nodal analysis

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Production Optimizationusing nodal analysis

Introduction

2Production Optimization - Introduction

The nodal systems analysis approach is a very flexible method that can be used to improve the performance of many well systems.

The nodal systems analysis approach may be used to analyze many producing oil and gas well problems. The procedure can be applied to both flowing and artificial

Introduction

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The nodal systems analysis schematic model

Introduction


To apply the systems analysis procedure to a well, it is necessary to be able to calculate the pressure drop that will occur in all the system components listed in Fig. 1-l.

These pressure drops depend not only on flow rate, but on the size and other characteristics of the components. Unless accurate methods can be found to calculate these pressure drops, the systems analysis can produce erroneous results

Introduction

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Kermit Brown, p. 88, Fig. 4.2

Pressure drop that will occur in all the systemIntroduction


The procedure consists of selecting a division point or node in the well and dividing the system at this point.

The locations of the most commonly used nodes are shown in Fig. 1-2.

Introduction

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Once the node is selected, the node pressure is calculated from both directions starting at the fixed pressures.

Therefore, a plot of node pressure versus flow rate will produce two curves, the intersection of which will give the conditions satisfying requirements

Introduction


The effect of a change in any of the components can be analyzed by recalculating the node pressure versus flow rate using the new characteristics of the componentThe procedure can be further illustrated by considering the simple producing system shown in Fig. 1-4 and selecting the wellhead as the node.

Introduction

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The effect on the flow capacity of changing the tubing size is illustrated in Fig. 1-5, and the effect of a change in flowline size is shown in Fig. 1-6.

Introduction


The effect of a change in tubing size on the total system producing capacity when pwf, is the node pressure is illustrated in Fig. 1-7.

Introduction

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If too much pressure drop occurs in one component or module, there may be insufficient pressure drop remaining for efficient performance of the other modules. This is illustrated in Fig. 1-8 for a system in which the tubing is too small.

Introduction


A case in which the well performance is controlled by the inflow is shown in Fig. 1-9. In this case, the exces-sive pressure drop could be caused by formation damage or inadequate perforations.

Introduction

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A qualitative example of selecting the optimum tubing size for a well that is producing both gas and liquids is shown in Fig. 1-10 and I-11.

Introduction


an example of determining the optimum gas injection rate for a well on gas lift is illustrated in Fig. 1-12 and 1-13.

Introduction

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a different inflow curve would exist for each perforating density. This is illustrated qualitatively in Fig. 1-14 and Fig. 1-15

Introduction


Introduction

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A suggested procedure for applying NODAL Analysis is given as follows :

• Determine which components in the system can be changed. Changes are limited in some cases by previous decisions. For example, once a certain hole size is drilled, the casing size and, therefore, the tubing size is limited

• Select one component to be optimized • Select the node location that will best emphasize the

effect of the change in the selected component. This is not critical because the same overall result will be predicted regardless of the node location

Introduction


• Develop expressions for the inflow and outflow.• Obtain required data to calculate pressure drop versus

rate for all the components. This may require more data than is available, which may necessitate performing the analysis over possible ranges of conditions

• Determine the effect of changing the characteristics of the selected component by plotting inflow versus outflow and reading the intersection.

• Repeat the procedure for each component that is to be optimized.

Introduction

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The nodal systems analysis approach may be used to :

1. Selecting tubing size.2. Selecting flowline size. 3. Gravel pack design. 4. Surface choke sizing.5. Subsurface safety valve sizing.6. Analyzing an existing system for abnormal flow re-strictions.7. Artificial lift design.8. Well stimulation evaluation.9. Determining the effect of compression on gas well performance.10.Analyzing effects of perforating density.11.Predicting the effect of depletion on producing ca-pacity.12.Allocating injection gas among gas lift wells. 13.Analyzing a multiwell producing system. 14.Relating field performance to time

Introduction


End of slide

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Predicting Current and Future IPR’s

2Production Optimization – Predicting IPR

Reservoir Performance

One of the most important components in the total well system is the reservoir. Unless accurate predictions can be made as to what will flow into the borehole from the reservoir, the performance of the system cannot be analyzed.

The flow from the reservoir into the well has been called "inflow performance" by Gilbert' and a plot of producing rate versus bottomholeflowing pressure is called an "inflow performance relationship" or IPR.

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WELL PERFORMANCE EQUATIONS

To calculate the pressure drop occurring in a reservoir, an equation that expresses the energy or pressure losses due to viscous shear or friction forces as a function of velocity or flow rate is required. Although the form of the equation can be quite different for various types of fluids, the basic equation on which all of the various forms are based is Darcy's law.

In 1856, while performing experiments for the design of sand filter beds for water purification, Henry Darcy proposed an equation relating apparent fluid velocity to pressure drop across the filter bed. Although the experiments were performed with flow only in the downward vertical direction, the expression is also valid for horizontal flow, which is of most interest in the petroleum industry.

Darcy's Law



Darcy's sand filters were of constant cross-sectional area, so the equation did not account for changes in velocity with location. Written in differential form, Darcy's law is:

or in terms of volumetric flow rate q


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I. Linear Flow

For linear flow, that is for constant area flow, the equation may be integrated to give the pressure drop occurring over some length L:

If it is assumed that k, µ and q are independent of pressure, or that they can be evaluated at the average pressure in the system, the equation becomes


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Integration gives:

where C is a unit conversion factor. The correct value for C is 1.0 for Darcy Units and 1.127 x 10-' for Field Units (See Table 2-1).




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Oil flow


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Gas flow



Darcy's law can be used to calculate the flow into a well where the fluid is converging radially into a relatively small hole.

Referring to the flow geometry illustrated in Figure 2-2, the cross-sectional area open to the flow at any radius is A = 2π r h.

Radial Flow


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Oil flow

For field units, became :



Gas flow

For field units, became :


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PREDICTING PRESENT TIME IPR'S FOR OIL WELLS

The factors affecting the inflow performance for oil wells were discussed qualitatively in the previous section. If all of the variables in the inflow equations could be calculated, the equations resulting from integration of Darcy's law could be used to quantify the IPR.

Unfortunately, sufficient information rarely exists to accomplish this and, therefore, empirical methods must be used to predict the inflow rate for a well

Several of the most widely used empirical methods for predicting an IPR for a well are presented in this section. Most of these methods require at least one stabilized test on a well, and some require several tests in which pwf test and qtest were measured.

Methods to account for the effects of drawdown only are first presented, that is, pR is assumed constant. Modification of the methods for depletion will then be discussed


Vogel Method

Vogel reported the results of a study in which he used a mathematical reservoir model to calculate the IPR for oil wells producing from saturated reservoirs.

The study deal with several hypothetical reservoirs including those with widely differing oil characteristics, relative per-meability characteristics, well spacing and skin factors.

The final equation for Vogel's method was based on calculations made for 21 reservoir conditions.

Although the method was proposed for saturated, dissolved gasdrivereservoirs only, it has been found to apply for any reservoir in which gas saturation increases as pressure is decreased

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Vogel's original method did not account for the effects of a non-zero skin factor, but a later modification by Standing extended the method for application to damaged or stimulated wells.

The Vogel method was developed by using the reservoir model proposed by Weller' to generate IPR's for a wide range of conditions. He then replotted the IPR's as reduced or dimensionless pressure versus dimension-less flow rate.

It was found that the general shape of the di-mensionless IPR was similar for all of the conditions studied. Examples of these plots from the original paper are illustrated in the next Figures

Vogel Method


Vogel’s dimensionless IPR

Vogel Method

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Vogel Method


Vogel Method

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Vogel arrived at the following relationship between dimensionless flow rate and dimensionless pressure :

Vogel Method


The dimensionless IPR for a well with a constant productivity index can be calculated from

Vogel pointed out that in most applications of his method the error in the predicted inflow rate should be less than 10%, but could increase to 20% during the final stages of depletion

Vogel Method

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In the original paper by Vogel, only cases in which the reservoir was saturated were considered. The method can be applied to undersaturatedreservoirs by applying Vogel's equation only for values of Pwf < Pb,

Application of Vogel Method-Zero Skin Factor

Vogel Method

a. Saturated Reservoirs.

b. Undersaturated Reservoirs.


Application of Vogel Method- non Zero Skin Factor(Standing Modification)

Vogel Method

The method for generating an IPR presented by Vogel did not consider an absolute permeability change in the reservoir. Standing6proposed a procedure to modify Vogel's method to account for either damage or stimulation around the wellbore.

The degree of permeability alteration can be expressed in terms of a Productivity Ratio PR or Flow Efficiency FE, where:

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Undersaturated Reservoirs with FE ≠ 1.

Standing's modification of Vogel's method to be used when the flow efficiency is not equal to one may also be applied to undersaturatedreservoirs.

Vogel MethodApplication of Vogel Method- non Zero Skin Factor

(Standing Modification)


Fetkovich proposed a method for calculating the inflow performance for oil wells using the same type of equation that has been used for analyzing gas wells for many years. The procedure was verified by analyzing isochronal and flow-after-flow tests conducted in reservoirs with permeabilities ranging from 6 md to greater than 1000 md. Pressure conditions in the reservoirs ranged from highly undersaturated to saturated at initial pressure and to a partially depleted field with a gas saturation above the critical.In all cases, oil-well back-pressure curves were found to follow the same general form as that used to express the inflow relationship for a gas well. That is:

Fetkovich Method

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That is:

Fetkovich Method


The value of n ranged from 0.568 to 1.000 for the 40 field tests analyzed by Fetkovich. The applicability of Equation to oil well analysis was justified by writing Darcy's equation as:

Fetkovich Method

For an undersaturated reservoir, the integral is evaluated over two regions as:

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Three types of tests are commonly used for gas-well testing to determine C and n. These tests can also be used for oil wells and will be described in this section. The type of test to choose depends on the stabilization time of the well, which is a function of the reservoir

Fetkovich Method

1. Flow-After-Flow TestingA flow-after-flow test begins with the well shut in so that the pressure in the entire drainage area is equal to pR. The well is placed on production at a constant rate until the flowing wellbore pressure becomes constant.

The test may also be conducted using a decreasing rate sequence.


The idealized behavior of production rate and wellbore pressure with time is shown in Figure.

Fetkovich Method

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2. Isochronal TestingIf the time required for the well to stabilize on each choke size or producing rate is excessive, an isochronal or equal time test ispreferred.

The values of PR 2 - Pwf

2 determined at the specific time periods are plotted versus qo and n is obtained from the slope of the line. To determine a value for C, one test must be a stabilized test. Thecoefficient C is then calculated from the stabilized test. The idealized behavior of producing rate and pressure as a function of time is shown in Figure.

Fetkovich Method


Fetkovich Method

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3. Modified Isochronal TestingIf the shut-in time required for the pressure to build back up to PR between flow periods is excessive, the isochronal test may be modified. The modification consists of shutting the well in between each flow period for a period of time equal to the producing time

Fetkovich Method


1. Horizontal Wells

IPR Construction for Special Cases

The productivity index for a horizontal well in which permeability difference in the vertical and horizontal directions is small was described by Giger, et al as:

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2. Waterflood Wells

It can be assumed that the IPR will be linear for values of pwf > pb. For pwf < pb, Vogel's equation may be used to account for the effect of gas saturation developing around the wellbore when pwf is below pb.

IPR Construction for Special Cases


PREDICTING FUTURE IPR's FOR OIL WELLS

As the pressure in an oil reservoir declines from depletion, the ability of the reservoir to transport oil will also decline. This is caused from the decrease in the pressure function as relative permeability to oil is decreased due to increasing gas saturation.

Standing MethodStanding" published a procedure that can be used to predict the decline in the value of qo (max) as gas saturation in the reservoir increases from depletion.

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Once the value of qo (max) or J has been adjusted, future IPR's can be generated from



Fetkovich MethodThe method proposed by Fetkovich to construct future IPR's consists of adjusting the flow coefficient C in his Equation for changes in ƒ(PR). He assumed that f( PR) was a linear function of PR, and, therefore, the value of C can be adjusted as

Future IPR's can thus be generated from

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Combining Vogel and FetkovichThe method proposed by Fetkovich for adjusting C can also be used to adjust qo(max) if a value for the exponent n is assumed. The expressions for qo(max)P and qo(max)F can be expressed using the Fetkovich equation as:

If a value of n equal to one is assumed, then:


PREDICTING PRESENT TIME IPR's FOR GAS WELLS

Darcy's equation for radial gas flow including permeability alteration and turbulence may be expressed as follows:

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This definition of B includes the assumption that re is much greater than rw. The effects of turbulence can also be accounted for by including an exponent in the pressure term of previous Equation. This results in the familiar back-pressure form of the equation.

Use of the Back Pressure Equation


Jones, Blount and Glaze MethodThe method of plotting test data, which was proposed by Jones, et al., can be applied to gas-well testing to determine real or present time inflow performance relationships. The analysis procedure allows determination of turbulence or non-Darcy effects on completion efficiency irrespective of skin effect and laminar flow.


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Predicting Future IPR's for Gas Wells

As reservoir pressure declines from depletion in a gas reservoir, the change in the IPR is not as significant as it is for an oil reservoir.

If no changes are made in re S or h, the values of C, or A and B can be adjusted for reservoir pressure changes as follows:

where the subscript P refers to present or real time and the subscript F refers to some future time.

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END OF SLIDE

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Inflow and Outflow Performance Curve

2Production Optimization – Inflow and outflow Performance curve


Tujuan:Menggabungkan kinerja dari berbagai komponen sumur minyakdan gas dalam sistem produksi untuk menentukan laju produksidan menentukan suatu sistem produksi yang optimal.

Sistem Produksi:Dalam pendekatan analisa nodal ini, sistem produksi meliputireservoir (aliran dari reservoir ke sandface), perforasi, gravel pack, screen, tubing, downhole safety valves, choke, pipapermukaan dan separator.

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Inflow and Outflow Performance CurveSkema Sistem Produksi



Inflow and Outflow Performance CurvePosisi “Node” dalam Analisa Nodal


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Inflow and Outflow Performance CurveAnalisa Nodal di Dasar Sumur

Posisi “node” di dasar sumur adalah yang paling umum digunakandalam analysis nodal.

Sistem dibagi menjadi dua bagian, reservoir dan sistem pipa (sumurdan permukaan).



Inflow and Outflow Performance CurveAnalisa Nodal di Dasar Sumur (Lanjutan)

Bagian reservoir dalam hal inimeliputi aliran fluida dari reservoir ke sand-face, aliran melaluiperforasi, gravel pack dan screen.

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Analisa Nodal di Dasar Sumur (Lanjutan)

Sistem pipa dalam hal inimeliputi aliran fluida daridasar sumur ke wellhead (melalui tubing string dandownhole valves) atau keseparator (melalui pipapermukaan dan chokes).




Kinerja dari setiap sistem dievaluasi pada “node” yang sama dalambentuk hubungan antara tekanan pada “node” dan laju alir. Untuk“node” di dasar sumur, hubungannya adalah antara tekanan alir dasarsumur (pwf) dan laju alir (q).

Konsep dari analisa nodal ini adalah pada “node”, yang merupakan titiktemu antara dua atau lebih sistem yang berbeda, kinerja dari sistemyang bertemu di “node” itu haruslah sama.

Kinerja reservoir dalam bentuk hubungan antara tekanan dan laju alirdisebut dengan “Inflow Performance Relationship” (IPR). Sedangkankinerja sistem pipa disebut “Outflow Pressures”.

Satu kurva IPR dibuat pada satu harga tekanan reservoir rata-rata.

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Inflow and Outflow Performance CurveAnalisa Nodal di Dasar Sumur (Lanjutan)

Kermit Brown, p. 91, Fig. 4.9a




Pemilihan “node” di dasarsumur digunakan untukmelihat pengaruh daripenurunan tekananreservoir terhadap lajuproduksi. Hal ini bergunadalam peramalanproduksi.

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Analisa Nodal di Wellhead

Sistem dibagi menjadi duabagian, reservoir+tubingstrings danflowline+separator.



Analisa Nodal di Wellhead (Lanjutan)

Flowline dan separator.


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Reservoir dan tubing strings.




Untuk berbagai laju produksi, dihitung tekanan wellhead yang diperlukan untuk mengalirkan fluida dari wellhead ke separator. Dari langkah ini kita mendapatkan “node” tekanan outlow.

Menggunakan laju produksi yang sama, dengan tekanan reservoir rata-rata yang tertentu hitung tekanan alir dasar sumur, kemudian tentukantekanan di wellhead dengan mengurangi tekan alir dasar sumur dengankehilangan tekanan di tubing strings. Prosedur ini menghasilkan “node”tekanan inflow.

Laju produksi untuk kombinasi dua sistem tersebut diperoleh dariperpotongan dua kurva tekanan outflow dan inflow.

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Inflow and Outflow Performance CurveAnalisa Nodal di Wellhead (Lanjutan)

Kermit Brown, p. 93, Fig. 4.15b





Pemilihan “node” di wellhead adalah untuk mengetahui pengaruh dariperubahan flowline terhadap produksi.

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Inflow and Outflow Performance CurveAnalisa Nodal di Separator




Analisa Nodal di Separator (Lanjutan)


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Inflow and Outflow Performance CurveAnalisa Nodal di Separator (Lanjutan)




Analisa Nodal di Separator (Lanjutan)

Sumur A memperlihatkan bahwapeningkatan produksi akan terjadicukup besar apabila tekananseparatornya rendah. Tetapi sumurD menunjukkan tidak adaperubahan produksi yang cukupberarti dengan perubahan tekananseparator.

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Analisa Nodal di Reservoir



Inflow and Outflow Performance CurveAnalisa Nodal di Reservoir (Lanjutan)

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END OF SLIDE

nodal analysis

Engineering