assessment of deliverability of a natural-gas-gathering and … · 2016. 7. 4. · on the...

PB Oil and Gas Facilities • August 2012 August 2012 • Oil and Gas Facilities 55

SummaryThe present work describes the development of a 1D steady-state isothermal reservoir/surface gas-pipeline-network model. The model was developed by combining the reservoir with surface-fa-cility description parameters to capture effectively the variations in reservoir flow dynamics with changes in surface-network op-erating conditions. The developed model is an extension of the general pipeline-network model in which the deliverability from the wells is calculated in addition to the nodal pressures and gas flows in different pipe sections in the system on the basis of a set of operating conditions. Validation of the developed model was acheived through history matching with field data obtained from a currently operating gas-gathering and -transportation network in the northeastern USA. After successful validation, the model was used as a diagnostic tool to evaluate “what if ” scenarios to identify the pressure and deliverability changes that can happen in the network. On the basis of the model predictions, recommenda-tions were made to the operator in terms of total production, total sales, and fuel consumed by the compressors present in the net-work. This integrated-modeling approach helped in analyzing the system response as a whole and gave good insight into how the well shut-in pressures used in the model had a significant impact on the deliverability predictions.

IntroductionNatural-gas production in the USA is estimated to increase from approximately 20.2 Tcf in 2008 to 26.4 Tcf in 2035, with most of the production coming from unconventional (e.g., coalbed methane, tight sands, shale gas) resources (US EIA 2011). The de-velopment or modification of necessary or existing infrastructure to handle new volumes of gas coming into a transportation network necessitates a systematic study to maximize the deliverability from the wells with minimum energy losses during transportation of the gas from wellhead to the customer. To understand and study the be-havior of a gas-transportation-network system, numerical models built on the basis of the thermodynamics of fluid flow in pipes are widely used in the natural-gas-transmission industry.

In early work by Stoner (1969), a method is described for mod-eling pipe sections, gas-storage fields, and compressors together as a single communicating system by representing them with their re-spective design equations and, subsequently, solving the continuity equations using a numerical iterative scheme for the flow rates and nodal pressures at steady-state conditions. In the following decade, several studies were carried out to develop integrated gas-network-pipeline models to characterize the surface gas-transportation system and the hydrocarbon formation as one interacting entity to aid better planning and management of the reservoir in terms of forecasting,

field development, and surface-infrastructure expansions (Startzman et al. 1977; Dempsey et al. 1971; Crafton and Dyal 1976).

In such integrated models specifically, a large amount of data was transferred back and forth during the computations and some of them were multidimensional/multiphase models developed for offshore/onshore fields (Baldwin 1980; Tingas et al. 1998; Litvak et al. 1997). Essentially, this data-exchange procedure between the two models (reservoir and surface) was conducted continu-ously and iterated until the flow rate or the pressure calculated by either of the models matched (Puchyr 1991; Mogensen et al. 1998). Integrated models (Hepguler et al. 1997; Dempsey et al. 1971; Crafton and Dyal 1976; Holst et al. 1999; Marsh and Kenny 2002; Stevenson and O’Shea 2006) were also developed in which inflow-performance relationships (IPRs) (Pshut, Cwell, nwell) were used to quantify the well deliverability with the backpressure equation proposed by Rawlins and Schellhardt (1935). In such models, the challenging task was using an appropriate well-deliv-erability constant (Cwell) to predict the well productivity during the simulations. In some cases, the well-deliverability constant was computed using well-test data and production data (Marsh and Kenny 2002) or calibrated using the wellhead pressure (Holst et al. 1999) computed by both models. These models were used for planning new well tie-ins and forecasting future pipeline and compression requirements.

As noted in the preceding, several models have been developed over the years to model the interaction between surface and sub-surface as a single entity. These models were “handshaking” in na-ture, with data being sent back and forth to solve for the different variables in the system. Initial field expansions can be studied by use of such integrated models, and successful predictions from these models rely on the data fed to them, and more importantly, the models handle large amounts of information during the com-putations. Developing a simple, reliable model becomes a ne-cessity during the prediction of field deliverability from mature fields when minimum known reservoir parameters are available and the use of a full-scale reservoir simulator is not possible. In this study, one such model is developed to capture the associated flow changes in the system whenever there is a change in the net-work pressure. This is acheived by incorporating the reservoir-de-scription parameters into the surface-pipeline-network model by use of the gas-well-deliverability equation. The subsurface prop-erties are incorporated into the model by three parameters (i.e., well shut-in pressure, well-performance constant, and a nonideal factor) to describe the laminar/turbulent nature of flow into the wellbore. An integrated model such as the one developed in this study can be used for a comprehensive analysis of a gas-network system to predict the accompanying flow changes because of the system pressure variation whenever a new well addition or a pipe-line expansion is made. The significance of such a model is its capability to predict the flow and pressure changes in the gas net-work, to decide on the physical feasibility of the proposed mod-ifications, and to guide the operators on the capital investment needed in such expansions.

Assessment of Deliverability of a Natural-Gas-Gathering and -Production System: Development of an Integrated

Reservoir/Surface Model

Dennis Arun Alexis, SPE, and Luis F. Ayala H., SPE, Pennsylvania State University

Copyright © 2012 Society of Petroleum Engineers

This paper (SPE 157713) was accepted for presentation at the SPE International Student Paper Contest at the SPE Annual Technical Conference and Exhibition, Denver, 30 October–2 November 2011, and revised for publication. Original manuscript received for review 9 December 2011. Paper peer approved 10 February 2012.

56 Oil and Gas Facilities • August 2012 August 2012 • Oil and Gas Facilities 57

Model DescriptionGas-Network Modeling. A gas network comprises nodes and node-connecting elements. The nodes can be the junction points between two node-connecting elements or the wellheads, which are supplying gas into the network, or a demand point at which gas is being sold. The node-connecting elements can be pipe legs, com-pressors, valves, or regulators present in the network to build a con-tinuous flow path between the supply and the demand points. Fig. 1 shows a simple gas-transportation network, describing the nodes and the node-connecting elements.

Modeling a gas network is performed by integrating the nodes and the node-connecting elements with appropriate design equa-tions. In the steady-state model discussed in this paper, the supply nodes are characterized by the well-deliverability equation, and the equations used for the node-connecting elements are the pipe equa-tion and the compressor-performance equation. The primary func-tion of these equations is to relate the volume of fluid transmitted through the facilities (or the volume produced by the wells) to var-ious other factors, and they are linked by constructing the node continuity equations for every node, which ensures that mass is con-served at every single node in the system. These node continuity equations are solved simultaneously to solve for the pressures at every node on the basis of a given set of boundary conditions. With the pressure simulated, the flow can be computed or vice versa.

1D Steady-State Gas-Flow Equation in Pipes. By writing a ther-modynamic balance invoking the first and second laws of thermo-dynamics at the inlet and outlet of the pipe section shown in Fig. 2, one can express the total pressure drop occurring in the pipe as

dd

dd

dd

ddtotal friction elevation acceleratio

Px

Px

Px

px( ) ( ) ( )

= + +nn( )

, ....................... (1a)

where

dd friction

Px( )

is the pressure drop because of friction,

dd elevation

Px( )

is the pressure drop because of elevation, and

dd acceleration

Px( )

is the pressure drop because of acceleration. The pressure drop be-cause of friction and elevation can be defined as

dd friction

Px

pv fg d

F

c( )= − 2

2

............................................................. (1b)

and

dd elevation

Px

pgg

pg hg Lc c( )

= − = −sinθ ∆ . ......................................... (1c)

The contribution of

dd acceleration

Px( )

is usually neglected when compared with the influence of the rest of the terms in Eq. 1a; thus, the total pressure drop occurring in the pipe section can be written as

dd total

Px

pg hg L

pv fg dc

F

c( )= − −∆ 2

2

. ................................................... (2)

Using the appropriate definitions of velocity, area, and density at average conditions, Eq. 2 becomes

−+

PMwT Z R

P Mw g hT Z R g L

m fg d

g

g

c

F

c

air

av av

air

av av

γ

γπ

2 2 2

2 2 2

2

2 532∆ '

∫ = ∫PP LP x1

20d d . ........................(3)

By integrating Eq. 3 and maintaining unit consistency, we obtain

q TP f

P e PT Z Le

dsc SCSC F

s

g

=

−38 774 1

2 22 5. .up down

av av γ. ......................... (4)

Eq. 4 (Menon 2005) represents the theoretical flow rate of the gas flowing through the pipe section if the pipe section is 100% ef-ficient in transmitting the flowing gas. The actual flow rate of gas is obtained by multiplying the theoretical flow rate with a factor called the flow efficiency Ef, which is the ratio of actual flow rate to the theoretical flow rate. Hence, Eq. 4 becomes

q TP f

P e PT Z Le

dsc scsc F

s

gactual

up down

av av =

−38 774 1

2 22.

γ..5Ef . ................. (5)

Eq. 5 can be expressed in the form

q C P e Psc ps n

actual up down= −( )2 2

1, ................................................. (6)

Internode Compressor

Demand nodes Supply node

Pipe leg

Fig. 1—Simple gas-transportation network to illustrate nodes and node-connecting elements.

L

θ∆h

Fig. 2—Illustration of a single-phase gas flow through a pipe section inclined at an angle θ.


where s is the elevation-adjustment parameter, Cp is the pipe con-ductivity, and the definition of both Cp and n varies with the partic-ular type of friction-factor model built into the equation.

Compressor-Modeling Equation. Compressors are an integral part of any gas-transportation network. They serve three primary purposes: to gather gas from any location in the network, to in-crease the pressure of the transported gas to feed the gas to a main pipeline network, and to increase the deliverability from the wells at the given operating conditions by lowering the wellhead pres-sures. Eq. 7 (Kumar 1987) represents the standard compressor-performance equation used in the industry:

hp( ) = −( )q k R ksck

1 23 , ................................................................ (7)

where k1, k2, and k3 represent the compressor-performance con-stants and are usually specified by the manufacturer. In this model, Eq. 7 is used for predicting the horsepower (hp) requirements when the compressor-performance constants and the suction or dis-charge pressure are specified as inputs. The model has the option to specify the hp, suction pressure, or the discharge to predict the other two variables.

Gas-Well-Modeling Equation. The gas-well-deliverability equa-tion is employed to model the gas-supply nodes in the network that are treated as wells in this model. The relationship representing the flow of gas into the wellbore from the formation is shown in Eq. 8 (Kelkar 2008):

q C P Psc whn

= −( )well shut well2 2 . .................................................... (8)The performance constant of the well (Cwell) is a function of res-

ervoir and fluid properties. The factor nwell to characterize nonideal flow behavior varies between 0.5 and 1.0, with unity representing laminar flow and 0.5 representing completely turbulent flow. The gas well, which is normally connected to a surface pipeline net-work, flows depending on the operating pressure of the pipeline in the system. The backpressure prevailing at the wellheads is more often the one that affects the sandface pressure to determine the amount of gas flowing into the wellbore. Eq. 8 is used in the model to predict the supply flow rate from a well for the existing pressure at the wellhead, which is the nodal pressure calculated at that par-ticular supply node by the model.

The model also has the capability to account for the con-sumption of gas by the compressors present in the network. By specifying the rate of fuel consumed (ft3/hp per hour), the gas con-sumption is taken into account. To account for the losses occurring in the system because of leaks or error in measurement, a factor (a fraction varying from 0.0 to 0.5) can be specified at all the supply nodes (wells). Hence, this fraction of gas is subtracted at all the supply nodes, and the remaining gas flows into the system.

Fluid Properties. The gas properties that are required as inputs into the model are the critical properties, compressibility factor, specific gravity, and gas viscosity. The critical temperature and pressure of the gas are calculated with a correlation relating to the specific gravity of the gas. The specific gravity has to be specified directly in this model. The compressibility factor (Z-factor) can be specified directly and can be used in the computations, or it can be computed by the model on the basis of the Dranchuk and Abou-Kassam (1975) iterative algorithm. The gas viscosity is computed using the Lee et al. (1966) correlation.

Formulation of the Node Continuity Equations. The node con-tinuity equations are formulated by use of the design equations for the pipe, compressor, and well. There are two fundamental

methods to construct the node continuity equations. One is the P-formulation approach, and the other is the Q-formulation ap-proach. In each method (explained in Appendix A), the formulation of the node equations is based on the principle of mass and energy conservation. In this model, the P-formulation method is used in which the primary unknown variables are the nodal pressures. The design equations are represented in terms of the unknown nodal pressures, depending on which nodes they are in communication with. The total number of node continuity equations that need to be constructed would be (N-1) because a pressure specification has to be made at any one node in the network.

The Concept of the Balance Node. This model simulates the in-dividual well-production flow rates using the shut-in pressure and the well-performance constant that are unique to each producing well. Out of the nodes specified as demand points, one node acts as the balance node (the node without any demand specification). The net production of the balance node is the algebraic sum of all the supply and demands in the network. The balance node is cre-ated to accommodate the production increase or decrease that can occur at the wellheads when the network pressure changes so that the steady-state solution is always enforced. Without this balance node at steady-state conditions, the model will not be able to con-verge to a solution because the total output from the network is now a variable quantity. This balance node avoids overspecification of the problem.

Numerical Solution. The node continuity equations are nonlinear in nature and have to be solved simultaneously. In this model, the equations are solved by the generalized Newton-Raphson iterative protocol. With the initial assumption of a single value of pressure at any node in the network, the Newton-Raphson iterative procedure runs until the difference in the value of pressure in the current itera-tion and the previous iteration at all the nodes is within a prespeci-fied tolerance level.

Case StudiesThe gathering system of interest handles production from approxi-mately 600 shallow gas wells, ranging in depth from 3,500 to 4,500 ft, and consists of a few hundred miles of gathering lines of various sizes. The pipeline-network map is shown in Fig. 3, where the en-tire pipeline network has been classified as the North, Middle, and South Sections, respectively, for ease of analysis. There are five compressor stations and four sales points. Flow through the system is powered by several compressors located at the five different lo-

Sales point

Compressor station

SouthSection

MiddleSection

NorthSection

: 6,000 ft

Fig. 3—Map of the pipeline network under study.


cations in the system. The four different sales points are located close to the distributing (or main trunk) line where custody transfer takes place. Though this field is a collection of hundreds of mature stripper wells, it still has the potential to harvest new volumes of natural gas from projected drilling activity. The production rates of the wells range from 1 to 250 Mcf/D.

Prescreening To Identify Production Trends. An arbitrary selec-tion of producing wells in the North Section of the network was per-formed to identify the relationship between the wellhead pressure and the flow rate of the well. Using the wellhead-pressure (Pwh) and flow-rate (qsc) data for these wells, a plot of Pwh vs. qsc was constructed to identify the trend in the plots. The expected trend should resemble the one shown in Fig. 4a (i.e., the higher the flow rate, the lower the wellhead pressure and vice versa). This trend is necessary to compute the IPR parameters for each producing well, which is explained in the next subsection.

Estimation of Well Shut-in Pressure and the Well-Performance Constant. A plot between Pwh2 and qsc(1/nwell) should yield a straight line, with a negative slope equal to (1/Cwell) (1/nwell) and an intercept equal to Pshut2, as shown in Fig. 4b. This plot is a direct conse-quence of Eq. 8. From the value of the slope and intercept, we can obtain the value of Cwell and Pshut for that particular well. It should be noted that the value of nwell (between 0.5 and 1.0) has to be as-sumed beforehand to obtain Cwell from the slope. The Cwell, Pshut, and nwell are collectively called the IPR parameters.

Preliminary Analysis. To study the deliverability predictions of the model, an initial IPR study was undertaken by modeling the North Section of the pipeline network. The well-performance con-stant and shut-in pressure were calculated from the Pwh2-vs.-qsc (1/n) plot. This section also had some new wells drilled and tied into the existing network. It would be interesting to see if the model is able to predict whether any wells in the network would get shut in as a result of the pressure changes in this section of the network. Figs. 5a and 5b show the crossplots, comparing the model and field predictions.

The match between the model predictions and field well flow rates is good. The points lying at the origin (0,0) in Fig. 5a show that there is a close agreement for the wells in which the production in the field and the model-predicted production are the same (in this case, zero). This is a result of the fact that with the new wells in the network, the wellhead pressure of those wells has changed. As the prevailing wellhead pressure became greater than the shut-in pressure of the wells, they naturally shut down. The points lying on the horizontal axis in Fig. 5a show the wells that are predicted by the model to be shut in though they are still producing in the field. There are a few significant outliers, which are circled in green. It was found that these wells did not have proper deliverability rela-tionships, and the approximations made to compute the Pshut and Cwell could have influenced the predictions.

History Matching the Entire Network. The shut-in pressures (Pshut) of the wells were provided by the operator, hence the Cwell

Fig. 4—(a) Pwh vs. qsc—expected production trend. (b) A well-deliverability plot.

0

20

40

60

80

100

120

140

160

14 15 16 17 18 19

qsc (Mcf/D)

Pw

h (

psi

a)

(a)

Intercept=Pshut2

Slope=−(1/Cwell) (1/nwell)

qsc 1/nwell

Pwh2 (psia2)

(b)

70

95

120

145

170

195

220

245

70 95 120 145 170 195 220 245

qsc Field (Mcf/D)

qsc

Mo

del

(M

cf/D

)

(b)

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60 70

qsc Field (Mcf/D)

qsc

Mo

del

(M

cf/D

)

(a)

Fig. 5—(a) Crossplot 1 for the entire North Section; (b) Crossplot 2 for the entire North Section.


values were computed using the production data and Eq. 8, instead of calculating Cwell and Pshut from the deliverability plot using the field production data. With this updated IPR information, the entire network system was modeled to observe the deliverability predic-tions of all the producing metered wells in the network. Figs. 6a, 6b, and 6c have the crossplots showing the model-predicted vs. field-recorded flow rates for three different months. The model pre-dictions were still good when the analysis was performed, when the network is considered as a whole. Wells that did not have deliver-ability information (i.e., unmetered wells with very small produc-

tion) were represented with a qsc of 0.001 Mcf/D in the model, as indicated by the operator. The dashed lines in Figs. 6a, 6b, and 6c represent an allowable bandwidth of 20% between the field flow rates and the model-predicted flow rates.

Sensitivity Analysis. A sensitivity analysis was carried out to determine how sensitive the model is with respect to deliverabil-ity predictions when different parameters are varied in the model. This is an important aspect in model development and evaluation. Experimenting with different operating parameters as inputs, one can test the behavior of the model under a variety of conditions. This exercise can assist in determining the boundaries up to which the model can be stretched without compromising the physical meaning of the generated results. In this study, the model was tested by varying the suction pressure of the various compressors located at different points in the network to determine the changes in the deliverability predictions in the entire network. The idea was to see how much loss of system deliverability is realized with lower-compression work. The parameters chosen here were the suction pressures of the compressors because a particular significance of incorporating compressors into a gas-transportation network is to increase the deliverability from the producing wells by lowering the wellhead pressures. Also, by lowering suction pressures, saving on compressor fuel consumption can be realized. Table 1 shows the different cases considered for sensitivity analysis. Table 2 sum-marizes the results of the sensitivity analysis. As we can see from Table 2, the production increase or decrease with the suction-pres-sure variations is not significant and is relatively unaffected when compared with the base-case scenario. The results are also plotted in Fig. 7.

The shut-in pressures used for the wells in the network are high, and though there is a change in pressure at the wellheads, the de-liverability is much less. This is because the well-performance con-stant Cwell (calculated using the shut-in pressures provided by the operator) is very small, making the change in the deliverability predictions relatively insignificant. Also, the use of high shut-in pressures is telling the deliverability model that there is enough en-ergy in the reservoir to transport the gas without much help from the compressor. The reliability of the model predictions depends primarily on the verification of shut-in pressures and the deliver-ability-plot shapes.

“What If” Scenarios. Having obtained good history matches, the network model was used for evaluating several scenarios to forecast the total network deliverability of the gas-gathering and -production system under study by employing a variety of operating conditions. One such scenario is presented here. The goal of this scenario is to introduce a new direct pipeline from the North Section to the sales point to divert most of the additional new gas produced upstream as a result of infill-drilling activity directly to the sales point of the North Section. The scenario is described in Fig. 8. The effect of the new pipeline on the infield compressor was to be studied with increasing pipe diameters. Table 3 shows that as pipe diameter in-

0

50

100

150

200

250

0 50 100 150 200 250

qsc Field (Mcf/D)

qsc

Mo

del

(M

cf/D

)

(b)

0

50

100

150

200

250

0 50 100 150 200 250

qsc Field (Mcf/D)

qsc

Mo

del

(M

cf/D

)

(a)

0

50

100

150

200

250

0 50 100 150 200 250

qsc Field (Mcf/D)

qsc

Mo

del

(M

cf/D

)

(c)

Fig. 6—Crossplot for total network: (a) Month 1, (b) Month 2, (c) Month 3.

TABLE 1—DESCRIPTION OF DIFFERENT CASES CONSIDERED FOR SENSITIVITY ANALYSIS

Case Variation in suction pressures

of compressors

1 5 psig decrease

2 10 psig decrease

3 10 psig increase

4 20 psig increase

5 30 psig increase

6 40 psig increase


creases, more gas reaches the sales point and less gas flows through the compressor, which is evidenced by the decrease in compressor hp. For economic reasons of laying out a pipeline over a distance of 3.75 miles, it is better to use a 2- to 3-in.-diameter pipeline. In this scenario, it is important to see the additional volume of gas com-ing into the system (balance-node quantity in Table 3) as a result of the new pipeline. We see a marginal increase of approximately 14 Mcf/D when compared with the base-case scenario. This same scenario was again modeled by employing the IPR parameters gen-erated from the deliverability plots instead of using the operator-specified Pshut and corresponding Cwell. The results are shown in Table 4. From the third column of Table 4, we see that the addition-al volume coming into the system is approximately twice that of the base case, with increasing pipe diameter. The numerical differences observed in the value of the quantity of gas at the demand node in comparison with the previous case result from the North Section being truncated from the rest of the section and modeled alone. In this case, it is important to note the change in the quantity of gas seen at the balance node.

Hence, the accuracy of the predicted volume increases because the new pipeline inclusion is based on the credibility of the Pshut and Cwell generated from the deliverability curves. In summary, this exercise showed that there will be a definite increase in production and substantial reduction in hp of the infield compressor because of the new pipeline addition, and the magnitude of the increase will depend largely on the accuracy of the shut-in pressures and the as-sociated well-performance constants.

ConclusionsA comprehensive description of the integrated reservoir/surface pipeline-network model was presented, and the following conclu-sions were derived:

1. The model was effective in predicting the well production by the inclusion of the well-deliverability equation embedded

into the surface-gas-network model on the basis of the good history matches obtained.

2. The accuracy of the graphical method described to estimate the IPR parameters depends largely on how far the production history of a particular well could be trusted because a level of approximation had to be accepted to generate the shut-in pressure for those particular wells having an erratic produc-tion history.

3. The sensitivity analysis carried out showed that the flow pre-dictions are quite unsensitive to changes in network pressure because the Cwell values are nearly zero, which makes the IPR curve a near-vertical line, meaning that the well deliverability is basically unaffected by the prevailing wellhead pressure.

4. By accounting for compressor fuel consumption and well-head losses, the model can assist in sizing compressors for a given compression ratio and capturing unknown physical losses, respectively.

5. This model could be further diversified by including modules to account for facilities such as regulators, valves, and under-ground gas storage, with special emphasis on multiphase flow in pipes.

Nomenclature Cp = pipe conductivity, Mcf/D/psi2 Cwell = well-performance constant, Mcf/D/psi2nwell d = pipe internal diameter, in. Ef = pipe flow efficiency, dimensionless fF = Fanning friction factor, dimensionless gc = gravitational constant, ft/sec2 h = height, ft h1 = elevation of pipe at upstream section of pipe, ft h2 = elevation of pipe at downstream section of pipe, ft k = compressor-performance constant L = length of pipe section, miles Le = equivalent length of pipe section, miles n = polytropic coefficient, dimensionless nwell = factor to account for laminar or turbulent flow of gas

into the wellbore, dimensionless Pb = pressure at base conditions, psia Pd = compressor-discharge pressure, psia Pdown = pressure at downstream section of pipe, psia Ps = compressor-suction pressure, psia Pshut = shut-in pressure at the average reservoir pressure,

psia Pup = pressure at upstream section of pipe, psia Pwf = flowing wellface pressure, psia qsc = flow rate of gas at standard conditions, Mcf/D R = compression ratio, dimensionless S = pipe-elevation-adjustment parameter, dimensionless Tav = average gas temperature, °R v = gas velocity, ft/sec Z = gas-compressibility factor, dimensionless ρ = gas density, lbm/ft3

θ = pipe inclination with respect to horizontal, radians

TABLE 2—RESULTS SUMMARY FOR SENSITIVITY ANALYSIS

Scenario Total Production (Mcf/D) Total Sales (Mcf/D)

Base Case 6,873 5,732

Case 1—5 psig decrease 6,878 5,737

Case 2—10 psig decrease 6,882 5,740

Case 3—10 psig increase 6,860 5,721




5500

5650

5800

5950

6100

6250

6400

6550

6700

6850

–20 0 20 40

Total Production

Total Sales

∆P (psi) at the Compressors

qsc

(M

cf/D

)

Fig. 7—Variation of total production and total sales with chang-es in compressor suction pressures.


Subscripts av = average b = base c = constant d = discharge e = equivalent f = flow F = Fanning p = pipe s = suction sc = standard conditions wh = wellhead

AcknowledgmentsThe authors would like to thank Mark Clavenna, Michael Lord, Mi-chael Nicol, and Ryan Cramer of NCL Natural Resources LLC for providing the data and financial support for performing this study.

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TABLE 3—RESULTS FOR THE NORTH SECTION WITH THE NEW LINE

New pipe diameter (in.)

Infield compressor (hp)

Demand at balance node

(Mcf/D) Q new pipe

(Mcf/D)

Fuel gas consumption

(Mcf/D)

No pipe 91.86 3,783.21 0.0 35.51

2 66.04 3,794.95 257.78 25.36

4 59.12 3,797.61 333.39 22.70

6 58.78 3,797.33 337.15 22.57

8 58.75 3,797.74 337.61 22.56

Direct new line3.75 miles

Fig. 8—Map section showing the prospective direct new line in the North Section of the network.


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Appendix A—Formulation of the Node Continuity EquationsThe node continuity equations are formulated with the design equa-tions for the pipe, compressor, and well. There are two fundamental methods to construct the node continuity equations. One is the P-formulation approach and the other is the Q-formulation approach. In each method, the formulation of the node equations is based on the principle of mass conservation, but in the Q-formulation ap-proach, the loop equations are constructed in addition to the node equations, ensuring energy conservation in the loop, which is a di-rect consequence of Kirchoff’s second law of network analysis. To demonstrate the difference between the two techniques, consider the simple network shown in Fig. A-1.

In Fig. A-1, the network has three nodes, one compressor, and two pipes. Node 1 receives the supply from a well and Node 2 and Node 3 serve as the two demand points in the network. There is a compressor between Nodes 1 and 2. At steady-state conditions, any flow that comes into the network at Node 1 leaves the network at Nodes 2 and 3, respectively. The flow through the compressor pipe (connecting Node 1 and Node 2) can be taken as qCOMP, the flow in Pipe 1 is q1 (connecting Nodes 1 and 3), and the flow in Pipe 2 is q2 (connecting Nodes 3 and 2).

The P-Formulation Approach. If the node continuity equations are to be built on the basis of the P-formulation approach, then the equations would resemble those in Eqs. A-1, A-2, and A-3 in which the primary unknowns are the nodal pressures. Eq. A-1 shows the

node continuity equation for Node 1 in which the flow coming into the network is from a well and the flow leaving Node 1 is conveyed through a compressor and Pipe 1. Also, the flow from a well, flow through a pipe, and flow through the compressor are represented by their respective design equations. Similar to Eq. A-1, the node con-tinuity equations are constructed for Node 2 and Node 3, as shown in Eqs. A-2 and A-3, respectively.

Node 1: hp

well shutwellC P P

k PP

k

n

k2

12

12

12

3−( ) − ( )

−

− −( ) = C P Pp n1 1 321

0. ................. (A-1)

Node 2: hp( )

−

+ −( ) − =k PP

k

C P Pk p n

12

12

32

22

1

3 2350 0

. ...... (A-2)

Node 3: C P P C P Pp n p n1 212

32

1

32

22

1

150 0−( ) − −( ) − = . ... (A-3)

In a conventional surface-gas-network model, the first term in Eq. A-1 would have been replaced by the constant 500 Mcf/D. In this integrated model, the constant-supply flow-rate node is treated as a well, and the gas-well-deliverability equation is used to model the flow from a gas well. If Cwell, Pshut, and nwell are known, then Eq. A-1 is still a function, relating variables P1 and P2 but with a stronger dependency on P1.

The Q-Formulation Approach. In the Q-formulation approach, the total number of node continuity equations required are (N-1)+L equations. The L equations refer to the number of loop equations that can be formed by analyzing the number of loops present in the network. In Fig. A-1, there is one loop. The loop equation is shown in Eq. A-7.

Node 1: COMP500 01− − =q q . ............................................ (A-4)

Node 2: COMPq q+ − =2 350 0. ........................................... (A-5)

Node 3: q q1 2 150 0− − = . .................................................. (A-6)

Loop 1: hp

COMP

Pk k q

R qk

n3

2

1 2

2

1 111 3−

+( )

−

− =R q n2 2 0

. ............... (A-7)

Well Source: 500 Mcf/D 350 Mcf/D

150 Mcf/D

21

3

Fig. A-1—Simple network for illustrating the development of node continuity equations.

TABLE 4—RESULTS FOR THE NORTH SECTION WITH THE NEW LINE WITH IPR PARAMETERS GENERATED FROM THE DELIVERABILITY PLOT

New pipe diameter (in.)

Infield compressor (hp)

Demand at balance node

(Mcf/D) Q new pipe

(Mcf/D)

Fuel gas consumption

(Mcf/D)

No pipe 72.2 650 0.0 27.9

2 48.5 916.8 327.2 18.7

4 30.8 1,123.7 594.1 11.9

6 29.1 1,143.4 620.7 11.2

8 28.9 1,145.8 624.1 11.2


As we can see from the node and the loop equations, the pri-mary unknown variables are the gas flows. The R in Eq. A-7 re-fers to the respective pipe resistivity, which is the reciprocal of the pipe conductivity (Cp). Though there are four equations and three unknowns (q1, q2, qCOMP), one of the node equations is redundant and can be neglected to have, finally, three equations with three un-knowns to solve for.

SI Metric Conversion Factor cp × 1.0* E-03 = Pa·s ft × 3.048* E-01 = m ft3 × 2.831 685 E-02 = m3 °F (°F-32)/1.8 = °C hp × 7.460 43 E-01 = kW in. × 2.54* E+00 = cm lbm × 4.535 924 E-00 = kg mile × 1.609 344* E+00 = km psi × 6.894 757 E+00 = kPa

*Conversion factor is exact.

Dennis Arun Alexis is currently a PhD candidate in the John and Willie Leone Family Department of Energy and Mineral Engi-neering at the Center for Quantitative Imaging at Pennsylvania State University. His research interests are in the areas of res-ervoir modeling of unconventional reservoirs, multiphase flow in porous media, reservoir characterization, multiphase network

analysis, carbon sequestration, and flow assurance. Alexis holds an MS degree in petroleum and natural gas engineering from Pennsylvania State University and a BS degree in chemical en-gineering from Anna University in India. He is a member of SPE and an active student volunteer in the Penn State SPE Chapter. He was awarded second place in the SPE Rocky Mountain/Mid-Continent/Eastern student paper contest in the MS division held in Lawrence, Kansas, USA in 2011.

Luis F. Ayala H. is an Associate Professor of Petroleum and Nat-ural Gas Engineering in the John and Willie Leone Family De-partment of Energy and Mineral Engineering at Pennsylvania State University. He has also been an instructor in the Chemical Engineering and Petroleum Engineering Departments at Uni-versidad de Oriente (Venezuela). His research activities focus on the areas of natural gas engineering, multiphase flow, nu-merical modeling, hydrocarbon phase behavior, and artificial intelligence. He holds PhD and MS degrees in petroleum and natural gas engineering from Pennsylvania State University and two engineering degrees with honors, one in chemical engi-neering (summa cum laude) and another in petroleum engi-neering (summa cum laude) from Universidad de Oriente. He is a member of SPE, the American Chemical Society, and the Na-tional Association of Engineers of Venezuela. He was awarded the 2007 Outstanding Technical Editor Award by SPE and the 2008 Wilson Award for Outstanding Teaching by Pennsylvania State University.

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