Application of cryogenic technologies for multiphase diagnostics in oil production industry
Filippov Yu.P., Panferov K.S.
Joint Institute for Nuclear Research, Joliot-Curie 6, Dubna, 141980, Russia
The report presents one of possible variants of using some cryogenic technologies
in oil production industry where three-phase flows “oil-water-gas” are often
observed. The method and algorithm to find the mass flow rate and the component
composition of such flows are discussed. The measuring system consists of a pair
of RF void fraction sensors, a narrowing device and temperature and pressure
(absolute and differential) sensors. A comparison of calculations with some
experiments on “oil-formation water-gas” flows has been demonstrated.
INTRODUCTION
The mass flow rate, G, and the quality, x, are important parameters of the cryogenic system of superconducting accelerators cooled with forced two-phase helium flows. For example, two-phase flow meters,
mounted in return two-phase helium headers, are needed to determine the corresponding mass flow rate
as well as the quality and distribute the flows between the neighbouring refrigerators of accelerators such
as the JINR Nuclotron and FAIR [1]. In principle, there is a problem in cryogenics to find the flow rate of
a two-phase flow for the whole range of quality x from 0 to 1. Certain advantages have been achieved in
this field in the last years. Thus, a two-phase correlation flow meter based on a pair of cryogenic RF void
fraction sensors is described in [2] and results of its preliminary test are presented. Another cryogenic
two-phase pressure-drop flow meter is discussed in [3]: it is a combination of an RF void fraction sensor
of a round cross-section and a cone narrowing device applied for helium and hydrogen.
Similar but much more complicated diagnostic problems arise in oil-producing industry while
determining the debit of oil wells, where three-phase “oil-formation water-gas” flows occur. Cryogenic
technologies are worth applying in this branch of industry, because the temperature here can vary in wide
range from –60°C (213 K) to +50 °C (323 K).
To perform full diagnostics of the three-phase
flow, the number of independent signals from sensors
should be equal to the number of unknown parameters. Assuming that the velocities of the phases are
equal and the salinity of the formation water is constFigure 1 The scheme of the diagnostics system for "oilant, there are three parameters of the “oil-formation
formation water-gas" flows
water-gas” flow: the volume fraction of gas, φ, the
volume fraction of water, w, and the total mass flow rate, G. Therefore, it is necessary to measure at least
three independent signals from any sensors. These sensors can be an RF-sensor of a round cross-section
[4], whose resonant frequency depends on the average permittivity of the flow, ε, a narrowing device,
which gives a value of a pressure drop, ΔP, depending on an average flow velocity, v, and average density,
ρ, as well as a correlator based on a pair of the two RF-sensors, which allows one to determine a correlation time, τc. The scheme of a measuring system based on these devices is shown in Figure 1, where one
can see the narrowing device 2, the two RF sensors 4, the sensor of the flow temperature 3 (Tf), and the
output cone 5. The whole system is mounted by means of connecting flanges 1 in a horizontal pipe where
a three-phase flow moves.
The aim of this report is to verify applicability of the proposed diagnostic system for real “oilformation water-gas” flow. For this aim, experiments on a test bench have been performed, and experimental values of the characteristics of the flow have been compared with values determined by the diag-
nostic system. The main attention is given to a specially developed complicated algorithm of data processing, which is necessary to calculate the characteristics of the flow from the measured signals of the sensors taking into account peculiarities of real oil-contained flows. This algorithm is an inalienable and essential part of the tested measuring system. We have not found descriptions of similar algorithms in
accessible literature because normally they are intellectual property of oil-producing companies that
manufacture multiphase flow meters for oil industry.
ALGORITHM TO PROCESS THE MEASURED DATA
Primarily, it is reasonable to introduce several restrictions to simplify the analysis of a quite sophisticated
“oil-salty water-gas” flow. Firstly, we regard the three-phase flow as a quasi two-phase flow. It means that
the flow is assumed to be a liquid-gas mixture, where the gas component is a true mono-phase medium
and the liquid component is a two-component medium consisting of oil and water. Secondly, we limit
ourselves with the case when the liquid component is an inverse emulsion “water-in-oil” (w/o) because it
is the simplest case of oil-water mixtures occurring most often in practice. Thirdly, we consider a socalled quasi-homogeneous flow pattern. It means that a difference between the velocities of the phases is
negligible, but there are still natural disturbances which enable the correlation method to be applied. And
finally, we consider the case when the liquid component prevails over the gas component, i.e. φ < 50%.
The use of the RF-sensor involves a problem of how to relate the ε-value with permittivities of the
components, which can be divided in two sub-problems. Firstly, one should relate the permittivity of the
liquid with the permittivity of its constituents – oil and water, taking into account that the liquid is a w/oemulsion. Secondly, one should relate the average permittivity of liquid-gas mixture with the permittivity
of liquid and gas components. Detailed solving of the first problem for can be found in [5], where HanaiBruggeman equation [6] was proposed. It is one of the most general and universal relation between the
permittivity of emulsion and permittivity of its components. It has the following form for the w/oemulsion:
1/ 3
 
∗em −∗wat ∗oil
∗
∗oil −∗wat em
=1−W ,
W=
w
.
1−
(1)
Here ε*wat, ε*oil, and ε*em are the complex permittivity of water, oil, and emulsion, respectively, W is
the relative volume fraction of the water in the emulsion. The permittivity of water and emulsion should
be regarded as a complex value because water always has a certain amount of salt and its conductivity
cannot be neglected. Hanai-Bruggeman equation was experimentally checked for many kinds of different
inverse emulsions, and it has been found that it describes experimental data better than other formulae as
it has been shown in [6]. Besides, the applicability of this equation for w/o-emulsion has been experimentally proved in [5]. As for the second problem, the same Hanai-Bruggeman equation can be applied
for the assumed quasi-homogeneous flow patterns:

1 /3
 
− gas  em
=1−
 em−gas 
.
(2)
Here εem, εgas, and ε are the real permittivity of emulsion, gas, and flow, respectively.
Thus, equations (1-2) allow ones to bind together the average permittivity, the permittivity of the
components and their volume fractions, but an additional variable εem appears. The dielectric
characteristics of pure substances, εgas, εwat, and εoil, should be found from in situ calibration, measuring the
frequency of the RF-sensor when it is filled with these pure components.
The use of the narrowing device requires a relation between the pressure drop, the flow rate and the
average density, ρ. The approach to obtain this relation is similar to analogous task for electrodynamics
characteristics and can be also divided in two stages. Firstly, one should establish the relation between the
values of ΔP, G and ρ, which includes physical properties of the gas and the liquid component such as
their effective density and viscosity. Secondly, one should relate effective properties of the liquid with the
W-value and the physical properties of oil and water.
As for the first stage, one can try to use the equation for the viscous two-phase flow derived in [5]. It
was obtained for oil-water flow but there appear to be no restrictions for using it for quasi-homogeneous
liquid-gas flow. The equation looks as follows:
G pd = Re  ∆ P  , =
1
.
1Re  2
(3)
Here κ(λ(Re), γ, ξ) is a calibration function which depends on values of the Darcy-Weisbach friction
factor λ and the geometrical constants γ and ξ. The λ-value depends on the Reynolds number, Re, whereas
the γ- and ξ-values can be determined exactly during calibration.
The problem appears how to determine the Re-value. To calculate Re = ρvD/μ, it is necessary to find
the effective viscosity of the flow, μ. One of the simplest equations for this purpose is the following [7]:
= g xem 1−x  ,

 1−
x= 1 em
g 
−1

,
 em =oil e  W
(4)
Here the viscosity of the oil-water emulsion, μem, can be found by means of the exponential formula [8].
Another problem is that the calculation of Re-value requires values of average velocity, v, or the total
mass flow rate, G, which are unknown. This problem can be solved by adding an additional equation
from the correlation method. Generally, it allows one to calculate the mass flow rate using the value of the
correlation time, τc, defined as a maximum point of the cross-correlation function R(τ) as follows [9]:
T
Gc =k c  A L / c ,
1
R=lim ∫ f 1 t  f 2 t  dt.
T ∞ T 0
(5)
Here kc is a calibration function, A is a cross-section area, L is the distance between two sensors, T is a
measuring time duration, and τ is a time shift between the signals.
Introduction of the calibration function kc in expression (5) is necessary because the velocity of flow
disturbances can differ from the average velocity of the flow [2]. The value of kc significantly depends on
the flow pattern, which, in its turn, depends on fractions of phases, their velocities and physical properties
such as density, viscosity and others. One can regard kc as a function of φ- and G-values.
The algorithm to determine characteristics of the flow should be iterative because such variables as
Re and kc depend on unknown G-value. One of the possible approaches is the following. Equations (1-5)
with several other ancillary equations are arranged in a set. All variables in it can be expressed in terms of
any chosen variable, say, εem. Thus, one can compose an equation for G-value:
G pd em −G c em =0,
(6)
where Gpd-value is determined by means of the pressure-drop method with the help of equation (3) and Gc
is determined by means of the correlation method with the help of equation (5). Equation (6) can be
solved by a computational method, whereupon the calculated εem-value allows one to determine all the
characteristics of the flow.
EXPERIMENTAL TESTS AND BRIEF DISCUSSION
The used test bench consists of a flow circuit, where multiphase flow is circulated by means of a gear
pump, and a cooling system. The tested diagnostics system of ID=100 mm and length between connecting
flanges of 1 m was embedded into the flow circuit. The rotation speed of the pump N and the total volume
flow rate Q were stabilized. More details about this test bench can be found in [5].
The flow circuit was filled with different mixtures under investigation, which had been prepared by
mixing oil and water in the given volume fractions. After preparing oil-water mixture in the flow circuit, a
portion of it was poured off. The partially filled flow circuit with air was firmly closed and the obtained
three-phase mixture was rotated by the pump. A disadvantage of this approach is that the pump was
initially intended for moving liquids only. Besides, there was no possibility to determine a slip ratio
between the gas and the liquid components. Yet the performed experiments allow one to estimate
qualitatively the possibilities of the diagnostics system.
Ten experimental points in the ranges of w-value from 30% to 40%, φ-value from 0% to 11%, and
G-value from 1 kg/s to 8 kg/s corresponding to the total volume flow rates Q from 4 to 34 m3/h, were processed by the developed algorithm. Results of this processing for three of ten points are presented in Table
1 as an example. Comparison of the real flow characteristics with the calculated values for the all investigated points allows one to estimate the errors as follows: δw ≈ 1.6%, δφ ≈ 6.1%, and δQ/Q ≈ 6%. These
preliminary results show that the measuring system based on the combination of the pair of RF-sensors
and the narrowing device can be used as an indicator of the three-phase flow at least. Relatively high
values of δφ-errors in certain points are caused by imperfection of the algorithm that is based on the
quasi-homogeneous model. To develop an improved version of the algorithm taking a slip ratio between
the liquid and gas components into account, additional experimental data are necessary. Besides, certain
theoretical assumption, for instance, equations (4), should be checked, and the exact values of the
calibration functions such as dependences kc(G, φ) and κ(λ), should be determined. For these purposes,
one should arrange a test on a full-scale test bench for “oil-salty water-gas” flows.
Table 1 Results of processing of three experimental points by the developed algorithm.
True values
Calculated values
The first point
w, % φ, % Q, m3/h
30
0.0
3.8
30
3.4
3.5
The second point
w, % φ, % Q, m3/h
38.0 5.0
34
37.5 6.0
36
The third point
w, % φ, % Q, m3/h
36
11.0 28
37
3.4
29
CONCLUSIONS
The system, consisting of a pair of meander RF-sensors of a round cross-section and a cone narrowing device, provides full information about three-phase flows like inverse water-in-oil emulsion (oil-water mixture at values of relative water fraction from 0 to about 70 %) and gas. This system produced on the basis
of the cryogenic technologies allows one to measure and find the values of temperature, pressure, mass
flow rates and the component composition of the flow. An algorithm to determine these characteristics of
the three-phase flow has been suggested. It uses the quasi-homogeneous model and values of resonant
frequencies, the correlation transit time and the pressure drop across the narrowing device. It can be
applied in case of constant salinity of water and requires measuring in situ such properties of oil, gas and
water as density, viscosity and complex permittivity. The latter quantity can be determined by means of
the used RF-sensor. The high value of viscosity of the water-oil flow, its dependence on water cut, and the
dependence of complex permittivity of water on its salinity have been taken into consideration.
Preliminary tests have demonstrated satisfactory agreement between experimental data and calculation
results. The errors to find gas volume fraction can be decreased by using the model with slip ratio of gas
phase with respect to oil-water mixture and additional experimental data obtained at three-phase test
facility “oil-salty water-gas”, which is planned later this year.
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