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Measurement of phase changes in live crude oil using an acoustic wave sensor: Asphaltene Instability Envelope Jean-Luc Daridon, and Herve Carrier Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b01655 • Publication Date (Web): 04 Aug 2017 Downloaded from http://pubs.acs.org on August 5, 2017
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Measurement of phase changes in live crude oil using an acoustic wave sensor: Asphaltene Instability Envelope
Jean-Luc Daridon* and Hervé Carrier
Laboratoire
des
Fluides
Complexes
et
leurs
Réservoirs-IPRA,
UMR5150,
CNRS/TOTAL/Univ Pau & Pays Adour, 64000, Pau, France.
*Corresponding author:
[email protected] ABSTRACT An experimental method is proposed for determining the Asphaltene Instability Envelope of a crude oil or crude oil + antisolvent system in reservoir conditions by using a Thickness Shear Mode acoustic wave sensor fully immersed in oil under pressure. The technique allows determining the Upper Asphaltene Instability Pressure by carrying out Constant Mass Expansion experiments whereas the Lower Asphaltene Instability Pressure can be determined during Constant Mass Compression tests. The basis of the Technique is presented and measurements have been carried out in a bottomhole oil + CO2 system with various CO2 contents at reservoir temperature. Finally, the effect of temperature on asphaltene instability envelope was studied on two systems with 45 and 55 mol% of CO2.
KEYWORDS Asphaltene, Crude oil, Pressure, acoustic wave sensors, Quartz Crystal Resonator
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GGRAPHICAL ABSTRACT
50.00 45.00 40.00 35.00
P / MPa
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30.00
L
25.00 20.00
L+As
Presevoir
15.00 10.00
L+V
5.00 0.00 0.00
10.00
20.00 30.00 40.00 xCO2 (mol%)
50.00
60.00
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1. INTRODUCTION Live crude oils are complex mixtures containing a large number of hydrocarbons mainly consisting of methane and short chain paraffins, naphtenes and aromatics. Some crude oils also contain in different proportions high molecular weight components belonging to different types of chemical group such as paraffin, resin and asphaltene. These heavy components which are soluble in crude oil under reservoir conditions may precipitate as waxy and/or asphaltenic solid phases when oil solvency power decreases as a consequence of changes in live oil pressure, temperature and composition during production. Blending crude oils coming from different wells can also increases risks of heavy components precipitation during pipeline transportation or storage. Moreover, changes in oil composition caused by gas injection such as methane or carbon dioxide may induce precipitation of asphaltenes during Enhance Oil Recovery processes. According to the nature and the quantity of heavy components, precipitation can lead to a significant deposition on solid surface. In reservoir, such deposition reduces the permeability of the pore altering the transport properties whereas accumulation of solid deposit in transport pipeline can plug production facilities1. Consequently, the precipitation and deposition of high molecular weight components at the various stages of oil recovery, transport and storage affects the production efficiency and leads to significant costs and economic losses. The first step to prevent precipitation and to avoid deposition during production operations consists in identifying either experimentally or by model prediction the thermodynamic conditions at which heavy components separate from live crude oil. In the case of heavy paraffins, this phase separation corresponds to a waxy crystallization that involves thermal effects and discontinuity in some thermodynamic properties. Such thermal effect and discontinuity in thermophysical properties enable an indirect detection of wax appearance conditions in live oils by different techniques2. In the case of asphaltene, the mechanisms of destabilization are more complex because they present several steps of aggregation3,4 including nano-aggregates, clusters, primary flocs, aged flocs characterized by different scales 1-2 nm, 2-5 nm, 50-100 nm and higher than 100 nm respectively. Consequently, few thermal effects and discontinuities in thermophysical properties are related to asphaltene precipitation making the detection of the onset of asphaltene destabilization far more difficult than measurement of a crystallization point. Despite these difficulties, several experimental techniques have been proposed to indirectly 3 ACS Paragon Plus Environment
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determine the asphaltene instability threshold. They mainly consist in measuring the physical properties of the oil during pressure scanning experiment. They include electrical conductivity5, viscosity6, refractive index7 and acoustic resonance8 measurements. Direct methods that consist in detecting solid-like particles by light scattering9 or by filtration10 are also used to investigate asphaltene destabilization from live crude oil samples under pressure. However, these direct methods require a minimum size for detecting solid particles corresponding to the size resolution of the apparatus which is generally around 0.5 to 1µm for optic high pressure microscopy and high pressure filtration. This value is ten times higher than the size of asphaltene flocs reported by Goual et al.11 in heptol (heptane/toluene) solutions at atmospheric pressure using a High Resolution Transmission Electron Microscopy.
With the aim of identifying an experimental technique sensitive to the asphaltene destabilization in the nanometer range and which can be easily extended to high pressure measurements we have tested in a previous work12 the capacities of quartz crystal resonators to probe asphaltenes flocculation. For that purpose, the response in resonant frequency and dissipation of a quartz crystal resonator totally immersed in a solution of toluene and asphaltenes was studied during heptane titration. During such titration, a huge change in the resonant behavior was observed and was related to the destabilization of asphaltene. Both the dissipation and resonant frequency appeared extremely sensitive to asphaltene destabilization in heptol mixtures. The main objective of the present work is to extend to high pressure and therefore to live crude oil, the method developed to probe asphaltene instability threshold by using Quartz Crystal Resonator technique. With this aim in mind, the response of a quartz crystal immersed in a live crude oil with various content of injected CO2 was studied during isothermal pressure scanning experiments. Experiments were carried out either by constant mass expansion or constant mass compression using a high pressure PVT cell with a quartz crystal thickness shear mode resonator inside. In both types of experiment, pronounced effects were observed on quartz response allowing an estimation of the Upper Asphaltene Instability Pressure (UAIP) and the Lower Asphaltene Instability Pressure (LAIP) which represent the extreme points of the Asphaltene Instability Envelope (AIE). The term “asphaltene instability pressure” rather than “onset of precipitation”, ”flocculation threshold” or “asphtene pressure” is used throughout the paper as it better fits the technique that consists in sensing the destabilization of asphaltenes from the crude oil during a pressure scanning. 4 ACS Paragon Plus Environment
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2. SENSITIVITY OF THICKNESS SHEAR MODE SENSORS IMMERSED IN A LIVE CRUDE OIL The thickness-shear mode (TSM) sensor used in this work consists in a thin AT-cut quartz disk with circular gold electrodes deposited on its faces on the central plano-plano portion. Due to the piezoelectric behavior of the quartz, the application of a rf voltage between its electrodes results in bulk acoustic waves that propagate through the sensor and reflect on its surfaces leading to the formation of standing waves across the thickness h of the disk. Such standing wave goes to a maximum at resonance when the half the acoustic wavelength is an odd multiple n of the thickness h. The resonance frequency fn of the nth harmonic is related to the disk thickness h and to the physical properties of the quartz according to the following relation:
f n = nf 0
(1)
with
f0 =
1 2h
µq ρq
(2)
where µq and ρq are the shear modulus and the density of quartz respectively and f 0 stands for the fundamental frequency of the resonator. When a TSM sensor operates in immersion in a viscous liquid it is more suitable to select quartz resonators with a low fundamental frequency in such a way to reduce perturbation of inharmonic modes13. For such reason, a TSM resonator with a fundamental frequency of 3 MHz was chosen for the present work. According to eq 2, the resonance frequency of TSM sensors can vary due to intrinsic changes of quartz properties caused by variations in temperature (∆fn,T) or pressure (∆fn,p). It can also vary due to extrinsic effects caused by the addition of an external load (∆fn,load) acting on the sensor surface in such way it modifies the path length h over which the bulk wave propagates. The load can be an additional solid layer, a fluid or anything in interaction with the quartz surface making the device sensitive to many different phenomena occurring in the vicinity of its surfaces. Thus, the overall shift in resonance frequency induced by the full immersion of a
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quartz resonator in a live crude oil under pressure can be written as a sum of three different contributions: ∆ = ∆, + ∆, + ∆,
(3)
The first term represents the influence of temperature on quartz properties. It can be nullified by considering the same temperature for the loaded and unloaded (in vacuum) quartz crystal resonator. The second accounts for the influence of pressure. It is proportional to both the overtone number and the pressure change according to the following equation14: ∆ , = nα ∆
(4)
where α is a coefficient related to the change of the elastic modulus of quartz with respect to pressure. As can be seen in Table 1, the sensitivity (nα ) in terms of frequency shift per pressure change is significant i.e. 80 Hz.MPa-1 for the third overtone. Accordingly, this contribution is of fundamental importance during pressure scanning experiments. The last term (∆, ) accounts for the electromechanical coupling between the sensor and the surrounding media at its surface. For a full immersion in a crude oil, it results from the combination of various effects including viscous damping, mass deposition and interfacial phenomena. The oscillating surfaces of the sensor in contact with the viscous oil generate a shear wave which travels away from the sensor over a short distance as shear waves are highly attenuated in liquids. The viscous dissipation produces an important damping that leads to a decrease in frequency proportional to the square root of the density viscosity product of the contacting oil according to Kanazawa equation15: ∆, = −√
!
(5)
Where, "# is the Sauerbrey constant16 defined as: "# =
$. !&
(6)
'( )(
In addition, viscous friction leads to an increase of dissipation that can be quantified by noting the change in half-band-half width Γ of the resonance peak. This increase of bandwidth is also related to oil density viscosity product of the oil by the Kanazawa equation15: ∆Γ, = √
!
(7)
Therefore, both ∆, and ∆Γ, are function of √. 6 ACS Paragon Plus Environment
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In presence of asphaltenes, adsorption and deposition may occur at the electrode-oil interface causing the formation of an asphaltene layer on the sensor’s surfaces. This additional layer decreases the resonance frequency of the sensor as its effective thickness increases. For a thin layer, Sauerbrey16 showed that the shift in resonance frequency caused by pure mass addition effect ∆,# is proportional to the thickness of the deposited layer. In the case of a symmetric deposition of thickness hD on both faces, it takes the following form: ∆,# = −2"# + ℎ+
(8)
In this expression, the shift in frequency appears as a linear function of the overtone number n. This behavior is truly valid only for a homogeneous thin film (in comparison to the acoustic wavelength) rigidly attached to electrodes in such way it does not dissipate energy and therefore does not damp the sensor (∆-,# = 0). As the deposited layer thickness increases, viscoelasticity of the layer dissipates a part of the energy and damps the sensor17,18. This additional damping leads to a deviation to Sauerbray equation that must be corrected by adding perturbation terms in both the shift in resonance frequency and bandwidth as proposed by Wolff et al.19 However, these corrections can be set at zero as long as the deposited layer keeps thin and the resonator operates in rigid mass loading hypothesis. Similarly, the Kanazawa equation 15 is strictly applicable to ideal quartz with smooth surfaces and non-slipping boundary conditions at liquid-solid interfaces. However, in reality, the surfaces of the resonator are rough and molecular slippage may occur at the solid-liquid interface. Such interfacial effects induce changes in both resonance frequency and dissipation20-23. Despite the complexity of physical phenomena occurring at the real quartz surfaces, the changes in resonance properties caused by interfacial phenomena can be written as the sum of two distinct contributions13. The first accounts for the mass effects related to liquid trapping in porous cavities of the quartz surface as well as to slippage acting as a negative mass. It has the form of a Sauerbrey term16. The second has the form of a Kanazawa term15. It accounts for the energy lost due to additional viscous friction on rough surface. In full immersion, the different effects (mass, viscous damping, interfacial phenomena) operate simultaneously and the loads combine in complex and intricate ways. However, by considering a small load, the superimposing of the mass and fluid loading can be expressed13 as a linear combination of Kanazawa type and Sauerbrey type terms: ∆,/ = −2"# ℎ+ − √
!
(9)
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∆Γ,/ = √ (1 + 1 )
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(10)
!
where R is an empirical correction term that accounts for viscous friction on rough surfaces and ℎ+ is a theoretical mass (per unit of area) that accounts for pure mass deposition but also for interfacial effects such as slippage. It can be negative when slippage has a dominant influence. It can be noticed, from eqs. 9 and 10, that any change in oil properties will result in a shift in resonant behavior of the contacting sensor. However, bandwidth appears only sensitive to a change in oil density viscosity product whereas resonance frequency is sensitive to both a change in adsorption and density viscosity product. The sensitivity in terms of frequency shift per unit of thickness corresponds to : ∆ 3,4567 2 ∆89
2
= 2"# +
(11)
That means that a sensor with a level of detection of 5 Hz is sensitive to an increase of thickness of 0.7 nm (Table 1) corresponding to a monolayer of asphaltene nanoagreates on the sensor surface. Such variation in deposit layer represents a change of volume fraction ∆: ;< => of 2×10-9 of the oil introduced in the experimental device. The sensitivity to viscosity is similar for both resonance frequency and bandwidth. It varies with viscosity and overtone number according to: ∆ 3,4567 2 ∆
2
=2
∆Γ3,4567 ?
2 = √
$ !
'5AB
@
(12)
5AB
The values of this sensitivity are reported in Table 1 for different oils with viscosities of 1, 10 and 100 mPa.s respectively. These values allow estimating the change in viscosity corresponding to the detection level of the experimental apparatus (5 Hz). When such change in viscosity is produced from the dispersion of unstable asphaltenes, it corresponds to an increase of the volume fraction of the disperse phase in oil φdisp that can be expressed as: C
∆: =< = − @'! E D
(13)
5AB
by considering a simple Einstein equation to represent the viscosity η of the dispersion in the dilute regime just below the destabilization threshold: = (1 + 2.5:)
(14)
The values of the minimum change in volume fraction φdisp detectable by the sensor are reported in Table 1 as function of overtone number for different oils. The values of φdisp reported in Table 1 being significantly higher than ∆: ;< => , the sensor appears more sensitive to mass deposition than to viscosity change during asphaltenes destabilization. 8 ACS Paragon Plus Environment
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The bandwidth and the resonance frequency are both sensitive to changes in oil properties. However, as the shear wave generated by the oscillating sensor surface falls off exponentially in oil in the direction of propagation, the sensor only probes the contacting oil characterized by the penetration depth δ of the shear wave in the oil given by:
G = @ 5AB '
(15)
! 5AB
This decay length corresponds to the one within which the shear wave amplitude decays to 1/e. It implies that the sensor is sensitive to any object in dispersion in oil with a characteristic size smaller than the penetration depth. Values of this property in oils with different viscosity are given for several overtones of a TSM sensor with a nominal frequency of 3 MHz in Table 1. It can be noted in this table that the decay length is inferior to 0.6 µm for oils with a viscosity less than 10 mPa.s. Consequently, the sensor appears sensitive to flocs having a size much lower than 0.6 µm corresponding to the detection level of microscopy and filtration techniques. The high sensitivity of TSM sensors to both mass loading and viscosity changes has been used in this work to investigate asphaltenes destabilization in live oils systems during pressure changes.
3. EXPERIMENTAL SECTION Chemicals and materials. Measurements were performed in a live crude oil coming from North Sea with various content of carbon dioxide. This crude oil is known to keep stable during depressurization in field conditions but carbon dioxide flooding is suspected of creating a risk of asphaltene destabilization. The oil was taken by downhole sampling and was stored in single-phase sample bottle before its transfer to the experimental cell. Some of the characteristics of this oil are provided in Table 2. The SARA (Saturate, Aromatic, Resin and Asphaltene) analysis performed on the dead oil is presented in Table 3. To perform this analysis, a sample of dead oil was taken from the bottom tank directly by flashing it in a cold trap. The dead oil was then topped at 323 K and 20 mbar to remove light ends (C15−). An Iatroscan instrument was used to quantify saturates, aromatics and polar fractions (resin + asphaltenes). Saturates were eluted with n-heptane whereas aromatics were eluted using a solvent composed of 25% (vol %) dichloromethane and 75% n-heptane. In addition, the asphaltene content was determined by precipitation using n-pentane as the precipitant agent with a weight/volume ratio of 1:40. 9 ACS Paragon Plus Environment
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The Asphaltene Stability Class Index-100 (ASCI-100)24, reported in Table 3, was determined in order to graduate the level of asphaltene stability. This index is assessed by adding a small drop of dead oil in 20 phials containing 2 ml of toluene + n-heptane binary mixtures with heptane content ranging from 0 to 100 w% by 5w% steps and by noting the heptane percentage value corresponding to the first phial in which asphaltene can be visually observed after 48 hours. The CO2 used was purchased from Linde with a given purity better than 99.995%. Instrumental Setup. A schematic of the experimental setup is shown in Figure 1. It mainly contains an automatic variable volume cell, a syringe pump, a sample cylinder and a network analyzer. The core element around which all other devices are connected is the PVT cell. It was designed to work at either constant temperature or constant pressure or even constant flow rate in the temperature range 273.15 to 403.15 K and pressures from vacuum to 100 MPa. This cell was presented in detail in a previous paper25. It consists of a non-magnetic cylinder, closed at one end by a moveable piston that allows changing the internal volume of the measurement enclosure from 20 to 50 cm3. The second end is closed by a plug with two HP electrical feedthroughs allowing the TSM sensor to be used in high pressure conditions. The sensor element is a highly polished AT-cut quartz crystal disc with a nominal frequency of 3 MHz. Electrodes made of a 100 nm layer of gold were deposited on each face. It is fixed horizontally inside the cell so as it is only surrounded by the liquid phase whatever the existence or nonexistence of a vapor phase in equilibrium with the liquid. These sensors with gold electrodes were chosen because they appear to be sensitive to asphaltene destabilization in a previous work carried out12 at atmospheric pressure. The external parts of the electrical feedthroughs are connected to a network analyzer that continuously measures the complex scattering parameters S11 of the sensor in order to determine the susceptance and conductance spectra of the quartz in a frequency range covering the fundamental mode and several overtones. In-situ stirring is accomplished using two Teflon-coated magnetic stirrers placed inside the cell and externally driven by a rotating magnet. The cell is held at constant temperature by circulating through channels arranged in the vessel wall a heat-carrier liquid connected to a thermostat bath circulator. The temperature is measured with an uncertainty better than 0.1 K by a platinum resistance implanted in the body of the PVT cell. The pressure is measured by using a pressure gauge in direct contact with the fluid inside the cell so as to avoid isolating a part of the fluid from the sensing area. It is calibrated as a function of 10 ACS Paragon Plus Environment
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temperature against a primary standard pressure sensor with an accuracy of better than 0.02 per cent in the pressure range 0.1-100 MPa. The PVT cell is equipped with an accurate position sensor that allows recording the position of the piston and therefore the variations of volume with a relative uncertainty of 0.05%. The cell is connected via a capillary tube to a high pressure syringe pump. This second pump is used to inject CO2 stepwise or continuously at constant temperature by circulating heat-carrier fluid from a second thermostat bath circulator. Furthermore, the syringe pump is equipped with a pressure gauge that measures the pressure of the fluid in the pump with an uncertainty of 0.1%. The CO2 density needed to convert the volume flow rate of the pump in mass flow rate is calculated from REFPROP26 using the temperature and the pressure measured inside the syringe pump. The full system is controlled by Labview software that drives the pump and the networks analyser during experiments. It monitors and displays the thermodynamic properties (P, V and T) of the fluid. It also records the complex scattering parameters of the sensor and converts them in conductance. For each harmonic the conductance spectrum is recorded using 1601 points around the resonant frequency in order to determine both the resonance frequency fn and the bandwidth Γn. The resonance frequency is estimated with an uncertainty of 4 Hz by noting the maximum of the conductance peak whereas the half bandwidth at half maximum is determined with an error less than 5 Hz. In order to get the unloaded reference values fn,0 and
Γn,0 needed for the calculation of ∆ and ∆Γ , measurements must be carried out in vacuum at the experimental temperature conditions before loading the crude oil into the measurement cell.
Sample preparation Experiments start by transferring a small volume of the live crude oil from the oil tank to the PVT cell at reservoir pressure and temperature. Due to the dead volume generated by the sensor element and its surrounding, loading is accomplished by performing a succession of small flashes in a transfer line composed of two buffer volumes of 1 cm3 separated by a valve. During each step, the pressure of the oil tank is adjusted to the reservoir pressure so as to keep the fluid in the oil tank in the single phase state, thereby guaranteeing oil composition in both oil tank and PVT cell. After its transfer, the oil is stirred to equilibriate at reservoir conditions. When equilibrium is achieved, the volume of the sample is measured and the oil mass introduced in the PVT cell is evaluated from this measurement and oil density. A Constant Mass Expansion experiment is then performed on the live crude oil at reservoir temperature in order to measure the bubble point pressure of the oil and thereby validating the transfer. The 11 ACS Paragon Plus Environment
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aim of this experiment is also to examine if asphaltene destabilization may occur during oil depressurization in the absence of a flocculating agent. When the system reaches a pressure lower than the LAIP in the liquid – vapor phase equilibrium domain, a given amount of CO2 is added into the PVT cell by operating the syringe pump. This antisolvent injection is performed far below the bubble point pressure in order to avoid flocculation during this operation. After gas injection the stirrer is turn off and the two phases system is compressed rapidly (1 MPa/s) up to high pressure in order to keep the system in a two phases non equilibrium state while crossing the asphaltene instability envelope. At this pressure the system is vigorously stirred in order to get a stable single phase CO2 + oil mixture. During this stabilization time the response of the sensor is monitored in order to verify that the dissolution of vapor leads to a decrease in bandwidth and therefore confirms that no destabilization occurs during the compression of the system.
Pressure scanning experiments For examining whether asphaltene destabilization may happen during decompression of a given system that can be either a reservoir oil or a mixture of oil and an injected antisolvent, a constant mass expansion experiment is carried out. The experiment consists in continuously decreasing the pressure of the system by expanding the volume of the cell while maintaining the temperature constant. The signal of the sensor is permanently recorded and resonant properties are calculated so as to evaluate the shift in resonance frequency and dissipation as a function of pressure. The influence of pressure on resonance frequency calculated by eq. (4) is removed from these values in order to get the experimental values of both ∆,/ and
∆-,/ . They correspond to the properties that are depicted in the diagrams used to determined phase changes. These diagrams are presented as functions of pressures but measurements are actually performed as a function of time. Thus, for translating time into pressure, the system must be kept in thermodynamic equilibrium throughout the scanning in pressure. This experimental constrain is taken into account by continuously agitating the system and by limiting the depressurization rate to 0.3 MPa/min. This rate represents an acceptable compromise between the lower rates that reduce kinetic effects but increase noise caused by the pump regulation and the higher rates that reduces noise but become sensitive to kinetic. Moreover, a good reproducibility was observed when working with a rate between 0.1 and 0.3 MPa/min.
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The pressure at which asphaltenes destabilization or phase transformations occurs is determined at the end of the experiment by analyzing the diagrams obtained and by noting sharp change in the curves slopes. Such indirect method can be applied for identifying destabilization or phase appearance in a homogeneous system but not for detecting restabilization or phase disappearance in a multiphase system. Consequently, only the bubble point pressure and the upper part of the asphaltene precipitation enveloped can be determined by this CME experiment. The lower part of the asphaltene precipitation envelope must be identified in an opposite way that is to say by performing a constant mass compression (CMC) test. Starting from liquid-vapor phase equilibrium region, the system is continuously compressed by reducing the volume of the cell. As for CME, CMC experiment is conducted with a compression rate of 0.3 MPa/min and the two phases system is vigorously stirred for facilitating dissolution of vapor in the liquid phase during the continuous compression process.
4. RESULTS AND DISCUSSION First measurements were carried out on live oil alone. The objective of this preliminary test was, firstly to check if the sensor immersed in the bottomhole oil verify the expectations of the model summarized in eqs 9 and 10, secondly, to measure the bubble point pressure at the reservoir temperature and evaluate whether asphaltene destabilization occurs during depletion. For this measurement, a sample of bottomhole oil was transferred to the PVT cell and maintain in equilibrium at reservoir pressure PR and temperature TR, continuously stirrred. The signal of the sensor was recorded in order to evaluate the conductance spectra. As it can be observed in Figures 2.a and 3.a for 3rd and 7th overtones respectively, immersion in crude oil broadens the resonance peaks and hugely decreases their amplitudes, thereby reducing the quality factor of the sensor. However, even with this level of damping, the signal remains exploitable. As can be seen in Figures 2.b and 3.b, real circular quartz resonators can vibrate in several other modes which are not harmonically related to the fundamental. These inharmonic modes always appear at frequencies above the harmonic overtones. However, the frequency interval between the main resonance and the spurious resonance decreases with increasing overtone number. The surrounding oil also broadens the inharmonic peaks of the sensor and brings them closer to the harmonic peaks (Figure 3.b). When these spurious peaks become too significant they distort harmonic peaks and consequently bias the calculation of fn and Γn. As this perturbation is all the more pronounced when the frequency is high, overtones 13 ACS Paragon Plus Environment
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beyond the 7th were not exploited and measurements were limited to fundamental and overtones 3, 5 and 7. Therefore, the linear combination of Kanazawa type and Sauerbrey expressed in eqs 9 and 10 can only be verified in this limited overtone range. For that purpose, ∆,/ ⁄ measured in oil at reservoir conditions is plotted as a function of 1/√ in Figure 4
whereas ∆-,/ is represented in Figure 5 as a function of √. As already observed in pure
liquids13, these figures show that the fundamental behaves singularly in comparison to the other overtones. This deviation comes from the finite size of the sensor that modifies the solution of the motion equation of the quartz obtained for an ideal infinite quartz plate. Such finite size effect becomes negligible in comparison to loading effects beyond the fundamental and therefore overtones follow the linear behavior expected by eqs. 9 and 10 as shown in Figures. 4 and 5. The low positive value of the y-intercept in Figure 4 indicates a negative mass loading (+ ℎ+ < 0) characteristic of slipping at the interface and low adsorption at the sensor surface. The sample was left in reservoir condition until the sensor signal stabilizes. Once stabilization has been achieved the constant mass expansion experiment was carried by a pressure scan from 30 to 5 MPa at 368.2 K. Sensor’s responses to this continuous decompression are presented in Figures 6 and 7. The 3rd overtone was only selected for presenting and comparing the results as the same behavior was observed for the three overtones recorded. The curves reveal a classical shape for a system presenting a liquid vapor phase transition in the pressure range covered by the experiment. Above the bubble point pressure, ∆,/ monotonically increases as pressure is reduced whereas ∆Γ,/ decreases with oil isothermal
decompression. This behavior is related to the decreases in density viscosity product in response to pressure fall. The reverse trend can be observed below the bubble point pressure due to the release of light components in the gas phase. In this part of the diagram ∆,/
decreases as pressure is reduced whereas ∆Γ,/ increases. These opposite behaviors lead to a sharp maximum in ∆,/ versus p curve and a minimum in ∆Γ,/ versus p. These
extrema can be used25 to determine the bubble point pressure of the bottomhole oil in addition to P,v data also recorded and plotted in Figures. 6 and 7. The bubble point pressure measured during this experiment is reported in Table 3. The trend of ∆,/ ⁄ versus 1/√ is plotted for different pressures above the bubble point in Figure 8. It can be seen in this figure that the y intercept keeps the same value whatever the pressure whereas the absolute value of the slope decreases with pressure. This observation reflects a continuing decrease whereas
+
remains unchanged throughout the
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Energy & Fuels
duration of the constant mass expansion. This conclusion was confirmed by calculating from eqs. 9 and 10 the relative oil density viscosity product and the apparent thickness change: '5AB (
