Nodal System Analysis of Oil and Gas Wells

Distinguished Author SeriesNodal Systems Analysis of Oil and Gas WellsBy Kermit E. Brown, SPE, and James F. Lea, SPE

Kermit E. Brown is F.M. Stevenson Professor of Petroleum Engineering at the U. of Tulsa.

Since 1966 Brown has served as head of the Petroleum Engineering Dept., vice president of research, and chairman of the Resources Engineering Div. He has conducted many courses on gas lift, multiphase flow, and inflow performance and served as a Distinguished Lecturer during 1969-70. Brown holds a BS degree in mechanical and petroleum engineering from Texas A&M U. and MS and PhD degrees from the U. of Texas, both in petroleum engineering. Brown served as the SPE faculty advisor for the U. of Tulsa student chapter during 1982-83. He also served on the SPE board during 1969-72, the Education and Professionalism Committee during 1966-67, and the Education and Accreditation Committee during 1964-66 and was Balcones Section chairman during 1964-65. He is currently on the Public Service Award Committee. is a research associate in the Production Mechanics Group of Amoco Production Co. in Tulsa. He works on computer implementation of existing design and analysis methods for artificial lift and improved application techniques. Previously, he worked with Pratt & Whitney Aircraft and Sun Oil Co. and taught engineering science at the university level. Lea holds BS and MS degrees in mechanical engineering and a PhD degree in thermal/fluid science from Southern Methodist U., Dallas.

James F. Lea

Summary1

Nodal analysis, defined as a systems approach to the optimization of oil and gas wells, is used to evaluate thoroughly a complete producing system. Every component in a producing well or all wells in a producing system can be optimized to achieve the objective flow rate most economically. All present componentsbeginning with the static reservoir pressure, ending with the separator, and including inflow performance, as well as flow across the completion, up the tubingOCTOBER 1985

string (including any downhole restrictions and safety valves), across the surface choke (if applicable), through horizontal flow lines, and into the separation facilitiesare analyzed.

Introduction

The objectives of nodal analysis are as follows. 1.To determine the flow rate at which an existing oil or gas well will produce considering wellbore geometry and completion limitations (first by natural flow). 2.To determine under what flow conditions (which may1751

be related to time) a well will load or die. 3.To select the most economical time for the installation of artificial lift and to assist in the selection of the optimum lift method. 4.To optimize the system to produce the objective flow rate most economically. 5.To check each component in the well system to determine whether it is restricting the flow rate unnecessarily. 6.To permit quick recognition by the operator's management and engineering staff of ways to increase production rates. There are numerous oil and gas wells around the world that have not been optimized to achieve an objective rate efficiently. In fact, many may have been completed in such a manner that their maximum potential rate cannot be achieved. Also, many wells placed on artificial lift do not

achieve the efficiency they should. The production optimization of oil and gas wells by nodal systems analysis has contributed to improved completion techniques, production, and efficiency for many wells. Although this type of analysis was proposed by Gilbert2 in 1954, it has been used extensively in the U.S. only in the last few years. One principal reason for this was the changing of allowable producing rates, and another has been the development of computer technology that allows rapid calculation of complex algorithms and provides easily understood data. Past conservation practices in the U.S. more or less restricted operators to 2- and 2 -in. [5.08- and 6.35-cm] tubing and 4 shots/ft [13.1 shots/m] for perforating. The use of larger tubing (4 and 5 in.

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JOURNAL OF PETROLEUM TECHNOLOGY

-AP,, SALES LINE h"P6=tpDSCpsep)7DSC'

GASr

sep

STOCK TANK SEPARATOR LIQUID

5 wh~P DSc'p =(pSURFACE

CHOKE

d i z

AP| AP2 AP3

= = : = . : . .

= Pr -

Pwfs =

LOSS IN POROUS MEDIUM LOSS ACROSS COMPLETION RESTRICTION SAFETY VALVE=

= Pwfs -Pwf =:

PUR Pusv Pwh" osc

' PDR =

~:

AP

Pwf ~ Pwh7

=

AP4 AP5 APG AP7 AP8

"PdsvP

:

DSC ~

SURFACE CHOKE IN FLOWLINE TOTAL LOSS IN TUBING

:p

-Psep = "Pwh = Psep =

: :

Pwf' Pwh-

" FLOWLINE

Fig. 1 Possible pressure losses in complete system.

P2 =(Pwfs-Pf)

[11.43 and 13.97 cm]) and 16 shots/ft [52.5 shots/m] is common today. Although the increase in flow rates in highproductivity wells has popularized nodal analysis, it is, nevertheless, an excellent tool for lowrate wells (both oil and gas) as well as for all artificial lift wells. Some of the greatest percentage increases in production rates have occurred in low-rate oil wells (from 10 to 30

B/D [1.59 to3 4.77 m /d]) and low-rate gas wells (from 50 up to 100 to 200 Mscf/D [1416 up to 2832 to 5663 std m3/d]). Numerous gas wells have needed adjustments in tubing sizes, surface pressures, etc., to prolong the onset of liquid loading problems. Nodal analysis can be used to estimate the benefits of such changes before they are made. One of the most important aspects of1751

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nodal analysis is to recognize wells that should be producing at rates higher than their current rate. Therefore, it can serve as an excellent tool to verify that a problem exists and that additional testing is necessary. For example, assume that a well is producing 320 B/D [51 m3/d] of oil. Applying nodal analysis to this well shows that it is capable of producing 510 B/D [81 m3/d]. This difference may be attributed to several factors, but nodal analysis can determine which component is restricting the rate or can determine that incorrect data are the cause of the higher predicted rate. A basic requirement for well analysis is the ability to define the current1752

inflow performance relationship (IPR) of the well. Accurate well test data must be obtained and the proper IPR applied for successful analysis. Then models of other well componen ts can be used to complete the predicted well performan ce. Fig. 1 shows components that make up a detailed flowing well system. Beginning with the reservoir and proceeding to the separator, the components are (1) reservoir pressure, (2) well productivity, (3) wellbore completion, (4) tubing string, (5) possible downhole restrictive device, (6) tubing, (7) safety valve, (8) tubing, (9) surface choke, (10) flowline, and (11) separator.


To optimize the system effectively, each component must be evaluated separately and then as a group to evaluate the entire well producing system. The effect of the change of any one component on the entire system is very important and can be displayed graphically with well analysis. Some aspects of the IPR component are covered in Appendix A; discussion of multiphaseflow pressure-drop correlations for pipelines is found in Appendix B. The most common positions for nodal analysis graphical solutions are listed below. 1.At the center of the producin g interval, at the bottom of the well.OCTOBER 1985

This isolates the well's inflow performa nce. 2.At the top of the well (wellhead). This isolates the flowline or the effects of surface pressure on production. 3.Differenti al pressure solutions (Ap) across the completion interval to evaluate the effect of the number of perforations on production in gravelpacked or standard completion wells.

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4. 5.Solutions

plotted at the bottom

at the separator, especially with gaslift wells. This isolates the effect of separator pressure on production. 6.Other solution positions for graphical solution are at surface chokes, safety valves, tapered string connection points, and downhole restrictions. The user must understand how pressureflow components of the well are grouped to form a graphical solution at a node point. For example, if the solution is1752

of the well (center of completed interval), then the reservoir and the completion effects can be isolated completely from the entire piping and production system. Caution should be taken in neglecting even 200 to 300 ft [61 to 91 m] of casing flow from the center of the completed interval to the bottom of the tubing. Because of lower velocities, the larger pipe may not be flushed out with produced fluids. This large section of pipe still


can be nearly full of completion fluids (water and mud), even though the well may be producing 100% oil. Numerous flowingpressure surveys have verified this occurrence. A major company recently surveyed a well producing 1,600 B/D [254 m3/d] of oil up 2%-in. [7.3cm] tubing. Because of a dogleg, tubing was set 1,000 ft [305 m] off bottom in the 11,000ft [3353-m] well. Both water and mud were found in the 7-in. [17.8cm] casing below the tubing, even though the well produced 100% oil. Cleaning this well resulted in an increase of the rate to more than 2,000 B/D [318 m3/d] of oil. This points out one type of practical limitation of nodalOCTOBER 1985

analysis when tubingpressuredrop calculations are used to calculate accurately a bottomhole flowing pressure (BHFP). Here, the analysis showed that the rate should be higher and, hence, served as a diagnostic tool that prompted the running of a pressure traverse. In many cases, the analysis predicts what should be expected, and the operator is advised to look for problems if the well is producing below that prediction. Specific Examples A limited number of examples are presented here; numerous examples, however, appear in 1-5 the literature. Two specific subjects have been selected for exampl1751

e solution s. 1.The effect of the downhole completion on flow rate is illustrated. An example solution for both a gravelpacked well and a standard perforated well is presented. Procedures to optimize the completions are outlined. 2.Quick recognition of those wells with a greater predicted potential than the present production rate is covered. These situations may be caused by a restriction in one of the components in the system. GravelPacked Oil and Gas Wells A paper presented by Jones et al.4 seemed to be1752

the catalyst that started operators looking more closely at their completions. This paper also suggests procedures for determining whether a well's inflow capability is restricted by lack of area open to flow, by skin caused by mud infiltration, etc. Ledlow and Granger3 have prepared an excellent summary of background material on gravel packing, including details on mechanical running procedures and selection of gravel size. The nodal analysis procedure for a gravelpacked well, illustrated with a sequence of figures, is presented here. The appropriate details, additional references, and equations can be found in Ref. 3.


The following procedure is valid for either an oil or gas well with the solution node at bottomhole. 1.Prepare the node IPR curve (Fig. 2). (This step assumes no Ap across the completion. ) 2.Prepare the node outflow curve (tubing intake curve in Fig. 3), which is the surface pressure plus the tubing pressure drop plotted as a function ofFig. 2Constructed IPR curve.

rate.

Fig. 3Constructed tubing intake curve.

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3. 4.Transfer the differential pressure available between the node inflow and node outflow curve on the same plot (Fig. 4) to a Ap curve. 5.Using the appropriate equations,3,4 calculate the pressure drop across the completion for various rates. Numerous variables have to be considered here, including shots per foot, gravel permeability , viscosity and density of the fluid, and length of the perforation tunnel for linear flow. Add this Ap curve on Fig. 4, as noted in Fig. 5.

6.Evaluate this completion (Fig. 5) to determine whether the objective rate can be achieved with an accepted differential across the gravel pack. Company philosophies on accepted Ap values differ. A reasonable maximum allowable Ap that has given good results ranges from 200 to 300 psi [1379 to 2068 kPa] for single-phase gas or liquid flow. Most operators will design for smaller Ap's for multiphase flow across the pack. 7.Evaluate other shot densities or perhaps other hole sizes until

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the appropriate Ap is obtained at the objective rate (Fig. 6). Perforation efficiency should be considered at this time. A good review on perforating techniques, which points out such factors as the number of effective holes expected and the effect of the number of holes and hole sizes on casing strength, was presented by Bell.6 8.The Ap across the pack can be included in the IPR curve, as noted in Fig. 7. Example Problem Typical

Gulf Coast Well With Gravel Pack. Below is a list of given data. pr = 4,000 psi [27.6 MPa], D= 11,000 ft [3352 m] (center of perforatio

Fig. 5Construct Ap across gravel pack.

ns), k = 100 md (permeabi lity to gas), h= 30 ft [9.1 m] (pay interval), hp = 20 ft [6.1 m] (perforate d interval),

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u

Fig. 7Gravel pack solution by including Ap completion in IPR curve.

RATE

120 100 40 20 140 60 80 RATE, MMCFD

J

_ 50 L

6 L 0

_ _L

7 0 10 20 30 40 RATE, MMCFDDEPTH = 11,000 Pwh = 1200 PSI

Fig. 8IPR curve for gas wellgravel-pack analysis.

/ Q . 5 X m Q

C

40/60-mesh gravel-packed sand, 640-acre [259-ha] spacing, 8%-in. [21.9P = 4000 PSI cm] casing; DEPTH = 11,000' K 103/4-in. [27.3= 100 MD cm] _ drilled hole, yg = 0.65, screen size = 5-in. [12.7-cm] OD, gas-sales-line pressure = 1,200 psi [8273 kPa], short flowline. This well is to be gravel packed. The tubing size and the number of shots per foot are to be evaluated with an underbalanced tubing-conveyed gun. It is assumed that there is nor

C L

1-

computable zone restriction around the perforation because of unconsolidated formationthat Q is, sand flows immediately into _ X all perforated holes until properly co prepacked. Procedure. 1.The IPR curve is prepared with Darcy's law, and the additional turbulence pressure drop4 is included (Fig. 8). 2.Tubing sizes of 2%, V/z, and 4'/2 in. [7.3, 8.89, and 11.43 cm] are evaluated at a wellhead pressure of 1,200 psi [8272 kPa], which is needed to flow gas into the sales line. From analysis of Fig. 9, 4'/2in. [11.43-cm] tubing is selected. Note that, if Fig. 9Evaluation of tubing sizes. market

OT CL

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Nodal System Analysis of Oil and Gas Wells

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