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Evaluation of Correlations of Compressibility Factor (z) of Natural Gas for Algerian Gas Reservoirs
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Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES18, Technologies and Materials for Renewable Energy, and Sustainability, TMREES18, 19–21 September 2018,Environment Athens, Greece 19–21 September 2018, Athens, Greece
Evaluation of Correlations of Compressibility Factor (z) of Natural International Symposium on District Heating and Cooling EvaluationThe of 15th Correlations of Compressibility Factor (z) of Natural Gas for Algerian Gas Reservoirs Gas for Algerian Gas Reservoirs AssessingH.M.SIDROUHOU the feasibility1*of using the2 heat demand-outdoor 3 , M.KORICHI and S.DADA 1* 2 3 , M.KORICHI and S.DADA temperature H.M.SIDROUHOU function for a long-term district heat demand forecast Laboratoire Dynamique, Interaction et Réactivité des Systèmes (DIRES), Hydrocarbon Processing Department, Kasdi Merbah University, 1 1
Ouargla – DZ- Algeria; Laboratoire Dynamique, Interaction et Réactivité des Systèmes (DIRES), Hydrocarbon Processing Department, Kasdi Merbah University, a a b c c 2 a,b,c DIRES, Hydrocarbon Processing Department, Kasdi Merbah University, Ouargla – DZ- Algeria Ouargla – DZAlgeria; 32 DIRES, Hydrocarbon Processing Department, Kasdi Merbah University, Ouargla – DZ- Algeria a 3 IN+ Center for Innovation, Technology and Policy Research - Instituto Técnico, Av.Ouargla Rovisco–Pais 1049-001 Lisbon, Portugal DIRES, Hydrocarbon Processing Department, KasdiSuperior Merbah University, DZ- 1, Algeria b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France
I. Andrić
*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre
Abstract Abstract The study of PVT properties of natural gas is essential for the development of its production and exploitation. The laboratory is Abstract The study of of natural gasproperties is essential of its production exploitation. Theand laboratory is considered thePVT mainproperties source of data for these as for it isthe alsodevelopment possible to compute these dataand using state equations empirical considered main sourceerror of data for these properties as it is also possible to compute these data using state equations and empirical correlationsthe with variable margins. District networks are margins. commonly in the literature as one ofonthethemost effectiveofsolutions for decreasing the correlations withto variable error This workheating aims study experimentally an addressed Algerian natural gas, concentrating calculation the compressibility factor, greenhouse gastoemissions from building sector. require high investments the heat This work aims study experimentally anthis Algerian natural gas, concentrating on the calculation ofare thereturned compressibility factor, using the relative correlations to the calculate factor,These whilesystems trying to modify these with whatwhich corresponds betterthrough with Algerian sales.the Due to the changed conditions and data. building renovation policies, heat what demand in the future decrease, using relative correlations to calculate this factor, while trying to modify these with corresponds better could with Algerian natural gas based on statisticalclimate tools and experimental prolonging the investment return period. natural gas based on statistical tools and experimental data. The results of this study show that it is possible to develop and update the correlation coefficients that correspond better with each Theresults main scope paper is toitassess the feasibility using the heat demand – outdoor temperature functionbetter for heat demand The of thisof study show that is to update the correlation coefficients that correspond with each geographic region inthis order to reduce thepossible margin ofdevelop error. ofand forecast. The district of to Alvalade, located in ofLisbon geographic region in order reduce the margin error. (Portugal), was used as a case study. The district is consisted of 665 vary in both construction ©buildings 2018 Thethat Authors. Published by Elsevierperiod Ltd. and typology. Three weather scenarios (low, medium, high) and three district © 2019 The Authors. Published by Elsevier Ltd. renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) compared with resultsarticle from aunder dynamic heatBY-NC-ND demand previously developed and validated by the authors. This is an and open access the CC license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection peer-review under responsibility of the model, scientific committee of Technologies and Materials for Renewable Energy, Selection andshowed peer-review underonly responsibility of the isscientific committee of Technologies andbeMaterials forfor Renewable Energy, The results that when weather change considered, the margin of error could acceptable some applications Selection and peer-review under responsibility of the scientific committee of Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES18. Environment and Sustainability, TMREES18. (the error inand annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation Environment Sustainability, TMREES18. scenarios,PVT, the production, error valuenatural increased up to 59.5% factor (depending on the weather and renovation scenarios combination considered). Keywords: gas, compressibility (z). The value of production, slope coefficient increased on average the range of 3.8% up to 8% per decade, that corresponds to the Keywords: PVT, natural gas, compressibility factorwithin (z). decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the 1.renovation GENERAL INTRODUCTION scenarios). The that values suggested could be usedlayers to modify function parameters for the scenarios considered, and 1.coupled GENERAL Natural gas isINTRODUCTION a fuel comes from the reservoir of thetheearth, it is essentially composed of methane (CH4), thegas accuracy of that heat comes demand is a odorless, fuel reservoir layers of the earth, it isinessentially composed (CH4), itimprove isNatural colorless and and it from isestimations. thethe simplest hydrocarbon that exists nature. Natural gas isofamethane non-renewable
it is colorless odorless, and itare is the simplest hydrocarbon that exists inareas. nature. Natural gas is a non-renewable fossil resourceand whose reserves concentrated in certain geographic The improvement of its supply, © 2017 The Authors. Published by Elsevier Ltd. fossil resource whose reserves are plays concentrated certain of itsof supply, transportation and storage conditions a strategicinrole for itsgeographic future in theareas. energyThe mix.improvement World production natural Peer-review under of the Scientific Committee Theits15th International Symposium on District Heatingofand transportation and responsibility storage conditions plays a strategic roleoffor future in the energy mix. World production natural Cooling.
1876-6102 © 2018 The Authors. Published by Elsevier Ltd. Keywords: Heat demand; Forecast; Climate change This is an open access under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 1876-6102 © 2018 Thearticle Authors. Published by Elsevier Ltd. Selection under responsibility of the scientific of Technologies and Materials for Renewable Energy, Environment This is an and openpeer-review access article under the CC BY-NC-ND licensecommittee (https://creativecommons.org/licenses/by-nc-nd/4.0/) and Sustainability, TMREES18. Selection and peer-review under responsibility of the scientific committee of Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES18. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES18. 10.1016/j.egypro.2018.11.231
H.M. Sidrouhou et al. / Energy Procedia 157 (2019) 655–669 H.M.SIDROUHOU/ Energy Procedia 00 (2018) 000–000
656 2
gas has tripled between 1970 and 2010, accounting for 21.4% of the total energy consumed worldwide in 2010, out of 12,717 megatons. Algeria ranks seventh in the world in terms of proven resources, the fifth in production and the third in export. It is considered as a true energy giant, Algeria, with 50% of reserves, 48% of total production and the impressive rate of 94% of natural gas exports, has no rival in the Mediterranean, where it is ranked as the leading producer and exporter of oil and natural gas. Pressure-volume-temperature (PVT) properties are the general terms used to express the volumetric behavior of a reservoir fluid as a function of pressure and temperature. These properties are very important for geophysicists and petroleum engineers, especially for material balance calculations, surge performance calculations, as well as for the analysis, identification, determination and estimation of reserves and quantities that can be recovered. They are also very important for the determination of oil or gas rates and simulations of digital reservoirs. The compressibility factor of the gas (Z) is a dimensionless quantity and is defined as a ratio of the actual volume of n-moles of the gas at temperature and pressure to the volume of the same ideal mole number at the same temperature and pressure. For many years, the most accurate method for determining the compressibility factors of natural gas has been the direct measurement in the laboratory using z-factor (standing and Katz) graphs for gas mixtures, but with the evolution of science; state equations and correlations have been developed for the determination of these factors. In this section, we apply correlations of these factors and try to develop correlation coefficients from the use of statistical tools and experimental data for these factors. So, the main goals of this work are summarized as follows: 1 - An experimental study of Algerian natural gas, with an accent at the expense of the compressibility factor. 2 - A statistical study of the different correlations existing to calculate the gas compressibility factor and an attempt to develop them with what corresponds best to the Algerian natural gas. Nomenclature P T V Vr Pb Pr Ppr Ppc D Mw Z GOR Fc Bo γg Yi n m ρ Ei Er S CCE CVD DTD
Pressure Temperatures volume Relative volume Bubble pressure Rose pressure Pseudo reduced pressure Pseudo-critical pressure Density of gas relative to air Average molar mass Compressibility factor of the gas Gas Oil Ratio Contraction factor (shrinkage) Formation Volume Factor Specific gravity of the gas Molar fraction of component i in the gas mixture Number of gas constituent Mass The density Error Medium error Standard deviation Constant composition expansion Constant volume differential Technology and Development Division radius of
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1. Experimental study 1.1. Data Characteristics Table 1. Field
STAH
Type of sampling
area
Fluid type
condensate gas
Static bottom pressure (Psig)
3550
Bottom temperature (°C)
133
Separation pressure (Psig)
305
Separation temperature (°C)
61
GOR "field" (cm3/cm3)
14014
Compressibility factor of the gas '' site ''
0.961
Density of separator gas '' site ''
0.698
1.2. Work Organization Chart Step 1: Reconstitution of the raw gas Surface Sampling Separator gas
Separator liquid
Validation
Validation
Thermodynamic study
Thermodynamic study
Calculated
Calculated RAW GAS
Step 2: Thermodynamic study of raw gas
PVT raw gas
Constant-composition expansion (CCE) test at (Tg)
Constant-volume depletion test (CVD) at (Tg)
Determination the compressibility factor (z).
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1.3. Reconstitution procedure for raw gas (reservoir fluid) The reconstitution of the reservoir fluid comprises the following steps: A. Validation of gas samples and separator liquid: For liquids, validation includes: - Determination of the opening pressure of the bottles; - The determination of the saturation pressure at the separation temperature, which must be identical to the separation pressure; For gases; the validation is done by: -A simple chromatographic analysis whose opening pressure must be close if not equal to the separation pressure. B. Thermodynamic study of the separation effluents: B. 1. Thermodynamic Study of Gas Separator: Table 2 This study is based on the following steps: Chromatographic analysis. Determination of the average molar mass. Determination of the density of the gas separator. Determination of the compressibility factor of the separator gas. B.2. Thermodynamic study of separator liquid: The PVT study of the separator liquid includes in the study of the Constant-composition expansion, the flash separation, is to determine the molar composition of the separator liquid. B.2.1. Constant-composition expansion of the Separator Liquid: Table 3; Table 4. This experiment makes it possible to determine the following parameters: Saturation pressure (Pb). Relative Volume. Density. B.2.2. Flash separation tests: Table 5. The flash separation in the laboratory is carried out in a separator of the type "Jefri GOR Apparatus", the flash separation makes it possible to calculate the following parameters: The gas-oil ratio "GOR": The contraction factor of the oil "Fc" or shrinkage "sh" The liquid volume factor "Bo" The density of the storage liquid (ρ 15 ° C). B.2.3.Determination of the composition of the separator liquid: A PVT Sim program performs calculations. The parameters of this recombination are: GOR Lab. The density of the storage liquid at 15 ° C. C. Recombination of raw gas: The purpose of this recombination is to reconstitute the reservoir fluid (raw gas). The physical parameters provided by the study of the gas and separator liquid would be used to: Correction of the GOR site Mathematical recombination of bottom effluents Physical Recombination Process of physical recombination: Table 6. 1. Correction of gas volume under standard conditions. 2. Calculation of the volume of liquid.
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Flash gas First recombination
Separator liquid
Second recombination
Raw gas
Flash liquid Separator gas
Separator liquid Fig 1: The steps of recombination.
1.4. PVT study procedure of raw gas: a) Constant-composition expansion of the raw gas (CCE): Having introduced a volume of 26.73 cm3 to 7000 Psig in the "visual" PVT cell, raised to the reservoir temperature (Tg = 133 ° C) in an air bath, regulated at +/- 0.2 ° C, and after stabilization temperature and pressure by magnetic stirring propeller; there is a decline in pressure. Table 7. b) Constant-volume depletion of raw gas (CVD). We have introduced in the study cell a volume of 29.18 cm3 of the raw gas at 6000 psig and the temperature of the field. The study of constant-volume depletion consisted of six (06) release pressure levels. During the gas release, a sample is taken at each level in a pycnometer for gas chromatographic analysis. 2. The empirical correlations of the factor Z Several empirical correlations for the Z-factor calculation have been developed in previous years; intended to accurately reproduce the Z-factor Standing-Katz graph. The most commonly used correlations are Hall-Yarborough (1973), Dranchuk-Abou-Kassem (1975), Papay (1985), S. Robertson and Beggs and Brill (1986). All correlations studied (Z-Natural Gas Factors) are calculated as a function of pseudo-reduced pressure (P pr) and pseudo-reduced temperature (T pr). In the case where the composition of the natural gas is not available, the pseudo-critical properties, Ppc and Tpc, can be predicted from the only specific gravity of the gas (γ g). Brown and all. (1948) presented a graphical method for convenient approximation of the pseudo-critical pressure and the pseudo-critical gas temperature only when the specific gravity of the gas is available. Later standing (1977) expressed this graphical correlation in the following form:
T pc 168 325 g 12.5 g2
(1)
Ppc 677 15.0 g 37.5 g2
(2)
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3. Numerical modeling of correlations of factor (Z) 3.1. data acquisition The data used in this study were obtained from the analysis of 42 samples from different types of gas and wells of the five fields of Algeria. The data used in this study are a range of separation pressures, separation temperature, pseudo-reduced pressure, pseudo-reduced temperature, specific gravity, and molar composition. Table 2. Table 2: Data Description (All Fields) FIELDS
T averages (K)
T Pr (averages) (K)
P averages (Pas)
P Pr (averages) (Pas)
Z averages
Hassi R’mel
327.42
1.68
6.85E+06
1.50
0.905
Ouad Noumer
325.15
1.61
2.50E+06
0.55
0.963
Ohant
312.32
1.65
5.36E+06
1.18
0.895
Brkin
342.15
1.59
7.31E+06
1.43
0.851
Stah
406.15
1.64
2.52E+07
5.56
1.045
3.2. work organization chart First step Application of correlations for each chosen field
Oued Noumer
Stah
Statistical analysis for each field Correlation selection unless error for each field Edit the selected correlation Apply the modified correlation
Hassi R'mel
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Second step Statistical analysis of group fields Select correlation unless error for grouped fields
Edit the selected correlation
Apply modified correlation for grouped fields for each field Hassi R’mel
Stah
Oued Noumer
3.3. Results of experimental study: Table 3: Results of the thermodynamic study of the separator gas. Constituents
Composition YI
Yi/100
Mi
Yi*Mi
N2
0.348
0.003
28.01
0.09
CO2
5.022
0.050
44.01
2.21
C1
82.191
0.821
16.04
13.18
C2
7.683
0.076
30.07
2.31
C3
2.608
0.026
44.09
1.15
iC4
0.454
0.004
58.12
0.26
nC4
0.743
0.007
58.12
0.43
iC5
0.279
0.002
72.15
0.20
nC5
0.205
0.002
72.15
0.14
C6
0.237
0.002
86.17
0.20
C7
0.129
0.001
96
0.12
C8
0.066
0.0006
107
0.07
C9
0.020
0.0002
121
0.02
C10
0.007
0.00007
134
0.009
C11
0.004
0.00004
147
0.005
C12
0.004
0.00004
161
MW
0.006 20.4434579
Density
0.70577428
Z (305psi) ; T (61c°)
0.9630
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Table 4: Result of calculates the density of the separating liquid. PYCNO N°
m pv
m pr
m pr – m pv(g)
V lt (cm3)
I
837,7
845,586
7,886
10,44
0,755
II
835,822
842,104
6,282
8,31
0,756
Density (g/cm3)
ρ average (g/cm3) 0,756
Table 5: Results of the thermodynamic study of the separator liquid. Pressure (psi)
3000
2500
2000
1500
1000
800
500
350
240
180
130
35,53
40,82
52,26
compound volume (cc)
32,31
32,44
32,59
32,75
32,93
33,01
33,14
33,22
Density (g/cc)
0,75
0,57
0,75
0,74
0,74
0,74
0,73
0,73
Table 6: Separation test results. Fc
GOR
Bo
d15°C
0,97
13,22
0,0103
0,7748
Table 7: Results of Recombination of Raw Gas. GOR recombination
ρ bp
13537,49 cm / cm
0,735 g/cm
3
3
3
V0 (gas) at (14,7psi and 15°C)
V liquid
V L (5000 psig)
18089,27 cm3
1,3362 cm3
1,2774 cm3
Table 8: Factor (Z) Results for Constant-composition expansion of Raw Gas at T = 133 ° C. Pressure (psi)
V compound (cc)
mass volume (cm2/g)
Z
7000
26.73
3.922
1.206
6500
27.85
4.086
1.167
6000
29.18
4.281
1.128
5500
30.84
4.525
1.093 1.061
5000
32.94
4.833
4500
35.56
5.217
1.031
4000
39.06
5.731
1.007
(Pr) 3550
43.15
6.331
0.987
3000
49.8
7.306
0.963
2500
59.35
8.707
0.956
2000
75.05
11.011
0.967
1700
89.96
13.198
0.985
1500
103.83
15.233
1.004
1100
148.5
21.786
1.053
1000
166.02
24.357
1.07
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Table 9: Factor (Z) Results for Constant-composition expansion of Raw Gas at T = 133 ° C. Pressure (psig)
Vg(cell)
Vg ( 150C)
Vg product
Z
3550
0.00
-
43.15
0.987
3000
7.20
1106.35
50.35
0.962
2000
21.01
2259.83
64.16
0.918
1200
16.87
1117.93
60.02
0.898
1000
20.46
1129.55
63.61
0.901
800
8.05
354.76
51.2
0.906
500
19.39
529.06
62.54
0.924
3.4. Results and discussions of statistical study of factor (Z) correlations. Table 10: Factor (Z) statistical study by standard correlations. Hassi R’mel field Correlations
Stah field
Oued Noumer field
Grouped Fields
Ea
S
Ea
S
Ea
S
Ea
S
Hall - Yarborough (1973)
1.42
0.65
5.63
2.36
1.75
2.91
2.88
3.64
Dranchuk and Abu-Kassem (1975)
17.32
2.68
63.0
71.23
5.97
0.97
32.90
47.57
Papay (1985)
1.19
0.69
5.03
6.42
1.73
3.03
2.63
4.03
beggs - brill (1986)
0.98
1.59
11.61
4.92
0.90
1.31
4.98
6.87
S.ROBERTSONl
2.53
2.09
13.98
7.68
0.88
1.44
6.38
7.75
Table 11: Z-factor statistical study by modified correlations.
Correlations
Hassi R’mel field
Stah field
Oued Noumer field
Grouped Fields
Ea
Ea
Ea
Ea
Papay (1985)
5.03
2.63
Papay (1985) modified correlation
5.03
2.54
beggs - brill (1986)
0.98
beggs - brill (1986) modified correlation
0.95
S.ROBERTSONl
0.88
S.Robertsonl modified correlation
0.86
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According to results: The statistical analysis of the errors shows in Table 9 that the correlation between beggs and brill (1986) surpasses the rest of the correlations studied with an average absolute error of 0.98% for the Hassi R’mel field, and the Papay correlation (1985). With an average absolute error of 5.03% for the Stah field and the S. ROBERTSONl correlation with an average absolute error of 0.88% for the Oued Noumer field. The statistical analysis of the errors shows in Table 10 that the Papay correlation (1986) surpasses the rest of the studied correlations with an average absolute error of 2.63% for the grouped fields. After selecting the correlation that gives less error for each field, this correlation was modified by new coefficients adapted to the data of each region and the statistical errors were recalculated. The statistical analysis shows a significant improvement in the overall mean absolute error with modified coefficients shown in Table 11: - The correlation beggs and brill (1986) with an average absolute error of 0.95% after modification for the Hassi R'mel field. - The Papay correlation (1985) with an average absolute error of 5.03% after modification for the Stah field. - The correlation of S. ROBERTSONl with an average absolute error of 0.86% after modification for the Oued Noumer field. The statistical analysis shows a significant improvement in overall mean absolute error with modified coefficients shown in Table 11, the Papay correlation (1985) with an average absolute error of 2.54% after modification for clustered fields. Fig 2 (a) shows the graphical comparison between experimental Z and Z estimated by correlation modification for the Stah field; R2 = 0.979; Fig 2 (b); field of Oued Noumer; R2 = 0.809; Fig 3; Hassi R'mel field; R2 = 0.997. In order to confirm the results obtained from the study of the correlations we will examine these results with results of experimental study. The results of the error between the compressibility factor values obtained by the experimental study (CCE) and the values obtained by the correlation that gives an overall error before the modified and after the modified are presented in Table 12. Table 12: Results of the Mean Absolute Factor (Z) Error between Experimental Values (CCE) and Value of Correlations. Pressure (psi)
Z experimental
Z Estimated by Papay
Z Estimated by modified Papay
7000
1.206
1.3451
1.3436
6500
1.167
1.266
1.2653
6000
1.128
1.1953
1.1952
5500
1.093
1.133
1.1334
5000
1.061
1.0791
1.0799
4500
1.031
1.0335
1.0347
4000
1.007
0.9963
0.9977
3550
0.987
0.97
0.9715
3000
0.963
0.947
0.9486
2500
0.956
0.9349
0.9365
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0.967
0.9312
0.9326
1700
0.985
0.933
0.9343
1500
1.004
0.9358
0.9371
1100
1.053
0.9456
0.9466
1000
1.07
0.9489
0.9498
Ea %
5.03
4.95
665 11
From Table 12 we find that the percentage of average absolute errors of the compressibility factor (Z) decreased in the case of the modified correlations (4.95) compared to the error before the modification of the coefficients of this correlation (5.03) (Papay 1986). The results of the error between the compressibility factor values obtained by the experimental study (separator gas) and the values obtained by the correlation that gives a global error before the modified and after the modified are presented in Table 13. Table 13: Results of the Mean Absolute Factor (Z) Error between the Experimental Values (Sep Gas) and Value of Correlations. Pressure (psi)
Z experimental
Z Estimated by Papay
Z Estimated by modified Papay
200
0.9749
0.9724
0.9747
210
0.9737
0.9711
0.9735
220
0.9726
0.9698
0.9723
230
0.9715
0.9685
0.9710
240
0.9703
0.9672
0.9698
250
0.9692
0.9659
0.9686
260
0.9681
0.9646
0.9674
270
0.9669
0.9634
0.9662
280
0.9658
0.9621
0.9650
290
0.9647
0.9608
0.9638
300
0.9636
0.9596
0.9626
305
0.9630
0.9589
0.9620
310
0.9624
0.9583
0.9614
320
0.9613
0.9571
0.9602
330
0.9602
0.9558
0.9590
Ea %
0.363
0.073
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From Table 13 we find that the percentage of average absolute errors of the compressibility factor (Z) decreased for the modified correlations (0.073), compared to the error before the modification of the coefficients of this correlation (0.363) (Papay 1986).
1.4 1.3 1.2 1.1 1 0.9 0.8
Préd(Z) / Z
R²=0,979
Z
Z
Préd(Z) / Z
0.8
0.9
1
1.1
1.2
1.3
1.4
1.4 1.3 1.2 1.1 1 0.9 0.8
0.8
0.9
1
1.1
Préd(Z) (a)
R²=0,809
1.2
1.3
1.4
Préd(Z) (b)
Fig 2: the graphical comparison between experimental Z and Z estimated by correlation modification. (a) Stah field; (b) Oued Noumer field.
Z (expérimental
0.98
R²=0,997
0.96 0.94 0.92 0.9 0.88 0.86 0.86
0.88
0.9
0.92
0.94
0.96
Z (calculer)
Fig 3: the graphical comparison between experimental Z and Z estimated by correlation modification. (Hassi R'mel field) (a)
(b)
Z Expériemental Z estimé par corrélation papay standared z estimé Par corrélation Papay modifié
1.40 1.35
0.974
1.30
0.972
1.25
0.970
Facteur Z
1.20
facteur Z
Estimé comme expérience Estimé par correlation papay Estimé par correlation papay modifié
0.976
1.15 1.10 1.05
0.968 0.966 0.964 0.962 0.960
1.00
0.958
0.95
0.956
0.90 1000
2000
3000
4000
5000
pression (psig)
6000
7000
0.954 180
200
220
240
260
280
300
320
340
pression (psig)
Fig 4: Graphical comparison between (Z) experimental, (Z) estimated before and after correlation modification. (a) (CCE); (b) (Gas sep).
2. CONCLUSIONS AND RECOMMENDATIONS This study is based on the calculation of the compressibility factor of natural gas by means of an experimental study and the use of various correlations in the calculation of this factor as well as the updating of the coefficients of these correlations with what corresponds to the best to Algerian natural gas and it is for this reason that the study was divided as follows: The study of this factor was calculated by means of an experimental study conducted on an Algerian natural gas (condensate gas) in a PVT laboratory at the Division of Technologies and Development (DTD).
H.M. Sidrouhou et al. / Energy Procedia 157 (2019) 655–669 H.M.SIDROUHOU/ Energy Procedia 00 (2018) 000–000
667 13
The calculation of this factor using the different correlations and the updating of their coefficients using experimental data for the different types of Algerian natural gas and statistical tools. This part of the study also compared the results of the calculation of this factor from the results obtained by experimentation and those obtained by using the correlations before and after their updating. As a result, the results of the study were as follows: 1- In the laboratory, the PVT study focuses on condensate gas and sometimes on wet gas to determine this factor. Dry gas requires a simple study to determine this factor. 2- The use of these empirical correlations for the calculation of this factor is more economical compared to the experimental study. 3- It is possible to develop these empirical correlations in accordance with the natural gas for each geographical area as the case of Algeria for example by using the statistical tools. According to these results, it is timely to recommend for future work: - The study should be undertaken on other PVT properties such as viscosity and formation volume factor. - The database needs to be broader and more accurate. - Extend this study to other regions and make a classification according to the type of reservoir. - Uses state equations to determine the factor and compare the results. References [1] A. rojey. "Natural gas, production, treatment and transport." technip editions, Paris, France (1994). [2] J.F. gravier. "Properties of reservoir fluids." edition technip, Paris, France (1986). [3] S.P. Karen and L.C. Peter. "Phase behavior of petroleum reservoir fluids." Taylor & Francis group, USA, (2007). [4] Danesh Ali. "PVT and phase behavior of petroleum reservoir fluids". (1998) elsevier Science .b.v. [5] IFP. "PVT fluid studies″. (2006).enspm. Industrial training. [6] Tarek Ahmed. "Hydrocarbon phase behavior". vol.7. (1989) by Gulf publishing company, Houston, Texas. [7] Tarek Ahmed. "Reservoir engineering handbook". Second edition. ©2000 by Gulf publishing company, Houston, Texas. [8] Tarek Ahmed. "Advanced reservoir engineering″. ©2005, Elsevier Inc. [9] Tarek Ahmed. "Equations of state and PVT analysis: applications for improved reservoir modeling". ©2007 by Gulf publishing company, Houston, Texas. [10] Perrin Denis, "oil and gas field; development techniques". ©1995 édition technip. [11] Samer Said, "Measurement and prediction of gas hydrate condensate formation conditions." memory magister 'option Refining. BOUMERDES 2012.
Appendix A. A.1. Correlation of PAPAY (1985); For the Stah field the graphical comparison is obtained by nonlinear regression without data validation and the new coefficients for the Papay (1985) correlation for the Z:
Ppr Ppr2 Z 1 A. B.Tpr C. D.Tpr 10 10
(3)
H.M. Sidrouhou et al. / Energy Procedia 157 (2019) 655–669 H.M.SIDROUHOU/ Energy Procedia 00 (2018) 000–000
668 14 Table 14
Parameters
Original
Modified
Modified
Stah field
grouped fields
A
3,35
0,0698
2,042
B
0,9813
0,1157
0,8620
C
0,274
2,9035E-08
4,7820 * 10 -3
D
0,8157
-2,78
-9,0910 * 10 - 2
A.2. Correlation BEGGS AND BRILL (1986) : For the Hassi R'mel field the graphical comparison is obtained by the nonlinear regression without validation of the data and the new coefficients have been obtained for the correlation beggs and brill (1986) for the Z:
Z A 1 A.e B C. Pr D
Such as:
(4)
A A1.Tpr A2 A4.Tpr A5 A3
A8 A12 6 2 .P .10 A10 .Ppr2 B A6 A7.Tpr .Ppr T A9 T 1 pr pr pr C A13 A14. logTpr
D 10
A15 A16.T
2 pr A16.Tpr
A1.Tpr A2 A4.Tpr A5 A3
Table 15
Parameters
Original
Modified
A1
1.39
-0.101
A2
-0.92
-9.626
A3
0.36
-0.607
A4
-0.101
0.691
A5
0.62
0.020
A6
-0.23
-0.027
A7
0.066
0.080
A8
-0.86
-4.020
A9
-0.037
0.006
A10
0.32
0.320
A11
0.132
-0.054
A12
-0.32
-0.281
A13
0.3016
0.754
A14
-0.49
0.835
A15
0.1824
0.336
H.M. Sidrouhou et al. / Energy Procedia 157 (2019) 655–669 H.M.SIDROUHOU/ Energy Procedia 00 (2018) 000–000
669 15
A.3. Correlation of S.ROBERTSON: For the Oued Noumer field the graphical comparison is obtained by the non linear regression without validation of the data and one obtained the new coefficients for the correlation for the Z:
P D Z 1 A.T . pr2 Tpr C T Tpr pr B pr
P p . 1 Exp E. pr F . pr T Tpr pr
Table 16 Parameters
Original
Modified
A
0.127
-0,0000183
B
0.638
9,444
C
7.76
-972,417
D
14.75
1391,691
E
0.3
0,0074
F
0.44
0,0021
2
(5)
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Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES18, Technologies and Materials for Renewable Energy, and Sustainability, TMREES18, 19–21 September 2018,Environment Athens, Greece 19–21 September 2018, Athens, Greece
Evaluation of Correlations of Compressibility Factor (z) of Natural International Symposium on District Heating and Cooling EvaluationThe of 15th Correlations of Compressibility Factor (z) of Natural Gas for Algerian Gas Reservoirs Gas for Algerian Gas Reservoirs AssessingH.M.SIDROUHOU the feasibility1*of using the2 heat demand-outdoor 3 , M.KORICHI and S.DADA 1* 2 3 , M.KORICHI and S.DADA temperature H.M.SIDROUHOU function for a long-term district heat demand forecast Laboratoire Dynamique, Interaction et Réactivité des Systèmes (DIRES), Hydrocarbon Processing Department, Kasdi Merbah University, 1 1
Ouargla – DZ- Algeria; Laboratoire Dynamique, Interaction et Réactivité des Systèmes (DIRES), Hydrocarbon Processing Department, Kasdi Merbah University, a a b c c 2 a,b,c DIRES, Hydrocarbon Processing Department, Kasdi Merbah University, Ouargla – DZ- Algeria Ouargla – DZAlgeria; 32 DIRES, Hydrocarbon Processing Department, Kasdi Merbah University, Ouargla – DZ- Algeria a 3 IN+ Center for Innovation, Technology and Policy Research - Instituto Técnico, Av.Ouargla Rovisco–Pais 1049-001 Lisbon, Portugal DIRES, Hydrocarbon Processing Department, KasdiSuperior Merbah University, DZ- 1, Algeria b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France
I. Andrić
*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière , O. Le Corre
Abstract Abstract The study of PVT properties of natural gas is essential for the development of its production and exploitation. The laboratory is Abstract The study of of natural gasproperties is essential of its production exploitation. Theand laboratory is considered thePVT mainproperties source of data for these as for it isthe alsodevelopment possible to compute these dataand using state equations empirical considered main sourceerror of data for these properties as it is also possible to compute these data using state equations and empirical correlationsthe with variable margins. District networks are margins. commonly in the literature as one ofonthethemost effectiveofsolutions for decreasing the correlations withto variable error This workheating aims study experimentally an addressed Algerian natural gas, concentrating calculation the compressibility factor, greenhouse gastoemissions from building sector. require high investments the heat This work aims study experimentally anthis Algerian natural gas, concentrating on the calculation ofare thereturned compressibility factor, using the relative correlations to the calculate factor,These whilesystems trying to modify these with whatwhich corresponds betterthrough with Algerian sales.the Due to the changed conditions and data. building renovation policies, heat what demand in the future decrease, using relative correlations to calculate this factor, while trying to modify these with corresponds better could with Algerian natural gas based on statisticalclimate tools and experimental prolonging the investment return period. natural gas based on statistical tools and experimental data. The results of this study show that it is possible to develop and update the correlation coefficients that correspond better with each Theresults main scope paper is toitassess the feasibility using the heat demand – outdoor temperature functionbetter for heat demand The of thisof study show that is to update the correlation coefficients that correspond with each geographic region inthis order to reduce thepossible margin ofdevelop error. ofand forecast. The district of to Alvalade, located in ofLisbon geographic region in order reduce the margin error. (Portugal), was used as a case study. The district is consisted of 665 vary in both construction ©buildings 2018 Thethat Authors. Published by Elsevierperiod Ltd. and typology. Three weather scenarios (low, medium, high) and three district © 2019 The Authors. Published by Elsevier Ltd. renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) compared with resultsarticle from aunder dynamic heatBY-NC-ND demand previously developed and validated by the authors. This is an and open access the CC license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection peer-review under responsibility of the model, scientific committee of Technologies and Materials for Renewable Energy, Selection andshowed peer-review underonly responsibility of the isscientific committee of Technologies andbeMaterials forfor Renewable Energy, The results that when weather change considered, the margin of error could acceptable some applications Selection and peer-review under responsibility of the scientific committee of Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES18. Environment and Sustainability, TMREES18. (the error inand annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation Environment Sustainability, TMREES18. scenarios,PVT, the production, error valuenatural increased up to 59.5% factor (depending on the weather and renovation scenarios combination considered). Keywords: gas, compressibility (z). The value of production, slope coefficient increased on average the range of 3.8% up to 8% per decade, that corresponds to the Keywords: PVT, natural gas, compressibility factorwithin (z). decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the 1.renovation GENERAL INTRODUCTION scenarios). The that values suggested could be usedlayers to modify function parameters for the scenarios considered, and 1.coupled GENERAL Natural gas isINTRODUCTION a fuel comes from the reservoir of thetheearth, it is essentially composed of methane (CH4), thegas accuracy of that heat comes demand is a odorless, fuel reservoir layers of the earth, it isinessentially composed (CH4), itimprove isNatural colorless and and it from isestimations. thethe simplest hydrocarbon that exists nature. Natural gas isofamethane non-renewable
it is colorless odorless, and itare is the simplest hydrocarbon that exists inareas. nature. Natural gas is a non-renewable fossil resourceand whose reserves concentrated in certain geographic The improvement of its supply, © 2017 The Authors. Published by Elsevier Ltd. fossil resource whose reserves are plays concentrated certain of itsof supply, transportation and storage conditions a strategicinrole for itsgeographic future in theareas. energyThe mix.improvement World production natural Peer-review under of the Scientific Committee Theits15th International Symposium on District Heatingofand transportation and responsibility storage conditions plays a strategic roleoffor future in the energy mix. World production natural Cooling.
1876-6102 © 2018 The Authors. Published by Elsevier Ltd. Keywords: Heat demand; Forecast; Climate change This is an open access under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 1876-6102 © 2018 Thearticle Authors. Published by Elsevier Ltd. Selection under responsibility of the scientific of Technologies and Materials for Renewable Energy, Environment This is an and openpeer-review access article under the CC BY-NC-ND licensecommittee (https://creativecommons.org/licenses/by-nc-nd/4.0/) and Sustainability, TMREES18. Selection and peer-review under responsibility of the scientific committee of Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES18. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES18. 10.1016/j.egypro.2018.11.231
H.M. Sidrouhou et al. / Energy Procedia 157 (2019) 655–669 H.M.SIDROUHOU/ Energy Procedia 00 (2018) 000–000
656 2
gas has tripled between 1970 and 2010, accounting for 21.4% of the total energy consumed worldwide in 2010, out of 12,717 megatons. Algeria ranks seventh in the world in terms of proven resources, the fifth in production and the third in export. It is considered as a true energy giant, Algeria, with 50% of reserves, 48% of total production and the impressive rate of 94% of natural gas exports, has no rival in the Mediterranean, where it is ranked as the leading producer and exporter of oil and natural gas. Pressure-volume-temperature (PVT) properties are the general terms used to express the volumetric behavior of a reservoir fluid as a function of pressure and temperature. These properties are very important for geophysicists and petroleum engineers, especially for material balance calculations, surge performance calculations, as well as for the analysis, identification, determination and estimation of reserves and quantities that can be recovered. They are also very important for the determination of oil or gas rates and simulations of digital reservoirs. The compressibility factor of the gas (Z) is a dimensionless quantity and is defined as a ratio of the actual volume of n-moles of the gas at temperature and pressure to the volume of the same ideal mole number at the same temperature and pressure. For many years, the most accurate method for determining the compressibility factors of natural gas has been the direct measurement in the laboratory using z-factor (standing and Katz) graphs for gas mixtures, but with the evolution of science; state equations and correlations have been developed for the determination of these factors. In this section, we apply correlations of these factors and try to develop correlation coefficients from the use of statistical tools and experimental data for these factors. So, the main goals of this work are summarized as follows: 1 - An experimental study of Algerian natural gas, with an accent at the expense of the compressibility factor. 2 - A statistical study of the different correlations existing to calculate the gas compressibility factor and an attempt to develop them with what corresponds best to the Algerian natural gas. Nomenclature P T V Vr Pb Pr Ppr Ppc D Mw Z GOR Fc Bo γg Yi n m ρ Ei Er S CCE CVD DTD
Pressure Temperatures volume Relative volume Bubble pressure Rose pressure Pseudo reduced pressure Pseudo-critical pressure Density of gas relative to air Average molar mass Compressibility factor of the gas Gas Oil Ratio Contraction factor (shrinkage) Formation Volume Factor Specific gravity of the gas Molar fraction of component i in the gas mixture Number of gas constituent Mass The density Error Medium error Standard deviation Constant composition expansion Constant volume differential Technology and Development Division radius of
H.M. Sidrouhou et al. / Energy Procedia 157 (2019) 655–669 H.M.SIDROUHOU/ Energy Procedia 00 (2018) 000–000
1. Experimental study 1.1. Data Characteristics Table 1. Field
STAH
Type of sampling
area
Fluid type
condensate gas
Static bottom pressure (Psig)
3550
Bottom temperature (°C)
133
Separation pressure (Psig)
305
Separation temperature (°C)
61
GOR "field" (cm3/cm3)
14014
Compressibility factor of the gas '' site ''
0.961
Density of separator gas '' site ''
0.698
1.2. Work Organization Chart Step 1: Reconstitution of the raw gas Surface Sampling Separator gas
Separator liquid
Validation
Validation
Thermodynamic study
Thermodynamic study
Calculated
Calculated RAW GAS
Step 2: Thermodynamic study of raw gas
PVT raw gas
Constant-composition expansion (CCE) test at (Tg)
Constant-volume depletion test (CVD) at (Tg)
Determination the compressibility factor (z).
657 3
4 658
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1.3. Reconstitution procedure for raw gas (reservoir fluid) The reconstitution of the reservoir fluid comprises the following steps: A. Validation of gas samples and separator liquid: For liquids, validation includes: - Determination of the opening pressure of the bottles; - The determination of the saturation pressure at the separation temperature, which must be identical to the separation pressure; For gases; the validation is done by: -A simple chromatographic analysis whose opening pressure must be close if not equal to the separation pressure. B. Thermodynamic study of the separation effluents: B. 1. Thermodynamic Study of Gas Separator: Table 2 This study is based on the following steps: Chromatographic analysis. Determination of the average molar mass. Determination of the density of the gas separator. Determination of the compressibility factor of the separator gas. B.2. Thermodynamic study of separator liquid: The PVT study of the separator liquid includes in the study of the Constant-composition expansion, the flash separation, is to determine the molar composition of the separator liquid. B.2.1. Constant-composition expansion of the Separator Liquid: Table 3; Table 4. This experiment makes it possible to determine the following parameters: Saturation pressure (Pb). Relative Volume. Density. B.2.2. Flash separation tests: Table 5. The flash separation in the laboratory is carried out in a separator of the type "Jefri GOR Apparatus", the flash separation makes it possible to calculate the following parameters: The gas-oil ratio "GOR": The contraction factor of the oil "Fc" or shrinkage "sh" The liquid volume factor "Bo" The density of the storage liquid (ρ 15 ° C). B.2.3.Determination of the composition of the separator liquid: A PVT Sim program performs calculations. The parameters of this recombination are: GOR Lab. The density of the storage liquid at 15 ° C. C. Recombination of raw gas: The purpose of this recombination is to reconstitute the reservoir fluid (raw gas). The physical parameters provided by the study of the gas and separator liquid would be used to: Correction of the GOR site Mathematical recombination of bottom effluents Physical Recombination Process of physical recombination: Table 6. 1. Correction of gas volume under standard conditions. 2. Calculation of the volume of liquid.
5 659
H.M.SIDROUHOU/ Energy Procedia 00 (2018) 000–000 H.M. Sidrouhou et al. / Energy Procedia 157 (2019) 655–669
Flash gas First recombination
Separator liquid
Second recombination
Raw gas
Flash liquid Separator gas
Separator liquid Fig 1: The steps of recombination.
1.4. PVT study procedure of raw gas: a) Constant-composition expansion of the raw gas (CCE): Having introduced a volume of 26.73 cm3 to 7000 Psig in the "visual" PVT cell, raised to the reservoir temperature (Tg = 133 ° C) in an air bath, regulated at +/- 0.2 ° C, and after stabilization temperature and pressure by magnetic stirring propeller; there is a decline in pressure. Table 7. b) Constant-volume depletion of raw gas (CVD). We have introduced in the study cell a volume of 29.18 cm3 of the raw gas at 6000 psig and the temperature of the field. The study of constant-volume depletion consisted of six (06) release pressure levels. During the gas release, a sample is taken at each level in a pycnometer for gas chromatographic analysis. 2. The empirical correlations of the factor Z Several empirical correlations for the Z-factor calculation have been developed in previous years; intended to accurately reproduce the Z-factor Standing-Katz graph. The most commonly used correlations are Hall-Yarborough (1973), Dranchuk-Abou-Kassem (1975), Papay (1985), S. Robertson and Beggs and Brill (1986). All correlations studied (Z-Natural Gas Factors) are calculated as a function of pseudo-reduced pressure (P pr) and pseudo-reduced temperature (T pr). In the case where the composition of the natural gas is not available, the pseudo-critical properties, Ppc and Tpc, can be predicted from the only specific gravity of the gas (γ g). Brown and all. (1948) presented a graphical method for convenient approximation of the pseudo-critical pressure and the pseudo-critical gas temperature only when the specific gravity of the gas is available. Later standing (1977) expressed this graphical correlation in the following form:
T pc 168 325 g 12.5 g2
(1)
Ppc 677 15.0 g 37.5 g2
(2)
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660 6
3. Numerical modeling of correlations of factor (Z) 3.1. data acquisition The data used in this study were obtained from the analysis of 42 samples from different types of gas and wells of the five fields of Algeria. The data used in this study are a range of separation pressures, separation temperature, pseudo-reduced pressure, pseudo-reduced temperature, specific gravity, and molar composition. Table 2. Table 2: Data Description (All Fields) FIELDS
T averages (K)
T Pr (averages) (K)
P averages (Pas)
P Pr (averages) (Pas)
Z averages
Hassi R’mel
327.42
1.68
6.85E+06
1.50
0.905
Ouad Noumer
325.15
1.61
2.50E+06
0.55
0.963
Ohant
312.32
1.65
5.36E+06
1.18
0.895
Brkin
342.15
1.59
7.31E+06
1.43
0.851
Stah
406.15
1.64
2.52E+07
5.56
1.045
3.2. work organization chart First step Application of correlations for each chosen field
Oued Noumer
Stah
Statistical analysis for each field Correlation selection unless error for each field Edit the selected correlation Apply the modified correlation
Hassi R'mel
H.M. Sidrouhou et al. / Energy Procedia 157 (2019) 655–669 H.M.SIDROUHOU/ Energy Procedia 00 (2018) 000–000
661 7
Second step Statistical analysis of group fields Select correlation unless error for grouped fields
Edit the selected correlation
Apply modified correlation for grouped fields for each field Hassi R’mel
Stah
Oued Noumer
3.3. Results of experimental study: Table 3: Results of the thermodynamic study of the separator gas. Constituents
Composition YI
Yi/100
Mi
Yi*Mi
N2
0.348
0.003
28.01
0.09
CO2
5.022
0.050
44.01
2.21
C1
82.191
0.821
16.04
13.18
C2
7.683
0.076
30.07
2.31
C3
2.608
0.026
44.09
1.15
iC4
0.454
0.004
58.12
0.26
nC4
0.743
0.007
58.12
0.43
iC5
0.279
0.002
72.15
0.20
nC5
0.205
0.002
72.15
0.14
C6
0.237
0.002
86.17
0.20
C7
0.129
0.001
96
0.12
C8
0.066
0.0006
107
0.07
C9
0.020
0.0002
121
0.02
C10
0.007
0.00007
134
0.009
C11
0.004
0.00004
147
0.005
C12
0.004
0.00004
161
MW
0.006 20.4434579
Density
0.70577428
Z (305psi) ; T (61c°)
0.9630
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662 8
Table 4: Result of calculates the density of the separating liquid. PYCNO N°
m pv
m pr
m pr – m pv(g)
V lt (cm3)
I
837,7
845,586
7,886
10,44
0,755
II
835,822
842,104
6,282
8,31
0,756
Density (g/cm3)
ρ average (g/cm3) 0,756
Table 5: Results of the thermodynamic study of the separator liquid. Pressure (psi)
3000
2500
2000
1500
1000
800
500
350
240
180
130
35,53
40,82
52,26
compound volume (cc)
32,31
32,44
32,59
32,75
32,93
33,01
33,14
33,22
Density (g/cc)
0,75
0,57
0,75
0,74
0,74
0,74
0,73
0,73
Table 6: Separation test results. Fc
GOR
Bo
d15°C
0,97
13,22
0,0103
0,7748
Table 7: Results of Recombination of Raw Gas. GOR recombination
ρ bp
13537,49 cm / cm
0,735 g/cm
3
3
3
V0 (gas) at (14,7psi and 15°C)
V liquid
V L (5000 psig)
18089,27 cm3
1,3362 cm3
1,2774 cm3
Table 8: Factor (Z) Results for Constant-composition expansion of Raw Gas at T = 133 ° C. Pressure (psi)
V compound (cc)
mass volume (cm2/g)
Z
7000
26.73
3.922
1.206
6500
27.85
4.086
1.167
6000
29.18
4.281
1.128
5500
30.84
4.525
1.093 1.061
5000
32.94
4.833
4500
35.56
5.217
1.031
4000
39.06
5.731
1.007
(Pr) 3550
43.15
6.331
0.987
3000
49.8
7.306
0.963
2500
59.35
8.707
0.956
2000
75.05
11.011
0.967
1700
89.96
13.198
0.985
1500
103.83
15.233
1.004
1100
148.5
21.786
1.053
1000
166.02
24.357
1.07
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Table 9: Factor (Z) Results for Constant-composition expansion of Raw Gas at T = 133 ° C. Pressure (psig)
Vg(cell)
Vg ( 150C)
Vg product
Z
3550
0.00
-
43.15
0.987
3000
7.20
1106.35
50.35
0.962
2000
21.01
2259.83
64.16
0.918
1200
16.87
1117.93
60.02
0.898
1000
20.46
1129.55
63.61
0.901
800
8.05
354.76
51.2
0.906
500
19.39
529.06
62.54
0.924
3.4. Results and discussions of statistical study of factor (Z) correlations. Table 10: Factor (Z) statistical study by standard correlations. Hassi R’mel field Correlations
Stah field
Oued Noumer field
Grouped Fields
Ea
S
Ea
S
Ea
S
Ea
S
Hall - Yarborough (1973)
1.42
0.65
5.63
2.36
1.75
2.91
2.88
3.64
Dranchuk and Abu-Kassem (1975)
17.32
2.68
63.0
71.23
5.97
0.97
32.90
47.57
Papay (1985)
1.19
0.69
5.03
6.42
1.73
3.03
2.63
4.03
beggs - brill (1986)
0.98
1.59
11.61
4.92
0.90
1.31
4.98
6.87
S.ROBERTSONl
2.53
2.09
13.98
7.68
0.88
1.44
6.38
7.75
Table 11: Z-factor statistical study by modified correlations.
Correlations
Hassi R’mel field
Stah field
Oued Noumer field
Grouped Fields
Ea
Ea
Ea
Ea
Papay (1985)
5.03
2.63
Papay (1985) modified correlation
5.03
2.54
beggs - brill (1986)
0.98
beggs - brill (1986) modified correlation
0.95
S.ROBERTSONl
0.88
S.Robertsonl modified correlation
0.86
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According to results: The statistical analysis of the errors shows in Table 9 that the correlation between beggs and brill (1986) surpasses the rest of the correlations studied with an average absolute error of 0.98% for the Hassi R’mel field, and the Papay correlation (1985). With an average absolute error of 5.03% for the Stah field and the S. ROBERTSONl correlation with an average absolute error of 0.88% for the Oued Noumer field. The statistical analysis of the errors shows in Table 10 that the Papay correlation (1986) surpasses the rest of the studied correlations with an average absolute error of 2.63% for the grouped fields. After selecting the correlation that gives less error for each field, this correlation was modified by new coefficients adapted to the data of each region and the statistical errors were recalculated. The statistical analysis shows a significant improvement in the overall mean absolute error with modified coefficients shown in Table 11: - The correlation beggs and brill (1986) with an average absolute error of 0.95% after modification for the Hassi R'mel field. - The Papay correlation (1985) with an average absolute error of 5.03% after modification for the Stah field. - The correlation of S. ROBERTSONl with an average absolute error of 0.86% after modification for the Oued Noumer field. The statistical analysis shows a significant improvement in overall mean absolute error with modified coefficients shown in Table 11, the Papay correlation (1985) with an average absolute error of 2.54% after modification for clustered fields. Fig 2 (a) shows the graphical comparison between experimental Z and Z estimated by correlation modification for the Stah field; R2 = 0.979; Fig 2 (b); field of Oued Noumer; R2 = 0.809; Fig 3; Hassi R'mel field; R2 = 0.997. In order to confirm the results obtained from the study of the correlations we will examine these results with results of experimental study. The results of the error between the compressibility factor values obtained by the experimental study (CCE) and the values obtained by the correlation that gives an overall error before the modified and after the modified are presented in Table 12. Table 12: Results of the Mean Absolute Factor (Z) Error between Experimental Values (CCE) and Value of Correlations. Pressure (psi)
Z experimental
Z Estimated by Papay
Z Estimated by modified Papay
7000
1.206
1.3451
1.3436
6500
1.167
1.266
1.2653
6000
1.128
1.1953
1.1952
5500
1.093
1.133
1.1334
5000
1.061
1.0791
1.0799
4500
1.031
1.0335
1.0347
4000
1.007
0.9963
0.9977
3550
0.987
0.97
0.9715
3000
0.963
0.947
0.9486
2500
0.956
0.9349
0.9365
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0.967
0.9312
0.9326
1700
0.985
0.933
0.9343
1500
1.004
0.9358
0.9371
1100
1.053
0.9456
0.9466
1000
1.07
0.9489
0.9498
Ea %
5.03
4.95
665 11
From Table 12 we find that the percentage of average absolute errors of the compressibility factor (Z) decreased in the case of the modified correlations (4.95) compared to the error before the modification of the coefficients of this correlation (5.03) (Papay 1986). The results of the error between the compressibility factor values obtained by the experimental study (separator gas) and the values obtained by the correlation that gives a global error before the modified and after the modified are presented in Table 13. Table 13: Results of the Mean Absolute Factor (Z) Error between the Experimental Values (Sep Gas) and Value of Correlations. Pressure (psi)
Z experimental
Z Estimated by Papay
Z Estimated by modified Papay
200
0.9749
0.9724
0.9747
210
0.9737
0.9711
0.9735
220
0.9726
0.9698
0.9723
230
0.9715
0.9685
0.9710
240
0.9703
0.9672
0.9698
250
0.9692
0.9659
0.9686
260
0.9681
0.9646
0.9674
270
0.9669
0.9634
0.9662
280
0.9658
0.9621
0.9650
290
0.9647
0.9608
0.9638
300
0.9636
0.9596
0.9626
305
0.9630
0.9589
0.9620
310
0.9624
0.9583
0.9614
320
0.9613
0.9571
0.9602
330
0.9602
0.9558
0.9590
Ea %
0.363
0.073
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From Table 13 we find that the percentage of average absolute errors of the compressibility factor (Z) decreased for the modified correlations (0.073), compared to the error before the modification of the coefficients of this correlation (0.363) (Papay 1986).
1.4 1.3 1.2 1.1 1 0.9 0.8
Préd(Z) / Z
R²=0,979
Z
Z
Préd(Z) / Z
0.8
0.9
1
1.1
1.2
1.3
1.4
1.4 1.3 1.2 1.1 1 0.9 0.8
0.8
0.9
1
1.1
Préd(Z) (a)
R²=0,809
1.2
1.3
1.4
Préd(Z) (b)
Fig 2: the graphical comparison between experimental Z and Z estimated by correlation modification. (a) Stah field; (b) Oued Noumer field.
Z (expérimental
0.98
R²=0,997
0.96 0.94 0.92 0.9 0.88 0.86 0.86
0.88
0.9
0.92
0.94
0.96
Z (calculer)
Fig 3: the graphical comparison between experimental Z and Z estimated by correlation modification. (Hassi R'mel field) (a)
(b)
Z Expériemental Z estimé par corrélation papay standared z estimé Par corrélation Papay modifié
1.40 1.35
0.974
1.30
0.972
1.25
0.970
Facteur Z
1.20
facteur Z
Estimé comme expérience Estimé par correlation papay Estimé par correlation papay modifié
0.976
1.15 1.10 1.05
0.968 0.966 0.964 0.962 0.960
1.00
0.958
0.95
0.956
0.90 1000
2000
3000
4000
5000
pression (psig)
6000
7000
0.954 180
200
220
240
260
280
300
320
340
pression (psig)
Fig 4: Graphical comparison between (Z) experimental, (Z) estimated before and after correlation modification. (a) (CCE); (b) (Gas sep).
2. CONCLUSIONS AND RECOMMENDATIONS This study is based on the calculation of the compressibility factor of natural gas by means of an experimental study and the use of various correlations in the calculation of this factor as well as the updating of the coefficients of these correlations with what corresponds to the best to Algerian natural gas and it is for this reason that the study was divided as follows: The study of this factor was calculated by means of an experimental study conducted on an Algerian natural gas (condensate gas) in a PVT laboratory at the Division of Technologies and Development (DTD).
H.M. Sidrouhou et al. / Energy Procedia 157 (2019) 655–669 H.M.SIDROUHOU/ Energy Procedia 00 (2018) 000–000
667 13
The calculation of this factor using the different correlations and the updating of their coefficients using experimental data for the different types of Algerian natural gas and statistical tools. This part of the study also compared the results of the calculation of this factor from the results obtained by experimentation and those obtained by using the correlations before and after their updating. As a result, the results of the study were as follows: 1- In the laboratory, the PVT study focuses on condensate gas and sometimes on wet gas to determine this factor. Dry gas requires a simple study to determine this factor. 2- The use of these empirical correlations for the calculation of this factor is more economical compared to the experimental study. 3- It is possible to develop these empirical correlations in accordance with the natural gas for each geographical area as the case of Algeria for example by using the statistical tools. According to these results, it is timely to recommend for future work: - The study should be undertaken on other PVT properties such as viscosity and formation volume factor. - The database needs to be broader and more accurate. - Extend this study to other regions and make a classification according to the type of reservoir. - Uses state equations to determine the factor and compare the results. References [1] A. rojey. "Natural gas, production, treatment and transport." technip editions, Paris, France (1994). [2] J.F. gravier. "Properties of reservoir fluids." edition technip, Paris, France (1986). [3] S.P. Karen and L.C. Peter. "Phase behavior of petroleum reservoir fluids." Taylor & Francis group, USA, (2007). [4] Danesh Ali. "PVT and phase behavior of petroleum reservoir fluids". (1998) elsevier Science .b.v. [5] IFP. "PVT fluid studies″. (2006).enspm. Industrial training. [6] Tarek Ahmed. "Hydrocarbon phase behavior". vol.7. (1989) by Gulf publishing company, Houston, Texas. [7] Tarek Ahmed. "Reservoir engineering handbook". Second edition. ©2000 by Gulf publishing company, Houston, Texas. [8] Tarek Ahmed. "Advanced reservoir engineering″. ©2005, Elsevier Inc. [9] Tarek Ahmed. "Equations of state and PVT analysis: applications for improved reservoir modeling". ©2007 by Gulf publishing company, Houston, Texas. [10] Perrin Denis, "oil and gas field; development techniques". ©1995 édition technip. [11] Samer Said, "Measurement and prediction of gas hydrate condensate formation conditions." memory magister 'option Refining. BOUMERDES 2012.
Appendix A. A.1. Correlation of PAPAY (1985); For the Stah field the graphical comparison is obtained by nonlinear regression without data validation and the new coefficients for the Papay (1985) correlation for the Z:
Ppr Ppr2 Z 1 A. B.Tpr C. D.Tpr 10 10
(3)
H.M. Sidrouhou et al. / Energy Procedia 157 (2019) 655–669 H.M.SIDROUHOU/ Energy Procedia 00 (2018) 000–000
668 14 Table 14
Parameters
Original
Modified
Modified
Stah field
grouped fields
A
3,35
0,0698
2,042
B
0,9813
0,1157
0,8620
C
0,274
2,9035E-08
4,7820 * 10 -3
D
0,8157
-2,78
-9,0910 * 10 - 2
A.2. Correlation BEGGS AND BRILL (1986) : For the Hassi R'mel field the graphical comparison is obtained by the nonlinear regression without validation of the data and the new coefficients have been obtained for the correlation beggs and brill (1986) for the Z:
Z A 1 A.e B C. Pr D
Such as:
(4)
A A1.Tpr A2 A4.Tpr A5 A3
A8 A12 6 2 .P .10 A10 .Ppr2 B A6 A7.Tpr .Ppr T A9 T 1 pr pr pr C A13 A14. logTpr
D 10
A15 A16.T
2 pr A16.Tpr
A1.Tpr A2 A4.Tpr A5 A3
Table 15
Parameters
Original
Modified
A1
1.39
-0.101
A2
-0.92
-9.626
A3
0.36
-0.607
A4
-0.101
0.691
A5
0.62
0.020
A6
-0.23
-0.027
A7
0.066
0.080
A8
-0.86
-4.020
A9
-0.037
0.006
A10
0.32
0.320
A11
0.132
-0.054
A12
-0.32
-0.281
A13
0.3016
0.754
A14
-0.49
0.835
A15
0.1824
0.336
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A.3. Correlation of S.ROBERTSON: For the Oued Noumer field the graphical comparison is obtained by the non linear regression without validation of the data and one obtained the new coefficients for the correlation for the Z:
P D Z 1 A.T . pr2 Tpr C T Tpr pr B pr
P p . 1 Exp E. pr F . pr T Tpr pr
Table 16 Parameters
Original
Modified
A
0.127
-0,0000183
B
0.638
9,444
C
7.76
-972,417
D
14.75
1391,691
E
0.3
0,0074
F
0.44
0,0021
2
(5)