GAS GA S FIEL FIEL D ENGINEE ENGINEERING RING Gas Well Performance © 2017 INSTITUTE OF TECHNOLOGY PETRONAS SDN BHD All rights reserved. No part of this document may be reproduced, stored in a retrieval system or transmitted in any form or by any means (electronic, mechanical, photocopying, recording or otherwise) without the permission of the copyright owner.
CONTENTS • Gas Well Performance • Static Bottom Hole Pressure (Static BHP) • Flowing Bottom Hole Pressure (Flowing BHP)
LEARNING OUTCOME OUTCOMES S At the end of the session, students students should be able to: • Determine static bottom-hole pressure (static BHP) using different methods • Determine flowing bottom-hole pressure (flowing BHP) using different methods
INTRODUCTION • Gas wells’ monitoring is important for the oil and gas industry because of the growth of the NG economic values • Figure 1 illustrates a schematic of a typical gas producing well • Ability of a gas reservoir to produce from a given set of reservoir conditions depends directly on the flowing bottom-hole pressure, Pwf • The ability of the gas reservoir to produce a certain quantity of gas depends both on the inflow performance relationship (IPR) and the flowing BHP • The flowing BHP depends on the separator pressure and the configuration of piping system
INTRODUCTION
Figure 1. Gas Producing Well Schematic
FLOWING BOTTOM-HOLE PRESSURE • Flowing bottom-hole pressure can be expressed as: = + ∆ + ∆ℎ + ∆ + ∆
= flowing pressure, psia = separator pressure, psia ∆ = pressure drop in flowline, psia ∆ℎ = pressure drop in surface choke, psia ∆ = pressure drop in well tubing, psia ∆ = pressure drop in in other restrictions, such as subsurface safety valves, and valves, fittings
Eq. (1)
INTRODUCTION • These conditions can be expressed as (Lee and Wattenbarger 1996, Eq. 4.100): = 1000 ∗ ( − )
Eq. (2)
• The straight line’s extrapolation to the square of the pressure difference evaluated at pwf = 14.7 psia determines the absolute open-flow (AOF) • AOF is the rate at which the well could produce if the BHFP were maintained at atmospheric pressure, it is also described as maximum allowable production rates for individual wells qg = gas flow rate (MMscf/D) C = stabilized performance constant, MMscfd/(psia2)n n = reciprocal of the slope of the line when log ( − ) is plotted vs log qg (0.5 for turbulent/mom-Darcy flow and 1 for Darcy flow) ҧ = shut-in average reservoir pressure, psia = flowing pressure, psia
ABSOLUTE OPEN FLOW
STATIC AND FLOWING BOTTOM-HOLE PRESSURES • Static or flowing pressure at the formation must be known in order to predict the productivity or absolute open flow potential (AOF) of gas wells • Preferred method to determine the bottom-hole pressure is to use a bottom-hole pressure gauge (down-hole pressure gauge) • Static BHP or flowing BHP can also be estimated from wellhead data (gas specific gravity, well head pressure, well head temperature, and well depth)
BASIC MECHANICAL ENERGY EQUATION • Mechanical energy balance in the case of steady-state flow (Lee and Wattenbarger 1996, Eq 2.26, Eq. 4.21): 144 + + + = −
Eq. (3)
• Mechanical energy balance in the case of steady-state flow with no mechanical work is done on the gas (compression) or by the gas (expansion through a turbine), the term ws is zero: 144 + + + = 0 ρ = density of the fluid, cuft/lbm p = pressure, psia g = local acceleration due to gravity, ft/sec2 gc = constant, 32.17 ft-lbm/lbf-sec2 Z = distance in the vertical direction, ft = average velocity of the fluid, ft/sec
Eq. (4)
= pressure drop due to kinetic energy, psia
F = energy loss resulting from friction, ft-lbf/lbm ws = total shaft work done by system, ft-lbf
BASIC MECHANICAL ENERGY EQUATION
STATIC BHP FOR SLANTED WELLS • Second term in Eq. (3) & Eq. (4) express kinetic energy, where changes in kinetic energy for gas flow are typically small (neglected)
• The reduced form of the mechanical energy equation may be written as: 144 + + = 0 2 ′ f = Moody friction factor, dimensionless L = distance along flow path, ft d‘ = internal pipe diameter, ft
= pressure drop due to friction, psia
Eq. (5)
STATIC BHP FOR SLANTED WELLS • For a static gas column, the basic mechanical energy balance is: 144 + = 0
Eq. (6)
• Assuming that g=gc = − 144
Eq. (7)
STATIC BHP FOR SLANTED WELLS • For slanted wells, the total length L and the depth Z are related: =
Eq. (8)
• In differential form: =
Eq. (9)
STATIC BHP FOR SLANTED WELLS • Density of a gas ( g ) at a particular point in a vertical pipe at pressure p and temperature T may be calculated as (assuming a single phase fluid that obeys real gas equation of state, EOS) (Lee and Wattenbarger 1996, Eq. 4.7): Eq. (10)
STATIC BHP FOR SLANTED WELLS • Combining Eq. (7), Eq. (9), and Eq. (10):
Eq. (11)
Basic Energy Equation • Equation (11) forms the basis for all the methods developed to estimate BHSP from surface measurements
AVERAGE T & Z – FACTOR METHOD • •
•
Both gas density and gas deviation factor are functions of pressure and temperature (Lee and Wattenbarger 1996, Eq. 4.9) Pressure and temperature dependent and change with well depth. Because of this dependency, it is difficult to solve the differential equation (Eq. (11)) In order to simplify the solution the average temperature and z factor method is used, it assumes the T and z-factor to be constant: Eq. (12)
The exact solution is:
pts = static tubing-head pressure, psia pws = BHSP, psia s = average T and z-factor method parameter, dimensionless
where
Eq. (13) Eq. (14)
AVERAGE T AND z – FACTOR METHOD • Because depends on iterative process:
which is unknown, solution requires an
1. Assume a value of BHSP, from:
, a good guess can be obtained
2. Compute avg pressure & temperature & use it to find avg zfactor 3. Calculate
with the earlier equation.
4. Iterate on steps 2 through 4 until
converges.
EXAMPLE 1 Calculate the BHSP of a gas well with the average T and zfactor method with the data given below:
EXAMPLE 1
EXAMPLE 1
EXAMPLE 1
•
Because of the simplifying assumptions made in its development, this method is not accurate for deeper wells and alternate methods should be used
REVIEW OF BSHP ESTIMATION • Average Temp. & z-Factor Method
Eq. (12)
Eq. (15)
The exact solution is: where
Eq. (13) Eq. (14)
POETTMANN’S METHOD • Assumes an average (constant) Temperature but allows the zfactor to vary with pressure thus requires a more rigorous calculation technique (Lee and Wattenbarger 1996, Eq. 4.12) • Substituting
into earlier equation and separating variable yields
Eq. (16)
• Integrate only the right side: Eq. (17)
POETTMANN’S METHOD • Equation (17) is re-written in terms of pseudo-reduced pressure for wider applicability (Lee and Wattenbarger 1996, Eq. 4.14) • : Eq. (18)
• Later, Poettmann broke the integral in two parts, choosing an arbitrary integration limit of 0.2: Eq. (19)
• Re-arranged:
Eq. (20)
POETTMANN’S METHOD • The integral
has been numerically evaluated and
tabulated as a function of Ppr and Tpr • This method does not require iteration • Inclusion of z-factor in the integral causes this technique to be potentially more accurate and applicable over a wider range of p & T conditions than the average T and z-factor method
POETTMANN’S METHOD • Lee and Wattenbarger (1996) Appendix B page 275
POETTMANN’S METHOD Solution procedure: 1. Compute value of non-integral term and call it K: Eq. (21)
2. Compute the pseudoreduced wellhead pressure, average pseudoreduced temperature, 3. Using the integral
and
, and the
, read from the table the value of the
POETTMANN’S METHOD Solution procedure: 4. Determine
by computing Eq. (20) using Eq. (21)
and appendix B
5. With the value of the integral in step 4 above, and the value of average Tpr , read the value corresponding to Ppr
6. From the definition of pseudoreduced pressure, compute:
EXAMPLE 2 Using the well data given in Example 1. calculate the BHSP using the Poettmann Method:
EXAMPLE 2
EXAMPLE 2
EXAMPLE 2
EXAMPLE 3 Pts = 2,450 psia T ts = 70 oF T ws = 300 oF L = 5,000 ft θ =
45.5o where
Gas Properties ɤ g = 0.7 p pc = 700 psia T pc = 400 oR
What is BHSP?
EXAMPLE 3 1. Calculate K 0.01875 0.01875 0.7 5000 cos(45.5) = = = 0.07 645 ത
2. Calculate pseudoreduced wellhead P and average pseudoreduced T , =
2450 = = 3.5 700
+ 300 + 460 + 70 + 460 2 2 = = = 1.6 400
3. Enter Ppr,ts and into table in Appendix B and read
= 2.642
EXAMPLE 3
EXAMPLE 3
2.642 + 0.07 = 2.712
= 2.712
1.6 3.818 ( )
CULLENDER AND SMITH METHOD • Makes no simplifying assumptions for T or z-factor • It has more rigorous and wider applicability • Begin with the Equation 12:
Eq. (12)
• Separate variable and rearrange:
Eq. (22)
CULLENDER AND SMITH METHOD • Equation (22) right hand side reduces to:
Eq. (23)
• Left hand side (LHS) of Eq. (23) contains both p and T dependent variable, it is difficult to evaluate the exact solution • Cullender & Smith proposed a numerical approximation for the LHS of Eq. (23) • Their method consisted of a two steps procedure that used the intermediate value for greater accuracy
CULLENDER AND SMITH METHOD • They defined the LHS integral as (Lee and Wattenbarger 1996, Eq. 4.19):
Eq. (24)
• Where I is the integrand evaluated at either the surface, midpoint, or bottomhole conditions as denoted by subscripts ts , mp , and ws , respectively • Integrand I is defined as: Eq. (25)
CULLENDER AND SMITH METHOD Solution procedure:
23
23
CULLENDER AND SMITH METHOD Solution procedure:
The main Equation Used for estimating BHSP
EXAMPLE 4 Using the well data given in Example 1. calculate the BHSP using the Cullender and Smith Method:
EXAMPLE 4
pseudoreduced
25
EXAMPLE 4
EXAMPLE 4
EXAMPLE 4
ACTIVE LEARNING 3 – CLOSURE REVIEW PAIRS • Make a group of 2 students • Discuss 1 major topic covered during this session • Each group explain for each topic the following: 1. What is the topic and why is it important? 2. What activities undergone to learn about the topic? 3. What interests you most about the topic? • Student volunteer to explain his/her answer for one topic, if your answer is great then you will get a PRIZE
COURSE SUMMARY – BOOKEND CLOSURE FOCUSED DISCUSSION 1. Determine static bottom-hole pressure (static BHP) using different methods 2. Determine flowing bottom-hole pressure (flowing BHP) using different methods
CLOSURE • Fill in the course survey only 4 short questions • (1 minute)
Rating (scale 1-5):
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Q&A Session
FOURTH WEEK QUESTIONNAIRE SUMMARY RED (STOP) Writing base assignment (hand written)prefer calculation Pop quiz at 8 am class/2 hours lecture/10 min late rule
Slow down teaching pace
More exercise/example/explanation/break
Closure review/Active learning
Smile more :) you have beautiful smile
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Sometimes don’t understand
FOURTH WEEK QUESTIONNAIRE SUMMARY GREEN (GO) 11am -1 pm class
Average Rating = 4.7/5
Patient/So kind/considerate Lecture pace/Time management Exercise/ Solutions Giving tips for test and fi nal exam/Summarize step/method in simple way The break Good explaination on Example (calculation) during lecture /tutorial Good/helpful and interesting lecture/ good slides/Everything/ All is well/ Keep Rocking 0
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BHFP • The methods developed for computing BHFPs from surface measurements consider the flowing wellhead pressure, pressure exerted by the weight of the gas column in the production string and the energy losses resulting from gas flowing through pipe • Energy balance equation simplifies to (Lee and Wattenbarger 1996, Eq. 4.21): Eq. (5)
Where gc is gravitational constant, in SI units gc=1 kg-m/N-s2, in field units gc=32.17 lb-ft/lbf-s2 • Using the Real Gas EOS, the equation becomes: Eq. (26)
BHFP • For a real gas flowing through a conduit with a circular cross section, the average gas velocity at any point is: Eq. (27)
• Substituting Eq. 27 into Eq. 26 yields: Eq. (28)
BHFP • If we convert the dimensions of the pipe diameter from feet to inches (d’ to d) and substitute dZ=cosθ dL, Eq. 28 becomes:
Eq. (29)
• This equation forms the basis for all methods developed to estimate BHFP’s from surface measurements in gas wells
PRESSURE LOSSES DUE TO FRICTION • BHFP’s equations have an “f ” term, the Moody friction factor, which is a function of:
• gas properties • gas flow rate • internal pipe roughness • type of flow regime (laminar, transitional, turbulent) • Except for laminar flow, the frictional losses are estimated using published correlations or develop in the lab
FLOW REGIME DETERMINATION • Reynolds Number, Nre (which is the dimensionless ratio of the fluid inertial forces to the viscous forces), it is often used to identify the nature of the flow regime. It is defined by:
• In terms of field units for gas flow:
Eq. (30)
LAMINAR FLOW • Fluid moves in imaginary layers, each layer gliding smoothly over an adjacent layer: • only molecular interchange of momentum • viscous shear force dominate & dampen turbulence • friction losses are caused primarily by the shear forces • Flow is laminar when • For laminar flow, Moody friction factor, “ f ” is inversely proportional to Reynolds number: Eq. (31)
TRANSITIONAL (UNSTABLE FLOW) • Reynolds number is between 2000 and 4000
• Both viscous and inertial forces become important • Cannot theoretically predict pressure losses and must rely on published empirical correlations derived from the lab experiments such as Colebrook’s: Eq. (32)
TURBULENT FLOW • Reynolds number is much higher than 4000 • Fluid particles move in a very erratic motion often interchanging momentum in the transverse direction • The friction factor is independent of Reynolds number and depends only on the relative roughness • Nikuradse’s empirical relationship can be used: Eq. (33)
JAIN AND SWAMEE’S CORRELATION • For unstable and turbulent flowing conditions (Nre > 2,000) and assuming E = 0.0023 inches, the following method can be used to calculate f directly:
Eq. (34)
FANNING FRICTION FACTOR • Equations 31 to 34 can be used to calculate f as a function of flow regime, gas properties, gas flowrate and internal pipe roughness • We can also use these equations to calculate the Fanning friction factor, f F which is related to the Moody Friction factor, f by Eq. (35)
B RE REA A K FO FOR R 3 MIN MINUT UTES ES © 2017 INSTITUTE OF TECHNOLOGY PETRONAS SDN BHD All rights reserved. No part of this document may be reproduced, stored in a retrieval system or transmitted in any form or by any means (electronic, mechanical, photocopying, recording or otherwise) without the permission of the copyright owner.
AVERAGE T AND z-FACTOR METHOD • Both gas density & z-factor z-fact or are p and T dependent and change with well depth • If T and z-factor are assumed constant then a solution can be obtained as follows • The base equation can be re-arranged as (Lee and Wattenba attenbarge rgerr 1996, 1996, Eq. 4.35): 4.35): Eq. (36)
AVERAGE T AND z-FACTOR METHOD • Separating variable yields:
• Multiply ply both sides by cos cos
and re-arr arrange:
AVERAGE T AND z-FACTOR METHOD • Further, if we multiply the numerator and denominator on the left side by p2 and apply the limits of integration, we have: Eq. (37)
• Following integration we can express Eq. (37) in terms of BHFP, pwf : Eq. (38)
SOLUTION TECHNIQUE • Because depends on Pwf which is unknown, solution requires an iterative process. 1. Assume a value of BHFP, Pwf , a good guess can be obtained from:
2. Compute avg pressure & temperature & use it to find avg zfactor and gas viscosity 3. Calculate the friction factor, “ f ”
Solution Technique 4. Calculate
5. Depending on the value of NRe, compute f using one of the four equations or correlations 6. Calculate Pwf with the earlier equation
7. Iterate on steps 2 through 4 until Pwf converges
EXAMPLE 5 • For the data given below, calculate the BHFP using the average temperature and z factor method. Assume that a one step calculation scheme is sufficiently accurate:
EXAMPLE 5
EXAMPLE 5
EXAMPLE 5
EXAMPLE 5
BREAK FOR 3 MINUTES © 2017 INSTITUTE OF TECHNOLOGY PETRONAS SDN BHD All rights reserved. No part of this document may be reproduced, stored in a retrieval system or transmitted in any form or by any means (electronic, mechanical, photocopying, recording or otherwise) without the permission of the copyright owner.
Sukkar & Conrnell Method for BHFP • Similar to the Poettmann’s method for BHSP.Assumes that Temp. can be represented by avg. value • No avg. z-factor assumption
• The base equation above can be re-arrange as:
Sukkar & Conrnell Method: Derivation
Eq. (39)
Sukkar & Conrnell Method for BHFP
Sukkar & Conrnell Method: Derivation
Eq. (40)
Sukkar & Conrnell Method: Derivation
Eq. (41)
Sukkar & Conrnell Method: Tables • The LHS integrals have been evaluated numerically and are tabulated in various references similar to the Poetmann’s method for BHSP.
Cullender & Smith Method for BHFP • Unlike the two previous methods, this method makes no simplifying assumptions for the variation of temperature and zfactor in the wellbore • To achieve accuracy, the wellbore is divided into two (or more segments) • Beginning with the base equation and separating variables:
Eq. (42)
Cullender & Smith Method for BHFP
Dividing the numerator and denominator of the left side of Eqn 32 by (Tz/p)2 and rearranging yields:
After
integrating the right side and reversing the limits of integration, we have
Cullender & Smith Method for BHFP LHS
integral cannot be evaluated.
Cullender
& Smith proposed a numerical integration scheme (similar as in BHSP)
Split
the well in two or more segments to improve accuracy
Cullender & Smith Method for BHFP RHS
Gas Viscosity from Lee and Wattenbarger Ch. 1 • Equation 1.63 – 1.67, where viscosity in cP and density in g/cm3
High P Gas Viscosity and 1 atm P Gas Viscosity Ratio from Carr et al. (Ikoku 1992) Ch. 2.8 • To determine high P gas viscosity, the gas viscosity at 1 atm has to be determined from plot that relates Molecular weight and T • Then using plot that relates Ppr and Tpr to give the ratio of high P viscosity and 1 atm viscosity • Lastly, the high P viscosity can be calculated as multiplication of the ratio with the 1 atm viscosity
Gas Viscosity at P=1atm from Ikoku (1992) Ch. 2.8
High P Gas Viscosity and 1 atm P Gas Viscosity Ratio from Ikoku (1992) Ch. 2.8
Cullender & Smith Calculations
Cullender & Smith Calculations
Cullender & Smith Calculations
BREAK FOR 3 MINUTES © 2017 INSTITUTE OF TECHNOLOGY PETRONAS SDN BHD All rights reserved. No part of this document may be reproduced, stored in a retrieval system or transmitted in any form or by any means (electronic, mechanical, photocopying, recording or otherwise) without the permission of the copyright owner.
Example 6 With
the same data given in Example 4, calculate the BHFP using the Cullender and Smith method assuming a two-step calculation scheme is sufficiently accurate.
Example 6
Example 6
Example 6
Example 6
Example 6
ACTIVE LEARNING 3 – CLOSURE REVIEW PAIRS • Make a group of 2 students • Discuss 1 major topic covered during this session • Each group explain for each topic the following: 1. What is the topic and why is it important? 2. What activities undergone to learn about the topic? 3. What interests you most about the topic? • Student volunteer to explain his/her answer for one topic
COURSE SUMMARY – BOOKEND CLOSURE FOCUSED DISCUSSION 1. Determine static bottom-hole pressure (static BHP) using different methods 2. Determine flowing bottom-hole pressure (flowing BHP) using different methods
CLOSURE • Fill in the course survey only 4 short questions • (1 minute)
Rating (scale 1-5):
THANK YOU © 2013 INSTITUTE OF TECHNOLOGY PETRONAS SDN BHD All ri gh ts res erv ed. No par t of th is do cu men t may be rep ro du ced , st or ed in a ret rie val sy st em or tr ans mit ted in any fo rm or by any mean s (elect ro nic , mechanical, photocopying, recording or otherwise) without the permission of the copyright owner.
Q&A Session
