Gas reservoir engineering ( U. Abdulhamid )

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•

A. A. Urayet, Ph.D.

Associate Professor /Al-Fateh University

· NATU,RAL-G.As

RESERVOIR ENGINEERING

Prepared By:

Dr. Urayet, Abdulhamid

,.

--

:

.

Part of the Technical Training Program organized

by:

The Petroleum Research Center, PRC

Tripoli, 2004

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---~---This course offers a comprehensive review of all aspects related to Natural-Gas Reservoir Engineering

from the Producing Formation to the surface:

i .... ..1r

-- The course has been :divided into 8 main chaplers as follows: .... o Definitions and Classifications

oGas Laws & Gas Deviation Factor

o Natural-Gas Physical Properties

o Gas Volumetrics and Gas Material Balance Calculations

o Inflow Performance & Deliverability Testing

o Transient Pressure Analysis o Vertical Flow Performance o Gas Field Development

This course does not consider advanced aspects related to Condensate-Bearing Gas reservoirs

such as vapor-liquid equilibrium, phase behavior, etc. The analytical solutions are presented without derivations

except when necessary

to understand the main assumptions involved and/or the sources of uncertainty in the results. Practical application to actual field data are discussed and practical analysis procedures are illustrated through

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Natural-Gas Reservoir Enqineerinq

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Cont'd Chapter 4.: GAS VOLUMETRICS 4.3.1 Mathematical formulation

4.3.2 Analysis of free-gas reservoirs 4.3.3 Volumetric reservoirs

4.3.4 Water-drive gas reservoirs

4.3.5 Treatment of condensates in the gas MBE

5.

• · Gas equivalent of hydrocarbon condensates

• Gas equivalent of condensing water vapor

~ Chapter 5 : INFLOW PERFORMANCE AND DELIVERABILITY

TESTING ~

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5.1 5.1.1 5.1.2 5.2 5.2.1 5.2.2 5.3 6. 6.1 6.2 6.3 6.4 7. 7.1 7.2 7.2.1 7.2.2 7.3 7.4 Flow-after-Flow Test Flow-after-flow procedure Flow-after-flow test analysis The Empirical method The Modified method

The Exact (Pseudo-gas Potential) method Isochronal Testing

Isochronal test procedure Isochronal test analysis

Accounting for the Condensates in the Analysis Chapter 6 : TRANSIENT PRESSURE ANALYSIS Introduction

The

P;

Analysis Method The

Pw

Analysis Method

The Pseudo-Gas Potential Method

Chapter 7 : VERTICAL FLOW PERFORMANCE General Flow Equation in Pipes

The Trial and Error

T -

z Method Static bottom-hole pressure calculations Flowing bottom-hole pressure calculations Sukkar & Cornell Method

Practical Aspects

Gas flow in the annulus

Temperature distribution in the wellbore Effect of liquid production

8. Chapter 8 : IMPORTANT RESERVOIR ASPECTS OF GAS FIELD DEVELOPMENT

8. 1 Introduction

8. 2 Recovery in Gas Reservoirs 8. 3 Reservoir Deliverability

8.4 Number of Wells and Well Spacing

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Natural Gas Reservoir Engineering Dr. A. A. Urayet

Chapter 1 DEFINITIONS AND CLASSIFICATION

NATURAL GAS is defined as a vaporous miXture of hydrocarbons, usually containing varying amounts of impurities .

To be more specific, a NATURAL GAS consists principally of the more volatile members of the Paraffin series (Cn H₂₀+_2).The "more volatile" members signify hydrocarbons containing one to four carbon atoms per molecule, such as Methane (CH_{4 ), Ethane}(C₂H _{6 ), Propane}(C3Hg), and Butane

(C4H10>·

In addition to the hydrocarbon components, different types of impurities, such as Carbon Dioxide

(C0

_{2 ), Hydrogen Sulfide}

(H

₂

S),

and Nitrogen

(Nz),

are commonly present in natural gases. The chemical composition of the natural gas is pre-determined by the geologic environment of the source rock, deposition, maturation, migration and trapping. ·

Natural free gas accumulations occure in different environments such as a single gas phase (i.e. no liquid hydrocarbons) with interstitial water in a volumetric reservoir, or as a single gas phase underlain by a thin column of condensing hydrocarbons, or as a gas cap overlying an oil reservoir, or finally as a single gas phase underlain by a water aquifer.

Natural gas occurs in different environments including conventional gas reservoirs, gas in tight sands, gas in tight shales, gas occluded in coal, and gas in geopressured reservoirs. However, in this course we only consider Conventional Gas Reservoirs.

Conventional Natural gas reservoirs are, commonly, classified into three main categories, as follows:

1. Dry natural gas reservoirs 2. Wet natural gas reservoirs

3. Condensate-bearing gas reservoirs

In general, Drv gas reservoirs are characterized by the negligible amount of hydrocarbon liquids condensing at the separator conditions, Wet gas reservoirs are characterized by more liquids condensing from the gas at separator conditions, and possibly in the production string, whereas, Condensate-bearing

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gas reservoirs are characterized by liquids condensing, not only in the separator and production string, but also in the formation, (most noticeably, in the area surrounding the well bore), as the pressure in the reservoir declines below the dew point pressure due to production. In practical field applications, the above classification has been based, in general, on the amount of the separator Liquid Hydrocarbons which are associated with the production of gas from the natural gas reservoir. ·

1.1 DEFINITIONS AND TERMINOLOGY

It is important to introduce, here, some basic definitions which are related to gas engineering in general, and which will be used throughout these notes. More definitions related to each specific topic will be introduced in following chapters.

Liquid Recovery , LR

LR

=

volume of hydrocarbon liquids (in STB) accumulating under separator conditions per one million scf (MM scf) of gas produced to the surface . LR is normally used to classify the gas reservoir into dry or wet. It is important to note that this definition should be used with caution when applied to the case of condensate-bearing gas reservoirs, since LR, in this case, represents the total amount of hydrocarbon liquids accumulating in the separator, which includes the liquids condensing from the gas under separator conditions, in addition to, liquids which have, already, condensed in the formation, and are produced once the critical saturation of liquid has been exceeded in the formation.

Even though some engineers use the term Gas Oil Ratio as the inverse of the Liquid Recovery, however, it is advisable to restrict the use of the GOR term to

oilreservoir calculations and terminology, and the term LR to the gas reservoir

terminoloqv. ·

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Mole Fraction .

x;

The chemical analysis of a gas mixture is normally expressed in terms of a mole fraction, x;, of each component, i, where,

number of moles of the component

(i)

Xi=~~~~~~~~~~~~~~~~~

total number of moles of the gas

Eq (1.1)

Typical examples of the chemical analysis of different natural gases will be given later in Tables (1.1, 1.2, 1.4, and 1.5). It is important to note that in these examples, the sum of the mole fractions of all components heavier than the normal Heptane, are grouped together under the term "Heptanes plus, C;''. Some laboratories report the gas analysis to

c;

_{0 ,}or to C~. especially in case of gas containing appreciable amounts of heavier hydrocarbon components.

Apparent Molecular Weight. M

Eq (1.2)

I

The Molecular weights of the different hydrocarbon and non-hydrocarbon ·components,

M;,

normally present in natural gases and crude oils are given in

Appendix-A, Table-1.1.

The number of pound-moles of a gas mixture, n, can be calculated as follows,

n

=

mass of the gas mixture (lb)

m

Apparent molecular weight

M

L,xi.Mi

Gas Specific Gravity,

y g

Mgas

Yg

= Mair

M

28.966

Eq (1.3) Eq (1.4)

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Example -1. 1

The chemical composition of the free gas produced from the Braebum field in Canada is given in columns (1 and 2) of the attached Table. Calculate the apparent molecular weight , M, and .the gas specific gravity,

r

g.

Solution

• Use Table 1.1/Appendix-A to read the molecular weights,of the different gas components, (column 3)

• Multiply the mole fraction of each component by its molecular weight as shown in column 4.:

• Using Eq (1.2), calculate the molecular weight of the gas as follows: M = LXi.Mi = 16.7794

• Using Eq ( 1.4) calculate the specific gravity of the gas as follows :

Mgas M

r

g = = = o.5793

Mair 28.966

Braeburn Gas field, Canada

Components composition molecular X;.M;

x;( mole%) weight, M (1) (2) (3) ( 4)=(2)X(3)/100 Methane _96.39 _16.043 _15.4638 Ethane _0.75 _30.070 _0.2253 Propane _0.11 _44.097 _0.0485 (lso. +N) Butane _0.03 58.124 0.0174 (lso. +N) Pentane _0.10 72.151 0.0722 Carbon Dioxide 0.97 44.010 0.4269 Hydrogen Sulfide _1.04 34.076 . 0.3544 Nitrogen _0.61 _28.013 _0.1709 100.00 . 16.7794 AAU/GAS/GAS I .doc 4 ~ t ' / · .. _{- -}_.~"'

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Recombined Reservoir-Gas Specific Gravity

The heavier components of the gas produced from a free gas reservoir would condense into liquid at the surface conditions. In order to obtain the composition of the reservoir gases and define the gas properties under · reservoir conditions, it is necessary to monitor the flow rates, the compositions, and the related properties of the gas and condensate streams. Once the necessary separator data is obtained, accurate determinations of the gas composition in the reservoir can be obtained experimentally or analytically. For quick estimation of the reservoir gas gravity, the following equation can be used: Yg =

4584

Yes Ygs

+

Res

1+132,800

Yes

MoRes

where,

r

g = specific gravity of the reservoir gas

r

gs = specific gravity of the separator gas

r

cs = specific gravity of the stock tank condensate

Eq (1.5)

Res =gas to condensate ratio, ( scf separator gas I one STB condensate)

M

₀ = Molecular weight of the tank oil

If the value of

M

₀ is not known, it can be estimated using the following equation:

IM

6084

0 ₀

AP!

-5.9

Eq (1.6)

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Natural Gas Reservoir Engineering _{Dr. A. A. Urayet}

Example -1. 2

Calculate the specific gravity of gas in the reservoir, given the following data : separator pressure

specific gravity of stock tank condensate specific gravity of the separator gas Liquid Ratio =680 psia

=

0.72

=

0.66

=

48 STB condensate I MM scf

Solution

141.5

1) calculate

AP!=

-131.5

=

-131.5

=

65.03 Yes

0.72

2)

R

=

1,000,000

=

1,000,000

=

_{20 833}

cs

LR

48 '

3) Calculate

M

₀

=

6084

-

6084

=

102.892

0

_AP!

-5.9

65.03-'- 5.9

4584

Yes Ygs

+

R

3J

r

g

=

cs

1+132 800

Yes

'

_MORCS

AAU/GAS/GAS I .doc

0.66 + 4584(0.72)

_ _ _ _

20_..::,_83_3 _ _ -

0.7835

1 + 132,800(0.72)

(102.892)(20,833)

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1.2 DRY GAS RESERVOIRS

Although small amounts of heavier hydrocarbon components can be present, most DRY natural gases consist predominantly of Methane

(CH

4 }, the mole percentage. of which may . be as . high as 98% ·of the hydrocarbon fractions. Furthermore, Methane

(CH

_{4 ) and Ethane}

(C

_{2 H6)}would constitute as high as 99% of the total hydrocarbon mole composition. Considering this Universally accepted classification, there are NO Dry Gas Reservoirs in Libya.

From a practical engineering point , the DRY gas is usually defined as a gas which is associated with less than TEN barrels of separator liquids per Million

scf of gas produced (i.e. LR< 10 STB I MM sen. The very small amount of

hydrocarbon liquids will usually have an API gravity of 70+, corresponding to liquid specific gravity less than 0.7.

TABLE 1.1

Typical Composition of natural DRY gas reservoirs

COMPONENTS COMPOSITION ( mole % )

Examole-A * Examole - B ** Methane 96.55 96.39 Ethane 2.15 0.75 Propane 0.45 0.11 (lso. +N) Butane 0.18 0.03 (lso. +N) Pentane 0.07 0.10 Hexane 0.25

---Heptanes plus 0.04

---Carbon Dioxide 0.31 0.97 Hydrogen Sulfide

---

1.04 Nitrogen

---

0.61 100.00 100.00 C1 % 96.85 98.98 (C1 + C2) % 99.01 99.75

* Example -A: West Cameron Pool, Louisiana Gulf Coast, USA ** Example - B : Belloy Formation , Braeburn Field , CANADA

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1.3 WET GAS RESERVOIRS

Some natural gas reservoirs yield condensed liquids at ratios of 10 - 20 barrels of separator liquids per Million scf of gas produced. Such gases are termed WET. They contain greater quantities of the less volatile {heavy) hydrocarbons (C3+) than do DRY gases. According to this Liquid Recovery criteria, only a small number of Libyan gas reservoirs can be correctly termed WET. Two examples of naturally occurring WET gas reservoirs in LIBYA are presented in TABLE 1.2. It is noted that the Liquid Recovery in both reservoirs is 10- 20 STB

I MM scf.

TABLE 1.2

Typical Composition of natural WET gas reservoirs

COMPONENTS COMPOSITION ( mole % )

Examole-C * Examole - D ** Methane 89.132 85.83 Ethane 3.433 5.16 Propane 1.064 2.32 {lso. +N) Butane 0.676 1.38 (lso. +N) Pentane 0.349 0.57 Hexane 0.320 0.29 Heptanes plus 0.990 0.35 Carbon Dioxide 3.303 3.85 Hydrogen Sulfide 0.733 0.25 100.00 100.00

Other fluid 12rogerties

Liquid Recovery 11 16

(STB/MM scf)

Seoarator conditions 449 psia /91° F NA

Gas specific qravitv 0.6764 0.688

Liquid qravitv (API) 51.3 NA

* Example - C : NC 41-G , offshore Trip.oli , Libya ** Example - D : Sahl Field I Shegega reservoir , Libya

AAU/GAS/GAS I .doc 8

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1.4 CONDENSATE-BEARING GAS RESERVOIRS

Condensate-Bearing gases differ in composition from the DRY and WET gases in that they contain appreciable amounts of the heavier hydrocarbons such as Butanes (C4),

P~ntanes

(C

_{5), Hexane}(C_{6 ) ,and Heptanes plus}(Cj).

Condensate-Bearing gas reservoirs will produce more than TWENTY barrels of separator liquids per Million scf of produced gas at normal field separator conditions. Rich Condensate-Bearing gases have been identified with producing ratios as high as (400) barrels of liquid condensate per Million scf of produced gas. The average API of the produced liquids ranges normally from an API gravity of the light crudes ( i.e. 45 ) to a maximum of 60 .

The International terminology for the different classes of NATURAL gases is presented in Table 1.3. Note that the Condensate-Bearing gases are classified into three categories which are termed RICH, MODERATE, and LEAN.

According to this classification, many of the Libyan Gas Reservoirs can be

correctly termed Condensate-Bearing Gas reservoirs. The chemical

compositions for three free gas reservoirs in Libya, representing the three classes of Condensate-bearing gases, are given in Table 1.4 for illustration.

TABLE-1.3

Practical Field Classification of Natural Gases

CLASSIFICATION LIQUID RECOVERY GOR

( STB I MM set) ( scf I STB) Dry <10 > 100,000 Wet 10 - 20 50,000 - 100,000 Condensate - Lean 20- 50 20,000 - 50,000 Condensate - Moderate 50 - 100 10,000 - 20,000 · Condensate - Rich > 100 < 10,000 NOTE:

In the normal field practice in Libya, no distinction is made between the "Moderate" and the "Rich" categories. Ttie term "Rich" is used to represent any free gas reservoir with LR > 50 STB I MM scf.

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Appendix-A I Table 1.1

Physical Constants of Hydrocarbons

1

No. Compound 1 Moth0tto 2 Ethono 3 Propotio 4 -autono 5 l•oltvt-6 -Pontono 7 l•opontono I Noo...,.tono 9 -Hoiruo - · 2-Mothrlpontono I . 3-Mothrlpontono Noohoir-13 2,3-0lmothrlbvtono 14 -Hoptono 15 2-Mothrlhoxono 16 3-Mothrlhoaono 17 3-E~rlpontono 11 2,2-01-thrlpontono 19 2,4-0lmothrlpontono 20 3,3-01-thylpontono 21 Trlptono 22 n-Octono 23 Dliaobutrl 2.C faooctofto 25 n-Nonono 2' n-Docono 27 Cyclopontono 28 Mothylcyclopontono 29 Cycloho•-30 Mothylcydoftoxono 31 Ethylono· 32 Propono 33 1-Bvtono :M Clo-2-Butono 35 Trono-2-But.fto . . . u t - . -1-Ponteno 38 1.2.:..allf041-39 1,3-BvtoclloRO" .co · · -.cl Acotrlono Q Bona-43 T o l -.c.c Ethrlbonaono 45 -x,,1one '6 111-Xylono 41 p-Xylono .cs Styrene 49 laopropylbonaono 50 Motftyl Alcohol 51 Ethyl Alcohol 52 Cor.bon Monoxide 53 · CorbOfl Oloaldo 5.C Hydrogen Sulfide 55 Sulfur Oloaldo 56 Ammonlo 57 Air S4 Hrdro9en 59 Oargen 60 Nitrogen 61 Chlorine 62 Wotor 63 Helium 6.C Ht'droaen Chloride

•

1 _•

IL NH1 HzOi Hz Ci Na Clz HaO Ho HCI 16.0.C3 30.070 .C.C.097 58.12.C 58.12.C 72.151 72.151 72.151 16.178 16.178 86•178 16.178 86.178 100.205 100.205 100.205 100.205 100.205 100.205 100.205 100.205 114.232 114.232 114.232 128.259 142.286 70.135 e.c.162 14.162 98.189 28.05.c 42.081 56.108 -56.108 56.108 56.108 70~135. .S.C.o92 S.C.092 68.119 26.038 78.114 . 92.1"1 ' 106.168 106.168 106.168 106.168 10.C.152 120.195 32.G.42 '6.069 28.010 .C.C.010 :M.076 6.C.059 17.031 28.96.C 2.016 31.999 28.013 70.906 18.015 .C.003 36 . .C61 -258.69 -127 • .CS -.C3.67 31.10 10.90. 96.92 . 12.12 .ct.10 155.72 140.c 1.C5.19 121.52 136.36 209.17 19.C.09 197..32 200.25 17.C.S.C 176.19 186.91 177.58 258.22 228.39 210.63 303 • .C7 345 . .CS '. 120.65 161.25 177.29 213.68 . -15.c.62 -53.90 20.75 38.69 33.58 19.59 85.93 : 51.53 2.C.06 . 93.30 -1.190 176.17 231.13 277.16 29L97 282 • .Cl 281.05 293.29 .306.:M . 148.1(2) 172.92(22) -313.6(2) -109.3(2) -76.6(2.C) 1.c.0(7) -28.2(2.Cl -317.6(2) -.C23.0(2.C) -297 . .C(2) -320 . .C(2) -29.3(24) 212.0 -121(16)

• ...

: i -••

...

l :

lk

·-> (5000) (800) 190 • 51.6 72.2 15.570 20.4.C 35.9 .c.956 6.767 6.098 9.856 7 • .CO.C 1.620 ·2.211 2.130 2.012 3.492 3.292 2.773 3.374 0.537 1.101 1.708 0.179 0.0597 9.91.C 4.503 3.26.C 1.609 226 • .C 63.05 45.s.c 49.80 63 • .CO 19.115 (20.) (60.) 16.672 3.22.c 1.032 0.371 0.26.C 0.326 o.:M2 (0.2.C) 0.188 .C.63(22) 2.3(7) 39".0(6) 88.(7) 212.(7) 154.(7) 0.9.C92(12) 925.(7) 0

·i

c

1!

1~

...

:u:

...

IL -296.46d -297.89d -305.8.Cd -217.95 '..;255.29 -201.51 -255.83 2.11 -139,58 -2«.63 -1.C7.72 -199.38 -131.05 -180.89 -181 • .CS -190.86. -182.63 -210.01 -12.12 -70.18 -132.07 -161.27 -6.C.28 -21.36 -136.91 -224.« 43.77 -195.87 -272 • .C50 -301 • .c5d -301.63d -218.06 -157.96 . -220.61 -265.39 -213.16 -164.02 -230.7.C -114.• .Cl.96 -138.9.C -138.91 -13.30 -5.C.12 55.86 -23.10 -140 .• 82 -1"3.82(22) -173 • .C(22) -3.C0.6(2) -117 .2(7) -103.9(7) -107.9(2) -.C3.C.8(2.C) -361.8(2.C) -3.C6.0(2.Cl -U9.8(2A) 32.0 -173.6(16)

•

;;

..

t

:

•

a': 667.8 707.8 616.3 560.7 529.1 .CS.8.6 490 • .C '6.C.0 436.9 436.6 453.1 4"6.8 .CS3.5 '396.8 396.5 408.1 '19.3 402.2 396.9 .C27.2 .C28 • .c • 360.6 360.6 372 . .C 332. 30.C. ·653.8 S.CS.9 591. 503.5 729.8 669. $83. 610. 595. 580 • 590. (653.) 628. (558 • .C) 890..C 710 • .C 595,9 523.5 5.CU 513.6 509.2 sao. "65 • .C 117.C.2(21) 925.3(21) 501 .(17) 1071.(17) 1306.(17) 11.C5.(2.Cl 1636.(17) 5.C7.(21 188.1(17) 736.9(2.C) .C9J.0(2.C) 1118 . .C(2.Cl 3208.(17) 1198.(17> Crltlcol conatonta -116.63 90.09 206.01 305.65 27.C.98 385.7 369.10 321.13 453.7 .C35.83 4"8.3 420.13 .C.C0.29 512.8 .C95.00 503.78 513 • .CS .cn.23 475,95· 505.85 496 • .C.C 56.C.22 530.« 519.46 610.68 652.1 '61.S .C99.35 536.7 570.27 .CS.58 196.9 295.6 32.C.37 311.86 292.55 376.93 (339.) 306. . "'12.) 95.31 552.22 605."55 . 651.2.C 615.0 651.02 6.C9.6 106.0 '76 . .C "62.97(21) .C69.58(21) -220.(17) 87.9(23) 212.7(17) 315.5(17) 270.3(2.Cl -221.3(2) -399.8(17) -181.1 (17) -232 . .C(2.Cl 291.(17) 705.6(17) 12.C.5(17) :! ~

a

f

0 > 0.0991 0.0788 0.0737 0.0702 0.072.C 0.0675 0.0679 0.067.C 0.0688 0.0681 0.0681 0.0667 0.0665 0.0691 0.0673 0.06'6 0.0665 0.0665 0.0668 0.0662 0.0636 0.0690 0.0676 0.0656 0.068" 0.0679 0;059 0.0607 0.0586 0.0600 0.0737 0.0689 0;0685 0.0668 0.0680 0.0682 0.0697 (0.0649) 0.065" (0.0650) . 0.0695 0.0531 0.05.C9 0.056• 0.0557 0.0567 0.0572 O.OS.Cl 0.0570 0.0589(21) o.o580C2U o.os32C17> o.03.C2C23) 0.0459(2.C) o.o306C2"> o.068H17> o.0517C3> o.5167(2.Cl 0.0382(2.C) 0.051.ccm o.028H17> o.o5oocm o.0208C17>

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TABLE 1.4

Typical Composition of CONDENSATE-bearing gas reservoirs

COMPONENTS COMPOSITION ( rnole

% )

Examole- E* Examole - F** Methane 78.90 80.77 Ethane 4.36 2.07 Propane 1.37 0.80 (lso.+N) Butane 0.78 0.72 (lso. +N) Pentane _- 0.53 0.45 Hexane 0.38 0.13 Heptanes plus 1.71 3.26 Carbon Dioxide 11.16 9.50 Hydrogen Sulfide

--

1.91 Nitrogen 0.72 0.39 100.00 100.00

Other fluid 12ro12erties

LR{STB/MM scf) 28.5 54

Gas specific aravitv 0.78 0.77

Liquid aravitv (API ) NA 52

Classification LEAN MODERATE

* Example - E: Hateiba Field, Zmam/Waha/Gargaf, Libya ** Example - F: 137 S/K Field, offshore Tripoli, Libya ***Example - G : NC 41-A ,offshore Tripoli , Libya

Examole-G*** 66.64 7.63 4.47 3.50 2.46 2.06 7.47 3.03

----2.74 100.00 125 0.84

37

RICH .~ { . " . ·'

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1.5 IMPURITIES

As mentioned earlier, natural gases contain impurities in varying amounts. This constitutes serious problems not only in the design of the field equipment and . . transportation facilities, but also in gas safes contracts. in gas flaring (especially · near metropolitan areas), in evaluating the heat content of fuel gas ,(i.e. Btu problem), in artificial lift design (i.e. corrosion problems), in the design of tertiary recovery projects (Miscibility problems), and of course in the gas treatment required to reduce the impurities to minimum tolerable levels which do not violate environmental regulations. .

Impurities associated. with natural gases may include one or more of the following items :

1. Carbon Dioxide 6. Water Vapor 2. Hydrogen Sulfide 7. Mercury 3. Sulfur Compounds 8. Dust 4. Oxygen 9. Helium 5. Nitrogen 10. Free liquids

New treatment and process technology allows the reduction of impurities to tolerable limits, however, the costs of special treatment may constitute a heavy load on the economics of the project, especially in the offshore gas development projects.

Almost all the Libyan natural gas reservoirs are contaminated by Carbon Dioxide, Nitrogen, and Hydrogen sulfide in varying amounts. Other types of impurities are rare occurrences, and (usually) with negligible concentrations. Typical Libyan gases containing impurities are illustrated in TABLE 1.5 . As can be seen from the table, the Carbon Dioxide ( C02 ), and Hydrogen Sulfide (

H2S) can be considered the major (and consequently the most troublesome)

impurity constituents in the Libyan gas production and treatment practices. It is very hard to set up a general guideline to "tolerable" concentrations of each of the above impurities, since this will depend on the specific use of the gas, the market place safety regulations, the Btu rating, the pressure base of the gas measurements, etc. However, in general, the industrial use of natural gas in most industrialized countries requires

ttw

concentration of water vapor to be less than (6) pounds per million standard cubic feet of gas, and the hydrogen sulfide content to be less than 1000 grains per million scf of gas .

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TABLE 1.5

Examples of some Libyan Gas Fields

containing high percentages of impurities

COMPONENTS Methane Ethane Propane (lso. +N) Butane (lso. +N) Pentane Hexane Heptanes plus Carbon Dioxide Hydrogen Sulfide Nitrogen * Example - H : ** Example - I : *** Example -J : COMPOSITION ( mole % )

Examole- H* Examole - I** Examole-J***

72.130 70.15 13.9 4.290 4.66 1.5 2.150 2.11 1.1 1.237 1.11 0.8 0.587 0.54 0.3 0.498 0.35 0.2 2.293 1.20 5.5 12.204 13.58 65.8 1.702 0.12 0.6 2.909 6.18 10.3

-100.000 100.00 100.00

NC 41 - C2 , Metlaoui formation , offshore Tripoli , Libya NC 41 - C1 , Reinche formation , offshore Tripoli , Libya

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I

Natural Gas Rese"YVoir Engineering Dr. A. A. Urayet

Water vapor. Carbon dioxide. and Hydrogen sulfide are normally present in varying amounts in all natural gas reservoirs. All three impurities can cause serious problems in the production of the wells. in the operation of the surface facilities. and in the transportation and marketing of the natural gas. This special treatment normally constitutes a heavy load on the initial investment · required for the field development; as well as, on the operating costs. In brief, .

the main production problems caused by these three types of impurities can be summarized as follows :

Effect of Water Vapor

Every natural gas reservoir has a certain initial liquid-water saturation which is determined by the geologic environment. In addition, the gas phase will always contain a certain amount of water vapors. Even if only the single gas phase is produced, the reduction of pressure and temperature in the well bore, in the flow lines, and in the surface facilities will result in the condensation of the water vapors to form a free water phase .

The presence of liquid water in communication with Carbon dioxide and/or hydrogen sulfide will result in severe corrosion of the equipment due to the formation of acids. In addition, the condensation of water in the flow lines will reduce the area available for the gas flow, which increases the pressure drop in the line, and consequently, the Horse Power requirements. In addition to that, a serious problem will appear when the temperature of the natural gas falls below a certain temperature limit, which allows the liquid water molecules and the gas molecules to combine and form a solid phase known as " Hydrates". The conditions necessary for the formation of Hydrates will be discussed in more detail in Chapter-3.

Effect of Hydrogen Sulfide , H

₂

S

The hydrogen sulfide is present in all natural gas reservoirs in concentrations ranging from a trace to as high as 25%. The presence of hydrogen sulfide represents one of the main problems to the production engineer, since the hydrogen sulfide will combine with water to produce corrosive acids .

Hydrogen sulfide also constitutes a severe health and environmental problem. The flaring of natural gas containing Hydrogen sulfide will result in sulfur dioxide

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I

Natural Gas Reservoir Engi.neering Dr. A. A. Urayet

which is very toxic. Extensive gas treatment is, especially, required if the flaring center is in the proximity of inhabited areas.

Effect of Carbon Dioxide .

C02

The effect of carbon dioxide is not as critical as the hydrogen sulfide, mainly, because it does not constitute an environmental problem. The main production problem associated with the presence of carbon dioxide in natural gases is the formation of corrosive acids in the presence of water. Another problem would be the lowering of the heat content of the natural gas, consequently, requiring special treatment before marketing .

Finally, from Reservoir Engineering point of view, it is important to remember that the presence of impurities (especially at high percentages) greatly affects the physical properties of the natural gas, especially the viscosity and compressibility, (as will be discussed in chapter-2). Neglect of the effect of impurities in any Reservoir or Production Engineering calculations will always result in erroneous evaluation of the fluid properties, leading, of course, to improper reservoir analysis, production and development.

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I

Chapter 2 GAS DEVIATION FACTOR

The most important gas properties are primarily determined by the Gas Composition, Pressure, and Temperature. Prior to introducing the different techniques of evaluating these properties, it is necessary to know understand the basic gas laws governing ideal single-component gases, and to learn how to account for the deviation of the Hydrocarbon natural gas performance from these laws.

2.1 DEFINITIONS AND TERMINOLOGY

Prior to discussing the different fundamental gas laws, and the techniques used in the evaluation of the different physical properties of natural gases, it is important to introduce the following important definitions:

Critical Pressure . Pc , and . Citica·1 Temperature . Tc

The critical pressure, Pc. and the critical temperature, Tc. for a single component gas are defined as the Pressure and the Temperature at the Critical Point (i.e. the point at which the intensive properties of the gas and liquid phases are identical). In simple terms, the critical temperature, Tc. can be defined as the temperature above which the gas CANNOT be liquified,

regardless of the pressure exerted on the svstem. Whereas, the critical

pressure, Pc. is defined as the pressure at which the gas phase will be in equilibrium with the liquid phase when the system is at the critical temperatrure. The critical values for the more common hydrocarbon components of natural gases and the impurities normally associated with them are given in Appendix-A, Table1 .1.

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• I

Pseudo-Critical Pressure. Ppc, and,Pseudo-Critical Temperature.

Tpc_

The Pseudo-Critical Pressure,

Ppc.

and the Pseudo-Critical Temperature,

Tpc.

for any hydrocarbon mixture are defined and calculated as follows :

and,

where,

n =number of components

x;

= mole fraction of the i-th component

Pei= critical pressure of the i-th component, and Tc;= critical temperature of the i-th component

Eqs (2.1)

Pseudo-Reduced Pressure,

P,,

and, Pseudo-Reduced Temperature,

T,

The Pseudo-Reduced Pressure, Pr, and the Pseudo-Reduced Temperature, Tr, for a pure natural gas system are defined and calculated as follows:

and,

T. =_I_

r

T

Pc

Eqs (2.2)

where, P and T are the Pressure and the Temperature of the gas system respectively.

The Law of Corresponding States

The Law of Corresponding States expresses that "All PURE gases have the same characteristics at the same values of reduced pressure and reduced temperature". By characteristics, it is meant the physical properties such as deviation factor, density, and viscosity. This Law has proven to be a very powerful tool in the analysis of the behavior (and the evaluation of the physical properties) of gases in general, and natural gas systems in particular.

AAU/GAS/GAS2.doc 2

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I

Different investigators have shown that this law applies very effectively for any gas mixture. as long as the gas components have similar molecular characteristics O.e. if the components are closely related· chemically).

Consequently, this law is expected to apply very effectively for pure hydro-carbon gases since they are all of the paraffin group. However, deviations will occur with increasing percentage of impurities (since they have a different molecular and chemical structures). The degree of deviation will depend on the type of impurity component in the natural gas; with the highest deviations occuring in the case of Hydrogen Sulfide (H2 S), lesser deviations in the case of

Nitrogen (N2), and the least deviations would be in the case of Carbon Dioxide (C02).

Extensive Properties

These are the physical properties which are dependent on the quantity of gas available, such as Volume (V), and, mass (m), and,

Intensive Properties

These are the physical properties that are independent of the quantity of gas, such as density, specific gravity, viscosity, and, gas compressibility. These are the properties which are basically of interest to the reservoir engineer.

Equation of State

The "Equation of State. EOS " can be defined as an equation which relates the

three fundamental thermodynamic properties of any gas system, namely, Volume (V), Pressure (P), and, Temperature (T).

An "Ideal Gas" is defined as a gas which has the following characteristics: 1) the total volume of the gas molecules is considered negligible with respect

to the volume occupied by the gas, (i.e. the volume of the container),

2) there are no attractive or repulsive forces between the gas molecules, nor, between the gas molecules and the container, and,

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Combining the three fundamental gas laws which govern ideal gas behavior, namely, Boyles Law, Charles and Gay Lussac Law, and Avogadro Principle, the Equation of State for an Ideal Gas can be written in the following form:

IPV=nRT

Eq (2.3)

I

where,

n =the number of pound (lb) moles of gas present in a Volume, V, P = Pressure of the system, psia,

T =Temperature of the system, degrees Rankin, and,

R = the Universal Gas Constant,

R

=

10.72

lb.;ole ,

(English system)

in .0

R

Example 2.1

The volume of

a

vessel containing 5 lbs of methane is 2 ft3. Assuming ideal gas

behavior, calculate:

a -

the pressure of the gas system, if the temperature is maintained at 50 °C,

b - the gas volume at standard conditions.

Solution

m 5

n = number of lb-moles = -

=

0.31166 lb-moles

M 16.043 a)

T° F

=

32 +

2_(T

0 C)

=

32 + 2_(50)

=

122°

F

5 5 PV= nRT P - nRT _ - - 0.31166(10.72)(122

+

460) _ - 972 23 . psta .

v

2.0

b) At standard conditions, P

=

14. 7 psia, and T

=

60

°

F

PV

=

nRT or, V

=

nRT

=

(0.31166)(10.72)(60

+

460)

=

118.18 scf

p 14.7

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I

Equation Of State for Natural Gases

At the standard pressure of 14.7 psia, and standard temperature of 60 °F, the form of Eq (2.3) can be used with negligible error for any gas system, since the assumptions regarding the definition of Ideal gas are generally met.

However, the ideal-gas law is completely inadequate to describe the behaviour of natural gases at the high reservoir. or even separator, pressures and temperatures, since at such conditions the molecules would be nearer to each other and consequently the volume of the molecules and the effect of the attractive forces cannot be considered Negligible. Also, the high gas temperatures would result in higher kinetic energy which would result in more frequent collisions.

Numerous forms of the EOS have been developed to describe the natural gas behavior. Some of the best known forms are:

The Beattie-Bridgeman Equation

this equation is best suited for single component gases, and consequently its use should be restricted to Dry natural gases composed mainly of Methane. The equation contains five constants which have been determined empirically from laboratory measurements.

The Benedict-Webb-Rubin Equation, (RF-2.1)

this equation is considered, currently, as one of the best and most suitable forms of the Equation of State describing the Pure (i.e. less than 2 mole % impurity) Dry, Wet and Lean Condensate-Bearing natural gases (LR<50) over the single and two phase regions. The BWR equation contains eight constants which have been determined semi-empirically. The BWR Equation have been tested by comparison of computed to experimental behavior of different gas samples world-wide, and was proven to be very accurate in describing natural gas behavior for all ranges of pressures, temperatures, and. compositions. However. corrections must be introduced in case of gases containing high heptane plus and/or impurity content.

The Avasthi-Kennedy Equation. (RF-2.2)

this correlation is considered as one of the most adequate and comprehensive equations of state for all types of natural hydrocarbon gases, including those which contain a high percentage ( >30%) of impurities. The equation contains 21 constants which have been determined from experimental data of 264

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I

reservoir pressure and temperature ranges, the main advantages of this equation is that its use is a direct procedure (i.e. does not require trial and error procedure), and it can be differentiated easily to obtain the gas compressibility.

2.2 GAS DEVIATION FACTOR

In the field of Petroleum Engineering, a much simpler method is used to account for the deviation of natural gas behavior from the Ideal Gas Law. This is achieved by introducing One single factor to correct for all the different sources of deviation; whether the deviation is due to the high pressure and temperature of the system, or to the presence of more than one hydrocarbon component, or due to presence of non-hydrocarbon components (i.e. impurities). This factor which is termed the "Gas Deviation Factor, z", is included into the Equation of State for an ideal gas, Eq (2.3), as follows:

I

PV =znRT

Eq (2.4)

The term "Gas Deviation Factor" will be used through out these notes, even though many technical people in the industry use the term "Gas Compressibility Factor" to signify the same factor, z. Our choice is made mainly to avoid confusion in terms, since the term "Compressibility factor, C", is used in all branches of science and engineering to signify the relative change in volume with respect to the change in pressure and/or temperature.

2.2.1 Deviation Factors for Single Component System

The Deviation Factors for different single hydrocarbon component gases were determined experimentally, and, then plotted and correlated as a function of pressure, P, and Temperature, T. These correlations are found in all Reservoir Engineering books. The characteristic shape of the z-factor correlation is illustrated in Figure (2.1) for Methane. This figure clearly indicate the following important features:

• The z -factor will decrease in value with increasing Pressure until a certain minimum is reached, then the z-factor will start increasing afterwards with any increase in pressure, (i.e. dzldp becomes positive).

AAU/GAS/GAS2.doc 6

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le

1.20 Methane 1.10 1.00 0.9 0.8

..

0 .... _u 0.7 .!': c 0 ·;; "' ·;; _0.6 <1> -0 .... "' (.'.) 0.5 0.4 0.3 -40 0.2 -22 - " " ' - I - - \ - - 4 -+---1----~---+---f 68 32 140 104 0.1 0 500 1000 1500 5000 6000 7000 _{Pressure psi a}8000

Pressure pounds per square inch absolute

Fig. 2_.I Gas deviation factor for methane

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j Natural Gas Reservoir Engineering Dr. A. A. Urayet

• The minimum value for the z-factor is dependent on the Temperature isotherm value (lower minimum value of z, for lower Temperature, as seen from Fig 2.1 ). Note that the minimum value of z will be lower for heavier gases (such as Ethane).

• It is noted that beyond a certain Pressure range (usually between 5000-7000 psia), the deviation factor, z, of the lower-Temperature isotherm will start having higher values than the deviation factor, z, of the higher-temperature isotherms.

2.2.2 Deviation Factors for Pure Natural Gases

Even though laboratory measurements are the most accurate method for determining the z-factor for any gas mixture, however, the extensive effort and time, and the sophisticated measuring devices required, have encouraged the trend toward developing semi-empirical techniques in order to evaluate the z-factor of any gas mixture.

Standing

I

Katz Correlation

The determination of the Deviation Factor for a PURE (i.e. negligible percentage of impurities) multi-component natural gas can be achieved, to a high degree of accuracy, by employing the concept of Pseudo-Reduced Pressure and Pseudo-Reduced Temperature. The Deviation Factors were determined experimentally for a large number of natural gases and were correlated as a function of Pr, and Tr, in line with the principle of Corresponding States. The results were presented in the "Standing I Katz z-factor charts"

shown in Appendix-A I Figure 2.1.

These extended charts cover the normal range of Field Pressures and Temperatures. Linear extrapolation of these curves beyond (Pr= 24) can be applied with minimum error.

Consequently, in order to calculate the z-factor for any pure natural gas system at a certain pressure and temperature, the following procedure can be applied : 1- Read from Appendix-A I Table 1.1 the critical values of pressure and

temperature for each component,

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I

2- Use the chemical analysis of the gas mixture to calculate Ppc, and Tpc for the gas, using Eqs (2.1 ),

3- Calculate Pr, and Tr, of the gas system, using Eqs (2.2),

4- Use the Standing I Katz charts, Appendix-A I Fig (2.1) to read the value of the z-factor corresponding to the calculated Pr and Tr values;

The proper procedure for the use of Standing I Katz charts to calculate the Gas

Deviation Factor is illustrated in Example Problem 2.2.

It is important to note that the accuracy of the above procedure, (which is developed for pure gases) can still be maintained, even in the case of gases contaminated by SMALL concentrations of C02 and N2 (less than 2% maximum for each), and by smaller concentrations of H2S (less than 1%), provided that these components are included in the calculation of the Pseudo-Critical Pressure and Temperature. Different investigators have shown that further corrections must be introduced if higher percentages of impurities are present in the gas mixture (Reference 2.3).

Example 2.2

The chemical composition of the gas produced from Braeburn field in Canada is given in the attached Table (columns 1 and 2). Calculate the gas deviation factor, z, for the following conditions:

a -

P = 3000 psia , and T = 230

°

F b - P

=

1000 psia , and T

=

150

°

F

Assume that x (iso-C4) = 0, and x(iso-C5 ) = 0

Solution:

1. Read the values of Pc and Tc for each component from Appendix-A I Tablet. 1, and enter into columns 3 and 4.

2. Calculate (x; . Pei) and (x; . T ci) for each component as shown in columns 5 and 6.

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I

Natural Gas Reservoir Engineering Dr. A. A. Urayet 3. Calculate: n n PPc

=

L:Xi·Pc; = 677.32 i=l ,and, Tp = LXi.Tc.

=

350.62 C I i=l

4. Calculate Pr and Tr as follows :

Case-a Case-b P,

=

_!...._

=

3000

=

4.429 r PPc 677.32 Pr

=

_!__

_PPc

=

_677.321000

=

1..476 Tr

=

_!_

=

230 + 460

=

1.₉₇ TPc 350.62 Tr=_!_= 150+460 =1.₇₄ TPc 350.62

Using Standing and Katz charls, Appendix-A I Fig 2. 1, read:

z

= 0.94

z

=

0.92

Calculation of pseudo-critical constants

( 1) (2) (3) (4) (5)

components composition _Pei _Tei _X;._Pei x;( mole%) _{( psia)} (o R) Methane 96.39 667.8 343.37 643.69 Ethane 0.75 707.8 550.09 5.31 Propane 0.11 616.3 666.01 0.68 (lso.+N) Butane 0.03 550.7 765.65 0.17 (lso.+N) Pentane 0.10 488.6 845.70 0.49 Carbon Dioxide 0.97 1071.0 547.90 10.39 Hydrogen Sulfide 1.04 1306.0 672.70 13.58 Nitrogen 0.61 493.0 227.60 3.01

I

100.00 677.32 AAU/GAS/GAS2.doc 10 (6) X;. Tei 330.97 4.13 0.73 0.23 0.85 5.32 7.00 1.39 350.62

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I

Brill and Beggs z-factor Correlation

I

Different investigators have tried to represent the Standing/Katz z-factor charts mathematically for computer use. However, most of the available mathematical expressions would require the solution of a system of Non-Linear equations numerically such as the "Hall-Yarborough correlation" and the "Dranchuk, Purvis and Robinson" correlation. One of the simplest and most practical expressions available in literature for the evaluation of the z-factor is the Brill and Beggs Correlation which has the following form:

1-A

D

z=A+--+c.Pr

Eq (2.5) eB where,

A=

1.39(T,. - 0.92)o.s - 0.36T,. -0.101

_

0.066 .

. 2

0.32Pr

6 B-(0.62-0.23Tr)Pr +(T _

-0.037)Pr + . (

₉

T. _

₉

)

r

0.86

10 r

· C

=

(0.132- 0.32

log

T,.)

\\

D

=

Anti

log(

0.3106 - 0.49

T,.

+

0.1824 T,.

2)

The Brill and Beggs correlation is within the accuracy requirements for all practical Reservoir Engineering problems. They are most accurate in the range 1.2 < Tr < 2.4 , and Pr < 13.

The proper procedure for the use of the Brill and Beggs correlation to calculate the Gas Deviation Factor is illustrated in Example Problem 2.3.

Example 2.3

Use the data given in Example 2.2 (part-a) to calculate the z-factor using the Brill and Beggs z-factor correlation

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Solution

The pseudo-reduced values, Pr and Tr (calculated in Example 2.2) are:

Pr

=

_!__

=

3000

=

4.429

PPc

677.32 Tr

=

_.!__

=

230 +

460 =

_1.97

TPc

350.62

Consequently,

A= l.39(Tr -

0.92)

0·5 -

0.36Tr

-0.101

A=

1.39(1.97 -0.92)

0·5 -

0.36(1.97)- 0.101=0.614126

6

B

=

(0.62 -

0.23Tr )Pr

+ (

0.0

66 -

0.037)P}

+

OC~;~

9 )

Tr

-0.86

10 r

B

=

(0.62 - 0.23xl .97)( 4.429)

+ (

0.0

66 - 0.03 7)( 4.429)

2

+

0.

3

~~;:;~?

1.97 - 0.86

10 .

-B

=

1.1707703

C

=

(0.132- 0.32

IogTr)

C

=

0.132 - 0.32 log(l .97)

=

0.03777081

D

=

Antilog(0.3106-0.49Tr

+

0.1824Tr

2)

D

=

Anti

log(0.3106 - 0.49(1.97)

+

0.1824(1.97)

2)

= 1.1302543

Consequently ,

1-A

D

z =A+

B

+c.Pr

e

z

=

0.614126

+

l

:

1 °;~

9 \~~;

6

+

0.03777081( 4.429)1.1

302543 z = 0.9358 AAU/GAS/GAS2.doc 12 6

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I

2.2.3 Gas Deviation Factor

I

Effect of Impurities

The presence of impurities (such as C0_2, N_2, H₂ S, etc.) in Natural Gases affects the values of the gas Deviation Factor. The magnitude of change in the value of z depends on the type and mole percent of the impurity.

Two approaches have been suggested in the literature for including the effect of the impurities in the calculation of the Deviation Factor. These two approaches can be termed the "Additive z-factor method", and the "modified Pc and Tc method". These two approaches can be summarized as follows:

The Additive z-factor Method

In this method the Deviation factor is considered to be equal to the arithmetic sum of the individual z-factors of the different components, each weighted according to its mole percentage in the gas mixture. Thus, the Deviation Factor of a natural gas can be represented by the following equation:

where,

Xhydr

Eq (2.6)

= sum of the mole fractions of the hydrocarbon components

xco2, Xtt2s , and _xN2

=

mole fractions of the different impurities, and, zco2, ZH2s, and _ZN2

=

deviation factors of the different impurities.

It is important here to note that the Deviation Factor for the hydrocarbon components, Zhydr, should be calculated as if only hydrocarbons are present in

the system. In other words the Tpc and Ppc used in Eq 2.5 (or entered to the Standing I Katz charts) to evaluate zhydr should be calculated as follows:

Ppc

=I

Pei ·Yi where, xi(hydr)

Yi=

LXi(hydr) and Eqs (2.7)

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(~

·---.---""'

- , , , , , , , , , , , , , _ , _ , __ ----, , , .

j

Natural Gas Rese~oir Engineering Dr. A. A. Urayet

It has been suggested to use certain eccentric factors to be multiplied by the z-factors of the different impurities to obtain more accurate estimate of the Natural Gas Deviation Factor. However, such accuracy is rarely required for Reservoir Engineering calculations. Different investigators have demonstrated that Eq (2.6) will have an error less than 0.1

%

for a Nitrogen mole percent of

10%. Similar demonstrations have been made for C02 and H2 S.

The Modified Pc and Tc method

In this method the calculated value of Ppc and Tpc are modified, and then the new values of Pr and Tr calculated on this basis are entered to the Standing I Katz charts or Brill and Beggs correlation, Eq 2.5, to evaluate the Deviation Factor. It is important to note that the modified values have NO physical significance, and should only be understood as a mathematical correction to the Katz charts.

One of the simplest (and yet very accurate ) methods available in literature for the modification of Ppc and Tpc was presented by Wichert and Aziz, (RF-2.6). In this method, the modified pseudo-critical properties can be calculated as follows: '

T =T

- & pc pc. ---' , PP .TP

p

=

c c Pc TPc

+

B(l -

B)&

Eqs (2.8) where,

Tpc and Ppc are the critical temperature and pressure for the gas mixture including the impurities, and,

A

= Sum of the mole fractions of Hydrogen Sulfide and Carbon Dioxide

B

= mole fraction of the Hydrogen Sulfide in the gas mixture= X (H2S)

AAU/GAS/GAS2.doc 14

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Note : Quick estimate of (8) can be obtained from the graphical form of the correlation given in Appendix-A I Fig (2.2) .

The Wichert and Aziz correlation should prove very useful in the analysis of Libyan gas reservoirs. The correlation has an average absolute error of 0.97% (for P < 7026 psia, and T < 300 F) for the range of data used in the development of the correlation which included C02 concentrations as high as 54.4 %, and H2 S concentrations as high as 73.8 %.

There are many other correlations available in the literature, however, most of them require a trial and error procedure, and consequently, make them fit for computer use mainly .

The proper procedure for the use of the Wichert and Aziz correlation to calculate the Gas·oeviation Factor is illustrated in Example Problem 2.4.

Example 2.4

Use the data given in Example 2.2 (parl-a) to calculate the z-factor using the

modified Pc and Tc method, (Wichert and Aziz correlation).

Solution:

the modified Pc - Tc method

A= X (H2S) + X ( C02)

=

(1.04+0.97)% =0.0201 i

e

B

=

X (H2S)

=

0.0104

s

=

120(A

0·9

-Al.

6

)+15(Bo.s

-B

4)

=120(0.0201°·

9

_-0.02011.

6

_{)+15(0.0104°}

5 _-

_0.0104

4₎₌

_4.8633

I TPc

=

TPc -

e

=

350.62-4.86

=

345.76

I I

pp

.Tp

p

= c c Pc TPc

+

B(l - B)s

(677.32)(345.76)

=

667.84 350.62+0.0104(1- 0.0104)( 4.8633)

and, consequently ,

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/-Natural Gas Reservoir Engineering

Tr

_{=_I__= 230+460=1.996}

TPc

345.76 Pr

=

_!_

= 3000 = 4.492

PPc

667.84

Dr. A. A. Urayet

Substitution of the modified Pr and Tr in the Brill and Beggs correlation, (as illustrated in Example 2.3) will give

a

value of ( z

=

0.9432 ), as compared to the value of (z

=

0.9358) obtained by using the Brill and Beggs correlation directly (without any modifications for impurities) in Example 2.3. The very small difference in the results clearly proves that Brill and Beggs correlation can be used with very small error for any natural gas with Low concentrations of C02 L

or Hz..S.

2.2.4 Gas Deviation Factor

I

Practical Aspects

Treatment of the heavier hydrocarbon components

The composition of a Natural Gas is reported, normally, in a form similar to that shown in Tables 1.1-1.5 (Chapter-1 ). It is important to note that the mole percentage of all the heavier components (i.e. C7 +, or C9+ or sometimes C13+) is normally reported as one single value. In such cases, the molecular weight and the specific gravity of this group of components should be reported. These two properties have been correlated in literature with (Pc) and (Tc) as shown in Appendix-A I Fig 2.3. And, consequently, the heavier components can

now be included in the normal procedure of calculating (Pr) and (Tr) which would be introduced to the Standing/Katz charts to calculate the z-factor.

Another method preferred by many reservoir engineers is to use the physical properties of Octane (

C

_{8H 18 )}for the C7+ fraction, properties of ( C10H 22) for the C9+ fraction, etc. This should always give good results for Dry and Wet gases.

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Unavailability of the gas chemical composition

In many instances the accurate chemical composition of the natural gas might not be available. This normally occurs when field calculations are required at the early life of the field (to make preliminary estimates of the gas in place and recoverable reserves). In this case the specific gas gravity can be used to esti-mate the values of (Pc) and (Tc) for the gas system from the available charts shown in Appendix-A I Fig (2.4).

Sutton R.P. presented the following relationships for the calculation of the pseudocritical properties using the specific gravity of the natural gas:

Ppc

=756.8-131.0(yg)-3.6(yg)

2+

{y.J..lzs.

+'+.'LG· Xc₆ z.- lt-

X

1

\J

₂ and,

This simple correlation should be corrected using the correction graphs given in Appendix-A I Fig 2.4 to account for impurities.

The proper procedure for the application of these practical techniques to calculate the Gas Deviation Factor is illustrated in Example Problem 2.5.

*

Effect of water vapor

Finally, the gas laboratory analysis is usually run after the gas sample has been dried. Consequently, the water vapor content is not reported. However, different investigators have concluded that the Deviation Factors calculated by the previous techniques are little affected by the water vapor content, and consequently no corrections are required for normal Reservoir and Well Productivity calculations.

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Problem 2.

5.

The chemical composition of a Libyan gas is given in columns 1 and 2 of the accompanying table. The following data is also available:

reservoir pressure reservoir temperature

specific gravity of the reservoir gas molecular weight of C₇+ specific gravity of C1 + = 2852 psia

=

227°F

=

0.688

=

100.1 = 0.80

Calculate the gas deviation factor. Use the pseudo-critical constants evaluated from:

a) the individual P ci and Tc; , b) the Sutton correlation

Solution:

a) using individual Pei and Tei

1) enter with the molecular weight and specific gravity of C7 + to Fig 2.3 (Appendix-A), and read Pc; (C1 +) = 1040 psia, and Te; (C1 +) = 505 °R

2) Read from Table 1. 1 (Appendix A) the values of P ci and Tc; for the individual

components, and enter into columns 3and 4

3) calculate x; .Pc; and x;. Te; as shown in columns 5 and 6

n

4) calculate

PPc

=

L,xi.Pq

=

680.7 psia i=I

5) enter with the values of C0₂and H₂S mole percentages to the Wichert and Aziz graph, Fig 2.2 (Appendix-A), and read 5 - 6

6) use Wichert and Aziz correlation, Eqs (2.8), to correct Ppc and Tpc as follows:

(40)

\ Natural Gas Reservoir Engineering Dr. A. A. Urayet

I

TPc

=

TPc -

8

= 382.3 - 6 = 376.3

I

p'

=

PPc .TPc

_

(680.7)(376.3)

=

67 0.0l

Pc

TPc +B(l-B)&

382.3+0.001(1-0.001)(6)

7) calculate :

Tr=_!__=

227+460=1.826

TPc

376.3

and,

P.

=

_.!!__

= 2852

=

4.26

r

PPc

670 e

8) finally, enter with the values of Pr and Tr to the Standing I Katz correlation, Fig 2. 1 (Appendix-A), and read z

=

0.905

b) using Sutton correlation

1) substitute the value of y g

=

0.688 into the Sutton correlation, Eqs.(2.9), as follows: 2

Ppc

= 756.8-131.0(y

g

)-3.6(y g)

= 756.8-131.0(0.688)-3.6(0.688)

2

= 665

and, 2

Tpc

= 169.2 + 349.5(y g)-74.0(y g)

= 169.2 + 349.5(0.688)- 74(0.688)

2

= 374.6

2) use the appropriate correction charts in Fig 2.4 (Appendix-A) to read: pseudo-temperature correction for C0₂

= -

3

°

F

pseudo-temperature correction for N₂

=

0 pseudo-temperature correction for H₂S = 0

Gas reservoir engineering ( U. Abdulhamid )

•

A. A. Urayet, Ph.D.

· NATU,RAL-G.As

RESERVOIR ENGINEERING

Prepared By:

Dr. Urayet, Abdulhamid

--

.

by:

..

Natural-Gas Reservoir Enqineerinq

CONTENTS

,.

•

9.

f

l

..;.

'

1 '

P;

Pw

T -

r

19

---~~~~~---I

Chapter 1

DEFINITIONS AND CLASSIFICATION

(C4H10>·

(C0

(H

S),

(Nz),

I

1.1

DEFINITIONS AND TERMINOLOGY

Liquid Recovery , LR

=

e

I

Mole Fraction .

x;

number of moles of the component

(i)

total number of moles of the gas

c;

Apparent Molecular Weight. M

I

M;,

n

mass of the gas mixture (lb)

m

m

Apparent molecular weight

M

L,xi.Mi

Gas Specific Gravity,

Yg

M

28.966

r

r

Solution

r

I

Recombined Reservoir-Gas Specific Gravity

4584

+

Res

1+132,800

Yes

MoRes

r

r

r

M

M

IM

6084

_{20 833}

_AP!

_MORCS