0.5Lc nc Ac  ,
expressed as:
independent of whether oil or gas flows through. The pressure loss from the reservoir to
the well pipe and through the nozzles can then be expressed
2
L
2
Gas is less dense than the oil at reservoir conditions and much lower viscosity. If the flow
through the reservoir is controlled a Darcy's law, the pressure drop from the reservoir to
the wellbore wall proportional to rate and viscosity pR   aqL (parameter: a
represents rock parameters and can be considered constant ). Pressure loss through the
nozzles follow from (6-10). The sum of these gives the pressure loss from the reservoir
to the well pipe
pR  p p  aqL  bqL2
(6-16)
By gas breakthrough the viscosity falls, so that the pressure loss through the reservoir:
decreases and the flow rate may increase. Pressure loss through the nozzles is
proportional to the squared rate, so when the rate increases, the pressure loss increases
relatively more. Choke based flow control will therefore reduce local inflow of gas,
relative to inflow without control. Thus it makes the well more robust with respect to gas
breakthrough.
Bernoulli valves are assumed to limit the flow regardless of pressure difference. Inflow
control by Bernoulli valves would should therefore make the well robust to local gas
breakthrough.
6.5.3 Robustness to water breakthrough
Fresh water has density close to 1000 kg/m3. Reservoir waters usually have slightly
larger density, due to dissolved salt. Oil density is usually smaller than water and density
considerably less than gas. The viscosity of water will be close to 1 cP, while the oil
viscosity can be anything from somewhat less to much larger.
Viscosity and density will affect the pressure loss through the reservoir and valves as
expressed by (6-15) above. Simple estimates regarding the robustness can be made
accordingly. Bernoulli valves may prevent the water flow exceeds a maximum rate.
Valves with floaters have the potential to make wells robust to water breakthrough. The
concept of osmosis control is interesting but currently more incomplete.
6.5.4 Constant choke size
A simple form of flow control is to select constant choke size along the completed
interval. Since the pressure loss through the nozzles is proportional to flow squared, this
prevents large local influx that could trigger sand production and damage sand screens.
Figure 6.16 shows the flow distribution calculated for Well Scenario 1, Table 6.1 above,
with constant tip size along the completed interval (dc = 1.5 mm, nc = 3, Lc = 12 m).
Figur 6.16 Innstrømning med like kontrollventiler langs komplettert intervall
Pressure drop and flow for Well Scenario 1, without flow control, was previously
illustrated in Figure 6.2. Comparison between Figures 6.2 and 6.16 shows that the
constant choke size provides a smoother flow along the completed interval, but slightly
reduces the discharge pressure at the heel
6.6 Flow in the annulus
Objectives: The importance of the annulus as the flow channel
If the annulus is not packed sand, or clogging by fines, it will pose a potential flow
channel. Local flow towards the well will be different from the inflow. This makes inflow
control is more complicated and unpredictable in that the conditions in the annulus will
be somewhat unpredictable and difficult to measure. Open annulus makes flow
resistance less and this can be beneficial.
6.6.1 Flow Relationships
Figure 6.17 illustrates the flow in the annulus and the well pipe. When the flow is
distributed between the annulus and the well pipe, the relationship between pressure
and flow becomes
pw  p R 
1
qw  q p 
jL
(6-16)
The influx to the annulus is here denoted: qw, while the inflow to the production pipe is
called: qp.
Figure 6.17: flow and flow in the annulus and well
With the control valves with choke characteristics (6-10), the relationship between
pressure and flow between the annulus and the well pipe becomes
p p  pw 
1
Cc q p q p
2
(6-17)
The pressure gradient along the well pipe relates to the flow as by (6-4) re-written below

dp p
dx
 C p Q p2
(6-18)
The pressure gradient along the annulus can similarly be linked to the flow

dpw
2
 C wQw
dx
(6-19)
The coefficient: Cw depends on the geometry and flow resistance. A crucial question will
be the amount of solids in the annulus.
6.6.2 With optimum flow control
We have previously shown that the homogeneous inflow can be achieved by sizing of
control valves. Along uniform reservoir sections, this means constant pressure along the
wellbore wall, ie no pressure gradient and no flow along the annulus.
Optimal flow control thus prevents flow in the annulus. With deviation from optimal
conditions, flow may occur in the annulus. How much depends on flow resistance in the
annulus.
6.6.3 Effect of flow in the annulus
Figure 6.18 illustrates the pressure and flow in the annulus and the well pipe calculated
for Well Scenario 2, Table 6.3 (corresponding to scenario 1, but with an open annulus).
The flow along the annulus makes the total pressure drop less and the flow then more
evenly distributed. At the heel the annulus closed, so the flow to is forced into the
production pipe.
Figur 6.18: Trykk og strømning med åpent ringrom
Table 6.3: Well Scenario 2
Reservoir pressure pR = 200 bar
Specific productivity index j = 0.1m3/d/bar,
Production Qt = 1000 m3 / d
Oil density 800 kg/m3.
Viscosity 1 cP
Inner diameter production pipe: d = 50 mm
Number of nozzles in ICD: nc = 3
Largest nozzle diameter dc,max = 1.5 millimeter
Outer diameter production tubing: 60 millimeters
Well diameter: dw = 200 mm
6.7 Well Maintenance
Objectives: Opportunities for maintaining the long-completed interval
In vertical wells casing is usually set and cemented through the producing interval. It is
common with the tail pipe hanging below the production packer. The well below the
perforations constitutes a sump where the sand and sediments can be accumulate.
In horizontal wells, there will not be similar sumps. The flow speed will be zero at the toe
and gradually increase towards the heel. In parts of the well pipe it will be so small that
the sediments can accumulate. It may therefore be necessary to intervene to remove
sand and perform other well maintenance.
It is not possible to reach down into horizontal sections with conventional wireline
technologies. Coiled tubings can be used, but requires heavy surface equipment. Easier
maintenance can be performed with an electrically driven cable tractor to pull the
equipment through the well pipe. Today's tractors, Figure 6.19, provides traction around
9000 N.
Figure 6.19 Cable Tractor (Aker Solutions/2010 /)
Figure 6.20 shows the cable tractor with equipment for milling and hole opening. There is also
equipment for sand removal, opening / closing of sliding sleeved, scale removal of valves and
other operations.
In practice, it is difficult, costly and risky to intervene in long horizontal wells and wells with
several branches. When planning an attempt to account for any future situations that may occur
and the necessary interventions, ie, think of all the well's life.
Figure 6.20 Cable tractor, fitted for milling (Aker solutins 2010)
Referanser
1990 Dikken, B.:
”Pressure Drop in Horizontal Wells and its Effects on their Production Performance”
JPT, Nov. 1990, 1426
1992 Brekke, K. og Sargeant, J.P. : “Fremgangsmåte og produksjonsrør for produksjon
av olje eller gass fra et olje- eller gassreservoar.”
Patent No 306127, Innlevert 18.09.1992
1997 Asheim, H. & Oudeman, P.: “Determination of Perforation Schemes to Control
Production and Injection Profiles along Horrizontal Wells”
SPE Drilling & Completion, March 1997, 13
2008 Aakre, H. & Mathiesen, V.:
“Method for flow control and autonomous valve or flow control device”
World Intellectual Property Property Organization, WO 2008/004875 A1
2010 Aker Solutions, produktinformasjon www.akersolutions.com/wellservice
2011 Mathiesen, V., Aakre, H., Werswick, R., Elseth,. G.:“The Autonomous RCP Valve
- New Technology for Inflow Control in Horizontal Wells” SPE 145737SPE Offshore
O&G Conf. & Exib., Aberdeen UK, 6-8 September 2011
2012 Halvorsen, M., Elseth, G., Nævdahl, O.,M.:
“Increased oil production at Troll by autonomous inflow control with RCP valves.”
SPE annual, San Antonio, TX, 8-10 Oct. 2012