The New Method of Gas Saturated Oil Viscosity Determination
V.I., Krikunov V.V.paper presents a mathematic technique for calculating viscosity of West Siberian reservoir oils.The viscosity is one of the most important fluids parameters, is submitted as a function of viscosities of components included in gas saturated oil, reservoir temperature and pressure.method uses concept of standard viscosity reservoir oil (at 200С and 0.1 МPа) - hypothetical values, since the mix at these conditions is double phase. The influence of temperature and pressure on standard viscosity has been defined by correlations obtained at research of behavior of West Siberian subsurface collected oil samples.laboratory practice of crude oil saturated with natural gas dynamic viscosity study in reservoir conditions high-pressure viscometers, which is included as additional components in complex and power-intensive PVT-equipment simulating reservoir pressure and temperature are used. In conditions of the analysis of the representative series of samples that show behavior of reservoir fluids, the realization of the large number of definitions is required that causes a lot of difficulties. Use of only experimental methods is connected to the time-consuming for realization of the analysis, presence of precision devices in laboratory, necessity of continuous operator observing for run, etc. Besides the factors listed above, there are a number of restrictions in using one or others viscometers depending on viscosity of a sample has been under study . Therefore creation of new calculation methods of the basic characteristics of oil-gas mixes used for oil fields development and surface facilities construction has both scientific and practical importance.development of a calculation method of dynamic viscosity determination of mixture its composition is chosen as initial parameter because it gives the best description of a mixture. The knowing of apparent viscosity of pure components at standard conditions is initial parameters for the method. Briefly, after composition as a whole has been analyzed followed by using the appropriate mixing rule for the apparent viscosity of a crude oil-gas mixture is defined. For further steps, the method uses the empirical correlations of standard viscosity, pressure and temperature for determination of oil saturated with gas viscosity at reservoir conditions.
where: μP, T dynamic viscosity of hydrocarbon fluid at P,T, mPa·s;
μ0 apparent viscosity of hydrocarbon fluid at standard conditions (0.1MPa, 293K), mPa·s, (standard viscosity)., the standard viscosity can be presented as simply combination of definitively functions of pure component standard viscosity according to its molar fraction. For example, in earlier published works the combination of additive viscosity function of cut fractions for tank oil takes place or the equation for gases at low pressure depending on molar composition is used:
Experimental Data Obtained
In process of obtaining experimental data the viscosities of reservoir liquid were obtained. The data were in temperature and pressure range 50-900C and 17-32 MPa. The way of experimental definition of viscosity consists of follow steps: sample of reservoir mixture has been transferred by non-mercury displacement RUSKA from first equilibrium cell into second cell thru the calibrated capillary of a known diameter at constant temperature (reservoir temperature) and fixed pressure difference, that equal to a difference between reservoir and some pressure that is bellow than reservoir, but higher than saturation point pressure. Composition of mixture has been calculated by means of result of gas chromatography analysis of liberated phases (gas and oil) and gas/oil ratio at standard (at 200C, 0.1MPa) flash separation.
Development of the Calculation Procedures
Apparent Viscosity at Standard Conditionsdefinition of standard viscosity of oil-gas mixture we propose the following mixing rule:
Earlier the similar equation was used by Kendall and Monroer for definition of binary mixes viscosity depending on value of viscosity of components included in their composition . In equation (3): xi is a molar fraction of i component; μ0,i is a standard viscosity of i component. The values of μ0,i for natural mixed components are presented in Table 1.
1 - Initial values of liquid density and dynamic viscosity of crude oil-gas mixes components at 200C and 0.1 MPa
ComponentMolar weightLiquid Density, kg/m3Liquid Viscosity, mPa·sCarbon dioxide…………………. 44.018500.26Nitrogen………………………...28.025700.12Methane………………………...16.04(300)(0.036)Ethane…………………………..30.07(460)(0.086)Propane…………………………44.095010.120Isobutane………………………..58.125570.179Norm. butane…………………...58.125800.171Isopentane………………………72.146200.224Norm. pentane………………….72.146260.234of components, since pentane, correspond to their actual value at standard conditions (Reference Data).components C3 and C4 in a mix have properties similar to normal liquid. The values of apparent viscosity for them are offered to be defined by extrapolation of the equation Chatteree, Kunte for organic liquids .
where: μt- viscosity of a liquid at given temperature, mPa·s
μb - viscosity of a liquid at boiling temperature, mPa·s- boiling temperature, 0C - current value of temperature;
А =-2.6677; B = 2.6613 (for paraffin hydrocarbons)values of apparent viscosity for methane and ethane are received by using of following expressions (Starling-Ellington methods ):
,(5): Y, К, Х - Lee coefficients adapted for temperature in Celsius degrees:
t - temperature, 0C;- molecular weight of component;
ρ - liquid density of component, kg/m3 (at 200C - apparent liquid density).determination of apparent density methane and ethane in the mixture Standing correlation expressions is applied :
Where: ρ0,mix - apparent density of mixture that is computed by the following equation (Standing):
Where: υi - molar volume of i component.
For apparent density of mixture calculation it is necessary to obtain the value of density of indivisible С6+-fraction. It can be obtained from equation (6) rewritten for C6+-residue density in tank oil:
Where: Mrto - cryoscopy molar weight of tank oil;
ρ0 - density of tank oil;
x′i - molar fraction of i component in tank oil;- molar weight of i component from Table 1. For С6+-fraction the value of molar weight obtained from following expression:
Where: xm′i - GC mass fraction of i component in tank oil., knowing of apparent density of a mixture it is possible to define density of methane and ethane with the equation (5). The final value of C1, C2 density is found out by Newtons successive approximation method with convergence criterion , where r is number of iteration. 3 or 4 approximations are enough for realization of the given algorithm. The apparent viscosity of methane and ethane is specified their density. Taken magnitude of C1, C2 viscosity is subsequently used for of oil-gas mixture apparent viscosity estimation. С6+-fraction the value of viscosity has been obtained by expression (3) rewritten for C6+ viscosity in tank oil:
Where: μ0 - viscosity of tank oil.
Temperature and Pressure Influence
As was earlier shown the viscosity of oil-gas system at reservoir conditions depends on given pressure, temperatures and standard viscosity. The kind of functional dependence such as (1) is received from a study more than 250 bottom-hole samples, which was collected from more than 80 West Siberian oil fields. It has been found out that viscosity is completely described by the following function:
Where: σ and τ - baric and thermal coefficients of viscosity, respectively.expressions for definition σ and τ depending on molar weight of reservoir mixture (rm) have sufficient prediction of accuracy for West Siberian oil-gas mixes and are following:
Use of the procedure
Table 2 summarized the results of bottom-hole study of typical West Siberian reservoir oil. Fig.1 shows the result of application of the method with experimental data for comparison. The average absolute deviation of these calculated and experimental viscosities is 11.1%. Thus some statistical increase of an error with increase of pressure and temperature is observed. The absolute value of standard viscosity practically has not influence on value of an error. It is comparable with errors of another known methods, but the basic rules of proposed method are justified in terms of physical chemistry and the calculations are easier realized. For these reasons it is possible to consider this method satisfactory for calculation of viscosity of West Siberian crude oil saturated with natural gas.
oil gas crude
Table 2 - Chart of experimental conditions and properties of crude oil saturated with natural gas samples
# of samplePressure, MPaTemperature, 0C0MrrmExperimentalCalculatedr,%119.23691.5311120.0120.0121.041.040.00%219.14691.5181120.0120.0121.041.030.96%329.12901.6231290.0150.0121.150.8426.96%421.65691.6361070.0120.0111.351.1713.33%517.1651.8271210.0130.0121.181.22-3.39%616.38672.5851400.0160.0131.361.5-10.29%723.69674.1521160.0130.0122.982.99-0.34%821.47615.0612000.0260.0152.452.421.22%925.1705.5291560.0180.0132.423.09-27.69%1014.86566.9151590.0190.0143