NORWEGIAN UNIVERSITY UNIVERSITY OF SCIENCE AND AND TECHNOLOGY Faculty of Engineering Science and Technology Department of Petroleum Engineering and Applied Geophysics
Natural Gas TPG 4140 Semester Project
Downhole Gas Compression
Mohammad Ostadi Maya Kusmaya Milad Kazemi Hatami Orkhan Ismayilov Kazeem Adetayo Awolola
Trondheim November 2011
Abstract
In all wells, reservoir pressure declines with the time. Boosting pressure becomes important to acquire high recovery and/ or accelerate production. Downhole Gas Compression (DGC) i s one of the latest technologies for pressure boosting. It has a number of benefits as an artificial lifting system. DGC allows increasing potential production, therefore prolongs the lifetime lif etime of field production. Currently this technology is on on the trial stage and is expected to enable gas extraction from otherwise uneconomic sites. The project summarizes the current status of this technology and shows its application in fields by simulation case studies. Both from literature and our case studies it was established that having a compression system as close to the reservoir as possible boosts the gas production and increases the ultimate gas recovery.
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Abstract
In all wells, reservoir pressure declines with the time. Boosting pressure becomes important to acquire high recovery and/ or accelerate production. Downhole Gas Compression (DGC) i s one of the latest technologies for pressure boosting. It has a number of benefits as an artificial lifting system. DGC allows increasing potential production, therefore prolongs the lifetime lif etime of field production. Currently this technology is on on the trial stage and is expected to enable gas extraction from otherwise uneconomic sites. The project summarizes the current status of this technology and shows its application in fields by simulation case studies. Both from literature and our case studies it was established that having a compression system as close to the reservoir as possible boosts the gas production and increases the ultimate gas recovery.
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List of Contents
Abstract
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1
Introduction ……………… …………………………… …………………………… ………………………….… ………….…..………….. ..………….. 1
2
Gas well production production limitations limitations and challenge challenges……… s……………… …………….… …….…..... ......…… .……
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Artificial lifting systems during gas production …………… …………………………… ……………………. ……. 3
2
3.1
Conventio Conventional nal compressi compression on ……… ………….…… ….…………… ……………… ……………… ……………… ……….. 3
3.2
Subsea Subsea compressi compression on at seabed seabed ……… ……………… ……………… ……………… ……………… ……………. ……. 4
3.3
Downhole Downhole gas compress compression… ion………… ……………… ……………… ……………… ……………… ……………. ……... 4
4
DGC and it’s working principles.................................... principles.......................................................... ......................................... ................... 4
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Downhole Downhole gas compressi compression on design design and specificat specifications ions ……… ……………… ………..... .......... .......… ..…
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6
5.1
Challenges and obstacles................................. obstacles........................................................ .............................................. ....................... 6
5.2
Design Design solutions solutions via advanced advanced engineerin engineering.... g......... .......... .......... .......... .......... .......... .......... .......... .......... ..... 6
Case study ……………… ……………………………… ……………………………… …………………………… ………………….…….. …….…….. 7 6.1
Deliverabi Deliverability lity profile profile of the well ……… ……………… ……………… ……………… ……………… ………….. ….. 9
6.2
DGC application as a solution …………… …………………………… ……………………...........… ……...........…… … 12
6.3
Increasing reservoir recovery by DGC installation …………… …………………...…… ……...…… 12
6.4
Potent Potential ial econom economic ic gain gain …… ………… ………… ………… ………… ………… ………… ………… ……... ....… .……. ….
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Conclusions ……………… ……………………………… ……………………………… ……………………………… ………………………. ………. 14
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Nomenclatures …………… …………………………… ……………………………… …………………………… ……………………… ………… 15
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References ……………… …………………………… …………………………… ……………………………… ………………………….. ………….. 16
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Tables……………………… Tables…………………………………… …………………………… ……………………………… ……………………….. ……….. 17
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Figures………………………… Figures………………………………………… …………………………… …………………….……… ……….…………… …… 18
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Appendice Appendices…… s…………… ……………… ……………… ……………… ……………… ……………… ……………… ……………… ………… … 29 12.1 Natural gas properties equations ……………… ……………………………… ………………..……….… ..……….… 29 12.2 Reservoir Reservoir deliverabi deliverability/in lity/inflow flow performan performance ce ……. ……...... .......... .......... .......... .......... .......... .......... .......
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12.3 Wellbore Wellbore performan performance/tu ce/tubing bing performan performance ce …......... ….............. .......... .......... .......... .......... .........… ....…..
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12.4 Choke performance………………… performance………………………………… ……………………………… ……………………… ……… 32 12.5 Pipeline performance…………………… performance………………………………… …………………………… ………………..…… ..…… 35 List of Tables
Table 6.1: Reservoir conditions ......................................... ................................................................. .............................................. ...................... 17 Table 6.2: Natural gas properties ............................................ ................................................................... ......................................... .................. 17 Table 6.3: Well tubing specifications .............................................. ..................................................................... ................................. .......... 17 Table 6.4: Choke, separator and pipeline data ............................................ ................................................................ .................... 17
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List of Figures
Figure Figure 2.1: Production Production profile of field life cycle……… cycle……………… ……………… ……………… …………... …......… ...… 18 Figure 3.1: Different types of artificial lifting for oil extraction..................................... extraction........................................ ... 18 Figure 3.2: Downhole hydraulic pump.................................... pump.......................................................... .......................................... .................... 19 Figure Figure 3.3: Water Water injection injection back to reservoir… reservoir………… ……………… ……………… ……………… …………... ….......… ....… 19 Figure Figure 3.4: Offshore Offshore alternative alternative gas compressi compression…… on…………… ……………… ……………… …………... ….......… ....….. 20 Figure 3.5: Subsea processing projects installed or announced……................ announced……..............................… ..............… 20 Figure Figure 3.6: Åsgard Åsgard subsea subsea compressi compression on layout…… layout…………… ……………… ……………… ……………… ………....… ....… 20 Figure Figure 3.7: 3.7: Åsgard Åsgard subse subseaa compr compressio essionn main main equipment equipments…… s…………… ……………… ……………… ………… … 21 Figure 3.8: Siemens PG’s Eco II centrifugal compressor…………………… compressor…………………………..…… ……..…… 21 Figure 3.9: Downhole compressor module………………………… module……………………………………… ………………….… …….… 22 Figure Figure 4.1: 4.1: Potential Potential yield improveme improvements nts from utilizing utilizing downhole downhole gas compress compression.. ion...... .... 22 Figure 5.1: Possible application range of DGC......................................... DGC................................................................ ........................... 22 Figure 6.1: Screenshot of HYSYS model……………………… model……………………………………… …………………….….. …….….. 23 Figure 6.2: System performance without DGC ……………… ……………………………… ……………………..…… ……..…… 24 Figure Figure 6.3: Velocity Velocity profiles profiles inside inside the tube at the different different wellhead wellhead pressures… pressures……… ……
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Figure 6.4: Pressure loss profiles inside inside the the tube at the different wellhead wellhead pressures…… 25 Figure 6.5: Gas velocity profile inside the tube at various various locations of DGC ................... 25 Figure 6.6: The ability DGC to increase the tubing transport capacity……………..…… capacity……………..…… 26 Figure 6.7: The performance performance in the first two year with with and without DGC ……………… ……………… 26 Figure 6.8: The performance performance with and and without without DGC at WHFP WHFP 195 195 psia psia ……………..… ……………..… 27 Figure 6.9: The performance with and and without without DGC at WHFP WHFP 195 195 psia psia (5 year) ……… ……… 27 Figure Figure 6.10: Well Producti Production on profile profile with and without without DGC at WHFP WHFP 195 psia…… psia………… …… 28
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1 Introduction One of the main tasks of the upstream gas industry is the selection of an optimum artificial lifting system to enhance gas production. Dynamic behavior of well flow characteristics makes this task rather challenging. It has been long recognized by all parties in oil and gas sectors that pressure boosting in the gas field located as close as possible to the reservoir has the most advantage. It leads to increase the well deliverability and recovery beyond that is achieved by using conventional gas compression system alone. Several efforts in the development of this kind of artificial lifting technology has been carried out. The most recent is downhole gas compression system. There are limited players that involved in technology development of the downhole gas compression. This is mainly because the design of this compressor demands advanced technology in many aspects. And also, natural gas fields are still vast and widely dispersed geographically. Most of oil and gas operators prefer to invest for new gas wells instead of prolonging production and increase the ultimate recovery in wells. Corac Group Plc is one of the pioneers in designing and testing of this type of compressors. Together with Eni, ConocoPhillips and Repsol-YPF, they made a joint industrial program (JIP) to carry out further technology development including field trial in an operated mature asset located in Southern Italy (Di Tulio, 2009). This technology is still at development phase. The joint industrial program has completed design, equipment construction and pilot scale test in a replicating downhole conditions (SPE 116406). However, commercialization stages of this technology are expected to come in the near future. The increasing demand for natural gas forces oil and gas operators to boost deliverability of their gas wells and extract available gas as much as possible. Downhole Gas Compression (DGC) offers unique opportunity of extracting available gas from previously unextractable reserves. DGC increases both the production and recovery factors of gas wells. DGC can be utilized during various phases of the well’s production life in order to overcome the increased reservoir drawdown pressure and to extend the life time of the well. The main economic advantage is gained when downhole compression is implemented during the “plateau” production period. This report tries to give the reader an overall introduction to DGC technology. It talks about gas well production limitations, design challenges, and provide practical information through simulated case studies.
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2 Gas Well Production Limitations and Challenges Production life of oil and gas field can be divided into three main stages, typically they are build up, plateau and decline. In order to demonstrate these stages special charts are used (Figure 2.1). Each part illustrates one of the production stages. The most important issue at exploitation operation is to keep production level high at each stage. To achieve desired deliverability from a particular field; the right flow rate of gas is needed. Indeed for keeping flow rate of gas, pressure is required. This required pressure is called Reservoir Pressure. The amount of reservoir pressure is a key parameter for deliverability of gas and should be enough to push the gas up to the surface. Each reservoir has a unique pressure. This pressure decreases along production period (Jahn 1998). The flowing bottom-hole pressure (FBHP) is another parameter for deliverability of gas. FBHP is the pressure at the bottom hole of the well. In order to achieve maximum production FBHP should be kept as low as possible in production period. There are several constrains to reach this target. At the primary stages of extraction the limitations include: fines migration, wear due to erosion, surface facility and gathering system capacity. By reduction in FBHP, operators should utilize some methods to stabilize the pressure. However a main problem to have a low FBHP is critical gas velocity particularly in tubing constrained gas wells. Critical velocity is the maximum velocity to avoid erosion effect in a specific tubing diameter. When gas is sucked from wellhead, the gas density inside the tubing is low due to compressibility of the gas at constant flow rate. At lower gas density gas velocity is higher, that may exceed the critical limit. Tubing and well can be damaged because of the erosion at this condition. Pressure losses increase at higher gas velocity. This condition is not expected. In order to avoid this problem production rate should be decreased (Tullio 2009). Liquid formation during the field life is another challenge. By reduction in reservoir pressure after some years, for the same bottom hole and wellhead conditions, the velocity of gas which goes through the well starts to decrease. As the pressure of the reservoir decreases it reaches to a point that liquid forms in the reservoir. At low flow rates, the gas does not have the capacity to transport liquid droplets to the surface. The result is liquid accumulation in the reservoir. It reaches to a point that makes reservoir unextractable. Therefore artificial lifting by boosting pressure becomes very important. There are several artificial lifting methods such as subsea compression and downhole gas compression. All those methods are discussed in next section. 2
3 Artificial lifting systems during gas production Artificial lift method applies when the pressure of gas reservoir begin to reduce. There are a variety of techniques to offset the reduction of flow of gas due to declining of the reservoir pressure. Boosting pressure is more often used in oil wells rather than gas wells. Several methods that are used for boosting pressure in oil production are beam Pump, gas lift, hydraulic pumping, electric submersible pump (Figure 3.1) (www.pdhengineer.com 2011) , downhole hydraulic pump (Figure 3.2) and water injection (Figure 3.3) (Peter O. Oyewole 2008) and (www.rigzone.com 2011). These methods are developed during previous years because of inherently less pressure in oil reservoir. Since oil has a better relative value and price among other energy resources, investment on developing of these ways is reasonable (Peter O. Oyewole 2008). By increasing demand for natural gas as a clean source of energy, gas wells began to develop. Over time, the pressure of the well decreases. In order to boost pressure for gas extraction, some techniques are used in latest years. Some of main techniques are briefly described below. 3.1 Conventional Compression
Conventional Compression is used both in onshore and offshore fields. In onshore fields it is easier to compress gas than in offshore. Conventional compressors are usually used at wellhead in onshore gas fields to maintain the required pressure. In offshore, especially in deep water gas fields, different techniques are available to stabilize pressure during the production (Figure 3.4). One way is to use conventional compressors in fixed platforms (Sirevaag 2009). Floating production system is the second alternative and utilizes the same compressors as fixed platforms. In both cases, compressors are installed at sea level and far from wellhead and this mean more powerful compressors and more demand for energy. Erosion in tubing as mentioned before could occur by utilizing of this type. 3.2 Subsea compression at seabed
Subsea compression system is other alternative with substantial advantages. Power requirement for the compressor becomes less when the compressor is installed near the wellhead. Because of this benefit and also development of subsea facilities suppliers; oil and gas industry are turning into subsea compression systems (Figure 3.5). Currently subsea compression is widely used and being developed by Statoil and its partners in some fields such as Gullfaks, Ormen Lange, Åsgard and Snøhvit (Figure 3.6 and 3.7) (Sirevaag 2009) and (Bass R.M. 2006). 3
Utilization of commercial and standard available types of compressors in subsea modules is another interesting issue. For instance, Siemens PG’s Eco II compact compressor (Figure 3.8) is used in subsea processing facilities at Statoil’s Tordis field in the Norwegian sector. Subsea gas compressors are cost-effective and save 30-40% of energy compared to their platform-based counterparts. In addition subsea gas compressors are providing the possibility of development of stranded gas fields which are far from infrastructures (www.rigzone.com 2011). In spite of considerable advantages of subsea compression, this kind of new technology has challenges ahead. Some of the challenges are high relative investment and service cost, need for special facilities and material to run at seabed, and being economically effective just for large fields (Bass R.M. 2006). 3.3 Downhole gas compression
Downhole gas compressor (DGC) (Figure 3.9) is the recent alternative to deal with the problem of pressure decline in gas reservoirs. This type of compressor is not in commercial use and is just in testing stage. More details about DGC are mentioned in the following section (www.ior.senergyltd.com 2011). 4 DGC and it’s working principles DGC is a new artificial lifting technology developed particularly to overcome the common erosional problem in natural gas wells. This new technology is expected to be a driver to boost the gas production rate and increase the ultimate gas recovery. As explained earlier, when a gas reservoir pressure declines, it reduces to the extent that it is insufficient to overcome the friction in the production tubing of the well. In this condition, the well production is down and it may no longer be economical to be extracted. In gas fields, central gas compression and/or wellhead compression are generally utilized to extend productive life. However, the conventional compression system which is installed at the well head has a limitation. When the pressure losses are too much in the production tubing, the compressor attempts to draw on a vacuum, at which point flow stops. DGC offers a good solution when the most significant ‘bottleneck’ to higher productivity is below ground (in the wellbore/tubing). DGC is purely designed to increase well potential and ultimate recovery which are the functions of both factors –reservoir drawdown and tubing friction. DGC compress the gas inside the tubing just after the gas leaves the bottom hole. Thus, it increases the gas density along the tubing and decreases the gas velocity for the same mass flow rate of the gas. 4
This reduces pressure losses due to friction and also reduces erosion problem inside the well tubing. A modest increase in tubing pressure obviously results in an increase in tubing transport capacity. Therefore DGC is able to deliver more gas than is produced using conventional central gas compression alone. Compression close to the source reservoir is more effective in lowering the field abandonment pressure and hence increasing ultimate recovery. DGC technology uses a compressor placed as near as possible to the point where gas is flowing from reservoir into the wellbore. By placing DGC near the bottom of the well, it sucks more gas from the bottom hole and reduces the FBHP. The lower FBHP results in more drawdown rate of gas from reservoir to bottom hole which itself accelerates gas production. By lowering FBHP, DGC decreases the reservoir abandonment pressure thus maximizes the recoverable reserves from the well reservoir (Liley 2004) The advantages of DGC to increase gas production and ultimate recovery are illustrated in Figure 4.1. This figure shows a graph of well flow potential (in thousand sm3/day unit) plotted against reservoir pressure for central compression, well head gas compression (WGC) and downhole gas compression, in this graph mentioned as DHGC (blue, yellow and green lines respectively). The theoretical absolute open flow (AOF) potential of the well which is our objective is shown in the black line. The figure clearly shows that DGC at the same reservoir pressure accelerates gas production particularly at higher reservoir pressures where the production driving force is big. And also, since the DGC can operate at lower FBHP than other compression technologies, it significantly increases the ultimate recovery. Central gas compression and well head gas compression systems are placed at a considerable distance from the reservoir. Thus, both compression technologies are facing the suction tubing high pressure losses due to friction and erosional problem which hinders the production acceleration . As the reservoir pressure declines a further problem is the liquid loading process. It occurs when the upward gas velocity falls below a critical value required for gas to move liquid droplets up to the surface. DGC solves this problem by extending the period of liquid droplet transport at the higher wellhead flowing pressure. Based on a comprehensive feasibility study done by Liley et.al. (2009), DGC is estimated to increase the production gain by 32 – 41%. It represents additional recovery of 14 – 20 Bscf per well over 5 years operation. All in all, DGC system brings the opportunity to develop stranded and sub-economic gas fields. 5
5 Downhole gas compression design and specifications 5.1 Challenges and obstacles
As you may imagine, downhole conditions can get very harsh. For every instrument to withstand and operate in these conditions there are some specifications. It requires innovative technologies to overcome the physical barriers downhole. One of the challenges is to provide 250-500 kW of compressor power 2-3 km below ground. But it is not that easy, the compressor should operate within the size of the tubing which is typically 7-9 inches. The harsh conditions are typically 20-60 bara in pressure and in excess of 100 °C in temperature (plc 2011). The second challenge is to design a high speed motor to drive compressor. To have high flow rates the compressor requires high speed motor. Within 7-inch-diameter tubing, compressor speed is in excess of 60,000 rpm (Reed 2009). The third challenge is the lubrication system. Conventional lubrication systems can not work in this environment. Gas flow, entrained contaminants, temperature and rubbing speeds of the seal surfaces degrade conventional lubrication system. The last challenge is the delivery of electricity to the unit downhole. The motors require alternating current (AC) power supply. Supplying AC current from the surface results in significant losses due to the long distance. Therefore there are two challenges to face with the electrical part: first, a lot of electronic equipment should be packed in a limited size, and second, there is a need to cool these electrical parts (Reed 2009). 5.2 Design solutions via advanced engineering
As mentioned before, operating downhole is full of challenges. But if we look at the bright side, these challenges enhance technology. And if these challenges are met, a higher economic benefit will be obtained. To improve production, the gas flow requires a moderate increase in pressure. Therefore centrifugal or axial compressors would be an ideal option, because they are suitable for high flow rates and moderate pressure ratios. The compressor system comprises of two to six independent compressor units arranged in series and mounted in a standard length of production tubing (Reed 2009). 6
To overcome the problem of high rotational speed, Corac Group Plc. has developed and patented high speed permanent magnet motor. It runs at 45,000 -60,000 rpm. The compressor is driven by motor on single shaft and there are no gear boxes, couplings or seals (plc 2011). The motor is supported on gas bearings that do not require oil lube. Instead well gas acts as lubricant. This lubrication system offers a very low-friction support system. The gas bearings ensure no wearing surfaces during operation. There are no liquid cooling circuits. Instead, the motor is cooled by the well gas f low around the outside of the motor. But there is a disadvantage to this, the performance of the compressor depends on the gas temperature. Currently, the technology is capable of operating with an inlet gas temperature of 105 °C (Reed 2009). The electricity is transmitted downhole as a direct current instead of alternating current. This is to minimize transmission losses. As the consequences, the whole motor drive and inverter are placed downhole. Due to space limitation, it is difficult to have separate cooling system for electronic equipment inside the tubing. Thus, the gas flow is used to cool it. Currently, the technology is available for casing diameters of 5.5 inches or above. It has been demonstrated that it can operate in wells with high liquid-gas ratios (greater than 27% by mass) with inlet temperature of 105 °C (Reed 2009). The range of applications of DGC technology related to the overall tubing diameter, flow rate, maximum inlet gas temperature and pressure ratio given by Corac Group Plc is shown in Figure 5.1. The power requirement of the compressor depends on the gas flow rate at same casing diameter. The higher the flow rate, the higher the power requirement. In our case study in the next chapter the flow rate is not in the range of this figure (it is lower). 6 Case study The objective of this case study is to evaluate the advantages of the DGC system by making comparison between the production profiles with and without DGC system over the depletion period. Commercial HYSYS simulator and Microsoft Excel are utilized to analyze and calculate the followings: 1- The deliverability profile of the well, 2- DGC compression work required to maintain the production 3- The optimum depth to locate DGC inside the well tubing. 7
Comparison between cost and energy requirements of DGC to that of conventional compression system is also briefly discussed. For the case study, the conditions of the well follow the requirements mentioned by Di Tulio et.al. (2009) which are: 1. Wet or dry gas well with minimum 178 mm (7 “) casing outer diameter, single completion string, medium to high productivity, wellhead flowing pressure (WHFP) at or below 20 bars, flowing bottom hole temperature (FBHT) less than 110 oC, and low liquid production. 2. Electricity available on well site 3. Production benefits are achievable by: increasing well drawdown, stabilizing well bore flow regime, integrating the DGC system with the conventional central/surface compression system. 4. Increase ultimate recovery by increasing the tubing unloading capacity and lowering the abandonment pressure. The reservoir conditions for the case study are described in Table 6.1. This is an artificial well, not a real one, in which data are taken from several sources with different assumptions. To evaluate the DGC application and advantages in depleted wells, the reservoir conditions are assumed to be 27.3 bar in pressure and 74 oC in temperature (Tullio 2009). Meanwhile, the C-constant and nexponent in backpressure Inflow Performance Relations (IPR) are assumed to be 0.09 Mcf/d-psi 2n and 0.86 respectively. In actual fields these numbers are taken from the well tests. The gas properties and conditions are described in Table 6.2. In the case study the gas has 0.56 and 1.28 of specific gravity (γg) and specific heat ratio (k), respectively. The specific gravity value is taken from Di Tulio et. al. (2009) in which candidate well selection criteria is described. There was no information about the gas composition in that article. However, the gas composition for this study is assumed to be 99% methane and 1% ethane to get the same specific gravity of 0.56. For the specific heat ratio (k), 1.28 is typical for natural gas (Guo 2007). The same well tubing dimensions as Di Tulio et.al. used for their study in 2009 is selected. All these dimensions data are shown in Table 6.3. In addition to this study, the choke and pipeline data are assumed and shown in the Table 6.4. All those parameters are the basis for calculating the deliverability of the well, calculating the DGC power required and optimum depth of DGC location inside the tubing.
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6.1 Deliverability Profile of the Well
After some years in operation, the gas well production rate is reduced. The production is maintained by installing conventional compression system at the downstream of the separator to reduce the surface pressure. HYSYS simulated model representing production line from the reservoir to the conventional compression system is shown in Figure 6.1. The reservoir conditions, the gas properties and compositions as explained earlier are inputs of the simulation. For natural flow case (without DGC), a pipeline module in HYSYS is used to represent the tube inside the well, with the input data taken from Table 6.3. For DGC case, a DGC unit is modeled as a compressor and is located in between of the two pipe segments. Each of the pipe segments represents the tubes at lower and upper parts of the compressor. Pipeline units, a valve, separator and conventional compressor are added at the downstream. The simulations are done in steady state conditions. Inflow and outflow performance and DGC compression works are determined by the simulation. HYSYS simulator used is a black-box calculation tool. To find out more about the calculations involved in the simulation, all equations and approaches (Guo 2007) to determine the inflow and outflow performance curves are described in Appendix 1. The Microsoft Excel is used to apply these equations and approaches. The calculations obtained from HYSYS simulation and the Excel show small deviations. Several equations used are explained below to show how simulator calculates the inflow and outflow performance. Inflow performance relationship of a well is a relationship between its producing bottom-hole pressures and its corresponding production rates under a given reservoir condition. It indicates the producing characteristics of a well. Its results are used in determining the economics of producing a well. Meanwhile the outflow performance relationship is a mathematical tool used in production engineering. It helps to assess the performance of the completion string by plotting the surface production rate against the flowing bottom hole pressure (FBHP). The fluid composition and behavior of the fluid phases affects the shape of the curve. The bottom hole of the well is selected for the solution node in this study. Flowing bottom hole pressure (FBHP) is calculated by the following equation: q C ( P 2 P 2 wf )
n
Where q is gas flow rate (Mscfd), P is reservoir pressure and Pwf is FBHP (both in psia). Meanwhile, the C-constant and n-exponent are backpressure Inflow Performance Relations (IPR) constants. Correlation line resulted from this equation is called inflow performance. 9
Since the bottom hole of the well is selected as node, the outflow performance is calculated starting from the separator system through the long pipeline, choke (valve), and well tubing back to the bottom hole point. The separator pressure is maintained constant at allowable operating pressure of the conventional compressor. Pressure, flow rate and pipeline dimensions are calculated by this equation: T b P 21 P 2 2 2.5 Q 77.54 D P GT LZf f b
Where the main variables are: Q for flow rate, P2 for separator pressure which is maintained at constant value, D is pipe diameter, f is friction losses along the pipe, L is the length of pipe and Z is the average compressibility of the gas. Thus, for a certain flow rate, pressure at upstream of the pipe (P1) can be determined. After calculating P1, pressure in the upstream of the choke/valve at the well head is determined by the following equations: If the flow in the valve is at sonic condition: Q sc 879C D Apup
2 k k 11 ( )( ) g Tup k 1 k
While, if the flow is at sub sonic condition, then this equation should be applied: Pdn 2 P dn k 1 q sc 1.248CD A2 Pup ( ) k ( ) k , (k 1) gTup Pup Pup k
Where, CD is choke characteristic constant, A is the choke nozzle area, and k is the specific heat ratio. Pdn and Pup are pressures at downstream and upstream of the choke. After having pressure at upstream of the choke (the same as well head pressure, P hf ), final step to determine outflow performance is to calculate bottom hole pressure by this equation: 6.67 104 Exp (s ) 1 f M q 2 z 2T 2 P wf Exp( s ) P hf d 5i cos 0.0375 g L cos s 2
2
zT
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This tubing string correlation is called Average Temperature and Compressibility Factor (TZ) Method. It is in US field units. Correlation line between FBHP (Pwf ) and flow rate (q) resulted from this equation is called as outflow performance. For more detailed equations and units used in this case study see Appendix 1. Thus, well deliverability is then determined by the intersection of the inflow and the outflow (tubing) performance curves. The future well deliverability (or minimum FBHP) over the depletion is also determined by the intersection of both curves. The HYSYS simulation result for the well deliverability projection is shown in Figure 6.2. In the first year, the wellhead operates at about 247 psia to produce 1100 Mscfd of gas. This is resulted from in intersection of IPR 1 and NF 247 lines in the figure. But in the second year, the reservoir pressure decrease to 365 psia and the inflow performance curve changes to IPR 2. The expected production rate cannot be achieved as in previous year with the same well head pressure of 247 psia. To maintain the same or even higher rate from the previous year, the well head pressure should be decreased further. In this case the well head pressure should be at 195 psia. The production rate can be increased to 1600 Mscfd by lowering the well head pressure to 131 psia. It is assumed that the system allows the wellhead pressure to go down to a minimum of 131 psia limited by operational condition of conventional compression system at the downstream facility. Excessive gas velocity in the upper part of the tubing is a problem when low wellhead flowing pressure is required for the optimal gas production (Tullio 2009) .This leads to erosion corrosion problems inside the tubing. One way to avoid erosion is raising the wellhead pressure but it decreases the production rate and increases the un-exploited reservoir drawdown. Figure 6.3 is HYSYS simulation result to show the impact of the well head pressure adjustment (to boost the well deliverability) to the velocity profile inside the tube. Three well head pressures used are 247 psia, 195 psia and 131 psia. The lower well head pressure, the more production rate, but at the same time, the higher velocity inside the tube. The possibility of having noise and erosion problems inside the tubing and pipeline rises as the gas flow velocity exceeds 60 ft/s [API RP 14E, 1991]. This is the case when the well is operated at lower pressure. Figure 6.4 shows higher pressure losses for lower the well head pressures due to higher flow velocity. Since the energy efficiency is a key figure in oil and gas industry, the lower well head pressure might not be economical to be applied.
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6.2 DGC application as a solution
Installing new conventional compressor at the surface to suck more gas from the well would not be an option when we have noise, erosion and high velocity problems at the wellhead. For this condition, the DGC system appears to be a good solution. By placing the DGC as close as possible to bottom hole of the well, the desired production rate can be maintained without causing any erosion problem inside the tubing. Figure 6.5 is HYSYS simulation result for optimum DGC location. The results show that the lowest gas velocity in the tubing occur when the DGC is placed nearly at the bottom hole of the well (in this case at the depth of 1,900 – 2,000 m, the well depth is about 2,358 m). The gas velocity increases as the DGC is placed nearer to the well head. The DGC increases the density of gas inside the tubing (at its discharge) and increases the wellhead flowing pressure. At the same time, DGC is also decreasing the flowing bottom hole pressure that results in higher drawdown of the gas from the reservoir. It enables a greater quantity of gas to be delivered to the processing facilities without suffering from erosion and potential energy losses (pressure losses). The DGC ability to increase the tubing transport capacity is shown in Figure 6.6. With a particular inflow performance, DGC delivers more gas compared to natural flow sucked by conventional compressor at same well head pressure. This unique DGC ability can be used to increase and/or maintain the deliverability of the depleted well. DGC effectively introduce an energy required by gas to flow at the desired flow rate. As common in other wells, the source of energy will be electrical power. The electrical power required at higher gas rate will determine the compressor power to install (Tullio 2009). If the well is operated at lower gas rate, lower compression power for DGC is required. Therefore it i s concluded that the DGC can be a solution to increase and/or maintain the deliverability rate of the depleted well without causing erosion problem in the well tubing. 6.3 Increasing Reservoir Recovery by DGC Installation
Abandonment reservoir pressure with and without the DGC installation will be different. Without DGC, the wellhead and bottom hole flowing pressures cannot be reduced further to increase the production. It is due to the erosion problems and limitations in operational range of the compressor at the downstream. Therefore the abandonment reservoir pressure would be higher.
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Inflow and outflow performance curves with and without DGC resulted from HYSYS simulation are compared in Figures 6.7, 6.8 and 6.9 during 5 years of depletion period. The well head is set at fixed pressure of 195 psia to have sufficient operational margin for the conventional compressor at the surface. DGC driver unit which is installed inside the well is supplied by 15 kW of electrical power. Based on inflow performance curves, the yearly gas production with and without DGC can be calculated and compared. This result is shown in Figure 6.10. From this Figure, it is revealed that DGC increases the reservoir recovery to an average of 70%, decreases the abandonment pressure from 223 psia to 132 psia, and prolongs the well production life. The minimum bottom hole flowing pressure can be further reduced to 3 bars (43.5 psia) according to the operational limitations set by (Tullio 2009). 6.4 Potential economic gain
It is rather difficult to estimate the exact economic gain of the DGC technology. Installation cost for a single DGC unit has not been established so far, since it is in its testing stage and has not been commercially implemented. However, the potential economic gain seems very attractive since this technology brings the opportunity to increase the production and reservoir recovery. From Figure 6.10, it can be seen that the well production increase by 730 MMscf in 5 years of DGC operation. This increase of production is equivalent to 130,076 B.o.e. DGC has an additional operating cost for the power consumption. Power consumed by a 15 kWDGC is about 1.2 MMBtu/day. This cost in 5 years operation is 26,280 USD at assumed 12 USD/mmbtu of gas price and it is about 20 cent USD/B.o.e of the gas produced. Di Tulio et.al. (2009) claims that DGC is still economically feasible by operational cost of 50 cent USD/B.o.e. As mentioned earlier, this additional operating cost does not have a significant impact on the revenue from the produced gas, considering the vast potential revenue remaining in the well. Careful assessment of gas production, gas price and operating expenditure should be made before implementing DGC in a gas well. Apart from the potential economic gain, DGC will bring bright future to the upstream gas industry by providing it with more gas to process.
13
7 Conclusions 1. The challenge at the end of the production life is to create the lowest achievable flowing bottom-hole pressure in order to improve the wells unloading capacity. 2. Several observations can be drawn from the case study using HYSYS simulation: - DGC appears to be a potential candidate as a means to increase or maintain the
deliverability rate of the depleted well without causing erosion problem in the well tubing. - DGC placed as close as possible to the bottom hole of the well gives optimum result in
terms of lower gas velocity and pressure drop inside the well tubing. The gas velocity and pressure drop increases as the DGC is placed nearer to the well head. - Installing DGC into the well tubing decreases the abandonment pressure and increases
ultimate reservoir recovery. - Installation of DGC adds an additional operating cost. However, it is insignificant
compared to the potential revenue obtained. 3. DGC will bring bright future to the upstream gas industry by providing it with more gas to process.
14
8 Nomenclatures NF
= Natural Flowing
Boe
= Barrel oil equivalent
DGC = Downhole Gas Compressor or Compression FBHP = Flowing Bottom Hole Pressure HP
= Horse Power or DGC shaft power
IPR
= Inflow Performance Relation
KW
= Kilo Watt
P
= Pressure
T
= Temperature
WHFP = Wellhead Flowing Pressure JIP
= joint industrial program
15
9 References: 1.
2. 3. 4. 5.
6.
7. 8.
9. 10. 11. 12.
13. 14. 15.
16. 17. 18.
Bass R.M. , S. I. E. P. (2006). Subsea Processing and Boosting-Technical Challenges and Opportunities. Offshore Technology Conference. Houston, Texas, Offshore Technology Conference Guðmundsson, J. S. (2011). NATURAL GAS PRODUCTION ENGINEERING. Guo, B. L., W.C.; Ghalambor, A. (2007). Petroleum Production Engineering, A ComputerAssisted Approach, Elseiver Science & Technology Books. Jahn, F., COOK, M. and GRAHAM, M. (1998). Hydrocarbon Exploration and Production, ELSEVIER. James F. Lea, P. T. L. a. H. W. W., Texas Tech University (2010) "PRODUCTION TECHNOLOGY, What’s new in artificial lift,." Introducing developments in natural gas well dewatering. Liley, J. E. N., Corac Group Plc, Verbeek, P. H. J. , Shell E&P BV (2004). Wellbore pressure boosting enhances recovery from natural gas wells. Offshore technology conference. Houston, Texas, U.S.A. Nelson, P. (2011) "Artificial lift systems benefiting by new technology." Peter O. Oyewole, S., BP, and James F. Lea, SPE, PL Tech LLC (2008). Artificial-Lift Selection Strategy for the Life of a Gas Well With Some Liquid Production. SPE Annual Technical Conference and Exhibition. Denver, Colorado, USA, Society of Petroleum Engineers plc, C. G. (2011). Downhole Gas Compression. Reed, J. (2009) "Downhole Gas Compression – A New Artificial Lift Technology for Gas Wells." 69. Sirevaag, R. B. (2009). Subsea Compression - from idea to reality? Tullio, M. T. D., Fornasari, S. , Ravaglia D. , Eni S.p.A. E&P Division, Bernatt N. , Liley J.E.N. , Corac Group plc (2009). Downhole Gas Compression: World's first installation of a new Artificial Lifting System for gas wells. EUROPEC/EAGE Conference and Exhibition, 8-11 June 2009. Amsterdam, The Netherlands, Society of Petroleum Engineers : 8-11. www.dukeswoodoilmuseum.co.uk . (2011). "Water injection well." from http://empedia.info/images/resource/698/large.jpg. www.ior.senergyltd.com. (2011). "Downhole Cas Compressor." from www.ior.senergyltd.com/issue13/research-development/smes/corac/. www.offshore-mag.com. (2011). "Subsea compression opens options for stranded deepwater gas." from http://www.pennenergy.com/index/petroleum/display/253470/articles/offshore/volume66/issue-4/norway/subsea-compression-opens-options-for-stranded-deepwater-gas.html. www.pdhengineer.com. (2011). "Gas Pipeline Hydraulics." from http://www.pdhengineer.com/pages/O-5001.htm. www.rigzone.com (2011) "How Does Artificial Lift Work?". www.rigzone.com. (2011). "Statoil: Subsea Compression Boosts Gas." from http://www.rigzone.com/news/article.asp?a_id=108151. 16
10 Tables: Table 6.1: Reservoir conditions (Tullio 2009) Properties
Unit
Value
Reservoir pressure Bottom hole temperature C-constant in back pressure IPR model n-exponent in backpressure IPR model
bar o C Mcf/d-psi2n
27.3 74 0.09 0.86
Table 6.2: Natural gas properties (Tullio 2009) Properties
Gas specific gravity (γg) Gas specific heat ratio (k) Pseudocritical pressure (Pc) Pseudocritical temperature (Tc)
Unit
Value
Bar o C
0.56 1.28 46.4 -80.93
Table 6.3: Well tubing specifications (Tullio 2009) Properties
Tubing inside diameter (D) Tubing absolute roughness ( ε) Tubing relative roughness (ε/D) Measured depth at tubing shoe (L) Inclination angle (Ѳ)
Unit
Value
In In
2.441 0.0003 0.0001229 2,358.85 0
m Degrees
Table 6.4: Choke, separator and pipeline data Properties
Unit
Value
In In in2
10 2 3.142
Bar o C In mile In Bar o C
9 27 10 1000 0.0006 1 27
Choke data
Upstream pipe diameter Choke diameter Choke cross-sectional area Separator & pipeline data
Separator pressure Separator temperature Pipeline diameter Pipeline length Absolute internal pipe roughness Base pressure Base temperature 17
11 Figures:
Figure 2.1: Production Profile of Field Life cycle (Guðmundsson 2011), (Jahn 1998)
Figure 3.1: Different types of artificial lifting for oil extraction. (Nelson 2011)
18
Figure 3.2: Downhole hydraulic pump (James F. Lea 2010)
Figure 3.3: Water injection back to reservoir (www.dukeswoodoilmuseum.co.uk 2011)
19
Figure 3.4: Offshore alternative gas compression (Sirevaag 2009)
Figure 3.5: Subsea processing projects installed or announced (Bass R.M. 2006)
Figure 3.6: Åsgard subsea compression layout (Sirevaag 2009)
20
Figure 3.7: Åsgard subsea compression main equipments (Sirevaag 2009)
Figure 3.8: Siemens PG's Eco II centrifugal compressor. (www.offshore-mag.com 2011)
21
Figure 3.9: Downhole compressor module (www.ior.senergyltd.com 2011)
Figure 4.1: Potential yield improvements from utilizing downhole gas compression
(www.ior.senergyltd.com 2011)
Figure 5.1: Possible application range of DGC (Reed 2009)
22
Figure 6.1: Screenshot of HYSYS model used for representing the reservoir to the conventional compression system
23
System Performance at Bottom Hole 500 450 400 350 a i 300 s p , 250 f w200 P 150 100 50 0 0
IPR 1
500
1000
IPR 2
1500 2000 qsc, Mscf/d NF 247
NF 195
2500
3000
NF 131
Figure 6.2: System performance without DGC (IPR = Inflow Performance Relation; the number
refer to year, NF = Outflow performance without DGC; the numbers refer to WHFP values, psia) Gas Veloc ity Profil e Inside the Tube
System Performance at Bottom Hole 500 450 400 350 a i 300 s p , 250 f w200 P 150 100 50 0 0
500
IPR 1
1000
IPR 2
1500 2000 qsc, Mscf/d NF 247
2500
NF 195
3000
NF 131
Figure 6.2: System performance without DGC (IPR = Inflow Performance Relation; the number
refer to year, NF = Outflow performance without DGC; the numbers refer to WHFP values, psia) Gas Veloc ity Profil e Inside the Tube 70 60 s / t f 50 , y t i 40 c o l e30 V s a20 G
10 0 0
500
1000
NF 131
1500 2000 qsc, Mscf/d NF 195
2500
3000
NF 247
Figure 6.3: Velocity profiles inside the tube at the different wellhead pressures (NF = Outflow
performance without DGC; the numbers refer to WHFP values, psia)
24
Pressure Loss es Inside the Tube 200 180 a160 i s p140 , s s120 o l 100 e r u 80 s s 60 e r P 40 20 0 0
500
1000
NF 131
1500 2000 qsc, Mscf/d NF 195
2500
3000
NF 247
Figure 6.4: Pressure loss profiles inside the tube at the different wellhead pressures
(NF = Outflow performance without DGC; the numbers refer to WHFP values, psia)
Well depth (m)
Figure 6.5: Gas velocity profile inside the tube at various locations of DGC from the wellhead
25
Increasing Tubin g Capacit y by DGC 400 350 300 a250 i s p , 200 f w P150
100 50 0 0
500
1000
1500 2000 qsc, Mscfd
DGC 131
NF 131
2500
3000
IPR 1
Figure 6.6: The ability DGC to increase the tubing transport capacity (IPR = Inflow
Performance Relation; the number refer to year, NF = Outflow performance without DGC; the numbers refer to WHFP values, psia) Inflow Performance Curve 400 350 300 a250 i s p , 200 f w P150
100 50 0 0
500
IPR 1
1000
1500 2000 qsc, Mscf/d
IPR 2
NF 195
2500
3000
DGC 195
Figure 6.7: The performance in the first two year with and without DGC at WHFP 195 psia
26
Inflow Performance Curve 400 350 300 a250 i s p , 200 f w P150
100 50 0 0
500
IPR 2
1000
1500 2000 qsc, Mscf/d
IPR 3
NF 195
2500
3000
DGC 195
Figure 6.8: The performance with and without DGC at WHFP 195 psia in the middle of DGC
operation period Inflow Performance Curve 400 350 300 a250 i s p , 200 f w P150
100 50 0 0
IPR 3
500
1000
IPR 4
1500 2000 qsc, Mscf/d IPR 5
NF 195
2500
3000
DGC 195
Figure 6.9: The performance with and without DGC at WHFP 195 psia in the end period of
DGC operation for the case study (5 year)
27
Yearly Gas Prod uct ion (at WHFP 195 psi a)
600
f c s 500 M 3 ^ 0 400 1 , n o 300 i t c u d 200 o r P
100 0 1
2
DGC
3 Year
4
5
NF (without DGC)
Figure 6.10: Well production profile with and without DGC at WHFP 195 psia
28
12 Appendices: 12.1 Natural gas properties equations (Guo 2007) 1.1 Determine pseudocritical temperature and pressure (psia, Rankine) from known gas
specific gravity ( γ g ). P pc 678 50( g 0.5) 206.7 y N 2 440 yCO2 606.7 y H 2 S T PC 326 315.7( g 0.5) 240 y N 2 83.3 yCO2 133.3 yH 2 S 1.2 Determine pseudoreduced properties:
P Pr T pr
P P pc T T pc
1.3 Determine gas viscosity
Correlation of Carr et al. 1954 involves a two-step procedure: The gas viscosity at temperature and atmospheric pressure is estimated first from gas- specific gravity and inorganic compound content. The atmospheric value is then adjusted to pressure conditions by means of correction factor on the basis of reduced temperature and pressure state of the gas. The atmospheric pressure viscosity (μi) can be expressed as 1 1 HC 1 N2 1CO2 1H2 S g
1 T pr
e r
1 HC 8.188 10 3 6.15 10 3 log( g ) (1.709 103 2.062 10 6 g )T 1 N2 [9.59 103 8.48 10 3 log( g )] y N 2 1CO2 [6.24 103 9.08 10 3 9.08 10 3 log( g )] yCO2 1 H 2 S [3.73 103 8.49 10 3 log( g )] y H 2 S
29
r ln(
g 1
T pr ) a 0 a1 Ppr a 2 P
2 pr
a 3 Ppr 3 T pr ( a4 a5 Ppr a 6 P 2 pr a 7 P 3 pr )
T 2 pr ( a 8 a 9 Ppr a10 P 2 pr a11 P 3 pr ) T 3 pr ( a12 a13 Ppr a14 P 2 pr a15 P 3 pr ) a 0 2.46211820 a1 2.97054714 a 2 0.28626405 a 3 0.00805420 a 4 2.80860949 a 5 3.49803305 a 6 0.36037302 a 7 0.01044324 a 8 0.79338568 a 9 1.39643306 a10 0.14914493 a11 0.00441016 a12 0.08393872 a13 0.18640885 a14 0.02033679 a15 0.00060958
1.4 Determine the gas compressibility, many methods are available but Hall and
Yarborough give a more accurate estimation: Hall and Yarborough Method
A 0.06125tr e
1.2(1t r ) 2
B tr (90.7 242.2tr 42.4t 2 r ) D 2.18 2.82t r and Z
Ap pr Y
Where Y is the reduced density to be solved from f (Y )
Y Y 2 Y 3 Y 4
(1 Y )
3
Ap pr BY 2 CY D 0
If the Newton and Raphson iteration method is used to solve the above equation for Y, the following derivative is needed.
1 4Y 4Y 2 4Y 3 Y 4 2 BY CDY D 1 4 dY (1 Y )
df (Y )
30
1.5 Gas Density (
g
)
2.7 g P zT
1.6 Formation Volume Factor of gas ( )
Gas formation volume factor is defined as the ratio of gas volume at reservoir condition to the gas volume at standard condition, that is, B g
V V sc
P scTZ PTsc Z sc
0.0283
zT P
1.7 Gas Expansion Factor ( )
It is normally used for estimating gas reserves. E
1 B g
35.3
P ZT
12.2 Reservoir deliverability/inflow performance (Guo 2007) 2.1 Flow Analytical Method
q
q=
kh( P 2 P 2 wf )
0.472r e 1424 zT ln( ) s Dq r w
When P 3000
k= md h= ft P= psi T= Rankine rw= ft
D= s= skin factor q
kh( P Pwf )
0.472r e 141.2 103 B g ln( ) s Dq r w
When P 3000
Bg=
31
b) Empirical Method
q C ( P 2 P 2 wf )n ,
Where C and n are empirical constants that can be determined based on test points. The value of n is usually between 0.5 and 1.
log( n
q1 q2
)
P P wf 1 2
, C
2
log(
P 2 P 2 wf 2
)
q1
P 2 P 2 wf 1
n
12.3 Wellbore performance/tubing performance (Guo 2007) 3.1 Average TZ Method
6.67 104 Exp (s ) 1 f M q 2 z 2T 2 P wf Exp ( s ) P hf d 5i cos 0.0375 g L cos s 2
2
zT
The Darcy-Wisebach(Moody) friction factor f f M f M
0.01750 d i 0.224
0.01603 d i 0.164
, for di 4.277 . , for di 4.277 .
Or
1 f M s 2 1.74 2 log( ) d i
2
12.4 Choke performance (Guo 2007) 4.1 Critical Pressure Ratio
2 k k 1 ( )c ( ) Pup k 1 P outlet
where Poutlet is the pressure at choke outlet, Pup is the upstream pressure, and k= is the specific heat ratio. The value of the k is about 1.28 for natural gas. For air: k=1.40 Critical P ratio 0.5283 For NG: k= 1.28 Critical P ratio 0.5494 When the actual ratio Critical ratio then subsonic flow exist When the actual ratio Critical ratio then sonic flow exist (the flow is choked at the valve) 4.2 Subsonic flow
32
Pdn 2 P dn k 1 q sc 1.248CD A2 Pup ( ) k ( ) k , (k 1) gTup Pup Pup k
Where qsc= gas flow rate, Mscf/d Pup= upstream pressure at choke, psia A2= cross-sectional area of choke, in.2 Tup= upstream temperature, °R g= acceleration of gravity, 32.2 ft/s2 γg= gas-specific gravity related to air N Re
20q sc g d 2
Where is gas viscosity in cp.
z up P down k 1 ( ) k , Velocity of the gas v v up 2 g cC pTup 1 zdn P up 2
Where C p = specific heat of gas at constant pressure (187.7 lb.ft/lbm.Rn for air) 4.3 Sonic flow Q sc 879C D Apup
2 k k 11 ( )( ) g Tup k 1 k
v v 2 up 2 g cC pTup 1
z up
(
Maximum flow
2 ) , or v 44.76 T up k 1
zoutlet The choke flow coefficient CD is not sensitive to the Reynolds number for Reynolds number values greater than 106. Thus, the CD value at Reynolds number of 10 6 can be assumed for CD values at higher Reynolds numbers. 4.4 Choke flow coefficient C D
d 2 d 1
0.3167 d 2 d 1
0.6
0.025 log N Re 4 ,
Where d 1 = upstream pipe diameter, in. d 2 = choke diameter, in. N Re = Reynolds number based on d 2
33
Find CD by the graph
The choke discharge coefficient CD can be determined based on Reynolds number and choke/pipe diameter ratio
4.5 Temperature at Choke Tdn
T up
z up zoutlet
P ( outlet ) P up
k 1
k
34
12.5 Pipeline performance (www.pdhengineer.com 2011) 5.1 General Equation
Without considering elevation T b P 21 P 2 2 2.5 Q 77.54 D P GT LZf f b Q = gas flow rate standard ft3/day (SCFD) L = pipe length, mi D = inside diameter of pipe, in. P 1 = upstream pressure, psia P b = base pressure, psia(usually 14.7 psia) P 2 = downstream pressure, psia T b = base temperature, °R (usually 60+460=540 °R) T f = average flowing temperature of gas, °R
G = gas specific gravity (Air=1.00) Z = gas compressibility factor at flowing temperature and pressure, dimensionless f = friction factor, dimensionless
With considering the elevation
T Q 77.54 b Pb Le
P 21 e 5 P 2 2 GT L Zf f e
0.5
D 2.5 ,
L (e5 1) s
H H 1 s 0.0375G ( 2 ) T f Z s = elevation adjustment parameter, dimensionless
H 1 = upstream elevation, ft H 2 = downstream elevation, ft
Always use absolute pressures, not gauge pressures.
1 f
2log10 (
e
3.7 D
2.51 ) Re f
f = friction factor, dimensionless D = pipe inside diameter e = absolute internal roughness of pipe, in.
Re = Reynolds number of flow, dimensionless 5.2 Weymouth Equation P 21 e 5 P 2 2 2.667 E = Efficiency pipeline factor (0-1) Q 433.5E ( )( )D Pb GT f Le Z Tb
35
