SEMESTER 5/3 PCB 3063 – PRODUCTION ENGINEERING I

PCB 3063 – PRODUCTION ENGINEERING I SEMESTER

5/3

By

Dr Aliyu Adebayo Sulaimon

([email protected]) (Telephone: 05368-7051) (Room No.: L-1-35) Dr Aliyu Adebayo Sulaimon

Learning Outcomes At the end of this lecture, students should be able to: 

Write down, understand and use Fetkovich’s Equation



To construct outflow performance curve



To describe flow regimes in two-phase vertical and horizontal pipes



Overlay the inflow and outflow curves to obtain a “Nodal” solution


IPR: Fetkovich’s Equation 𝟐

𝟐 𝒏

𝒒 = 𝑪(𝑷 − 𝑷𝒘𝒇 ) where C and n are empirical constants

NOTE:  This equation is more accurate than Vogel’s equation IPR modeling.  Like Vogel’s equation, Fetkovich’s equation is also valid for average reservoir pressure less than or equal to the initial bubble point pressure (𝑷 ≤ 𝑷𝒃,𝒊 ) Dr Aliyu Adebayo Sulaimon

EXAMPLE Given the following data, construct IPR of a well in a saturated oil

reservoir using both Vogel’s equation and Fetkovich’s equation. First Well Test: • •

𝑷 = 𝟑, 𝟎𝟎𝟎 𝒑𝒔𝒊𝒂 𝑷𝒘𝒇,𝟏 = 𝟐, 𝟎𝟎𝟎 𝒑𝒔𝒊𝒂

•

𝒒𝟏

= 𝟓𝟎𝟎 𝒔𝒕𝒃/𝒅𝒂𝒚

Second Well Test:

• •

𝑷 = 𝟑, 𝟎𝟎𝟎 𝒑𝒔𝒊𝒂 𝑷𝒘𝒇,𝟐 = 𝟏, 𝟎𝟎𝟎 𝒑𝒔𝒊𝒂

•

𝒒𝟐

= 𝟖𝟎𝟎 𝒔𝒕𝒃/𝒅𝒂𝒚


Solution Vogel’s Method:

𝒒𝒎𝒂𝒙 =

𝒒𝒎𝒂𝒙 =

𝒒𝟏

𝑷𝒘𝒇,𝟏 𝑷𝒘𝒇,𝟏 𝟏 − 𝟎. 𝟐 − 𝟎. 𝟖 𝑷 𝑷 𝟓𝟎𝟎

𝟐

𝟐𝟎𝟎𝟎 𝟐𝟎𝟎𝟎 𝟏 − 𝟎. 𝟐 − 𝟎. 𝟖 𝟑𝟎𝟎𝟎 𝟑𝟎𝟎𝟎

𝟐

= 𝟗𝟕𝟖 𝒔𝒕𝒃/𝒅𝒂𝒚

Generate the IPR by using the following equation 𝒒 = 𝒒𝒎𝒂𝒙 𝟏 − 𝟎. 𝟐

𝑷𝒘𝒇 𝑷

− 𝟎. 𝟖

𝑷𝒘𝒇

𝟐

𝑷 Dr Aliyu Adebayo Sulaimon

Solution (Cont’d) Fetkovich’s Method:

𝒒𝟏 𝟓𝟎𝟎 𝐥𝐨𝐠 𝒒𝟐 𝟖𝟎𝟎 𝒏= = = 𝟏. 𝟎 𝟑𝟎𝟎𝟎𝟐 − 𝟐𝟎𝟎𝟎𝟐 𝑷𝟐 − 𝑷𝒘𝒇,𝟏 𝟐 𝐥𝐨𝐠 𝐥𝐨𝐠 𝟐 𝟐 𝟑𝟎𝟎𝟎𝟐 − 𝟏𝟎𝟎𝟎𝟐 𝑷 − 𝑷𝒘𝒇,𝟐

𝐥𝐨𝐠

𝑪=

𝒒𝟏 𝑷𝟐 − 𝑷𝒘𝒇,𝟏 𝟐

𝒏

=

𝑷𝒘𝒇 (psia)

𝟓𝟎𝟎 𝟑𝟎𝟎𝟎𝟐 − 𝟐𝟎𝟎𝟎𝟐

𝟏.𝟎

= 𝟎. 𝟎𝟎𝟎𝟏

𝒒𝑽𝒐𝒈𝒆𝒍 (stb/day)

𝒔𝒕𝒃 /𝒑𝒔𝒊𝟐 𝒅

𝒒𝑭𝒆𝒕𝒌𝒐𝒗𝒊𝒄𝒉 (stb/day)

0

978

900

500

924

875

1000

826

800

1500

685

675

2000

500

500

2500

272

275

3000

0

0


Solution (Cont’d)


NODAL ANALYSIS  We wish to predict achievable fluid production rates from reservoirs with specified production string characteristics. This can be achieved by a technique called Nodal analysis.

 To simulate the fluid flow in the system, it is necessary to “break” the system into discreet nodes that separate system elements (equipment sections)  Nodal analysis is a system analysis for determination of fluid production rate and pressure at specified node (Figures 1 & 2) Dr Aliyu Adebayo Sulaimon

Pressure Losses in Well System Pwh

P6 = (Posc - Psep) P8 = (Pwh - Psep) Psep Surface choke P5 = (Pwh - PDSC)

Gas Separator Liquid

Sales line

Stock tank

Pwf

P = (Pusv - PDsc) Pwf

P7 = Pwf - Pwh

Bottom hole restriction

Pwf

P3 = (Pur - PDR) Pwf

Pwf

P2 = (Pwfs - Pwf)

P1 = Pr - Pwfs P2 = Pwfs - Pwf P3 = Pur - PDR P4 = Pusv - PDSV P5 = Pwh - PDSC P6 = Posc - Psep P7 = Pwf - Pwh P8 = Pwh - Psep Pwfs

Pr

= = = = = = = =

Loss in porous medium Loss across completion Loss across restriction Loss across safety valve Loss across surface choke Loss in flowline Total loss in tubing Total loss in flowline Pe

U = Upstream D = Downstream

P1 = (Pr - Pwfs)

FIGURE 1


Pressure Losses in Well System

U = Upstream

D = Downstream

FIGURE 2


General Applications of Nodal Analysis 

Selecting tubing size



Surface choke sizing



Subsurface safety valve sizing



Selecting flowline size



Analyzing existing restriction in the system



Artificial lift design



Well stimulation evaluation



Analyzing effect of perforating



Gravel pack design



Determine effect of compression on gas well performance



Allocating injection gas among gas lift wells Dr Aliyu Adebayo Sulaimon

Performance Curves 

A performance curve is a “pressure-rate” relation



The performance curve of upstream equipment is called “Inflow Performance Curve”



The performance curve of downstream equipment is called “Outflow Performance Curve”



The intersection of the two performance curves defines the operating point, i.e. operating q and 𝑷𝒘𝒇 at the specified node



For convenience, Nodal analysis is usually conducted using the bottom-hole or wellhead as the solution node Dr Aliyu Adebayo Sulaimon

Combine Inflow and Outflow 4000 FIGURE 3

𝑷𝒘𝒇 (psia)

3000

2000

1000

0 0

2000

4000

6000

𝒒 (Mscf/day)

8000

10000

12000


Review of Wellbore Hydraulics (Cont’d)  Single phase flow can be characterized as laminar or

turbulent, depending on the value of a dimensionless group, the Reynolds number, 𝑵𝑹𝒆 ,

𝑵𝑹𝒆 =

𝝆𝒗𝑫 𝝁

 Flow Regimes (or Flow Patterns) 

This is a qualitative description of the phase distribution



The manner in which two phases (liquid and gas) are distributed in pipes significantly affects slippage between phases and the pressure gradient. Dr Aliyu Adebayo Sulaimon

Review of Wellbore Hydraulics (Cont’d)  Flow Regimes in Two-phase Vertical Upward Flow (4 general types): These flows occur as a progression with increasing gas rate for a given liquid rate  Bubble flow: Dispersed bubbles of gas in a continuous liquid phase  Slug flow: At higher rates, the bubbles coalesce into larger bubbles (Taylor bubbles) that eventually fill the entire pipe cross section. Between the large gas bubbles are slugs of liquid that contain smaller bubbles of gas entrained in the liquid


Review of Wellbore Hydraulics (Cont’d)  Churn flow: With further increase in gas rate, the larger gas bubbles become unstable and collapse, resulting in churn flow, a highly turbulent flow patter with both phases dispersed. It is characterized by oscillatory, up-and-down liquid motion. In small diameter tubes, churn flow may not develop at all and the flow passes directly from slug to annular flow. This flow is typically avoided because of its destructive consequence on the piping system.

 Annular flow: At very high gas rates, gas becomes the continuous phase, with liquid flowing in an annulus coating the surface of the pipe and with liquid droplets entrained in the gas phase. Annular flow is particularly stable and is the desired flow pattern for twophase pipe flows.


Review of Wellbore Hydraulics (Cont’d)

Two-phase flow regimes in vertical pipe


Review of Wellbore Hydraulics (Cont’d) The flow regime in gas-liquid vertical flow can be predicted with a flow regime map [i.e. a log-log plot of the liquid (𝑵𝒗𝒍 ) vs gas (𝑵𝒗𝒈 ) velocity numbers e.g. Duns and Ros, 1963] 𝑵𝒗𝒍 = 𝒗𝒔𝒍

𝟒

𝝆𝒍 𝒈𝝈

and

𝑵𝒗𝒈 = 𝒗𝒔𝒈

𝟒

𝝆𝒍 𝒈𝝈

where 𝝆, 𝒈 𝒂𝒏𝒅 𝝈 are density, acceleration of gravity and interfacial tension of the gasliquid system respectively. NOTE: For a given gas-liquid system, the only variables in the dimensionless groups are the superficial velocities of the phases. Other maps are those of Taitel, Barnea, and Dukler (1980)



Figure: Duns and Ros flow regime map Dr Aliyu Adebayo Sulaimon

Review of Wellbore Hydraulics (Cont’d)  Flow Regimes in Two-Phase Horizontal Flow 



Two-phase flow in horizontal pipes differs markedly from that in vertical pipes. Completely different correlations (except for Beggs and Brill, 1973) are used for horizontal flow. The flow regime does not significantly affect the pressure drop as in vertical flow because there is no P.E contribution to the pressure drop


Review of Wellbore Hydraulics (Cont’d)  Segregated Flow: The two phases are mostly separated • Stratified flow: At relatively low rates of both phases, liquid flows along the bottom of the pipe and gas flows along the top of the pipe with a smooth interface between the phases.

• Wavy flow: At higher flow rates, the interface becomes wavy, and stratified wavy flow results.

• Annular flow: At high gas rates and relatively high liquid rates, annular flow consisting of an annulus of liquid coating the wall of the pipe and a central core of gas flow, with liquid droplets entrained in the gas occurs.



 Intermittent Flow: Gas and liquid are alternating •

Slug: Large liquid slugs alternates with high-velocity bubbles of gas that fill almost entire pipe.

•

Plug (or elongated bubble): Large gas bubbles flow along the top of the pipe, which is otherwise filled with liquid.


Review of Wellbore Hydraulics – Pressure Traverse 

The aim is to generate the total pressure loss in the tubing in order to calculate the 𝑷𝒘𝒇 𝒐𝒓 𝑷𝒘𝒉



The pressure increment ΔP can be calculated in a piecewise manner at short depth incremental Δh



The Outflow Performance is generated by considering Single-Phase or Multiphase Flow



For a single-phase liquid flow (𝑷𝒘𝒉 > 𝑷𝒃 ; unrealistic), the pressure drop in the tubing can be calculated from 𝟐𝑳 𝒈 𝝆 𝟐𝒇 𝝆𝒖 𝑭 ∆𝑷 = 𝑷𝟏 − 𝑷𝟐 = 𝝆∆𝒛 + ∆𝒖𝟐 + 𝒈𝒄 𝟐𝒈𝒄 𝒈𝒄 𝑫 P.E term

K.E term

Friction term Dr Aliyu Adebayo Sulaimon

Review of Wellbore Hydraulics – Pressure Traverse 

The overall pressure drop is obtained with a pressure traverse calculation procedure.



A differential form of the mechanical energy balance equation is 𝒅𝑷 𝒅𝑷 = 𝒅𝒛 𝒅𝒛



+ 𝑷𝑬

In most 2-phase correlations, the density, 𝝆,

where

𝒅𝑷 𝒅𝒛

𝒅𝑷 𝒅𝒛

𝑲𝑬

𝒅𝑷 𝒅𝒛 𝑷𝑬

=𝝆 𝑷𝑬

+

𝒅𝑷 𝒅𝒛

𝑭

is based on the in-situ average

𝒈 𝐬𝐢𝐧 𝜽 𝒈𝒄

𝝆 = (𝒚𝒍 )𝝆𝒍 + (𝟏 − 𝒚𝒍 )𝝆𝒈

 Various definitions of the 2-phase average velocity, viscosity, and friction factor are used in different correlations to calculate the K.E and frictional pressure gradients.


Review of Wellbore Hydraulics – Pressure Traverse  Two-phase flow correlations:          

Hagedorn and Brown (One of the consistently best correlations) Aziz et al Duns and Ros Hasan and Kabir Beggs and Brill Payne et al Orkiszewski Mukherjee and Brill (1999) – Detailed review of the correlations Gray correlation Griffith correlation

The modified Hagedorn and Brown (m H&B) method (Brown 1977) and the Beggs and Brill (1973) are commonly used correlations oil wells. The m H&B is recommended only for near-vertical wellbores. The Beggs & Brill is applicable for any wellbore inclination and flow direction while the Gray correlation is commonly used for gas wells that are also producing liquid. Dr Aliyu Adebayo Sulaimon

Review of Wellbore Hydraulics – Pressure Traverse

 Hagedorn-Brown correlation ∆ 𝒖𝒎 𝟐 𝒅𝑷 𝒇 𝑭 𝑴𝒕 𝟐 𝟏𝟒𝟒 =𝝆+ +𝝆 𝟏𝟎 𝟓 𝒅𝒛 𝟐𝒈𝒄 ∆𝒛 𝟕. 𝟒𝟏𝟑 × 𝟏𝟎 𝑫 𝝆 𝑴𝒕 =total mass flow rate, lbm/d;

𝒖𝒎 = mixture velocity, ft/s


Determination of the Operating Point  Bottom-Hole and Wellhead Nodes in Nodal Analysis 

When the bottom-hole is used as a solution node in Nodal analysis, the inflow performance is the well “Inflow Performance Relationship (IPR)” and the outflow performance is the “Tubing Performance Relationship (TPR)” – if the tubing shoe is set at the top of the pay zone.



When the wellhead is used as a solution node, the inflow performance curve is the “Wellhead Performance Relationship (WPR)” while the outflow performance curve is the wellhead “Choke Performance Relationship (CPR)”



The IPR can be generated by using the Darcy or PI equation, and the Vogel’s or Fetkovich’s equation. The TPR can be established either by using several traverse curves for a defined set of properties and characteristics of the well or by using the computer to solve the existing multiphase flow correlations. Dr Aliyu Adebayo Sulaimon

Determination of the Operating Point (Cont’d)  Analysis with the Bottom-Hole Node 

Oil Well: o

IPR:

𝒒 = 𝑱 𝑷 − 𝑷𝒘𝒇 𝒐𝒓 𝑷𝒘𝒇 = 𝑷 −

o

TPR:

𝑷𝒘𝒇 = 𝑷𝒘𝒉 +

𝑳 𝟏𝟒𝟒

𝝆+

𝒒 𝑱

𝒌 𝝆

The operating point (𝒒𝒔𝒄 , 𝑷𝒘𝒇 ) can be determined graphically or analytically by

𝒒 = 𝑱 𝑷 − 𝑷𝒘𝒉 −

𝑳 𝟏𝟒𝟒

𝝆+

𝒌 𝝆


Determination of the Operating Point (Cont’d)  Analysis with the Bottom-Hole Node 

Gas Well: o o

𝒒𝒔𝒄 = 𝑪 𝑷𝟐 − 𝑷𝒘𝒇

IPR:

𝟐

𝑷𝒘𝒇 =

TPR:

𝒆𝒔 𝑷

𝒉𝒇

𝟐

+

𝟐 𝒏

𝒐𝒓 𝑷𝒘𝒇 𝟐 = 𝑷𝟐 −

𝟏 𝒒𝒔𝒄 𝒏

𝑪

𝟔.𝟔𝟕×𝟏𝟎−𝟒 𝒇𝑴 𝒒𝒔𝒄 𝟐 𝒛𝟐 𝑻𝟐 𝒆𝒔 −𝟏 𝒅𝒊 𝟓 𝐜𝐨𝐬 𝜽

The operating point (𝒒𝒔𝒄 , 𝑷𝒘𝒇 ) can be determined graphically or analytically by

𝒒𝒔𝒄 𝟐 𝑷 − 𝑪

𝟏 𝒏

−

𝒆𝒔 𝑷

𝒉𝒇

𝟐

+

𝟔. 𝟔𝟕 × 𝟏𝟎−𝟒 𝒇𝑴 𝒒𝒔𝒄 𝟐 𝒛𝟐 𝑻𝟐 𝒆𝒔 − 𝟏 𝟓

𝒅𝒊 𝒄𝒐𝒔 𝜽

=𝟎


Determination of the Operating Point (Cont’d)  Analysis with Wellhead Node 

Oil Well: o

IPR:

𝒒 = 𝑱 𝑷 − 𝑷𝒘𝒇 𝒐𝒓 𝑷𝒘𝒇 = 𝑷 −

o

TPR:

𝑷𝒘𝒇 = 𝑷𝒘𝒉 +

𝑳 𝟏𝟒𝟒

𝝆+

𝒒 𝑱

𝒌 𝝆

The equation that describes inflow for the wellhead node (WPR) is given as:

𝒒 = 𝑱 𝑷 − 𝑷𝒘𝒉 −

𝑳 𝟏𝟒𝟒

𝝆+

𝒌 𝝆


Determination of the Operating Point (Cont’d)  Analysis with Wellhead Node 

Oil Well: If the Choke Performance Relationship (CPR) is given by 𝑪𝑹𝒎 𝒒 𝑷𝒘𝒉 = 𝑺𝒏 The operating point (𝒒𝒔𝒄 , 𝑷𝒘𝒇 ) can be obtained by substituting 𝑷𝒘𝒇 into the WPR to obtain:

𝑪𝑹𝒎 𝒒 𝑳 𝒒=𝑱 𝑷− + 𝑺𝒏 𝟏𝟒𝟒

𝒌 𝝆+ 𝝆

which can be solved with a numerical technique (See Guo et al for “q” for a gas well) Dr Aliyu Adebayo Sulaimon

Gradient Curves


Pressure Traverse Curves

• OLD FILES\appendix c - PRESSURE TRAVERSE CURVES.pdf

• See the attached files.


Example Nodal Solution of a Well  Find the flow rate for a well producing under the following conditions if 2-7/8 inches tubing is used: • • • • •

GLR = 𝟒𝟎𝟎 𝐬𝐜𝐟/𝐒𝐓𝐁 𝑷𝒓 = 𝟑𝟒𝟖𝟐 𝐩𝐬𝐢𝐠 𝑷𝒃 = 𝟑𝟔𝟎𝟎 𝐩𝐬𝐢𝐠 𝑷𝒘𝒉 = 𝟒𝟎𝟎 𝐩𝐬𝐢𝐠 𝜸𝒈 = 𝟎. 𝟔𝟓

• • • •

𝑫𝒆𝒑𝒕𝒉 = 𝟏𝟎, 𝟎𝟎𝟎𝐟𝐭 𝒇𝒘 = 𝟎. 𝟓 𝑨𝑷𝑰 = 𝟑𝟓 𝑷𝒘𝒇 = 𝟑𝟒𝟒𝟓 𝐩𝐬𝐢𝐠 𝐰𝐡𝐞𝐧 𝐪 = 𝟑𝟐𝟎 𝐒𝐓𝐁/𝐃 Dr Aliyu Adebayo Sulaimon

Solution Nodal Solution of a Well  Using the well test results, calculate 𝒒𝒎𝒂𝒙 from Vogel equation  By assuming different 𝑷𝒘𝒇 , use the same equation to generate the inflow performance curve  Using the traverse curve for 2-7/8” and based on the well information, the outflow curve can be generated.

 𝒒𝑳 = 𝟏𝟐𝟔𝟎

𝑺𝑻𝑩 𝑫

@ 𝟑𝟑𝟐𝟖 𝒑𝒔𝒊𝒈

 𝒒𝒐 = 𝟔𝟑𝟎 𝐒𝐓𝐁/𝐃 Dr Aliyu Adebayo Sulaimon

Tubing Performance Relationship Models Two categories of TPR models:  Homogenous flow models (Poettmann and Carpenter, Cincchitti, Dukler et al.) 

Treats multiphase as homogenous mixture



Neglects liquid holdup effects (no-slip assumption)



Less accurate and requires calibration with local operating conditions in field applications



Advantageous in handling gas-oil-water three-phase and gas-oilwater-sand four-phase system



Can be programmed easily


Review of Wellbore Hydraulics (Cont’d)  Separated-flow models o o o o

Lochhart and Martinelli correlation Duns and Ros correlation Gray correlation Hagedorn and Brown method



Separated-flow models are more realistic than the homogenousflow models



Often presented in the form of empirical correlations



Effects of liquid holdup (slip) and flow pattern are considered



It is difficult to code them in computer programs since most correlations are presented in graphic form Dr Aliyu Adebayo Sulaimon

Use of Nodal Analysis in Tubing Sizing 

As much as 80% of the total pressure loss in a well can occur in producing the fluids from bottom-hole to the surface



The tubing size must be selected before the well is drilled; tubing size dictates the casing size which dictates the hole size



There is an optimum tubing size for any system.



Tubing too small might restrict the flow-rate due to excessive friction loss, and tubing too big might cause a well to load up with liquids and die


Use of Nodal Analysis in Tubing Sizing 

To determine the optimum size of tubing to be installed several of different sizes of tubing outflow curves must be calculated maintaining the rest of the well characteristics as constant



Sometimes it is necessary to use the traverse curve for each particular size of tubing to get a solution point and compare with the others.



Several software programs exist in the market to select tubing size


Outflow Performance for Different Tubing 4000

d = 1.995

d = 2.441

Pwf, psia

3000

2000

1000

0 0

10000

20000

q, Mscf/day

30000

40000


Lecture Review 





Besides the reservoir and lower completions, which other two are considered components of the production system? • • • •

Tubing Wellhead Flowlines Control valves

• • • •

Gradient curves Inflow curves Outflow curves Nodal curves

• • • •

Slug flow Mist flow Churn flow Stratified flow

What type of curve can be constructed using flow correlations, which incorporate the two-phase equation modified upon flow mapping?

Besides bubble and annular, which other two are flow regimes in vertical pipes?


Lecture Review 

How is a “nodal solution” determined? • • • •



Which of the following is an application of the Nodal Analysis approach? • • • •



By doing a balance material of the flow-rate coming into the node and leaving out the node By drawing the inflow and outflow in the same scale and getting a cross point By selecting a point (node) at any place of the production system By calculating the pressure losses of the production system

Selecting Frac pumping schedule Selecting choke size Selecting artificial lift method Selecting wellhead pressure rating

In a nodal solution graph, what would probably happen to the outflow curve if the wellhead pressure is increased? • • • •

It would stay the same It would shift to the right It would shift to the left Wellhead pressure does not influence outflow curve


QUESTIONS?

THANK YOU


SEMESTER 5/3 PCB 3063 – PRODUCTION ENGINEERING I

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