G19PA
Production Technology-1 Tutorials
Chapter 3 – Reservoir and Tubing
Performance
Heriot-Watt University
Edinburgh EH14 4AS, United Kingdom
2
Tutorials: Chapter 3 - Reservoir and Tubing Performance
CONTENTS
PART1
1.1
1.2
1.3
1.4
1.5
1.6
WELL PERFORMANCE SENSITIVITY TUTORIAL
Reservoir Inflow and Tubing Outflow Restrictions
Tubing Size and Liquid Loading
Effect of Water Cut and Depletion
Opportunities for Skin Removal by Stimulation
Completion Design
Well Head Pressure
PART2
RESERVOIR AND TUBING PERFORMANCE TUTORIALS
Produced by Heriot-Watt University, 2015
Copyright © 2015 Heriot-Watt University
All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system or transmitted in any form or by any means
without express permission from the publisher.
This material is prepared to support the degree program in Petroleum
Engineering.
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1
WELL PERFORMANCE SENSITIVITY TUTORIAL
Combinations of the Well Inflow and Well Outflow along with the concept of systems
analysis of production systems (nodal analysis) (Chapter 3) allow us to estimate the
well productivity under today’s actual or future expected producing conditions. The
sensitivity of the well design (or its robustness) to the many factors which effect well
production as the well ages can then be tested. So as to minimise the “Total Well
Capital and Operating Costs” over its complete lifetime.
Figure 1 Nodal Analysis.
Figure 1 illustrates the systems analysis concept. The point (or node) at which the
analysis is carried out can be chosen to be anywhere in the producing system - the
inflow and outflow being calculated for the complete system up- and down-stream
from the chosen node. The sensitivity of the production rate to changes in the
dimensions of a particular component (situated next to the node) can then be
evaluated. This allows the performance of each individual well component to be
analyzed separately. Typical examples of node selection are:
•
Wellhead: evaluate the effect of flow line size
•
Safety Valve: evaluate the effect of the reduced flow caused by the diameter of
the safety valve being smaller than that of the tubing (important in high rate gas
wells)
•
Sandface: select the optimum tubing size or evaluate well inflow performance
(is there a requirement for reperforation, stimulation {to remove a positive skin
(acidisation) or create negative skin (hydraulic fracturing)}
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Other possible node points can be seen in Figure 1 from Chapter 3 notes (Reservoir
and Tubing Performance) which analyses pressure losses in the complete production
system. Some of the more frequently encountered sensitivity analyses are described
below.
1.1
Reservoir Inflow and Tubing Outflow Restrictions
The impact of (relatively) inadequate reservoir inflow (case 1) with a (larger than
necessary) tubing is illustrated in Figure 2. The opposite case, production restriction
by a too small tubing (case 2) is shown in Figure 3 for the same reservoir inflow
performance. It comes as no surprise to see that:
q 1 >> q 2 and p reservoir ≈ p sandface (2) >> p sandface (1)
Figure 2 Reservoir outflow restricts production.
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Figure 3 Small tubing restricts production.
1.2
Tubing Size and Liquid Loading
The well production will normally increase as the tubing size increases. The pressure
drop in the tubing thus decreases so that a greater well drawdown is possible for the
same reservoir and separator pressure. However, at a certain point, the upward (gas)
flow velocity has decreased so much (due to the tubing diameter increase) that it is no
longer sufficient to efficiently lift the liquid to the surface i.e. phase slip and liquid
holdup (or liquid loading) increases (Figure 4).
Figure 4 Liquid loading analysis.
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Figure 5 Nodal analysis predicts production rate as tubing diameter increases.
Eventually, the increased hydrostatic head (due to the liquid loading) will be greater
than the reduced friction pressure losses as the tubing diameter increases further. This
leads to a maximum production rate (Figure 5) at a certain tubing diameter. Unstable
flow is encountered with even larger tubing diameters – it is not recommended to
operate in this region since liquid loading will eventually progress to the stage that the
well ceases to flow.
1.3
Effect of Water Cut and Depletion
Figure 6 Effect of water cut on oil production.
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Figure 7 Effect of depletion on production rate.
Figure 8 Sensitivity of production rate to simultaneous pressure depletion
and increasing water cut
Table 1 Reservoir Simulator Predictions.
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An increasing water cut reduces the gas liquid ratio as well as increasing the
hydrostatic head between the reservoir and the surface. This is illustrated in Figure 6
for a slightly over pressured reservoir. Reservoir simulation can be used to predict the
reservoir pressure depletion with time as well as any increase in water cut. (Table 1).
The effect of this pressure depletion on the production rate is summarised in Figure 7
and the two are combined in Figure 8. The oil production rate at time t2 is only 25% of
the initial production, while a small further reduction in reservoir pressure or an
increase in water cut beyond 50% will cause the well to cease production altogether.
1.4
Opportunities for Skin Removal by Stimulation
Well testing frequently identifies that a positive skin effect is restricting well
production. The economic incentive for removing this skin (or even inducing a
negative skin) can be evaluated with the help of nodal analysis. Figure 9 shows the
current well inflow (skin = +8) together with its partial (skin = +2) and complete (skin
= 0) removal. The carrying out of a hydraulic fracture (skin = -3) is also illustrated.
Figure 9 Opportunities for increased production
by skin removal and increase in tubing diameter.
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The flat outflow profile of tubing results in large gains in production that might allow
these treatments to be carried out. Tubing 2 (with a more vertical outflow profile) is
already restricting production with the impaired (skin = +8), while only minor
(probably uneconomic) production gains are recorded when the skin is removed – the
most favourable production (-3) being still less than that achieved with the larger
tubing and the high (+8) reservoir skin.
The most appropriate remedial action can only be chosen – and economically justified
– when the pressure losses within the complete well system are understood.
1.5
Completion Design
Figure 10 Effect of number of perforations on production rate.
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The high skin discussed in the previous case could have many causes e.g. formation
damage, partial completion etc. One factor under the control of the production
engineer is the number and type of perforations. Figure 10 illustrates an increase in the
numbers of perforations {N 1 <N 2 <N 3 <N 4 , all of diameter D 1 } while Figure 11 shows
that effect of a restricted number of perforations (N 1 ) can be (partially) compensated
for by an increase in the diameter from D 1 to D 3 (i.e. reduction in the frictional
pressure loss in the perforation tunnel itself). Theoretically increasing the number of
perforations is more beneficial since it improves the inflow from the reservoir as well
as decreasing the (average) frictional pressure drop in the perforation tunnel (see
Figure 12 for comparison). The cost of the perforation operation will increase as the
number and diameter of the perforations are increased – an economic optimum will be
found when both factors are varied simultaneously.
These theoretical calculations are a useful, but not complete guide. It is being
frequently observed in the field that not all perforations are effective e.g. in gravel
packed wells it is standard practice to assume only 33%–50% of the perforations are
effective (i.e. open to flow).
Figure 11 Effect of perforation diameter on production rate.
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Figure 12 Optimisation of perforating schedule.
1.6
Well Head Pressure
The separator pressure is often the main component in the surface pressure losses. It
exerts a restrictive “back pressure” on the well production which limits the total
pressure drop available for fluid inflow from the reservoir and onward transportation
to the surface. This effect is illustrated in Figure 13 – where the wellhead is used as the
nodal point. Reducing the separator pressure is often an effective way of increasing the
wells production capacity during later well life when the reservoir pressure is depleted
and the water cut is high.
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Figure 13 Effects of separator pressure on production rate.
This type of “backpressure” on the wells is often encountered in more subtle ways e.g.
the gas collecting in the tubing/casing annulus of a well equipped with an artificial lift
pump can limit the maximum available drawdown by acting as a back pressure.
Venting this casing gas increases the drawdown with a corresponding production rate
improvement (See Chapter 4, Selection and Design of Artificial Lift)
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2
RESERVOIR AND TUBING PERFORMANCE TUTORIALS
Question 1. Calculate the increase in production from a well if a
remedial workover reduces the skin factor from 3.9 to 0.4. for the
following data:
Oil permeability, k o = 110 mD
Thickness of formation, h = 50 m
Oil viscosity, µ o = 1.3 x 10-3 Pas
External radius, r e = 480 m
Wellbore radius, r w = 0.15 m
Oil formation volume factor, B o = 1.2 rm3/stm3
Average reservoir pressure, = 270 bar
Flowing bottomhole pressure, P wf = 190 bar
(assume no rate dependent skin (i.e. Dq=0) and semi-steady state flow)
SOLUTION 1
a) Flow rate before workover
Skin factor = 3.9
q o = 0.016 m3/s
q o = 1382 m3/day
q o = 8692 b/day
b) Flow rate after workover
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Skin factor = 0.4
q o = 0.023 m3/s
q o = 1987 m3/d
q o = 12497 b/d
The increase in production is therefore 12479 - 8692 = 3805 b/d
Question 2. An initial well test in a reservoir gave a stabilised oil flow
rate of 9781 b/d for a stabilised flowing bottomhole pressure of 105 bar
with a skin factor of zero. After 18 months’ production, the flowing
bottomhole pressure was 90 bar to maintain this initial production
rate. Calculate the mechanical skin factor for this well after 18 months’
production:
Oil permeability, k o = 95 mD
Formation thickness, h = 50 m
Oil viscosity, m o = 1.3 x 10-3 Pas
External radius, r e = 300 m
Wellbore radius, r w = 0.15 m
Oil formation factor, B o = 1.21 rm3/stm3
Average reservoir pressure, = 170 bar
(assume no rate dependent skin and semi-steady state flow)
SOLUTION 2
Check that the values given are correct.
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q o = 0.018 m3/s
{Check original data: initial flowrate = 9781 b/d = 9781x0.159/3600/24 m3/d = 0.018
m3/s}
Therefore the original data are correct.
For P wf = 90 bar, the skin factor for the same flowrate will be:
Question 3.
The following data are relevant to a well in a reservoir
Average reservoir pressure, = 4000 psi
Actual flowing bottomhole pressure, P wf = 2600 psi
Ideal flowing bottomhole pressure, P wf = 3000 psi.
Determine the flow efficiency of the well.
SOLUTION 3
Flow Efficiency,
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Question 4. A well has been tested and found to have a positive skin
factor. Pressure test analysis shows the pressure drop over the skin to
be 150 psi. Calculate the flow efficiency given the following test data:
DATA
average reservoir pressure,
= 3600 psi
actual flowing bottomhole pressure, P wf = 1950 psi
SOLUTION 4
Flow Efficiency (FE),
FE =
ideal drawdown 3600 − (1950 + 150)
=
= 91%
3600 − 1950
actual drawdown
Question 5. A 2.5 in tubing string is 8000 ft long. It produces 1000 b/d
(all water) against a wellhead pressure of 120 psi with a gas liquid ratio
of 200 scf/b and an average reservoir pressure of 3000 psi. Using
gradient curves, determine the average productivity index (assume it is
linear).
SOLUTION 5
Chart 110, all water curves.
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Calculate the average linear productivity index,
PI =
1000
q
=
= 2.1 b / d / psi
Pr − Pwf 3000 − 2520
Question 6. A well produces all oil at a rate of 800 b/d against a wellhead
pressure of 120 psi. The average reservoir pressure is 2300 psi. The
bubble point pressure is 2400 psi. The diameter of the tubing is 2.5 in
and it is 8500 ft in length. The gas liquid ratio is 400 scf/b.
Calculate
a) The average productivity index (assume it is linear)
b) The maximum oil flow rate (assume Vogel behaviour)
c) Plot the inflow performance relationship.
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SOLUTION 6
Select chart C104
a) Average productivity index,
PI =
q
800
=
= 1.48 b / d / psi
Pr − Pwf 2300 − 1760
b) The reservoir pressure is below bubble point. Vogel is a better description of the
inflow behaviour:
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= 2114 b/d
c)
Select various flowing bottomhole pressures to delineate the inflow
performance curve:
where P wf is in the range of the following table:
and is plotted as
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Question 7. The following test data pertain to a well in a reservoir. Find
the tubing size which would be suitable for this well to produce.
DATA
SOLUTION 7
1
Determination of the required drawdown
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2
Tubing size
This is determined by matching the required flowing bottomhole pressure, P wf to a
selection of tubing sizes. As a first attempt, try 2 in and 2.5 in tubing. Assume 95%
water cut is equal to 100% water cut.
i) 2 in tubing, chart C95
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ii) 2.5 in tubing, chart C110
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iii) requirement for flow:
By inspection, the 2 in. tubing requires a pressure which is too high for the reservoir to
produce 1000 b/d. The 2.5 in. tubing is below the pressure required by the reservoir to
produce 1000 b/d. However, the pressure for the 2 in. tubing is close to the reservoir
requirement and it may be that other factors such as the capital cost of the tubing and
the cost of installation over ride this purely technical assessment. Also, the charts for
100% water were used which is likely to slightly overestimate the pressure.
Question 8. A well design has chosen a specific tubing size as shown
below. Use gradient curves to determine the gas liquid ratio required to
flow the well.
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DATA
SOLUTION 8
1
The required flowing bottomhole pressure for the reservoir is
= 2346 psi
2
The appropriate gradient curve must be chosen for 1000 b/d, all water, i.e. chart
C95. Assume the gas liquid ratio to start such that the minimum gradient curve
is used.
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Project across from the equivalent depth to the intersection with 2346 psi. This falls
around 380 to 400 scf/b.
3
Check that use of this gradient curve is still valid for the choice of the
equivalent wellhead depth - i.e. that the equivalent welled depth for 80 psi is
still 580 ft: this is correct, therefore the gas liquid ratio is 380 to 400 scf/b.
Question 9. The following reservoir and completion data are pertinent to a
specific well.
DATA
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Calculate the following
a) The gas liquid ratio to flow the well.
b) If gas is injected at the bottom of the tubing, calculate the amount of injection gas
per day required.
SOLUTION 9
a)
Calculate the flowing bottomhole pressure, P wf
= 1500 psi
b) to determine the gas liquid ratio, the amount of gas already present in the oil
must be determined from the gas oil ratio. Then the total gas liquid ratio can be
determined from the appropriate gradient curve and the extra gas required to
flow the well determined.
liquid flow rate, q = q o + q w
water cut =
gas oil ratio, GOR = 400 scf/b
gas flow rate = 0.5 x 4000 x 400 scf/d
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gas liquid ratio,
= 400 (1-0.5) = 200 scf/b
Choose curve C126
Extend the gradient at 9600 ft from the minimum gradient curve over until a flowing
bottomhole pressure of 1500 psi is reached. This falls around 720 scf/b.
Check that use of this gradient curve is still valid for the choice of the equivalent
welled depth - i.e. that the equivalent wellhead depth for 120 psi is still 1100 ft: this is
correct, therefore the gas liquid ratio is 720 scf/b.
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The gas required is now calculated from:
Flow rate, q = 4000 b/d
Gas liquid ratio = 720 scf/b
Therefore gas flow rate = 720 x 4000 b/d = 2880000 scf/d
Solution gas from oil = 2000 b/d x 400 scf/b = 800000 scf/d
Therefore the injected gas rate = 2880000 - 800000 = 2080000 scf/d = 2.08 MMscf/d.
Question 10. A well and reservoir have the following completion and
reservoir data. The flow is all oil.
Determine the operating point.
SOLUTION 10
1) Determine the inflow performance relationship
Develop the following table
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2) For the given tubing and fluid properties, assume various flow rates and
calculate the flowing bottomhole pressure required to flow the fluid up the
tubing at that particular flow rate. Try the following flow rates:
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Plot the Inflow Performance Relationship (IPR) and Tubing Performance Curve (TPC)
From the plot, the operating point is where the two curves intersect: 3602 b/d and 1134
psi
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confirm these values;
= 1134 psi
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