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Abstract The most common centrifuges used in the petroleum industry for capillary pressure measurements are made by Beckman. The Beckman centrifuge has, long been found problematic due to its rotor design. The gravity degradation phenomenon at low speeds has been identified as one of the problems for high permeability and porosity sandstone samples, in which the gravitational acceleration distorts the horizontal centrifugal force distribution inside core plugs and thus leads to inaccurate interpretation of capillary pressure information in the high saturation region. The possible remedial countermeasures to this problem may include developing a rotor head with a new configuration that minimizes the effect while maximizing the quality of row experimental data. This paper presents a theoretical analysis of the centrifugal field of rotor systems with pivoted heads. The analysis from the proposed theory shows that a pivoted rotor head makes the gravitational nd centrifugal fields more closely aligned, thereby greatly educing this effect. The new rotor configuration provides n alternative for the centrifuge experiments. A simple approximation is provided to extend the Hassler-Brunner method for use with a pivoted rotor head. Introduction Two of the most important parameters required by petroleum reservoir engineers in order to calculate the performance of oil and gas reservoirs are capillary pressureand relative permeability. Unfortunately, these are he two most difficult parameters to measure. Since the mid-1940'S, centrifuges have been used to collect data from which capillary pressure data can be interpreted. The basis of this method is that if a sample of porous edium contains two components, one of which wets the solid, internal surface of the sample, then capillary pressure tends to hold this wetting component inside the sample. If the sample is spun in a centrifuge, the centrifugal force acts to expel the wetting component from the sample, while the capillary pressure forces act to hold the wetting component in the sample. By measuring the amount of wetting component produced as a function of the speed (RPM) at which the sample is spun, a data set may be obtained from which capillary pressure versus saturation may be interpreted. Such interpretations may be very complicated.. In recent years, there has been increasing interest in using a centrifuge to obtain relative permeability. This is done by measuring the rate at which the wetting component is expelled, and interpreting this rate data, again using a complex procedure. Even though centrifuge techniques have been in use for almost 50 years, they have not yet been perfected. Three basic problems remain: obtaining a complete understanding of the mechanisms that are involved in fluid displacement by centrifugal forces, performing true imbibition experiments, and interpreting the data to obtain capillary pressure and relative permeability curves. Considering the first basic problem in particular, two typical phenomena have held people's attention. One is the radial effect due to core width. . Traditionally people assume either a constant or a linear centrifugal acceleration distribution inside the core plug. Such assumptions will cause errors when a short, large diameter core plug is used (unfortunately this is the case for most commercial Beckman centrifuges).
Abstract This paper gives a comparative study of empirical viscosity correlation expressions. The documented expressions include Lee et al.'s exponential expression, Dempsey-Standing's polynomial expression, Dranchuk-Islam- Bentsen's representation of Carr et al's data, Gurbanov and Dadash-Zade's expression, Lohrenz et al's expression, and a regression expression of Gonzalez and Lee's data. The first four expressions are two-step procedures, while the equation representing Gonzalez and Lee's data is a one-step procedure, and Lohrenz et al's expression is basically a semi-empirical composition dependent method. Some of these expressions are capable of estimating viscosities of impure natural gases which contain non-hydrocarbon components like N2 CO2and H2S. A detailed analysis of application region, accuracy, and computational superiority for these empirical expressions of viscosity correlations is presented and a two-step procedure with combined equations is recommended. Introduction In the petroleum industry, natural gas viscosities at reservoir conditions or elevated pressures and temperatures are of particular importance for reservoir engineering calculations. The only accurate way to obtain the viscosity of a gas is to determine it experimentally, using apparatus such as a rolling-ball pressure viscometer or a capillary-tube viscometer. In the early petroleum industry, many experimental efforts were made and many data were obtained. In practical applications, however, petroleum engineers always rely on empirical correlations of natural gas viscosities. The reason is perhaps twofold: performing good experiments is quite tedious, and also compared with the inaccuracy of some of the other data that are used in the same equations with the gas viscosity, the viscosity might be the most accurate even though it comes from empirical data which were correlated graphically for engineering convenience. With the advent of computers, many semi-empirical equations for gas viscosities were developed to meet the industry's demand. Most of these equations stemmed directly from the regression of experimental charts that were already well correlated, while others were developed based on experiment, supported by molecular theories. The viscosity of a pure gas depends on temperature and pressure, but for a natural gas, or a gas mixture, it is also a function of the composition of the gas. In addition, when a natural gas is not pure, or there are some non-hydrocarbon components (such as N2, CO2 and H2S) present in the gas, its viscosity under pressure and temperature has to be corrected. Conventionally, a two-step procedure is usually used to estimate natural gas viscosities under pressure and temperature.. In the first step, µg the viscosity at low pressure or atmospheric pressure and the desired temperature T is estimated if the apparent molecular weight Mg or the gas gravity G and the desired temperature are known. When it is not a pure hydrocarbon gas, the viscosity µg has then to be corrected for all non-hydrocarbon components. In the second step, the viscosity of the natural gas under pressure and temperature is calculated through equations that predict the ratio of µ to µg based on the principle of corresponding states, that is, the ratio of µ to µg is expressed as a function of both the reduced pressure.
Abstract A numerical simulation of an unsteady state gas permeameter has been developed which takes into account non-ideal gas and thermodynamic (non-isothermal) effects. It is shown that these effects have a profound influence on the pressure response of the apparatus. Although some Influences may be designed out, important effects associated with rock/gas interacting cannot be modified. These influences should be taken into account when analysing the data. Introduction In a previous paper, the performance of an unsteady state gas permeameter was modelled by means of a one dimensional numerical simulation. The model was used to analyse the influence of both slippage and inertial effects on the response of the instrument. The response of the instrument was then examined in the context of experimental errors and it was shown that, for certain permeability ranges, it is difficult, if not impossible, to measure Klinkenberg and/or Forchheimer coefficients. It was recommended that these parameters not be accepted as valid unless the Klinkenberg or Reynolds number respectively was greater than 0.1. The model on which the previous paper was baaed contained these simplifying assumptions:The gas is ideal There are no thermodynamic effects associated with the decompression, that is, it is isothermal. There are no heat transfer effects. (this Follows from 2) The current paper presents the results obtained from an extended numerical model which removes these three assumptions. With these three assumptions negated, the approximate method proposed by Jones is no longer formally valid. However, this does not mean that the approximate method necessarily gives erroneous results. For this reason the approximate method' will be reconsidered in light of the new model. In the past, many approximate analytical solutions besides that of Jones has been presented for this problem. One of these (Hsieh et a1) has often been referred to as an exact solution. It is not, however, exact since it solves a linearized version of the governing equation. For isothermal, Darcy flow, the equation solved in the approximate solutions, including that of Hsieh, is of the form: Equations 1 (available in full paper) while the equation solved numerically in the present paper is of the form: Equations 2 (available in full paper) The parameters a and a are constants. To the authors' knowledge, no exact solution exists to Equation 2. Non Ideal Gas Behaviour In the original numerical model, the pressure (P), temperature (T) and density (P) were assumed to be related by the ideal gas law: that is, Equations 3 (available in full paper) where R is the ideal gas constant for the particular gas used. In the present, revised model, the gas is assumed to obey the Benedict-Webb-Rubin (BWR) equation: Equations 4 (available in full paper) Neglecting the influence of slippage and inertia, results for the pressure decline vary with the parameter tk (time multiplied by permeability), regardless of permeability (see reference 1).
The Analysis Of Laboratory Fluid/Flow Displacement Data To Obtain Relative Permeability Curves
Ruth, D.W. (Geotechnical Resources Ltd.) | Nikakhtar, B. (Geotechnical Resources Ltd.) | Wong, S. (Geotechnical Resources Ltd.) | Mitchell, B.T. (Geotechnical Resources Ltd.) | Mcleod, G. (Geotechnical Resources Ltd.)
Abstract The approaches to analysing unsteady state displacement experiments in order to determine relative permeability curves are reviewed. A new version of the welge technique, which incorporates explicit functional forms for relative permeability is developed. The sensitivity of the production and pressure history to the shape of the relative permeability curves is analysed. The influence of capillary pressure is then predicted by comparing results from the welge technique and from the numerical simulator. Introduction Relative permeability measurement methods may be broadly classified into two types: steady state and unsteady state. For the steady state method, the phases are injected at a Fixed volumetric ratio until pressure and flow equilibrium have been established. The pressure drops across the core of each phase (Δ Pa) and the flow rates of each phase (qa) are then used to calculate the relative permeabilities (kra) by means of the Darcy equation Equation 1 (available in full paper) where µa is the Viscosity, k is the absolute permeability, A is the cross sectional area of the sample and L is the length of the sample. A saturation of the sample is also required, this is typically determined by weight. The unsteady state method is based on interpreting an immiscible displacement process. This interpretation is based on one of the two approaches: application of the welge Theory (see Johnson, Bossler and Naumann or Jones and Roszelle) or numerical simulation (see Sigmund and McCafFery). The welge approach requires the determination of the derivative of fractional flow with saturation. These derivatives are usually found either graphically or by means of curve fitting of the data. furthermore, application of this method requires the following experimental restrictions:The pressure drop across the sample must be sufficiently large so that capillary pressure effects are negligible. The pressure drop restriction often necessitates the use of the flow rates much in excess of those used in the field. Because graphical or point to point methods are used, a reasonable number of data points must be available after injection fluid breakthrough. for water displacing oil experiements, this is often achieved by using an oil which has a viscosity much higher than that in the field. The second method (numerical simulation) of reducing the data, is a more direct and sophisticated means of calculating the relative permeability curves, I t is applied by assuming explicit functions to relate relative permeability and saturation. The equations most often used are referred to as Corey equations which for two phases (i and d for injected and displaced) are: Equation 2a & 2b (available in full paper) where kie and kde are the effective end point permeabilities (effective permeability when the other phase is immobile), 5i and 5d are the saturations, and ni and nd are exponents which determine the shapes of the two relative permeability curves (shape exponents). Data reduction by the numerical 9imulatlon method can explicity take account of capillary pressure effects. Therefore, there is no need to remove these effects by means of high flow rates.