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Comparing methods for calculating Z-factor
Abstract
From an examination of computational methods, one can select the most accurate method for calculating a gas deviation factor (Z), the method that needs the least computer time, and whether a microcomputer or larger machine is needed. This examination covered thirteen computational methods for describing the Standing-Katz natural gas deviation factor chart that has been used for more than 40 years. Petroleum engineering calculations often require knowledge of Z-factors for natural gases, but experimental data from pressure-volume-temperature (p-V-T) measurements are seldom available. In such cases, use of the Standing-Katz Z-factor chart or its tabulated form is generally accepted.
... Ansari models need PVT properties and thus the PVT properties are estimated using the black oil correlations, which are listed in Table 2. These correlations are the most accurate ones based on different literature surveys ( Brill et al., 1991;Takacs, 1989;Takacs, 1989;Bendakhlia et al., 1989;Renanto et al., 1998;Patton et al., 1980). For estimating the PVT properties, the temperature of the fluid should be known; thus using the temperature of the top node and the Hasan-Kabir's (Hasan-Kabir, et al., 1994) model, the temperature of the bottom of the section can be estimated. ...
... Ansari models need PVT properties and thus the PVT properties are estimated using the black oil correlations, which are listed in Table 2. These correlations are the most accurate ones based on different literature surveys ( Brill et al., 1991;Takacs, 1989;Takacs, 1989;Bendakhlia et al., 1989;Renanto et al., 1998;Patton et al., 1980). For estimating the PVT properties, the temperature of the fluid should be known; thus using the temperature of the top node and the Hasan-Kabir's (Hasan-Kabir, et al., 1994) model, the temperature of the bottom of the section can be estimated. ...
One of the problems that sometimes occur in gas allocation optimization is instability phenomenon. This phenomenon reduces the oil production and damages downhole and surface facilities. Different works have studied the stability and suggested some solutions to override it, but most of them (such as making the well intelligent) are very expensive and thus they are not applicable to many cases. In this paper, as a new approach, the stability has been studied in gas allocation optimization problems. To prevent the instability, instability has been assumed as a constraint for the optimizer and then the optimizer has been run. For the optimization, first a genetic algorithm and then a hybrid of genetic algorithm and Newton-Quasi have been used, and their results are compared to ensure the good performance of the optimizer; afterwards, the effect of adding the instability constraint to the problem on production reduction have been discussed. The results show that the production loss with adding this constraint to the system is very small and this method does not need any additional and expensive facilities for preventing the instability. Therefore, the new method is applicable to different problems.
... At the beginning there is a need for some empirical correlations for fluid and flow properties estimation. Here, for fluid properties, modeling the most accurate models based on different literature (Brill and Beggs, 1991a) (Takacs, 1989) (Khamehchi, et al., 2009) have been used. For example, for critical pressure and temperature Standing (Vatani and Mokhatab, 2004a), for gas compressibility factor Standing and Katz (Standing and Katz, 1942) and Papay (Papay, 1968) and for viscosity of gas and oil Lee (Takacs, 2005) and Beal (Beal, 1946) have been used respectively and solution gas oil ratio has been modeled by Laster (Lasater, 1958a) equation. ...
... In this calculation, different correlations were used. These are the most accurate ones based on different literature (Brill and Beggs, 1991b), (Takacs, 1989), (Pourafshary, 1979), (Bendakhlia and Aziz, 1989), (Renanto and Economides, 1998), (Patton et al., Septamber 19 80). In order to apply the effect of gas lift, the gas lift effect is added by considering a different gas liquid ratio (GLR) in the above injection point. ...
... Studies of the compressibility factors for natural gases of various compositions (Brown et al., 1948;Wichert et al., 1972;Burnett, 1979;Dranchuk et al., 1975;Hall et al., 1973;Garb, 1978) have shown that Z-factors can be generalized with sufficient accuracies for most engineering purposes by introducing the concepts of pseudo-reduced pressure and temperature based on pseudo-critical pressure and temperature as follows: In common natural gas applications, it is accepted by wide usage to the use the chart of Standing and Katz (Standing et al., 1942) for compressibility factors (Saleh, 2002). A summary and comparison of thirteen methods for describing the Standing and Katz chart is available by Takacs (1989). Of these methods, the Dranchuk-Kassem (Dranchuk et al., 1975) method was chosen for use in GasGrid for estimating the Zfactor, because this method offered combined merits of having a wide range of applicability (0.2 ≤ P r ≤ 30.0, 1.0 ≤ T r ≤ 3.0) with an average error of only 0.6% according to the study by Takacs (1989). ...
... A summary and comparison of thirteen methods for describing the Standing and Katz chart is available by Takacs (1989). Of these methods, the Dranchuk-Kassem (Dranchuk et al., 1975) method was chosen for use in GasGrid for estimating the Zfactor, because this method offered combined merits of having a wide range of applicability (0.2 ≤ P r ≤ 30.0, 1.0 ≤ T r ≤ 3.0) with an average error of only 0.6% according to the study by Takacs (1989). In this method, the authors, using the Starling- ...
Thesis (M.S.)--Pennsylvania State University, 2003. Library holds archival microfiches negative and service copy.
... In this calculation, different correlations were used. These are the most accurate ones based on different literature (Brill and Beggs, 1974;Takács, 1989;Pourafshary, 2007;Bendakhlia and Aziz, 1989). After calculating the bottom hole pressure for a fixed rate, other production rates were assumed and their corresponding bottom hole pressure was calculated. ...
Lapangan gas “MC” reservoir “SDM” terletak dibagian barat blok Sumatera Selatan. Reservoir “SDM” telah diproduksi oleh 4 sumur, mulai produksi Juli 1987. Kumulatif produksi gas per 31-01- 2017 adalah 38.771 MMSCF. Perusahaan bermaksud membuat rencana pengembangan lanjut lapangan (POFD) dalam rangka untuk mengoptimalkan perolehan gas. Permasalahan utamanya adalah berapa cadangan gas per 31-01-2017. Data teknik pendukung untuk prediksi cadangan gas, seperti data reservoir, produksi, karakteristik gas fungsi waktu telah dicatat oleh perusahaan sejak lapangan “MC” mulai berproduksi, termasuk data cadangan gas mula-mula volumetrik. Metodologi yang digunakan, pertama mengumpulkan data teknik pendukung, kedua analisa perilaku reservoir, ketiga menentukan tekanan reservoir rata-rata menggunakan tiga model tekanan rata-rata (sumuran, area dan volume), keempat menentukan faktor kompresibilitas gas (Z) menggunakan tujuh model faktor kompresibilitas Z (metode Standing & Katz, Thomas Hankinson Phillips, Soave Redlich Kwong, Beggs & Brill, Dranchuk Abu Kassem, Peng-Robinson, dan M.A. Mahmoud), kelima menentukan jenis mekanisme pendorong dengan Metode Cole Plot , keenam menentukan Original Gas In Place (OGIPi) dan Ultimate Recovery (URi) berdasarkan pendekatan Material Balance P/Z , ketujuh prediksi Cadangan Gas per 31-01-2017. Hasilnya adalah cadangan gas per 31-01-2017 reservoir “SDM” sebesar 7.200 MMSCF setelah divalidasi dengan cadangan gas per 31-01-2017 volumetrik. Kata kunci: tekanan reservoir, rata-rata, faktor Z, cadangan sisa gas.
Compressibility factor, z, values of natural gases are necessary in most petroleum gas engineering calculations. Most common sources of the compressibility factor values are experimental measurements, equations of state method and empirical correlations. If laboratory measured data were unavailable, empirical correlations can be used to determine the compressibility factors. However, there might be discrepancies between laboratory-measured values with those obtained by correlations which, in turn, might affect the outcome of a study. Sensitivity analysis is a technique used to determine how different values of the compressibility factor would affect well testing and material balance equation calculations. Under a given set of data, this technique is used within specific boundaries that will depend on one or more methods, such as the effect that changes in reservoir's parameters obtained from build-up test and calculations of gas initial in place by using material balance equation. This study highlights how changes in the compressibility factor affect well testing results and volume of gas initially in reservoir calculated using material balance equation. Three wells producing under partial water drive mechanism were considered for this study. Dranchuk and Abu-Kassem’s method was found to have the lowest error.
One of the most common methods for calculating the production oil rate in a gas lift well is nodal analysis. This manner is an accurate one, but unfortunately it is very time consuming and slow. In some modern studies in petroleum engineering such as close loop control of the wells this slowness makes it impossible to have an online optimization. In fact, before the end of the optimization the input parameters have changed. Thus having a faster model is necessary specially in some of the new studies. One of the sources of slowness of the nodal analysis is the temperature profile estimation of the wells. There are two general approaches for temperature profile estimation, some like heat balance are accurate but slow. Others, similar to linear profile assumption are fast but inaccurate and usually are not used commonly. Here, as a new approach, a combination model of heat balance and linear temperature profile estimation has represented which makes the nodal analysis three times faster and it is as accurate as heat balance calculations. To create this, two points (gas injection point and end of tubing) are selected, then using heat balance equations the temperature of those two points are calculated. In normal nodal analysis the temperature of each wanted point in the well is estimated by heat balance and it is the source of slowness but here just two points are calculated using those complex equations. It seems that between these points assuming a linear temperature profile is reasonable because the parameters of the well and production such as physical tubing, and casing shape and properties and gas oil ratio are constants. But of course, it still has some deviation from the complete method of heat balance which using regression and assigning a coefficient to the model even this much of the deviation could be overcame. Finally, the model was tested in various wells and it was compared with the normal nodal analysis with complete heat balance models. Results showed that the new model is as accurate as normal heat balance but three times faster.
One of the most common methods for calculating the production oil rate in a gas lift well is nodal analysis. This manner is an accurate one, but unfortunately it is very time consuming and slow. In some modern studies in petroleum engineering such as close loop control of the wells this slowness makes it impossible to have an online optimization. In fact, before the end of the optimization the input parameters have changed. Thus having a faster model is necessary specially in some of the new studies. One of the sources of slowness of the nodal analysis is the temperature profile estimation of the wells. There are two general approaches for temperature profile estimation, some like heat balance are accurate but slow. Others, similar to linear profile assumption are fast but inaccurate and usually are not used commonly. Here, as a new approach, a combination model of heat balance and linear temperature profile estimation has represented which makes the nodal analysis three times fasterand it is as accurate as heat balance calculations. to create this, two points (gas injection point and end of tubing) are selected, then using heat balance equations the temperature of those two points are calculated. In normal nodal analysis the temperature of each wanted point in the well is estimated by heat balance and it is the source of slowness but here just two points are calculated using those complex equations. It seems that between these points assuming a linear temperature profile is reasonable because the parameters of the well and production such as physical tubing, and casing shape and properties and gas oil ratio are constants. But of course, it still has some deviation from the complete method of heat balance which using regression and assigning a coefficient to the model even this much of the deviation could be overcame. Finally, the model was tested in various wells and it was compared with the normal nodal analysis with complete heat balance models. Results showed that the new model is as accurate as normal heat balance but three times faster.
Z-factor determination in a digital computer
- E H Gray
- H L Sims
Gray, E.H., and Sims, H.L., Z-factor determination in a digital computer," OGL July 20, 1959,
pp. 80-81.
Z-factor equation developed for use in digital computers
- A M Sarem
Sarem, A.M., "Z-factor equation developed for
use in digital computers," OGL Sept. 18, 1961,
p. 118.
A great number of petroleum-engineering calculations require knowledge of deviation factors for natural gases. But experimental data from P-V-T measurements are seldom available. In such cases, use of the Standing-Katz Z-factor chart, or its tabulated form, is generally accepted. This article evaluates eight methods that have been devised to make the original Standing-Katz chart of supercompressibility, or Z-factor, readily usable in complex calculations. A chart and a table are presented to help choose the proper method for a given range of reduced temperature and pressure. Considerations on the computer programming of every method are given with an eye on possible use of minicomputers.
Previous article on the title method (see Engineering Index 1973, Abstract No. 040920) is expanded by an explanation of use of an equation of state that represents the classic Z-factor chart.
Mathematical representation of the Standing-Katz chart for natural gas supercompressibility factors is essential in computer programs to solve complex gas production and transmission problems. This article describes a set of 13 equations that has been developed for this purpose. These equations cover the pseudo-reduced pressure (Pr) range from 0. 2 to 15. 0 and the pseudo-reduced temperature (Tr) range from 1. 05 to 3. 0.
Density data are reported on 16 saturated hydrocarbon vapors at pressuresranging from 1000 to 8220 lb. per sq. in. and at temperatures ranging from 35?to 250?F. These data have been used to extend the compressibility-factor chartfor natural gases up to 10,000 lb. per sq. in. The relatively large quantity ofhigh-boiling constituents present in high-pressure vapors in equilibrium withcrude oils makes it necessary to include in the analysis of the gas themolecular weight, density, and possibly boiling range of the heptanes andheavier fraction. Relationships have been presented by which the density ofgases may be obtained directly from the temperature, pressure, and gas gravityprovided the gases have a common source or are similar in composition.
Introduction
The densities of natural gases are necessary in many engineeringcomputations in petroleum production and utilization. Gas reserves, changes inreservoir pressure, gradients in gas wells, metering of gases, pipeline flow,and compression of gases are typical problems requiring the density of the gas.A decade ago, engineering computations used ideal gas laws with deviations upto 500 lb. per sq. in. Recent discoveries of pools having pressures up to 7500lb. per sq. in., and installation of pressure-maintenance and recycling plants,have increased the need for data on gas density at high pressures.
Methods Of Computation
The accepted method of computing the density or specific volume of naturalgases is the use of the ideal gas law corrected by a compressibility factor.The method proposed by Kay of correlating compressibility factors for gaseousmixtures on pseudo critical properties appears to be satisfactory for naturalgases. The methane-compressibility factor has been shown to deviatesystematically from the behavior of natural gases and a chart giving thesecorrected factors is available.
A method of computing specific volume of gaseous mixtures from partial molalvolumes has been reported by Sage and Lacey. Complete data for the computationare not yet available for all hydrocarbon gases.
Most of the reported data on gas densities have been in the single-phaseregion removed from the dew point or saturation condition. Since most gases inthe reservoir or while on contact with liquid during flow are saturated, thedetermination of densities under conditions of saturation is particularlyimportant.
T.P. 1323
Compressibility factors have been calculated by means of computer for almost twenty-five years. During this period, the techniques available for effecting such calculations have been gradually improved and refined. In the recent past, experimental data have been fitted with various equations of state and these fitted equations have been used to generate Z factors. In this article the generalized Starling equation of state has been fitted to the Standing and Katz Z-factor correlation and a computer program is presented for the generation of Z factors by means of this equation. A comparison is made of the performance of the Hall and Yarborough, Dranchuk et al. and above-mentioned methods and the results are discussed.