SPE 95282 Modelling the Gas Well Liquid Loading Process N. Dousi, Delft U. of Technology; C.A.M. Veeken, Shell E&P Europe; and P.K. Currie, SPE, Delft U. of Technology
Copyright 2005, Society of Petroleum Engineers This paper was prepared for presentation at Offshore Europe 2005 held in Aberdeen, Scotland, U.K., 6–9 September 2005. This paper was selected for presentation by an SPE Program Committee following review of information contained in a proposal submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to a proposal of not more than 300 words; illustrations may not be copied. The proposal must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.
Abstract Liquid loading is a serious problem in areas where gas fields are maturing. An analysis is provided of the production behaviour over time of liquid-loaded wells. This shows clearly that these wells can operate at two different rates, a stable rate at which full production is taking place and a lower metastable rate at which liquid loading effects play a role. A model has been constructed which enhances the understanding of the process of water build up and drainage in gas wells. It assumes a single gas and water co-production point and a single water re-injection point. As expected a water column is built up in the well as soon as production takes place below the critical rate. As observed in the field, for good inflow performance a metastable flowrate can be observed. At this state the water re-injection and water coproduction rate are equal to one another and the water column height stabilizes. A sensitivity analysis has been carried out to determine how well parameters influence the metastable flowrate, the time required to reach this metastable rate, the corresponding water column height and the shut-in time required to drain this water column. The results of the analysis indicate that significant metastable flow rates occur in wells which have good inflow performance, a low water gas ratio and a large distance between injection and production point. Furthermore a steady state analytical solution has been derived for the metastable rate and stabilized water column height confirming the numerical analysis results.
Introduction
Many of the mature offshore gas fields in the Southern North Sea have already experienced considerable pressure depletion resulting in significantly reduced gas flowrates and, eventually, liquid loading. Insight into the flow characteristics of these liquid-loaded wells will help manage tail-end production i.e. will help define the most effective means of accelerating and maximising their ultimate recovery. Liquid loading All wells producing from depleting gas reservoirs will eventually exhibit so-called liquid loading. The liquid loading process occurs when the gas velocity within the well drops below a certain critical gas velocity. The gas is then unable to lift the water co-produced with the gas (either condensed or formation water) to surface. The water will fall back and accumulate downhole. A hydrostatic column is formed which imposes a back pressure on the reservoir and hence reduces gas production. The process eventually results in intermittent gas production and well die-out. This paper will describe the liquid loading behaviour by modelling the build-up and drainage of water in gas wells. There is an extensive literature on liquid loading. Duggan1 introduced the concept of a critical minimum wellhead gas velocity for the onset of liquid loading. Oudeman2 gives a review of the literature. The most widely applied method for predicting liquid loading is based on an analysis of droplet transport in vertical turbulent gas flow by Turner et al3, leading to the prediction of a critical flowrate, which we shall call the Turner rate. Coleman et al4 confirmed that the Turner rate is a good predictor of the onset of liquid loading, and examined the influence of other parameters on the process. Lea and Nickens5 discussed ways of solving liquid loading problems. Guo et al.6 presented a further improvement on the Turner criterion. Although the Turner rate (or a modification thereof) is accepted as a good criterion for predicting the onset of liquid loading, Oudeman2 pointed out that it is not a good predictor of when the well will die, which may occur at a lower rate. Recently, Sutton et al7 noted that wells may operate at subcritical rates, and gave a review of the methods for analyzing this phenomenon. Here we report on field data which clearly show the existence of subcritical “metastable” flow rates, at which the well still produces, even though liquid loading is occurring. A
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simple conceptual model is introduced which helps to understand and interpret this data. Field data demonstrating metastable flow The production data of mature gas fields has been analyzed for evidence of stable flow rates below the Turner flowrate. Five examples are presented to illustrate the effects of liquid loading. A number of techniques have been used to analyze this production data.
Fig. 2 Example 2. Sorted annual tubing head temperatures of a well that is occasionally liquid loading.
These results are interpreted to indicate that the well produces at a stable rate corresponding to the temperature 90 °C. As liquid loading starts, there exists a metastable rate at which the production rate is less and the tubing head temperature correspondingly decreases to 40 °C. An individual liquid loading event for this well is displayed in Fig. 3, illustrating the time it takes for this well to load up. In this example liquid loading takes place within about one day.
Example 1. The transition period between stable and subcritical flow can be observed in Fig. 1. In this example the flowrate drops from a stable rate of about 220,000 m3/d to 50,000 m3/d. Liquid loading takes place within about 10 days.
Production data, year 2000 90 Stable regime 80 70
Production data Tfth, C Pth, bara
60
300
20
200
10 150
0 20-apr
21-apr
22-apr
100
23-apr Tfth
Pth
24-apr
25-apr
Tamb
Fig. 3 Example 2. Individual recorded liquid loading event
0 17-feb
27-feb
9-mrt
19-mrt
29-mrt
8-apr
18-apr
Qg, x1000m3/d
Fig. 1 Example 1. Production data demonstration start of liquid loading
Example 2. The data consists of the daily flowing tubing head temperature (Tfth), in the period 1997 – 2002 of a NAM well. Fig. 2 shows the temperature data for one well. For each year, the data has been sorted, so that the lowest temperature recorded is assigned to day 1, and the highest temperature to day 365, and plotted as in Fig. 2. From this figure, it is seen that in 1997 the Tfth had the value of about 90 °C for all but 50 days in the year. In subsequent years, the number of days at lower temperatures increases steadily, reaching 160 in year 2002. Moreover, when the temperature falls below 90 °C, it takes discrete values, either about 20 °C (ambient surface temperature, indicating that the well is shut in) or about 40 °C. In 1997, the well flowed at this Tfth for about 10 days. In 2002, the number of days had increased to about 60. The downtime also increases from 15 days in 1997 to 100 days in 2002.
100 90 Temperature at stable flow
70 60 50 40 30
Temperature at metstable flow
20 10
Ambient Temperature
0 0
50
100
150
200
Time, days 1997
1998
1999
2000
2001
2002
Production data 100
40
90
30
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70
10
60
0 Stable flowrate
50
-10
40
-20
30
-30
20
-40
10
-50 Metastable flowrate
0 20-sep
30-sep
10-okt
20-okt
30-okt
Qg, x1000m3/d
9-nov
19-nov
29-nov
-60 9-dec
Pth, bar
Fig. 4 Example 3. Individual recorded liquid loading events
One can clearly distinguish two stable flowrates. The stable and metastable flowrates are about 50,000 m3/d and 10,000 m3/d respectively. It takes about 8 to 10 days for the well to load up. When we sort the hourly flowrate data in the same way as the temperature data in example 2, a similar profile is obtained, which can be observed in Fig. 5.
Sorted flowing tubinghead temperature data
80
Example 3. Here we introduce data from another NAM well. In Fig. 4 a series of consecutive liquid loading events are displayed. The tubing head pressure and flowrate are plotted as a function of time.
Pth, bar
50
Tfth, C
40 30
Qg, x1000 m3/d
Qg,x1000m3/d
250
Metastable regime
50
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30
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25
35 30
60 Stabe rate
20
40 Critical rate
Pth, bar
25
15
Qg, x1000m3/d
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Qg, x1000m3/d
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20 60 15 40 10 20 0 28-jan
Pbh, bar
Production data
Sorted flowrate data
5
7-feb
17-feb
27-feb
0 9-mrt
10
20
Qg, x1000m3/d 5
Metastable rate 0 0
1000
2000
3000
4000
5000
6000
Pbh, bar
Fig. 7 Example 5. Bottom hole pressure in response to liquid loading
0 7000
T, hours Sorted flowrate data
Sorted tubing head pressure data
Fig. 5 Example 3. Sorted hourly flowrate and tubing head pressure data of a well that is occasionally liquid loading.
We can distinguish a regime in which the well produces at a stable rate, between 40,000 and 60,000 m3/d and a regime at which it produces at a lower metastable flowrate, between 9,000 and 11,000 m3/d. The metastable plateau observed is not long because the operator systematically shuts in the well upon observing liquid loading. Example 4. Extended periods of metastable flow can be observed in Fig. 6. In this example the well produces at a metastable flowrate of about 14,000m3/d. Production data 70
30
60
25 20 15
40
10 30
Pth,bar
Qg,x1000m3/d
50
5 20
Methods to analyse liquid loading Study of the behaviour of individual wells confirms that when certain wells are liquid loading the gas flowrate can drop to a lower metastable flowrate. Furthermore the data indicates that the time span, in which liquid loading occurs, varies. The objective of the modelling work is to determine what the processes are behind the field observations, and to quantify them for various given well conditions. Two methods are presented to analyse liquid loading. Firstly, a simple numerical model was constructed to simulate the transient behaviour of liquid loading and its impact on various parameters. The second method encompasses a procedure to determine the metastable flowrate analytically, assuming a steady state situation. Both methods are largely based on the modelling assumptions described in the next chapter.
0
10 0 2-jun
As expected, the bottom hole pressure increases sharply upon liquid loading. A significant metastable flowrate can be observed as well.
-5 -10 22-jun
12-jul Qg,x1000m3/d
1-aug
21-aug
Pth,bar
Fig. 6 Example 4. Extended metastable flowrate
Notice that the metastable flowrate remains fairly constant even though the flowing tubing head pressure fluctuates significantly.
Model construction To predict how water build-up takes place within a gas well a simple conceptual model has been created illustrating the effect of liquid loading, as reported in Dousi8. The model incorporates well behaviour (build-up and drainage of a liquid column) but does not take into account reservoir behaviour (depletion and re-pressurisation).
Example 5. In order to see the bottom hole pressure in response to liquid loading, Fig. 7 has been constructed. In this example the flowing tubing head pressure remains fairly constant at about 13.5 bar. Batch foam was used to kick off this well periodically.
Depth X1
Reference point
X2
Gas and Water Production point
X3
Water Injection point
Water column Fig. 8 Schematic of the well model
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In Fig. 8 the model is depicted schematically. The following assumptions are made: • • • •
• •
•
• • •
•
Below x1 the well is assumed to be vertical. It is assumed that the tubing head pressure is equal to the surface export pressure when the well is not shut in. The reservoir pressure at the production point x2 equals Pres,g. At the injection point x3 the reservoir pressure equals Pres,w. Above depth x1 the flow behaviour within the well is described by the model introduced by CullenderSmith 9. At x1 the pressure is Pfbh1. The interval below x1 is a relatively small part of the well. Below x1 the pressure drop due to frictional flow effects is neglected. At depth x2 a gas production point is located. A simple Darcy model for single-phase gas describes the inflow into the well. Water is produced together with the gas, at a constant water gas ratio Fwg. At x2 the pressure is Pfbh2. At the bottom of the well (x3) a water injection point is located. A simple Darcy inflow model for singlephase liquids describes the flow into the reservoir. At x3 the pressure is Pfbh3. A water column can be built up between x1 and x3. Depth x1 is always chosen higher than the top of the liquid column. The initial gas flowrate can be set to operate in the liquid loading regime by changing the reservoir pressure such that the initial gas flowrate is equal to or lower than the critical rate described by a simplified Turner critical rate relationship. Upon liquid loading it is assumed all water coproduced with the gas (with constant water gas ratio) will fall back to form the water column.
(1)
where Pfth is the flowing tubing head pressure, Qg is the gas production flowrate and B and C are outflow constants reflecting hydrostatic head and friction respectively. The relationship relating the pressure Pfbh1 to the pressure Pfbh2 at the production point is taken as purely hydrostatic, neglecting any friction effects: P fbh2 = P fbh1 + G w h wc1 + G g h gc1
P fbh3 = P fbh1 + G w hwc2 + G g h gc2
(2)
where Gg and Gw are the hydrostatic gradients at the bottom of the well. hwc1 equals the water column length above the production point and hgc1 equals the height of the gas column between the top of the water column and x1. If the top of the water column is below x2, hgc1 equals the distance between x1 and x2.
(3)
in which hwc2 equals the height of the water column length above the injection point and hgc2 equals the height of the gas column between the top of the water column and x1. If the height of the water column is zero, hgc2 equals the distance between x1 and x3. Assuming production and injection take place in the same gas reservoir at pressure equilibrium: Pres,w = Pres,g + G g h gc
(4)
where hgc equals the distance between x2 and x3. The inflow relationship at the production point x2 is:
(Pres,g ) 2 − (Pfbh2 ) 2 = Ag Q g
(5)
If Pfbh2 is larger than the reservoir pressure then the production rate equals zero. The model neglects possible re-injection at x2. The injection relationship at the injection point x3 is: P fbh3 − Pres,w = Aw Q w, inj
(6)
If the reservoir pressure is larger than Pfbh3, than the flowrate equals zero. The model neglects possible inflow at x3. The water co-produced with the gas is written as follows: Q w, prod = Q g Fwg
The Cullender Smith9 well flow model provides:
(Pfbh1 )2 = B(Pfth )2 + C(Qg )2
The relationship relating the pressure Pfbh1 to the pressure Pfbh3 at the injection point is also taken as hydrostatic:
(7)
For modelling purposes a simplified form of the Turner2 critical rate relationship has been used where surface area, temperature and Z-factor are chosen as be constant such that the relationship can be written as follows:
Qc = Cst Pfth
(8)
The Cullender-Smith outflow factors B and C, the gas inflow resistance factor Ag, the simplified Turner factor Cst, and the average water gas ratio Fwg, are usually known for a production well. In addition, the model requires knowledge of the usually-unknown water re-injection resistance factor Aw. This factor is usually determined in an iterative manner by matching the model results against the actual production data. The numerical program takes discrete timesteps and calculates and solves the model equations in an iterative manner.
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Describing the process
45
Pth, bara
40 35 30 25 20 0
1
2
3
4
5
6
7
8
9
10
Tim e, days
Fig. 10 Example 6. Assumed tubing head pressure over time
300
6
250
5
200
4
150
3
100
2
50
1
0
Water injected/produced, m3/d
Flowrates & height water column as a function of time Gas flowrate, x1000m3/d Height water column, m
The modelled process that takes place in the well during liquid-loading is depicted in Fig. 9 and can be described as follows: At time t=0 the well is producing stably at a constant flowrate. As soon as the tubing head pressure increases above a certain tubing head pressure, the rate drops below the critical Turner rate. At this time the water co-produced with the gas cannot be transported to surface and will drop to the bottom of the well imposing a backpressure on the reservoir. Due to water column build up, the pressure at the injection point will rise until it exceeds the reservoir pressure. Then water will start to be re-injected into the reservoir, essentially draining the well partially. The column may build up so that at some point in time it starts to cover the production interval. At this time the column will impose a higher pressure on the production interval as well. The increased pressure will reduce the drawdown resulting in a drop in gas flowrate and consequently also a drop in water production rate. A new stabilized metastable gas rate is reached when the water production rate becomes equal to the water re-injection rate. At this point the water column height will stabilize as well.
Tubing head pressure as a function of time
0 0
1
2
3
4
5
6
7
8
9
10
Time, days Height water column
Gas flowrate
Water production rate
Water injection rate
Fig. 11 Example 6. Production and re-injection rates and water column height over time
Bottomhole pressures at injection and production point as a function of time 70
Pbh, bara
60 50 40 30 Gas and water production
0
1
Water injection Water column
2
3
4
5
6
7
8
9
10
Tim e, days
Reservoir pressure
Pbh injection point
Pbh production point
Fig. 9 Schematic of model liquid loading process
Fig. 12 Example 6. Bottomhole pressures over time.
Numerical model calculations
In Fig. 11 the gas and water production rates, the water reinjection rate and the water column height as a function of time are displayed. Fig. 12 displays the pressures at the injection and production point. At t=1 day the gas and water production rates immediately reduce, because of the increased flowing tubing head pressure. Also the water column builds up to 100 m, the distance between the production point and injection point. At that point in time the column will start to cover the production point and the gas flowrate (and water production rate) consequently decreases further. At t=1.6 days water will start to be re-injected. This takes place as soon as the bottom hole pressure becomes higher than the reservoir pressure at the injection point. At t=2.5 days the height of the water column stabilizes at 250 m. This happens as soon as the
An example of the predictions of the model is given here. It illustrates the processes that occur during liquid loading. Example 6. The distance between the injection and production points equals 100 m. Fig. 10 depicts the assumed tubing head pressure over time. At time t=0 the well is producing at above the critical Turner rate. At t=1 day the tubing head pressure is slightly increased such that the well will produce below the critical rate. At t=3 days the tubing head pressure is reduced to its original level. At t=5 days the well is shut in. At t=8 days the well is brought back onstream.
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water injection rate equals the production rate. At t=3 days the tubing head pressure is lowered having an immediate positive impact on the gas flowrate. However the gas flowrate remains lower than the critical rate. Therefore instead of draining the water column, the height of the water column increases further to 280 m. This is because decreasing the tubing head pressure results in a slight decrease of pressure at both the injection point and production point. Thus the gas flowrate and water production rate will increase and the water injection rate will decrease. Hence water will continue to build up. At t=4 days a new stable point is reached. At t=5 days the well is shut in and the water column drains at a constant rate, until the top of the water column has reached the production point. Then the water re-injection rate decreases until all the water is drained. Comparison of numerical model with field data In order to determine if the model can mimic liquid loading realistically, the model results have been compared to actual field data for a well with 3.5’’ tubing and a 7’’ production liner down to a reservoir depth of about 1700 m. A downhole pressure gauge was installed in this well to monitor the liquid loading event. In Fig. 13 the actual and modelled gas flowrates and the modelled height of the water column are displayed.
Ag Aw B C Cst ρg ρw Fwg Distance between production and re-injection point
17 4 1.4 0.038 ~12 0.68 1000 6 35
[bar2/e3m3/d] [bar/m3/d] [-] [bar2/(e3m3/d)2] [e3m3/d/(bar)0.5] [kg/m3] [kg/m3] [m3/e6 m3] [m]
Figs. 13 and 14 show that the model realistically mimics the liquid loading process. Note that the bottom hole pressure gauge is located about 20 meters above the perforated interval. Therefore when a column of water exists in the well 2 bar needs to be added to the field data resulting in a better match with the model prediction in Fig. 14.
250
50
200
40 150 30 100 20
Height water column, m
Flowrate, x1000m3/d
Table 1 - Field Example, Inflow-, Outflow- and Critical Rate Parameters
Sensitivity analysis
Gas production rates & Height water column 60
50
10
0
0 0
5
10
Gas flowrate model
15
20
Time, days Gas flowrate field Length water column
Fig. 13 Field and model gas flowrates and water column height over time
The important properties of a liquid loaded well are: 1. Qms, the metastable flowrate 2. Qc, the critical flowrate 3. Water column height 4. Time to reach the metastable flowrate 5. Drainage time at shut in A sensitivity analysis was carried out to investigate the impact of changing the input parameters on these properties. The values in Table 2 present the base case parameters for an existing well where the B and C outflow factors represent a well with 5” tubing down to 4000 m. and Aw has been determined by matching the model against field data. Table 2 – Base case, Inflow-, Outflow- and Critical Rate Parameters
Pressures field data and model
Ag Aw B C Cst ρg ρw Pfth Fwg Distance between production and re-injection point
40 35 30 Pressure, bara
Table 1 gives the relevant model parameters, where Aw and Fwg have been varied to provide the best match. In this case Aw controls the level of the metastable flowrate and the water gas ratio mainly impacts the time the metastable flowrate is reached. In the model the liquid loading sequence was initiated manually after 2 days.
25 20 15 10 5
10 7.5 2.2 0.015 16 0.8 1000 30 50 150
[bar2/e3m3/d] [bar/m3/d] [-] [bar2/(e3m3/d)2] [e3m3/d/(bar)0.5] [kg/m3] [kg/m3] [bar] [m3/e6 m3] [m]
0 0
5
10
15
20
Time, days Pbh production point model
Pbh field
Pfth
Pfth field
Fig. 14 Field and model pressures over time
The actual and modelled tubing head and bottomhole pressures are presented in Fig. 14.
The following parameters were varied: Ag, Fwg, Pfth, and the distance between the production and re-injection point. Also Aw was varied proportionally to Ag. The critical and metastable rate, stable water column height, time to drain the water column and time to reach the metastable water level were recorded. For each scenario the reservoir pressure is
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chosen such that the well in the liquid loaded regime will initially produce slightly below the critical rate.
300
80
250 200
60
150 40
100 50
20 0
0 0
Flowrate and height water column as a function of inflow resistance factor Ag
400 40 200
20
20
40
60
80
100
Ag, bar2/1000m3/d
Qms, Metastable rate
Qc, Critical rate
Height water column
Fig. 15 Critical rate, metastable rate and water column height for varying Ag
4 3 2 1 0
50
Time to reach metastable flowrate
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60
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Ag, bar2/1000m3/d Time to reach metastable flowrate
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150
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Fwg, m3/mln m3
12 10 8 6 4 2 0
t shut in, days
t, days
Shut in time and liquid loading time
20
Height water column
9 8 7 6 5 4 3 2 1 0
0
0
Qc, Critical rate
Shut in time and liquid loading time
0
0
200
Fig. 17 Critical rate, metastable rate and water column height for varying Fwg
t, days
0
150
t shut in, days
600
60
100
Fwg, m3/mln m3
Water column,m
Qg, x1000m3/d
80
50
Qms, Metastable rate
800
100
Water column, m
Figs. 15 and 16 depict the sensitivity to the gas inflow resistance factor Ag.
100
Qg, x1000m3/d
In this paper only the sensitivity to Ag and Fwg are highlighted. The complete results are given in Dousi 8.
Flowrate and height water column as a function of Fwg
Drainage time at shut in
Fig. 16 Loading time and drainage time at shut-in for varying Ag
Four interesting conclusions can be drawn: • The metastable flowrate increases rapidly for decreasing inflow resistance factor Ag. • The water column grows approximately linearly with Ag. • For low Ag factors the well can load within a period smaller than 5 days, in agreement with field observations. • Shut-in times required to drain the well increase linearly with increasing Ag factor. Figs. 17 and 18 depict the sensitivity to the water gas ratio, Fwg.
Drainage time at shut in
Fig. 18 Loading time and drainage time at shut-in for varying Fwg
Again four interesting conclusions can be drawn: • The metastable flowrate decreases rapidly with increasing water gas ratio. • The water column height increases marginally for increasing water gas ratio. • The time to reach a metastable level decreases rapidly for increasing water gas ratio. • The drainage time at shut-in is relatively insensitive to the water gas ratio. It can be concluded from the sensitivity analysis that wells which produce significant metastable flowrates typically have good inflow performance, a low water gas ratio and/or a large distance between re-injection and production point. Analytical predictions The metastable flowrate and the stabilized water column height can be derived analytically assuming steady state conditions. Metastable flowrate. The metastable flowrate, Qms, is the gas rate at which the rate of co-produced water Qw,prod (or FwgQms) is equal to the amount of re-injected water Qw,inj:
Qw,inj = FwgQms
(9)
Qms and Qw,inj are respectively described by: (Pres,g ) 2 − (P fbh,g ) 2 = Ag Q ms
(10)
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and Pfbh,w − Pres,w = Aw Q w,inj
(11)
Assuming the full column between production and injection point is water filled a relation exists between Pfbh,w and Pfbh,g as follows: P fbh,w = P fbh,g + Z pi G w
(12)
where Zpi is the true vertical distance between the production and injection points and Gw is the hydrostatic gradient of the co-produced water. Further assuming production and injection take place in the same gas reservoir at pressure equilibrium: Pres,w = Pres,g + Z pi G g
(13)
Where Gg is the hydrostatic gas gradient in the reservoir. Then Eq. (11) can be re-written as: Pfbh,g - Pres,g + Z pi (G w − G g ) = Aw Q w,inj
(14)
Given Eq. (9), Eq. (10) and (14) can be solved to calculate Pfbh,g: 1 ⎡ ⎤ ⎞2 ⎥ ⎢⎛ ( Pres,g ) 2 ⎜ ⎟ + ⎢ 1+ ⎥ ⎜ ⎟ M2 ⎥ = M ⎢⎜ 1 − ⎢ 2( Pres,g − Z pi (G w − G g )) ⎟ ⎥ ⎜ ⎟ ⎢⎜ ⎥ ⎟ M ⎠ ⎢⎝ ⎥ ⎣ ⎦
P fbh,g
Note that Eqs. (15) and (17) can be generalised to situations where production and injection take place in different reservoirs with different pressures by replacing Zpi(Gw-Gg) by the pressure difference. The sensitivity analysis performed using the numerical model for Qms and hwc as function of Ag has been repeated using the analytical predictions. The results are identical to the numerical model results presented in Fig. 15. Note that for very low Ag the analytical prediction gives a metastable rate which exceeds the stable rate while the water column height required to re-inject the produced water becomes less than the distance between the production and injection points. Water column height. The above analysis indicates that the metastable rate does not depend on the flowing tubing head pressure. This statement is also supported by the production data in Fig. 6. Obviously for a metastable rate to occur the flowing tubing head pressure must be high enough or the reservoir pressure must be low enough to result in liquid loading. However if liquid loading occurs the flowing tubing head pressure no longer influences the metastable rate. However the effective true vertical height H of the water column that forms above the production point does depend on the flowing tubing head pressure. It is derived by matching the pressure difference between tubing head and flowing bottom hole pressures as follows: 1
(15)
H=
P fbh,g − ( B(P fth ) 2 + C(Q ms ) 2 ) 2
(19)
Gw − G g
The total height of the stabilized water column then becomes: where (16)
2 Fwg Aw
Qms then follows using Eq. (10). For realistic parameters Eq. (15) can be approximated by: Pres,g - P fbh,g ≈
Z pi (G w − G g ) ⎛ Pres,g ⎜1 + ⎜ M ⎝
⎞ ⎟ ⎟ ⎠
True vertical water column height above production point vs flowing tubing head pressure
(17)
Z pi (G w − G g )2 Pres,g ⎛ Pres,g ⎞ ⎟ Ag ⎜⎜1 + M ⎟⎠ ⎝
250 Maximum FTHP for stable flow
200
where (Pres,g – Pfbh,g) is the drawdown pressure corresponding to the metastable flow rate. Also, the metastable rate can be approximated by: Q ms ≈
(20)
Fig. 19 shows how H varies as function of Pfth for the base case parameters in Table 2 where the reservoir pressure is assumed fixed at 54.5 bar.
H, m
M =
h wc = H + Z pi
Ag
Metastable flow regime
150 Maximum CITHP for given reservoir pressure
100 50 0
(18)
20
25
30
35
40
Pfth, bar
Fig. 19 Height above production point versus flowing tubing head pressure, base case parameters
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Four regimes can be distinguished: • Pfth > 36.7 bar: no gas flow possible as hydrostatic head of gas column creates overbalance at production point, • 34.6 bar < Pfth < 36.7 bar: metastable flow is less than indicated in Eq. (18) as there is insufficient drawdown pressure available to produce Qms, accordingly there will be no full water column between production and injection point, • 30 bar < Pfth > 34.6 bar: metastable flow rate as described by Eq. (18), the height of the water column increases as Pfth decreases, and • Pfth < 30 bar: stable flow regime with gas rates above the critical rate, however metastable flow with an increased water column is also possible. See for example Fig. 10 and 11 for the period 3
9
mentioned is that active control should prevent build-up of long columns of water which take longer to drain away. Another reason is that it could reduce the potential impairment caused by re-injecting fresh condensed water into water sensitive formations. Certainly active control will provide a means of managing the available well capacity. The numerical model presented in this paper could be expanded to include reservoir pressure recovery in order to simulate and optimise intermittent well production. Managed metastable production. Metastable production should ideally be considered as an opportunity to maximise gas recovery and to reduce surface water processing and disposal. The model presented in this paper could help mature this opportunity into practical solutions. Conclusions The following conclusions can be drawn from this study: • Production data from mature gas fields clearly show that gas wells can produce at metastable flowrates below the minimum stable or Turner flowrate. • A numerical model has been developed which reproduces the gas-well liquid-loading behaviour observed in the field, including the metastable flowrate. The results of the numerical model have been confirmed by a steady-state analytical solution. • The results of sensitivity analyses show that a significant metastable flowrate can be observed in a well with good inflow performance, a low water gas ratio and a large gas column. • The model can be used to analyse and optimise the control of intermittent gas well production and to mature the active use of metastable gas production.
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SPE 95282
Nomenclature
Ag Aw B C Cst Fwg g Gg Gw H hgc hwc Pfbh Pfth Pres Qc Qg Qms Qw,prod Qw,inj Tfth x Zpi ρg ρw
= Gas inflow resistance factor, bar2/e3m3/d = Water re-injection resistance factor, bar/m3/d = Factor related to head,= Factor related to friction, bar2/(e3m3/d)2 = Constant in simplified Turner Eq., e3m3/d/(bar)0.5 = Water gas ratio, m3/e6m3 = Gravitational constant, 9.81 m/s2 = Hydrostatic gas gradient, bar/m = Hydrostatic gradient of formation water, bar/m = Height water column above the production point, m = Height gas column, m = Height water column, m = Flowing bottomhole pressure, bar = Flowing tubing head pressure, bar = Reservoir pressure, bar = Critical gas flowrate, x1000 m3/d = Gas flowrate, x1000 m3/d = Metastable gas flowrate, x1000 m3/d = Water production flowrate, m3/d = Water injection flowrate, m3/d = Flowing tubing head temperature, °C = Position in well, m = Vertical distance production-injection point, m = Gas density, kg/m3 = Water density, kg/m3
Acknowledgements We express our gratitude to the Nederlandse Aardolie Maatschappij B.V. for their cooperation and permission to publish this material. Special thanks to Chad Wittfeld for supplying the bottom hole pressure data. References 1. 2. 3.
4.
5. 6.
Duggan, J.O., “Estimating flow rates required to keep gas wells unloaded,” J.Petrol.Tech.,Dec 1961, 1173 1176 Oudeman P., “Improved Prediction of Wet-Gas-Well Performance,” Paper SPE 19103, SPE Production Engineering (Aug. 1990) Turner, R. G., Hubbard, M.G., and Dukler, A.E., “Analysis and Pediction of Minimum Flow for the Continuous Removal of Liquids from Gas Wells,” Paper SPE 2198, JPT (Nov. 1969) 1475; Trans., AIME 246 Coleman S.B., Clay H.B., Mccurdy D.G and Norrie H.L., “A New Look at Predicting Gas-Well LoadUp,” Paper SPE 20280, J.Petrol.Tech.,March 1991, 329-333 Lea, JF and Nickens, H.V., “Solving gas-well liquidloading problems,” J.Petrol.Tech., Dec 1961, 1173 – 1176 Guo, B., Galambor, A., Xu, C., “A Systematic Approach to Predicting Liquid Loading in Gas Wells,” Paper SPE 94081, presented at the 2005 SPE Production and Operations Symposium held in Oklahoma City, USA, 17-19 Apr. 2005
7.
8. 9.
Sutton R.P, Cox S.a., Williams E.G., Stolz R.P., Gilbert J.V., “Gas Well Performance at Subcritical Rates,” Paper SPE 80887 presented at the SPE Production and Operations Symposium held in Oklahoma City, Oklahoma, U.S.A., 22-25 March 2003 Dousi, N., “Modelling Liquid Loading and Gaslift for Gas Wells,” M.Sc. Thesis, Delft University of Technology (June 2004), TA/PW/04-05 Cullender, M.H. and Smith, R.V., “Practical Solution of Gas-Flow Equations or Wells and Pipelines with Large Temperature Gradients,” Trans., AIME, (1956) 207
SI Metric Conversion Factors bar x 1.0* bbl x 1.589 873 °F (°F − 32)/1.8 ft x 3.048* ft2 × 9.290 304* ft3 × 2.831 685 lbm x 4.535 924 psi x 6.894 757 *Conversion factor is exact.
E + 05 = Pa E − 01 = m3 = °C E − 01 = m E − 02 = m2 E − 02 = m3 E − 01 = kg E + 00 = kPa
