Diffusion Model Coupled with the Flory–Huggins–Zuo Equation of

Feb 4, 2015 - SAS Schlumberger, D105, TTC Industrial Estate, Thane Belapur Road, Nerul EAST, Navi Mumbai 400706, India. §. Cairn India Ltd., 4th Floo...
0 downloads 0 Views 5MB Size
Download PDF
Article pubs.acs.org/EF

Diffusion Model Coupled with the Flory−Huggins−Zuo Equation of State and Yen−Mullins Model Accounts for Large Viscosity and Asphaltene Variations in a Reservoir Undergoing Active Biodegradation Julian Y. Zuo,*,† Richard Jackson,‡ Ankit Agarwal,‡ Bernd Herold,§ Sanjay Kumar,§ Ilaria De Santo,∥ Hadrien Dumont,⊥ Cosan Ayan,# Martyn Beardsell,∇ and Oliver C. Mullins○ †

HPS Center, Schlumberger, 150 Gillingham Lane, MD-3, Sugar Land, Texas 77478, United States SAS Schlumberger, D105, TTC Industrial Estate, Thane Belapur Road, Nerul EAST, Navi Mumbai 400706, India § Cairn India Ltd., 4th Floor, Vipul PlazaSector 54, SunCity, Golf Course Road, Gurgaon, Haryana 122002, India ∥ Schlumberger Geoservices, 127 Avenue du Bois de la Pie, 95971 Roissy-en-France, France ⊥ NAO, Schlumberger, 1325 S. Dairy Ashford, Houston, Texas 77077, United States # WLH, Schlumberger, 1 Rue Henri Becquerel BP202 Building 1, 3rd Floor, Clamart 92142, France ∇ SIS Schlumberger, Lambourn Court, Wyndyke Furlong, Abingdon Business Park, Abingdon, Oxfordshire OX14 1UJ, United Kingdom ○ Schlumberger-Doll Research, Cambridge, Massachusetts 02139, United States ‡

ABSTRACT: A very large monotonic variation of asphaltenes and viscosity has been measured by downhole fluid analysis (DFA) in crude oils in five-stacked sandstone reservoirs in the northern part of the Barmer Basin, northwest India, undergoing active biodegradation; each of the five-layered sand bodies shows overlaying fluid gradients with depth providing replicate validation of the measurements. Fluid data from four wells across the field shows that the gradients are uniform across the formation. The crude oil in the upper half of the oil column exhibits an equilibrium distribution of asphaltenes matching predictions of the Flory−Huggins−Zuo Equation of state (FHZ EoS) with the gravity term only using asphaltene nanoaggregates of the Yen−Mullins model. However, the bottom half of the reservoir reveals a large asphaltene gradient approximately three times larger than the equilibrium predictions from the FHZ EoS. This increase in asphaltenes creates a very large (8×) viscosity gradient and is a major production concern. In addition, these shallow reservoirs are undergoing active biodegradation at temperatures of 55−61 °C. A simple diffusive model coupled with the FHZ EoS is shown to account for the entire observed asphaltene distribution in each of the five sand layers. Alkanes (and some aromatics) are rapidly consumed at the oil−water contact at the base of the oil column. The rate-limiting step is the diffusion of these compounds to the oil−water contact. The loss of these oil components decreases the oil volume yielding an increase in asphaltene concentration and a significant increase in viscosity. The limited geologic time of the oil in the reservoir limits the vertical extent of the diffusive process accounting for the observation of asphaltene equilibrium at the top of the column. Specifically, petroleum system modeling of this basin indicates that the oil commenced undergoing biodegradation approximately 50 million years ago, and this duration matches the analysis using the diffusion model plus the FHZ-EoS. Gas chromatography applied to the oils from the top to the bottom of the oil column provides detailed compositional confirmation of the diffusive mechanism proposed. In particular, all measured compositional properties of the oil column are shown to be consistent with this simple diffusive model. The ability to account for asphaltene and viscosity variations in the five stacked sand layers with a simple diffusive model coupled with the FHZ EoS and the Yen−Mullins model provides a robust model for improving efficiency of reservoir engineering and oil production.

■

INTRODUCTION Downhole fluid analysis (DFA) has successfully been used to measure the properties of reservoir fluids downhole in situ in oil wells and in real time during downhole sample acquisition.1 DFA has excellent accuracy in measuring fluid gradients, which in turn enables accurate thermodynamic modeling. The cubic EoS2 has been used for decades to model gas−liquid compositional gradients and saturation pressure gradients of reservoir fluids. In contrast, there had been no thermodynamic treatment to model gradients of dissolved (or colloidally suspended) asphaltenes in reservoir fluids. This deficiency is traceable to the lack of © 2015 American Chemical Society

understanding of the molecular and colloidal sizes of asphaltenes in crude oil and even in laboratory solvents. In recent years, the molecular and nanocolloidal structures of asphaltenes has been clarified and codified in the Yen−Mullins model.3,4 Recently, important confirmation of this model has been obtained from various sources. NMR spectroscopy and relaxometry have shown agreement with molecular architecture and PAH (polycyclic Received: November 18, 2014 Revised: February 4, 2015 Published: February 4, 2015 1447

DOI: 10.1021/ef502586q Energy Fuels 2015, 29, 1447−1460

Article

Energy & Fuels

Figure 1. (left) 3D view of reservoir structures penetrated by four wells. (right) Schematic diagram of the reservoir with five-staked sand bodies and the same initial oil−water contact.

aromatic hydrocarbon) size and asphaltene cluster size.5 Other NMR studies obtained similar cluster sizes.6 Centrifugation studies and DC-conductivity studies have confirmed the existence of asphaltene nanoaggregates7 and asphaltene clusters8 and have confirmed small aggregation numbers of each. The aggregation number of approximately six for asphaltene nanoaggregates has been obtained by laser mass spectrometry.9,10 The critical nanoaggregate concentration has been confirmed by other mass spectrometry studies albeit with somewhat higher yet comparable aggregation numbers.11 Interfacial tension measurements have obtained confirmation of the asphaltene molecular architecture proposed in the Yen− Mullins model and have also obtained confirmation of the nanoaggregate structure.12,13 With the size of asphaltene nanostructures resolved in the Yen−Mullins model, the effect of gravity on asphaltenes can be expressed explicitly. As such, the gravity term has been added to Flory−Huggins polymer solution theory to obtain the Flory− Huggins-Zuo equation of state (FHZ EoS).14−18 The FHZ EoS has been successfully employed to treat gradients in many reservoir studies. It is the only one that has been shown to treat gradients of asphaltenes in all types of crude oils spanning the range from condensates [with high gas/oil ratio (GOR)] to heavy oils (with low GOR and high asphaltene content).19 In particular, the FHZ EoS with nanoaggregates has been used to evaluate asphaltene gradients in so-called black oils, those with moderate GOR and moderate asphaltene content, for the purpose of addressing reservoir connectivity.20−22 Furthermore, the FHZ EoS with asphaltene nanoaggregates from the Yen− Mullins model was used to evaluate an oil column that had undergone both biodegradation and multiple charging. DFA data was only available for a single well; within this well, the analysis showed that the asphaltene gradients in the oil column were equilibrated.23 Thus, sufficient time had passed to overcome transients of biodegradation and multiple charges of hydrocarbon into the reservoir for equilibration to prevail.23 The FHZ EoS with nanoaggregates was also shown to apply to a large asphaltene gradient produced in a centrifugation experiment of a live (gas containing) black oil.24 The FHZ EoS with clusters has been shown to account for an asphaltene gradient of a factor of 10 in a 50 m column of heavy oil over a 100 km circumferential rim of an anticlinal oilfield.25 The assumption of a single asphaltene chemistry in this highly graded column was confirmed by sulfur X-ray absorption near edge spectroscopy26 and by

establishing the same asphaltene molecular weight and nanoaggregate aggregation number independent of the location within the oil column.27 With the equilibrium model of reservoir fluids determined with the FHZ EoS, it is now possibly to treat dynamic process from a thermodynamic perspective, where a transient is occurring in the reservoir. One transient process that is of great significance in oilfields is biodegradation. Biodegradation of oil columns occurs at the oil−water contact; as the microbes live in the water but consume oil chemical components.28 The microbes preferentially consume specific chemical species in the crude oils. For example, n-alkanes are the first chemical species consumed by microbes in the biodegradation process as indicated in the Peters−Moldowan rank of biodegradation.29 Large fluid gradients have been observed in cases of biodegradation.28−30 Diffusion is well-known to be a critical component of controlling rates of biodegradation.31 Nevertheless, the inability to model asphaltene gradients largely precluded the ability to develop specific thermodynamic models of the effect of biodegradation on asphaltene and viscosity gradients. In this paper, we examine large asphaltene and viscosity gradients, along with large gradients in other fluid properties in an oil reservoir with five stacked sand bodies undergoing active biodegradation. Extensive fluid property measurements, both downhole and laboratory, are performed in this study. Fluid data from four wells across the field is acquired showing consistency across the reservoir. In particular, accurate asphaltene gradient measurements are performed utilizing downhole fluid analysis. The combination of the FHZ EoS together with a diffusive model and with asphaltene nanoaggregates is used to perform the thermodynamic modeling of the asphaltene gradients. Diffusion of alkanes to the oil−water contact is presumed to be the ratelimiting step in this process. The predominant effect on asphaltene concentration is consistent with consumption of alkanes and some alkylaromatics. The thermodynamic model is shown to account for both the upper oil column, which is thermodynamic equilibrium, and the lower section of the oil column, which is dominated by the dynamic processes of diffusion and biodegradation. All of the five stacked sandstone reservoirs are shown to exhibit the same fluid properties establishing the robustness to the measurements and analysis. The ability to provide an explicit thermodynamic model of asphaltene gradients even in cases where the reservoir is 1448

DOI: 10.1021/ef502586q Energy Fuels 2015, 29, 1447−1460

Article

Energy & Fuels undergoing dynamic processes advances reservoir-engineering modeling for efficient oil production.

■

OVERVIEW OF THE BIODEGRADATION RESERVOIR AND ITS ENCLOSED FLUIDS The oilfield located in the northern part of the Barmer Basin in the west of Rajasthan, northwest India is a Paleogene fluvialdominated five-layered sandstone formation consisting of ∼250 m of medium- to thick-bedded fine- to coarse-grained sandstones with interbedded mudstones. The 3D view of the formation structures penetrated by four wells is given in the left panel of Figure 1, and a schematic diagram is shown in the right panel of Figure 1. The reservoir was discovered in 2005. Wells 1 and 2 were drilled in 2005. The reservoir started to produce oil in January 2012. Then, wells 3 and 4 were drilled in 2012. The reservoir has different sandstone layers named by FB1, FB2, FB3, FB4, and FB5. Production data establishes the connectivity within each reservoir and the lack of connectivity between these different stacked reservoirs. Thus, this study involves five separate, stacked reservoirs with each reservoir revealing the same fluid gradients. The five sand layers have the same initial oil−water contact (OWC). The formation contains excellent reservoir quality sands with porosity of 18% to 33% (average 25%), permeability up to 20 D (average 5 D). The reservoir is a shallow reservoir with depths from 290 to 455 m true vertical depth subsea (TVDSS) and measured well depth (MD) is 479 to 666 m. The reservoir temperature varies from 55 to 61 °C and the formation pressure changes from 4275 to 6116 kPa. At the top of the oil column, bubble point pressures of the reservoir fluids are close to formation pressures. Stock tank oil (STO) API gravity varies from 19 to 32°API. Gas/oil ratio (GOR) is low, from 9 to 16 m3/m3. Oil viscosity significantly changes from 20 to 150 cP at reservoir conditions.

Figure 2. Schematic diagram of the MDT, a wireline formation sampling tool with the DFA and focused sampling modules. The 3rd generation of DFA, the IFA (Insitu Fluid Analyzer), is illustrated at the top right, which measures some hydrocarbon compositions, GOR, density, viscosity, and color, among other measurements. A focused sampling probe (bottom right) uses a concentric sampling arrangement and two synchronized pumps, which acquires samples with low contamination of filtrate from oil-based-mud (OBM) drilling fluid in a much shorter time frame.34

■

SAMPLE ACQUISITION AND DOWNHOLE FLUID ANALYSIS DFA measurements are conveyed by the MDT (Modular Formation Dynamics Tester), a wireline formation sampling tool.1 Figure 2 illustrates the schematic diagram of the MDT tool with the DFA tool and with a focused sampling probe module. One of the basic methods employed for DFA is optical spectroscopy, as shown in Figure 2 (top right). Optical spectrometers measure the visible-near-infrared (vis-NIR) spectrum of the formation fluids passing through the flowline of the MDT tool as a function of time.1 The vis-NIR absorption spectrum provides the magnitude of electronic absorption which is dependent on the asphaltene content. In addition, the CH vibrational overtones and combination bands in the NIR spectral range are sensitive to the alkane composition. In the case of crude oil, the methane CH4, the −CH3 and −CH2 groups have characteristic peaks in the NIR region that can be treated to give information on fluid composition.32,33 Figure 3 depicts the vis-NIR absorption spectra of several common reservoir fluids. Large variations in the absorption response are observed for different types of hydrocarbons, with a graded transition from the “colorless” gases and condensates to much darker heavy oils.1 At any wavelength (λ), the absorption (Aλ) of a sample is defined as the logarithm of the transmittance, that is, the log of the intensity ratio of the incident light (I0) and transmitted light (I). The optical density (ODλ) is expressed as

Figure 3. Vis-NIR absorption spectra of different types of reservoir and well fluids.1 Visible light is best suited for distinguishing relative asphaltene content (“color”). The NIR spectrum is useful for water detection, distinguishing water from oil and identifying the type of oil and oil composition.

⎛I ⎞ ODλ = Aλ = log10⎜ 0 ⎟ ⎝I⎠

(1)

The new DFA tool, the IFA (In Situ Fluid Analyzer), incorporates a filter absorption spectrometer, a grating absorption spectrometer, a fluorescence and reflectivity sensors, density measurement, and resistivity, pressure, and temperature sensors. This provides real time fluid GOR, compositions (C1, C2, C3−C5, and C6+), CO2 content, live fluid density and viscosity, live water pH (using pH dyes), fluorescence/reflection intensities and resistivity, coloration (linearly associated with asphaltene content), and OBM (oil-based muds) filtrate contamination level. When drilling oil wells, drilling fluids with clays are used, so-called drilling fluid muds. The clay acts to seal 1449

DOI: 10.1021/ef502586q Energy Fuels 2015, 29, 1447−1460

Article

Energy & Fuels

Figure 4. Yen−Mullins model3,4 depicting the predominant molecular and colloidal structures of asphaltenes in crude oils and in laboratory solvents. At low concentrations such as in light oil, asphaltenes are dispersed as a true molecular solution (left). At higher concentrations such as in black oils, asphaltenes are dispersed as nanoaggregates (center). At yet higher concentrations such as in mobile heavy oils, asphaltenes are dispersed as clusters of nanoaggregates (right).

permeable zones by mud cake formation at the borehole wall, thereby limiting drilling fluid loss. Nevertheless, when OBM drilling fluids are used, some miscible contamination occurs with formation crude oils. Focused sampling probes use an annular and central sampling regions (cf. Figure 2), each with its own pump, thereby greatly reducing this miscible contamination in the central sampling line. As pumping continues, contamination is reduced until required sample purity is achieved, typically less than 5% or even 1% of contamination.34

depths h1 and h2, respectively. It should be pointed out that the solubility parameter, molar volume, and density of bulk fluids, temperature, pressure, and compositions are dependent on depth. For low-GOR fluids, the solubility and entropy terms can approximately be canceled out due to the opposite and small influence on the asphaltene concentration gradient. Thus, eq 2 can be rewritten as

THE FLORY−HUGGINS−ZUO EOS AND YEN−MULLINS MODEL OF ASPHALTENES The Flory−Huggins−Zuo equation of state was developed by Freed et al.14,18 and Zuo et al.,15−17 to account for asphaltene gradients in oilfield reservoirs and in laboratory centrifugation experiments. It is the first EoS for predicting asphaltene concentration gradients with depth in oil reservoirs and is the only EoS that has successfully modeled condensates through heavy oils.19 The FHZ EoS relies on the colloidal characterization of the crude oils. For example, for heavy oils, large asphaltene gradients are obtained due to the relatively large cluster size. If an EoS does not incorporate asphaltene clusters from the Yen−Mullins model, it will be unable to obtain the observed large gradients in heavy oil columns.19,25 Because of the simple form of the FHZ EoS, it can use various measurements of reservoir fluid properties in particular by employing asphaltene concentration ratios or optical density ratios at two different depths in the reservoir. It should be noted that the Flory− Huggins theory has been used successfully to account for aspects of asphaltene phase behavior.35−37 The FHZ EoS adds a gravity term to the Flory−Huggins theory and accounts for asphaltene gradients, a significant object for EoSs. The FHZ EoS is given by

(3)

■

⎧ vag (ρ − ρ )(h2 − h1) ⎫ φ (h 2 ) OD(h2) a ⎬ = a = exp⎨ OD(h1) RT φa(h1) ⎩ ⎭

(2)

The first application of eq 3 to an oilfield column was for a highly undersaturated low-GOR black oil, with incorporation of nanoaggregates from the Yen−Mullins model.20 In eq 2, OD, T, ρ, and h are available from DFA and other measurements. The five unknowns are the asphaltene density as well as the molar volumes (v) and solubility parameters (δ) of both oil and asphaltenes. The asphaltene density and solubility parameter are estimated by the correlations. The molar volume and solubility parameter of live fluids are estimated by a cubic EoS. The remaining unknown is the size of asphaltenes, which is tightly constrained by the Yen−Mullins model of asphaltenes.3,4 The Yen−Mullins model3,4 depicts the predominant molecular and colloidal structures of asphaltenes in crude oils and in laboratory solvents as shown in Figure 4. At low concentrations such as in light oil, asphaltenes are dispersed as a true molecular solution (left, ∼1.5 nm in diameter). At higher concentrations such as in black oils, asphaltenes are dispersed as nanoaggregates (center, ∼2 nm in diameter). At yet higher concentrations such as in mobile heavy oils, asphaltenes are dispersed as clusters of nanoaggregates (right, ∼5 nm in diameter). The FHZ EoS is the only one that has been shown to treat gradients of asphaltenes in all types of crude oils and at equilibrium and disequilibrium conditions. The details about advances in the FHZ EoS for asphaltene gradients and formation evaluation are given in ref 19. Optical density is linearly related to asphaltene content.19 This oil column also follows the linear relationship between n-C7 asphaltene content and optical density at 1290 nm as shown in Figure 5. This is consistent with many previous determinations of crude oil color and asphaltene content.20

where OD, R, ϕ, v, δ, T, g, ρ, and h are the optical density, universal gas constant, volume fraction, molar volume, solubility parameter, temperature, gravitational acceleration, density, and depth, respectively. Subscript a denotes the properties of asphaltenes; subscripts h1 and h2 stand for the properties at

APPLICATION OF THE CUBIC EOS TO A SINGLE SAMPLE FROM THE OIL COLUMN The fluid at 315.5 m TVDSS (517 m MD) was selected to validate application on the cubic EoS for laboratory measure-

⎧ φ (h 2 ) ⎪ vag (ρ − ρ )(h 2 − h1) OD(h2) a = a = exp⎨ ⎪ φa(h1) RT OD(h1) ⎩ +

⎫ ⎡⎛ v ⎞ va ⎛ v ⎞ ⎤⎪ ⎬ [(δa − δ)h21 − (δa − δ)h22 ] + ⎢⎜ a ⎟ − ⎜ a ⎟ ⎥⎪ RT ⎢⎣⎝ v ⎠h2 ⎝ v ⎠h1⎥⎦⎭

■

1450

DOI: 10.1021/ef502586q Energy Fuels 2015, 29, 1447−1460

Article

Energy & Fuels

predicted by the cubic EoS is close to the experimental data with a deviation of 1.7% and then matched by tuning a binary interaction parameter. Figure 6 gives the phase behavior results. The formation pressure is a little bit higher than the bubble point pressure. The results are in good agreement with the experimental data for this sample. Compositional and phase behavior measurements of crude oils in this field are consistent. However, as shown in Figure 6d, the corresponding state (CS) viscosity model40 could not describe viscosity variation with pressure nicely (the CS model gives much bigger viscosity at higher pressure) although a couple of parameters in the viscosity model were tuned. Therefore, the viscosity at the bubble point was matched by adjusting the CS viscosity model.

Figure 5. Asphaltene wt % versus optical density. A linear relationship (dashed line) is observed: Asphaltene wt % = 15.813 OD.

■

CRUDE OIL PROPERTIES OF THE RESERVOIR FLUID The MDT tool configured with DFA tools and with focused sampling34 was used to measure fluid compositions and properties and to acquire fluid samples with low OBM filtrate contamination downhole. The downhole fluid samples were

2

ments of this single sample. The Peng−Robinson EoS was employed to calculate phase behavior of this sample with the characterization method described in the literature.38,39 The bubble point pressure at the formation temperature (57 °C)

Figure 6. PVT measurement and analysis for a single sample of crude oil at a depth of 315.5 m TVDSS. (a) Phase envelope (red curve, EoS bubble point; blue curve, EoS dew point; green circle, EoS critical point; yellow triangle, experimental bubble point; blue asterisk, formation pressure). (b) Oil density as a function of pressure in CCE (constant composition expansion) test at 57 °C (red curve-EoS; green circles-experimental data). (c) Solution GOR as a function of pressure in DL (differential liberation) test at 57 °C. (d) Viscosity as a function of pressure. 1451

DOI: 10.1021/ef502586q Energy Fuels 2015, 29, 1447−1460

Article

Energy & Fuels

Figure 7. Variations of saturates, aromatics, and resins + asphaltenes from degassed oil in well. The dashed curves denote the best curve fitting. Increasing biodegradation toward the base of the oil column results in decreasing saturated hydrocarbons and increasing resins + asphaltenes. There is more OBM filtrate contamination for the lowest sample because it is the most viscous, thus causing increased collection of the (low viscosity) OBM filtrate.

Figure 8. GC chromatograms for the entire oil column. The GC of OBM filtrate appears in the upper right. The crude oils from the upper half of the column have very similar chromatograms with plentiful n-alkanes. The chromatograms in the lower half of the oil column show decreasing n-alkane composition with depth. OBM contamination becomes more pronounced at the base of the oil column due to sampling problems with viscous crude oils. The blue circles are the DFA measured optical density and solid curve is the best curve fitting.

acquired and at surface degassed with subsequent SARA (saturates, aromatics, resins, and asphaltenes) analysis. Gas chromatography (GC) was performed for the degassed samples. Figure 7a shows the variations of saturates, aromatics and resins +

asphaltenes for the degassed oil samples in well 1. The curves are simple polynomial curve fitting to show the trends. The gas chromatograms of the degassed oil samples are illustrated in Figure 7b. Large compositional gradients are apparently 1452

DOI: 10.1021/ef502586q Energy Fuels 2015, 29, 1447−1460

Article

Energy & Fuels

and 7 shows that there is mild biodegradation at 360 m depth, but without much increase in asphaltene concentration. That is, slight loss of n-alkanes occurred up to this depth. At more shallow depths, the n-alkanes are uniform implying the lack of biodegradation above this depth. Figure 10 depicts variations of the optical density measured by DFA, the live fluid viscosity and degassed oil API gravity measured by the PVT laboratory for the four wells. The dashed curves denote the best curve fitting of the data. The fluid properties slightly change at the top of the oil column whereas the fluids significantly become heavier toward the base of the oil column owing to severe biodegradation at the oil−water contact. Based on the reference fluid and isothermal equilibrium assumption, compositional gradients with depth were calculated by the method of Zuo et al. using the cubic EoS.41−44 The predicted results show that there are almost no compositional gradients in the oil column. Therefore, the cubic EoS failed to predict the asphaltene and viscosity gradients, in particular, in the lower half of the oil column. This is very low GOR oil (9 to 16 m3/m3) consisting of a large amount of asphaltenes. As expected, the cubic EoS cannot treat asphaltene gradients with success.14−19 The FHZ EoS was then employed to predict the asphaltene (or optical density) gradient using 2 nm in diameter of asphaltene nanoaggregates in terms of the Yen−Mullins model.3,4 The FHZ EoS with the gravity term only can be used to estimate the asphaltene gradient due to lowGOR oil.14−19,44,45 That is, the solubility term of the FHZ EoS is largely invariant for a relatively homogeneous low-GOR crude oils at low pressure as predicted by the cubic EoS. The predictions by the FHZ EoS with the gravity term only are illustrated in Figure 11. The FHZ EoS is working well at the top of the oil column. The lower sands have much bigger optical density (asphaltene wt %) than the equilibrium distribution predicted by the FHZ EoS. The optical density is higher than the equilibrium value by a factor of 3 at the base of the oil column. The implication is that thermodynamic equilibrium of asphaltenes applies over the upper half of the oil column, while a significant disequilibrium in asphaltene concentration applies in the lower half of the oil column. Therefore, a new model is required to estimate the disequilibrium asphaltene gradient in the lower half of the oil column due to biodegradation.

observed toward the base of the oil column. Increasing biodegradation toward the base of the oil column results in decreasing saturated hydrocarbons and increasing resins + asphaltenes. In the upper ∼1/2 of each reservoir, the crude oil samples contain large and comparable quantities of n-alkanes which indicates that they are not biodegraded. However, in the lower 1/2 of the oil column, n-alkanes are seen to be decreasing and are almost all missing at the base of the oil column. The OBM filtrate contamination of the oil sample with its narrow nalkane distribution is observed in these samples. The gas chromatogram of the oil based mud filtrate is also shown in Figure 7 for reference. The GC trace of the OBM filtrate is readily distinguishable from that of the crude oil. Figure 8 shows GC chromatograms of the degassed crude oils versus depth in the entire column. The GC chromatogram of the OBM filtrate is also shown (top-right), which does contaminate some of the crude oil samples. The GC chromatograms for the crude oil samples in the upper section of the oil column are very similar to dominant n-alkane composition. In contrast, in the lower half of the oil column, there is a strong trend toward reduced n-alkane contribution. This is seen in comparison of the sharp n-alkane peaks versus the elevated, broad unresolved complex mixture (UCM). At the very base of the column, there is almost no n-alkane contribution (except for the OBM filtrate contamination, which is circled). This GC chromatography data is consistent with extensive biodegradation at the base of the column, with decreasing biodegradation at points above the base of the oil column. Virtually no biodegradation is detected in the upper section of the oil column as the n-alkanes are uniformly prominent. OBM filtrate contamination is generally worse at the base of the column where the viscous nature of the crude oils makes sample acquisition more challenging. Figure 9 shows an analysis of the GC chromatograms in Figure 8. For the GC ratio in Figure 9, the average of the three largest n-

■

SIMPLE DIFFUSION MODEL FOR BIODEGRADATION Multiple oil charges must be taken into consideration for some reservoirs involving biodegradation. For instance, in a case study in Brazil, the reservoir crude oil was shown to be enriched in nalkanes indicating little biodegradation, and in 25-norhopanes indicating extensive biodegradation. The explanation in this case was that the first charge occurred when the reservoir temperature was less than 80 °C, and extensive biodegradation of this oil occurred (leading to formation of 25-horhopanes).23 Subsequently the reservoir underwent subsidence and heated beyond 80 °C thereby causing paleopasteurization of the reservoir. Subsequent to this event, a further charge of oil into the reservoir occurred accounting for the presence of n-alkanes in the reservoir crude oil.23 Moreover, after all these processes, the asphaltenes then equilibrated at least locally.23 In the shallow reservoir of the current study in this paper, the reservoir temperature remains quite low, so biodegradation is current. A multiple charge scenario of the sort discussed immediately above does not apply. Actually, the geochemistry study from core and

Figure 9. GC ratios. n-Alkane divided by unresolved complex mixture (UCM) versus true vertical depth subsea (TVDSS). The destruction of n-alkanes toward the base of the column is pronounced. The similarity of the GC chromatograms in the upper section of the column indicates uniform (and no) biodegradation. The dashed blue curve is drawn only to guide the eye.

alkane peaks at/near n-C27 (over and above the broad UCM peak) is the numerator of the ratio and the unresolved complex mixture (UCM) maximum peak at the same retention time is the denominator. This selection avoids artifacts from the OBM filtrate while emphasizing any loss of n-alkane. The n-alkanes are the most susceptible to biodegradation. Comparison of Figures 9 1453

DOI: 10.1021/ef502586q Energy Fuels 2015, 29, 1447−1460

Article

Energy & Fuels

Figure 10. (a) Optical density variation. (b) Live fluid viscosity variation. (c) API gravity variation. The dashed blue curves are the best polynomial fit. Fluid properties slightly change at the top of the oil column whereas fluids significantly become heavier toward the base of the oil column owing to severe biodegradation at the oil−water contact.

sequence. The length of time to equilibrate asphaltenes via diffusion in the upper half of the column is directly comparable to the length of time required to diffuse alkanes to the oil−water contact in the lower half of the reservoir. Because the asphaltenes are determined to be equilibrated in the upper half of the reservoir, we conclude that current charging is not significant and is not determining the distribution of hydrocarbon types in this reservoir. This analysis is enabled by employing the industry’s first EoS for asphaltene gradients, it is now possible to know what an equilibrated asphaltene gradient is. Consequently, the analysis of the reservoir in question as a diffusive gradient is reinforced, the contribution of current charging is not significant. To simplify the issue in question, one dimension model is employed in this work. For the five-stacked anticline reservoirs with the same initial oil−water contact, as shown in Figure 1(left), its dip angle (α) can be used to convert the real distance [ h/sin(α) ] to the true vertical depth subsea (TVDSS, h) as shown in Figure 12. At the oil−water contact, depth h = 0. There is a common water zone below the oil−water contact and a multilayered sandstone oil zone above the oil−water contact. Following the same approach as the development of the FHZ EoS, whole oil components are divided into two groups: maltenes (m) and asphaltenes (a). Microbes can consume components of alkanes (and some alkylaromatics) in the group of maltenes. In the following, for simplicity, the components consumed by microbes are referred to as alkanes. To establish a simple diffusive model for biodegradation, the following assumptions are made: (1) Microbes consume the alkanes rapidly in comparison with diffusion times of the components to the oil−water contact. The rate-limiting step is presumed to be alkane diffusion down to the oil−water contact. (2) Initial oil compositions of the reservoir are equilibrated (homogeneous). (3) Biodegradation occurs at the oil−water contact where microbes live.29,30

Figure 11. Comparison of DFA optical density with FHZ EoS predictions using the gravity term. The upper half of the oil column is accounted for successfully using the FHZ EoS with asphaltene nanoaggregates. However, the lower sands have much bigger optical density (asphaltene wt %) than the equilibrium distribution predicted by the FHZ EoS. Thus, the conclusion is that the lower half of the oil column is not equilibrated.

fluid samples indicates that the oil in the northern part of the Barmer basin where the oilfield in this paper is located was generated from the same source rock.48 Nevertheless, we must consider whether current charging is playing a significant role in establishing the hydrocarbon distributions in this reservoir. We presume the Stainforth charge mechanism applies where a charge of late, light hydrocarbons undergoes piston-like displacement of an earlier charge of heavier hydrocarbon.46 Such a sequence applies to the norm subsidence process, where the later charge is more mature. Active biodegradation would only increase the density of the earlier charge strengthening the gravity segregation which causes the layering in the Stainforth charge mechanism. If significant charging were current, then there would not be equilibrated asphaltenes in the upper half of the reservoir. Instead, the asphaltene gradient would be in accord with that of the charge 1454

DOI: 10.1021/ef502586q Energy Fuels 2015, 29, 1447−1460

Article

Energy & Fuels

Figure 12. Schematic diagram for a biodegradation process. (a) Maltene (mainly alkane) concentration distribution; (b) Asphaltene concentration distribution. C and h are the mole concentration (it can be replaced by mass concentration) and TVDSS. At the oil−water contact, h = 0, h increases upward.

⎧ ⎪ ρm ̅ at h < ∞ ρm̅ = ⎨ ⎪ ̅ at h = ∞ ⎩ ρm0

(4) Diffusion of asphaltenes upward the oil column is ignored because biodegradation makes solvents (maltenes) better for dissolving asphaltenes that may compensate upward diffusion of asphaltenes. Based on these presumptions, maltene diffusion is governed by Fick’s second law: ∂ρm̅ ∂t

According to the initial and boundary conditions mentioned above, an analytical solution to diffusive eq 4 is expressed as ⎛ ⎞ ρm̅ − ρm1 h ̅ = erf⎜ ⎟ ρm0 ⎝ 2sin(α) Dt ⎠ ̅ − ρm1 ̅

2

=D

∂ ρm̅ ∂h2

(4)

at

t=0

ρa̅ = ρ − ρm̅

for

h=0

wi =

t>0

(9)

ρi̅ ρ

i = m, a

(10)

The fluid density (ρ) at downhole conditions can be measured by DFA or in the PVT laboratory. Therefore, three parameters are at most required to be determined: ρ̅m0, ρ̅m1, and t.

(5)

at

(8)

where ρ is the fluid mass density. The mass fraction is then calculated by

where ρ̅m0 is the initial mass concentration (partial density) of the maltenes. Because biodegradation occurs at the oil−water contact where microbes live and consume all alkanes (alkane concentration is almost zero), concentration of maltenes at the oil−water contact can be considered approximately as a constant although the loss of alkane components decreases the oil volume yielding an increase in asphaltene concentration. ρ̅m1 can be treated as an adjustable parameter if no data is available. The first boundary condition is given by ρm̅ = ρm1 ̅

ρm0 ̅ > ρm1 ̅

where erf is the error function and α is the dip angle. As mentioned previously, due to lack of connectivity from one sand layer to another, alkanes cannot diffuse down vertically from one sand layer to another. However, it can diffuse down the oil−water contact in the same sand layer as depicted in Figure 1 (left). Therefore, the dip angle is included in eq 8. Therefore, concentration of asphaltenes is computed by

where ρ̅m is the mass concentration (partial density) of the maltenes which contain alkanes that can be consumed by microbes. D, t, and h are the effective diffusion coefficient of the maltenes (actually alkanes) independent of concentration, time, and depth, respectively. Because it is assumed that the initial reservoir is equilibrated, compositional gradients are very small and negligible for such low-GOR heavy oil.1 As expected, the equilibrium oil property gradient predicted by the cubic EoS2 is negligible. That means the initial reservoir is homogeneous. Therefore, initial conditions of the reservoir just prior to biodegradation at all depths (h) are given by ρm̅ = ρm0 ̅

(7)

■

RESULTS AND DISCUSSIONS The diffusive model was employed to the five-stacked biodegradation reservoirs. According to ref 47, diffusion coefficients of alkanes in crude oil are about 5 × 10−6 cm2/s. For heavy oils with subsurface viscosities estimated to be around 100 cP, diffusion coefficients of alkanes could be from 5 × 10−7 cm2/s to 10−8 cm2/s.30 Therefore, it is assumed that the effective diffusion coefficient D = 10−7 cm2/s for maltenes (actually alkanes) in the heavy oil with viscosity from 20−150 cP and the dip angle is assumed to be 13°. Therefore, eq 8 was used to calculate the maltene distribution with time and depth. To utilize eq 8, two partial densities (ρ̅m0 and ρ̅m1) of maltenes at initial conditions (or at the top of the oil column and at the base of the oil column) are required. At the top of the oil column, the FHZ EoS was employed to compute the equilibrium asphaltene

(6)

Because the concentration of maltenes remains unchanged at shallow depths far away from the oil−water contact due to no biodegradation or fresh oil charges into the top of the reservoir, the second boundary conditions are given by 1455

DOI: 10.1021/ef502586q Energy Fuels 2015, 29, 1447−1460

Article

Energy & Fuels gradient (then obtaining asphaltene weight fraction, wa0) and fluid mass density (ρ0) was measured. Therefore, ρ̅m0 is known due to ρ̅m0 = (1 − wa0) ρ0. Similarly, at the base of the oil column, mass density and mass fraction of maltenes were also measured. Thus, ρ̅m1 is known as well. Therefore, the only undetermined parameter is time, which can be obtained by fitting the measured asphaltene gradient data of the lower half of the oil column. The mass concentration distribution of maltenes with depth and time calculated by the diffusive model is shown in Figure 13,

Then, time (t) is adjusted to match the DFA measured OD data where asphaltene weight fraction is converted to OD using the correlation in Figure 5. The optimized time t = 50 Ma if D = 10−7 cm2/s and α = 13°. As mentioned previously, the oilfield is the Paleogene fluvial-dominated multilayered sandstone reservoir. According to ref 48, the reservoir started charge at the Eocene period (55 Ma with substantial oil at 44 Ma). The geochemistry study indicates that the oil in the northern part of the Barmer basin was generated from the same source rock. The source rock was uplifted at the early Miocene period ending reservoir charging.48 The formation temperature varies from 55 to 61 °C. The biodegradation started with the initial reservoir charge and continues today; 50 Ma for the start of biodegradation is reasonable. The results are also consistent with the geological, petrophysical, and production data that the five stacked sandstone reservoirs are lack of connectivity. If they were connected (only vertical diffusion), time would be much less (t = 2.5 Ma), which is unrealistic. Pressure measurement during production shows the different sands are not vertically connected. Figure 15 shows the results of a 1D petroleum system model of the Barmer basin.48 Subsidence causes the petroleum source rock to enter the oil generation thermal window in the lower Eocene. This is when the vitrinite reflectance Ro enters the range 0.5−1.3. Uplift in the lower Miocene terminates oil generation. Biodegradation commences immediately with oil charging into the reservoir. (The GC data shows little biodegradation occurred in oil migration.) With biodegradation, the density of the oil increases. Subsequent oil charging into the reservoir is light both because it is higher maturity and because it is not (yet) biodegraded. Consequently, the newly charged, lighter oil is positioned above the existing oil in the reservoir, thereby pushing the existing reservoir oil down in a piston-like displacement with very little mixing.46 This charge scenario has been called the Stainforth charge scenario.1 This scenario is consistent with the diffusional analysis herein. The OD fitting result from optimized time (t = 50 Ma) is depicted in Figure 16. The FHZ EoS with the gravity term only gives the equilibrium distribution of optical density, which matches the DFA measured OD very well in the upper half of the oil column where no biodegradation occurs. The diffusive model matches the OD gradient nicely in the lower half of the oil column. Because the biodegradation time is not long enough, the fluids at the upper sands still contain full of n-alkanes. This is consistent with the gas chromatograms as shown in Figures 7b and 8. This also explains why the FHZ EoS can handle the upper sands nicely. As stated by Head and Larter,31 heavy levels of biodegradation have typically lost up to 50% to 70% of their mass of C6+ components. This is in very good agreement with the 3× increase of asphaltenes from equilibrium distribution predicted by the FHZ EoS (the gravity term only) with 2 nm in diameter at the base of the oil column. The loss of alkane and some alkylaromatic components decreases the oil volume yielding an increase in asphaltene concentration. As mentioned previously, diffusion of asphaltenes upward the oil column is ignored because biodegradation makes solvents (maltenes) better for dissolving asphaltenes that may compensate upward diffusion of asphaltenes. Let us look at the density variation in this oil column as shown in Figure 17a. The upper half of the oil column almost has no density gradient whereas the lower half has a large density gradient due to biodegradation. The

Figure 13. Maltene mass concentration distributions with time and depth. Concentration of maltenes (basically alkanes and some alkylaromatics) decrease with time at the same depth.

where Ma is mega-annum (million years). At the beginning of biodegradation, microbes consume all alkanes at the oil−water contact, thus yielding alkane (maltene) concentration contrast. Such alkane concentration contrast makes alkanes diffuse downward. Then, microbes consume the alkanes diffused down at the oil−water contact. Because biodegradation is more rapid than diffusion, the limiting step is alkane diffusion. This process continues slowly. Alkanes gradually disappear upward and concentration of maltenes decreases upward to shallower depth with time. The density gradient with depth was measured by DFA and/or in laboratory. The oil density is able to be populated based on the measurements. With the density gradient distribution, mass concentration of asphaltenes is then calculated by eq 9. Mass fraction of asphaltenes is computed by eq 10. The calculated asphaltene mass percentage with depth and time is shown in Figure 14.

Figure 14. Asphaltene mass percentage with time and depth. The green solid curve is the equilibrium distribution calculated by the FHZ EoS with the gravity term only. Biodegradation leads to an increase in asphaltene content. 1456

DOI: 10.1021/ef502586q Energy Fuels 2015, 29, 1447−1460

Article

Energy & Fuels

Figure 15. 1D burial model with the oil maturity window (Ro = 0.5−1.3) superimposed illustrating the late Cretaceous−Early Tertiary rifting event and a calibrated uplift event commencing in the Miocene. Oil generation (and reservoir charging) in the Barmer basin initiated in the Lower Eocene.48

With these parameters, the full FHZ EoS with the gravity, solubility and entropy terms is then used to predict the OD gradient by assuming asphaltenes are locally equilibrated with oil. The full FHZ EoS gives good OD gradient predictions (dashed blue curve) as shown in Figure 16. This means that if reasonable solubility parameter and molar volume variations are able to be estimated, reasonable asphaltene gradients can be computed using the FHZ EoS and assuming asphaltenes are locally equilibrated with oil. On the other hand, such a large solubility parameter gradient in the lower half of the oil column greatly compensate diffusion of asphaltenes toward lower concentrations. Viscosity plays a central role in well productivity and displacement efficiency and impacts completion strategies and field development plans. Accurately assessing areal and vertical variations of viscosity will lead to more realistic reservoir simulation and field development models. Since viscosity varies exponentially with asphaltene concentration,50 the viscosity can be directly related to the OD because a linear relationship between OD and asphaltene concentration. The large viscosity variation is mainly resulted from the big asphaltene gradient due to biodegradation. The Pal−Rhodes model51 and the Mooney model52 were modified to calculate viscosity for heavy oil in the open literature.50,53,54 The two models are also used for viscosity estimation in this paper. Viscosity (μ) can be calculated by the Pal−Rhodes model51

Figure 16. Optical density gradient predicted by the FHZ EoS and the diffusion model at t = 50 Ma and α = 13°. The FHZ EoS with the gravity term only matches the DFA measured OD very well at the upper section of the reservoir where no biodegradation occurs. The diffusive model is in good agreement with the OD gradient at the lower portion of the oil column.

solubility parameters of oil can be estimated in terms of oil density according to Zuo et al.49

δ = 17.347ρ + 2.904

(11)

where ρ and δ are the density in g/cm and the solubility parameter in (MPa)0.5, respectively. The oil molar volume can be calculated by the oil molecular weight divided by the oil density. The variations of the calculated oil solubility parameter and molar volume are illustrated in Figure 17b). Again, the lower half of the oil column has large solubility parameter and molar volume gradient due to biodegradation. It should be noticed that the FHZ EoS with the gravity term only is equivalent to the full FHZ EoS applied to the formation with no density, solubility parameter, and molar volume gradients from the top to bottom of the oil column. 3

μ = μ0 (1 − K ′·A)−ν

(12)

where A is the mass fraction of asphaltenes which can be replaced by OD and μ0 denotes the viscosity at the reference where no asphaltenes are present (A = 0). Lin et al.53 found K′ = 1.88 and ν = 6.9 for heavy oil. We keep ν the same as Lin et al. but K′ is treated as adjustable parameters in this paper. We can also select a depth where asphaltene concentration and viscosity are known 1457

DOI: 10.1021/ef502586q Energy Fuels 2015, 29, 1447−1460

Article

Energy & Fuels

Figure 17. (a) Density gradient. (b) Variations of calculated solubility parameters and molar volume.

combination of the equilibrium and disequilibrium asphaltene distributions work well.

as a reference as well. In that case, there is only one adjustable parameter. Viscosity (μ) can also be estimated by the modified Mooney model ⎛ kA ⎞ ⎟ μ = μ0 exp⎜ ⎝1 − A ⎠

■

CONCLUSIONS Large asphaltene and viscosity gradients were studied, along with large gradients in other fluid properties, in an oilfield reservoir with five stacked sand reservoirs, each with oil undergoing active biodegradation. Extensive fluid property measurements, both downhole and laboratory, were conducted in this study. Fluid data from four wells across the field intersecting the five stacked reservoirs were acquired showing consistency across the all formations. In particular, accurate asphaltene gradient measurements were performed utilizing downhole fluid analysis. Combined with the FHZ EoS, a simple diffusive model was developed for the entire observed asphaltene distribution in each of the five sand reservoirs of the formation undergoing active biodegradation. Alkanes (and some alkylaromatics) are rapidly consumed at the oil−water contact at the base of the oil column. The diffusion of these compounds to the oil−water contact is the rate limiting step; subsequent biodegradation is relatively fast in comparison. The loss of the alkane components results in a decrease in the oil volume, thus yielding an increase in asphaltene concentration and thus in viscosity. The charging of oil into the reservoir occurred approximately 50 million years ago, and biodegradation commenced at that time. In this duration, oil at the bottom half of the reservoir suffered alkane diffusion coupled with alkane loss due to biodegradation. The top half of the oil column, where the asphaltene gradient follows the equilibrium distribution predicted by the FHZ EoS with the gravity term only, is not biodegraded due to the limited residence time of the oil in the reservoir. The substantial gas chromatography data of the entire oil column support the diffusive mechanism proposed. That is, the n-alkane contribution to the oil is seen to vary as expected with the diffusive model. The diffusive model is in good agreement with all the measured compositional properties of the oil column. The capability of accounting for asphaltene and viscosity variations in five stacked sand layers using a simple diffusive model together with the FHZ EoS and the Yen−Mullins model provides a robust model for improving efficiency of reservoir engineering and oil production. This study shows yet another oilfield where a simple thermodynamic model (here with diffusion) accounts for a large range of measured properties including those such as viscosity that have a major impact on field development planning. The ability to account for the asphaltenes

(13)

where k is treated as an adjustable parameter in this paper. For live heavy oil, effects of GOR, pressure, and temperature on viscosity can be corrected by the following expression50 1/3⎤ ⎡⎛ ⎛ η ⎞ R sref ⎞ ⎥⎛ Tref ⎞4.5 ⎢ ⎟ exp[1.392 ⎜⎜ ⎟⎟ = ⎜ ⎟ ⎜ ⎝ ηref ⎠live ⎢⎣⎝ R s ⎠ ⎥⎦⎝ T ⎠

× 10−2(p − pref )]

(14)

where ref stands for reference conditions. Pressure (p) is in MPa, temperature (T) in K, and GOR (Rs) in m3/m3. The computed viscosity results for this oil column at reservoir conditions are shown in Figure 18. The fitted K′ = 1.3 in the Pal− Rhodes model and k = 8.5 in the modified Mooney model. The correlated results are in good agreement with the measured data. It can be seen that the equilibrium asphaltene distribution predicted by the FHZ EoS cannot represent viscosity well in the lower half of the oil column (left-side curve) whereas the

Figure 18. Viscosity gradient predicted by both the Pal−Rhodes model and the Mooney viscosity model. Viscosity increases by a factor of ∼8 due to biodegradation at the base of the oil column. The modeled viscosity is in good agreement with the experimental data. 1458

DOI: 10.1021/ef502586q Energy Fuels 2015, 29, 1447−1460

Article

Energy & Fuels from a first-principles foundation is key to optimization of fluid considerations in production of oil.

■

at SPE Annual Technical Conference and Exhibition, Florence, Italy, Sept. 19−22, 2010. (18) Freed, D. E.; Mullins, O. C.; Zuo, J. Y. Heuristics for Equilibrium Distributions of Asphaltenes in the Presence of GOR Gradients. Energy Fuels 2014, 28, 4859−4869. (19) Zuo, J. Y.; Mullins, O. C.; Freed, D.; Elshahawi, H.; Dong, C.; Seifert, D. J. Advances in the Flory−Huggins−Zuo Equation of State for Asphaltene Gradients and Formation Evaluation. Energy Fuels 2013, 27, 1322−1335. (20) Mullins, O. C.; Betancourt, S. S.; Cribbs, M. E.; Creek, J. L.; Andrews, A. B.; Dubost, F.; Venkataramanan, L. The Colloidal Structure of Crude Oil and the Structure of Reservoirs. Energy Fuels 2007, 21, 2785−2794. (21) Betancourt, S. S.; Ventura, G. T.; Pomerantz, A. E.; Viloria, O.; Dubost, F. X.; Zuo, J. Y.; Monson, G.; Bustamante, D.; Purcell, J. M.; Nelson, R. K.; Rodgers, R. P.; Reddy, C. M.; Marshall, A. G.; Mullins, O. C. Nanoaggregates of Asphaltenes in a Reservoir Crude Oil. Energy Fuels 2009, 23, 1178−1188. (22) Dong, C.; Petro, D.; Pomerantz, A. E.; Nelson, R. L.; Latifzai, A. S.; Nouvelle, X.; Zuo, J. Y.; Reddy, C. M.; Mullins, O. C. New Thermodynamic Modeling of Reservoir Crude Oil. Fuel 2014, 117, 839−850. (23) Pomerantz, A. E.; Ventura, G. T.; McKenna, A. M.; Cañas, J. A.; Auman, J.; Koerner, K.; Curry, D.; Nelson, R. L.; Reddy, C. M.; Rodgers, R. P.; Marshall, A. G.; Peters, K. E.; Mullins, O. C. Combining Biomarker and Bulk Compositional Gradient Analysis to Assess Reservoir Connectivity. Org. Geochem. 2010, 41 (8), 812−821. (24) Indo, K.; Ratulowski, J.; Dindoruk, B.; Gao, J.; Zuo, J. Y.; Mullins, O. C. Asphaltene Nanoaggregates Measured in a Live Crude Oil by Centrifugation. Energy Fuels 2009, 23, 4460−4469. (25) Mullins, O. C.; Zuo, J. Y.; Seifert, D.; Zeybek, M. Clusters of Asphaltene Nanoaggregates Observed in Oil Reservoirs. Energy Fuels 2013, 27, 1752−1761. (26) Pomerantz, A. E.; Bake, K. D.; Craddock, P. R.; Qureshi, A.; Zeybek, M.; Mullins, O. C.; Kodalen, B. G.; Mitra-Kirtley, S.; Bolin, T. B.; Seifert, D. J. Sulfur Speciation in Asphaltenes from a Highly Compositionally Graded Oil Column. Energy Fuels 2013, 27, 4604− 4608. (27) Wu, Q.; Seifert, D. J.; Pomerantz, A. E.; Mullins, O. C.; Zare, R. N. Constant Asphaltene Molecular and Nanoaggregate Mass in a Gravitationally Segregated Reservoir. Energy Fuels 2014, 28, 3010− 3015. (28) Bennett, B.; Adams, J. J.; Gray, N. D.; Sherry, A.; Oldenburg, T. B. P.; Huang, H.; Larter, S. R.; Head, I. M. The Controls on the Composition of Biodegraded Oils in the Deep Subsurface. Part 3. The Impact of Microorganism Distribution on Petroleum Geochemical Gradients in Biodegraded Petroleum Reservoirs. Org. Geochem. 2013, 56, 94−105. (29) Peters, K. E.; Walters, C. C.; Moldowan, J. M. The Biomarker Guide: Biomarkers and Isotopes in Petroleum Systems and Earth History; Cambridge University Press: Cambridge, U.K., 2005; Vol. 1 and 2. (30) Larter, S. R.; Wilhelms, A.; Koopmans, M.; Aplin, A.; Di Primio, R.; Zwach, C.; Erdmann, M.; Telnaes, N. The Controls on the Composition of Biodegraded Oils in the Deep Subsurface. Part 1: Biodegradation Rates in Petroleum Reservoirs. Org. Geochem. 2003, 34, 601−613. (31) Head, I. M.; Jones, D. M.; Larter, S. R. Biological Activity in the Deep Subsurface and the Origin of Heavy Oil. Nature 2003, 426, 344− 352. (32) Mullins, O. C.; Daigle, T.; Crowell, C.; Groenzin, H.; Joshi, N. B. Gas−Oil Ratio of Live Crude Oils Determined by Near-Infrared Spectroscopy. Appl. Spectrosc. 2001, 55, 197−201. (33) Fujisawa, G.; Van Agthoven, M. A.; Rabbito, P.; Mullins, O. C. Near-Infrared Compositional Analysis of Gas and Condensate Reservoir Fluids at Elevated Pressures and Temperatures. Appl. Spectrosc. 2002, 56, 1615−1620. (34) Akkurt, R.; Bowcock, M.; Davies, J.; Del Campo, C.; Hill, B.; Joshi, S.; Kundu, D.; Kumar, S.; O’Keefe, M.; Samir, M.; Tarvin, J.; Weinheber,

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Mullins, O. C. The Physics of Reservoir Fluids: Discovery through Downhole Fluid Analysis; Schlumberger: Sugar Land, TX, 2008. (2) Peng, D.-Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59−64. (3) Mullins, O. C. The modified Yen model. Energy Fuels 2010, 24 (4), 2179−2207. (4) Mullins, O. C.; Sabbah, H.; Eyssautier, J.; Pomerantz, A.; Barre, L.; Andrews, A.; Ruiz-Morales, Y.; Mostowfi, F.; McFarlane, R.; Goual, L.; Lepkowicz, R.; Cooper, T.; Orbulescu, J.; Leblanc, R.; Edwards, J.; Zare, R. N. Advances in Asphaltene Science and the Yen−Mullins Model. Energy Fuels 2012, 26, 3986−4003. (5) Dutta Majumdar, R.; Gerken, M.; Mikula, R.; Hazendonk, P. Validation of the Yen−Mullins Model of Athabasca Oil-Sands Asphaltenes using Solution-State 1H NMR Relaxation and 2D HSQC Spectroscopy. Energy Fuels 2013, 27 (11), 6528−6537. (6) Korb, J. P.; Louis-Joseph, A.; Benamsili, L. Probing Structure and Dynamics of Bulk and Confined Crude Oils by Multiscale NMR Spectroscopy, Diffusometry, and Relaxometry. J. Phys. Chem. B 2013, 117, 7002−7014. (7) Goual, L.; Sedghi, M.; Zeng, H.; Mostowfi, F.; McFarlane, R.; Mullins, O. C. On the Formation and Properties of Asphaltene Nanoaggregates and Cluster by DC-Conductivity and Centrifugation. Fuel 2011, 90, 2480−2490. (8) Goual, L.; Mostowfi, F.; Pomerantz, A. E.; McFarlane, R.; O.C. Mullins, O. C. Cluster of Asphaltene Nanoaggregates by DCConductivity and Centrifugation. Energy Fuels 2014, 28, 5002−5013. (9) Wu, Q.; Pomerantz, A. E.; Mullins, O. C.; Zare, R. N. Laser-Based Mass Spectrometric Determination of Aggregation Numbers for Petroleum- and Coal-Derived Asphaltenes. Energy Fuels 2014, 28, 475−482. (10) Wu, Q.; Pomerantz, A. E.; Mullins, O. C.; Zare, R. N. Fragmentation and Aggregation in Laser Desorption Laser Ionization and Surface Assisted Laser Desorption Ionization Mass Spectrometry. J. Am. Soc. Mass Spec. 2013, 24 (7), 1116−1122. (11) McKenna, A. M.; Donald, L. J.; Fitzsimmons, J. E.; Juyal, P.; Spicer, V.; Standing, K. G.; Marshall, A. G.; Rodgers, R. P. Heavy Petroleum Composition. 3. Asphaltene Aggregation. Energy Fuels 2013, 27 (3), 1246−1256. (12) Rane, J. P.; Harbottle, D.; Pauchard, V.; Couzis, A.; Banerjee, S. Adsorption Kinetics of Asphaltenes at the Oil−Water Interface and Nanoaggregation in the Bulk. Langmuir 2012, 28, 9986−9995. (13) Rane, J. P.; Pauchard, V.; Couzis, A.; Banerjee, S. Interfacial Rheology of Asphaltenes at Oil−Water Interfaces and Interpretation of the Equation of State. Langmuir 2013, 29, 4750−4759. (14) Freed, D. E.; Mullins, O. C.; Zuo, J. Y. Theoretical Treatment of Asphaltenes in the Presence of GOR Gradients. Energy Fuels 2010, 24 (7), 3942−3949. (15) Zuo, J. Y.; Mullins, O. C.; Freed, D.; Zhang, D.; Dong, C.; Zeng, H. Analysis of Downhole Asphaltene Gradients in Oil Reservoirs with a New Bimodal Asphaltene Distribution Function. J. Chem. Eng. Data 2011, 56 (4), 1047−1058. (16) Zuo, J. Y.; Freed, D.; Mullins, O. C.; Zhang, D.; Gisolf, A. Interpretation of DFA Color Gradients in Oil Columns Using the Flory−Huggins Solubility Model. SPE Paper 130305. Presented at CPS/ SPE International Oil & Gas Conference and Exhibition, Beijing, China, June 8−10, 2010. (17) Zuo, J. Y.; Freed, D.; Mullins, O. C.; Zhang, D. DFA Profiling of Oil Columns with Asphaltene Gradients. SPE Paper 133656. Presented 1459

DOI: 10.1021/ef502586q Energy Fuels 2015, 29, 1447−1460

Article

Energy & Fuels P.; Williams, S.; Zeybek, M. Focusing on Downhole Fluid Sampling and Analysis. Oilfield Rev. 2006/2007, 18 (4), 4−19. (35) Wang, J. X.; Buckley, J. S. A Two-Component Model of the Onset of Asphaltene Flocculation in Crude Oils. Energy Fuels 2001, 15, 1004− 1012. (36) Wang, J. X.; Creek, J. L.; Buckley, J. S. Screening for Potential Asphaltene Problems. SPE Paper 103137. Presented at the 2006 SPE Annual Technical Conferences and Exhibition, San Antonio, TX, Sept. 24−27, 2006. (37) Creek, J. L.; Wang, J.; Buckley, J. S. Verification of AsphalteneInstability-Trend (ASIST) Predictions for Low-Molecular-Weight Alkanes. SPE Prod. Oper. 2009, 5, 360−367. (38) Zuo, J. Y.; Zhang, D.; Dubost, F.; Dong, C.; Mullins, O. C.; O’Keefe, M.; Betancourt, S. S. EOS-Based Downhole Fluid Characterization. SPE J. 2011, 16 (1), 115−124. (39) Zuo, J. Y.; Zhang, D. Plus Fraction Characterization and PVT Data Regression for Reservoir Fluids near Critical Conditions. SPE Paper 64520. Presented at SPE Asia Pacific Oil and Gas Conference and Exhibition, Brisbane, Australia, Oct. 16−18, 2000. (40) Pedersen, K. S.; Fredenslund, A. An Improved Corresponding States Model for the Prediction of Oil and Gas Viscosities and Thermal Conductivities. Chem. Eng. Sci. 1987, 42, 182−186. (41) Zuo, J. Y.; Mullins, O. C.; Dong, C.; Zhang, D.; O’Keefe, M.; Dubost, F.; Betancourt, S. S.; Gao, J. Integration of Fluid Log Predictions and Downhole Fluid Analysis. SPE Paper 122562. Presented at the SPE Asia Pacific Oil and Gas Conference and Exhibition, Jakarta, Indonesia, Aug. 4−6, 2009. (42) Zuo, J. Y.; Mullins, O. C.; Dong, C.; Betancourt, S. S.; Dubost, F. X.; O’Keeffe, M.; Zhang, D. Investigation of Formation Connectivity Using Asphaltene Gradient Log Predictions Coupled with Downhole Fluid Analysis. SPE Paper 124264. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, LA, Oct. 4−7, 2009. (43) Elshahawi, H.; Ramaswami, S.; Zuo, J. Y.; Dong, C.; Mullins, O. C.; Zhang, D.; Ruiz-Morales, Y. Advanced Reservoir Evaluation Using Downhole Fluid Analysis and Asphaltene Flory−Huggins−Zuo Equation of State. Petrophysics 2013, 54 (1), 20−29. (44) Zuo, J. Y.; Mullins, O. C.; Dong, C.; Zhang, D. Modeling of Asphaltene Grading in Oil Reservoirs. Nat. Resour. 2010, 1 (1), 19−27. (45) Zuo, J. Y.; Elshahawi, H.; Mullins, O. C.; Dong, C.; Zhang, D.; Jia, N.; Zhao, H. Asphaltene Gradients and Tar Mat Formation in Reservoirs under Active Gas Charging. Fluid Phase Equilib. 2012, 315, 91−98. (46) Stainforth, J. G. New Insights into Reservoir Filling and Mixing Processes. In Understanding Petroleum Reservoirs: Toward an Integrated Reservoir Engineering and Geochemical Approach; Cubit, J. M., England, W. A., Larter, S., Eds.; Geological Society: London, 2004. (47) Freed, D. E.; Burcaw, L.; Song, Y.-Q. Scaling Laws for Diffusion Coefficients in Mixtures of Alkanes. Phys. Rev. Lett. 2005, 94, 1−4 (067602, published Feb. 17, 2005). (48) Naidu1, B. N.; Kothari, V.; Whiteley, N. J.; Guttormsen, J.; Burley, S. D. Calibrated Basin Modelling to Understand Hydrocarbon Distribution in Barmer Basin, India. Paper No. 10448. Pesented at AAPG International Convention and Exhibition, Singapore, Sept. 16−19, 2012. (49) Zuo, J. Y.; Mullins, O. C.; Freed, D.; Zhang, D. A Simple Relation between Densities and Solubility Parameters for Live Reservoir Fluids. J. Chem. Eng. Data 2010, 55 (9), 2964−2969. (50) Zuo, J. Y.; Mullins, O. C.; Mishra, V.; Garcia, G.; Dong, C.; Zhang, D. Asphaltene Grading and Tar Mats in Oil Reservoirs. Energy Fuels 2012, 26 (3), 1670−1680. (51) Pal, R.; Rhodes, E. Viscosity/Concentration Relationships for Emulsions. J. Rheol. 1989, 33, 1021−1045. (52) Mooney, M. The Viscosity of a Concentrated Suspension of Spherical Particles. J. Colloid Science 1951, 6, 162−170. (53) Lin, M. S.; Lunsford, K. M.; Lover, C. J.; Davison, R. R.; Bullin, J. A. The Effects of Asphaltenes on the Chemical and Physical Characteristics of Asphalt. In Asphaltenes: Fundamentals and Applications; Shu, E. Y., Mullins, O. C., Eds.; Plenum Press: New York, 1995; pp 155−176.

(54) Luo, P.; Gu, Y. Effects of Asphaltene Content on the Heavy Oil Viscosity at Different Temperature. Fuel 2006, 86, 1069−1078.

1460

DOI: 10.1021/ef502586q Energy Fuels 2015, 29, 1447−1460