Advances in the Flory–Huggins–Zuo Equation of State for Asphaltene

Review pubs.acs.org/EF

Advances in the Flory−Huggins−Zuo Equation of State for Asphaltene Gradients and Formation Evaluation Julian Y. Zuo,*,† Oliver C. Mullins,‡ Denise Freed,‡ Hani Elshahawi,§ Chengli Dong,§ and Douglas J. Seifert∥ †

DBR Technology Center, Edmonton, Alberta T6N 1M9, Canada Schlumberger Doll Research, 1 Hampshire Street, Cambridge, Massachusetts 02139, United States § Shell International Exploration and Production Company, Houston, Texas 77079, United States ∥ Saudi Aramco, Dhahran 31311, Saudi Arabia ‡

ABSTRACT: Recent advances in the understanding of the molecular and colloidal structure of asphaltenes in crude oils are codified in the Yen−Mullins model of asphaltenes. The Yen−Mullins model has enabled the development of the industry’s first asphaltene equation of state for predicting asphaltene concentration gradients in oil reservoirs, the Flory−Huggins−Zuo equation of state (FHZ EOS). The FHZ EOS is built by adding gravitational forces onto the existing Flory−Huggins regular solution model that has been used widely to model the phase behavior of asphaltene precipitation in the oil and gas industry. For reservoir crude oils with a low gas/oil ratio (GOR), the FHZ EOS reduces predominantly to a simple form, the gravity term only, and for mobile heavy oil, the gravity term simply uses asphaltene clusters. The FHZ EOS has successfully been employed to estimate the concentration gradients of asphaltenes and/or heavy ends in different crude oil columns around the world, thus evaluating the reservoir connectivity, which has been confirmed by the subsequent production data. This paper reviews recent advances in applying the FHZ EOS to different crude oil reservoirs from volatile oil (condensate) to black oil to mobile heavy oil all over the world to address key reservoir issues, such as reservoir connectivity/compartmentalization, tar mat formation, non-equilibrium with a late gas charge, and asphaltene destabilization. The workflow incorporates the integration of new technology, downhole fluid analysis (DFA), coupled with the new scientific advances, the FHZ EOS and Yen−Mullins model. The combination proves a powerful new method of reservoir evaluation. Asphaltene or heavy end concentration gradients in crude oils are treated using the FHZ EOS, explicitly incorporating the size of resin molecules, asphaltene molecules, asphaltene nanoaggregates, and/or asphaltene clusters. All of the parameters in the FHZ EOS are related to DFA measurements, such as compositions, GOR, density, etc. The variations of gas and oil properties with depth are calculated by the classical cubic equation of state (EOS) based on DFA compositions and GOR using specifically developed delumping, characterizing, and oil-based drilling mud (OBM) contamination correcting techniques. Field case studies have proven the value and simplicity of this asphaltene or heavy end treatment. Heuristics can be developed from results corresponding to estimation of asphaltene gradients. Perylene-like resins with the size of ∼1 nm are dispersed as molecules in high-GOR volatile oils with high fluorescence intensity and virtually no asphaltenes (0 wt % asphaltene). Heavy asphaltene-like resins with the size of ∼1.3 nm are molecularly dissolved in volatile oil at a very low asphaltene content. Asphaltene nanoaggregates with the size of ∼2 nm are dispersed in stable crude oil at a bit higher asphaltene content. Asphaltene clusters are found in mobile heavy oil with the size of ∼5 nm at even higher asphaltene content (typically >8 wt % based on stock tank oil). Two types of tar mats are identified by the FHZ EOS: one with a large discontinuous increase in asphaltene content versus depth typically at the base of an oil column (corresponding to asphaltene phase transition) and one with a continuous increase in asphaltene content at the base of a heavy oil column simply by extending the oil column in the downdip direction because of an exponential increase in viscosity with asphaltene content. All of these studies are in accordance with the observations in the Yen−Mullins model within the FHZ EOS analysis.

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ratio (GOR), density, compositions of CO2, C1, C2, C3−C5, and C6+, fluid optical density (OD) or fluid “color” that is linearly related to the heavy end (asphaltene) content, and fluorescence intensity that is associated with the perylene-like resin content and is also linear in the low-concentration limit. For low-GOR, highly undersaturated black oils, the GOR

INTRODUCTION

The effects of gravity, thermal gradients, biodegradation, active charging, etc.1 often cause complicated compositional gradients of reservoir fluids in oil columns. Moreover, reservoir compartmentalization can result in discontinuous distributions of fluid compositions and properties. The recognition of flow barriers, compartmentalization, and tar mats is key to effective and efficient reservoir characterization, production, and management, especially in deepwater environments. Downhole fluid analysis (DFA) is an essential tool for measuring the compositional gradients in real time at reservoir conditions. The new generation DFA tool measures the gas/oil © 2012 American Chemical Society

Special Issue: 13th International Conference on Petroleum Phase Behavior and Fouling Received: July 24, 2012 Revised: November 6, 2012 Published: November 11, 2012 1722

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dealt with in fields, the gravitational force must be taken into account. Thus, the FHZ EOS is built by adding the gravitational term onto the existing Flory−Huggins model that has broadly been used in modeling of phase behavior of asphaltene precipitation in the oil and gas industries.12−17 Previously, the Flory−Huggins model could not be used to predict asphaltene concentration gradients in oil columns because the gravitational term requires the sizes of asphaltenes, which have been unclear until recently.7 On the other hand, conventional cubic EOS cannot represent asphaltenes accurately because they are a variant of the van der Waals EOS, which is based on a modification of the ideal gas law. The cubic EOSs are well-developed for vapor and liquid equilibria for reservoir fluids in part using the component critical properties in calculations. Asphaltenes are amorphous and not amenable to treatment with equations for fluids because their critical properties cannot be measured. To apply the cubic EOS to systems containing asphaltenes, empirical correlations are often used to estimate critical properties of asphaltene pseudocomponents. Because of inaccurate asphaltene characterization and because no critical points exist for asphaltenes, the cubic EOSs are highly parametric and, consequently, are not employed in this manner to reservoir evaluation, especially in real time. The FHZ EOS is developed to describe equilibrium concentration distributions of heavy ends in oil columns. To make it simple and easily used in real time, two steps are often followed. In the first step, the cubic EOS is used to characterize reservoir fluids in the oil columns and, thus, provides key parameters (variables) for the FHZ EOS, the liquid phase (oil) solubility parameter, and the molar volume because the cubic EOSs are widely used for describing vapor- and liquid-phase behavior of reservoir fluids. All of the parameters in the FHZ EOS can be related to DFA measurements, such as compositions, GOR, density, etc. In particular, the ubiquitous use of DFA, in over 90% of the world market, for evaluation of reservoir fluids in open holes and the strong link between the FHZ EOS and DFA enable broad application of this new theoretical development. The variations of gas or liquid fluid properties with depth are calculated by the cubic EOS based on DFA compositions and GOR using specifically developed delumping, characterizing, and oil-based mud (OBM) contamination-correcting techniques.18−23 Although the EOS can be employed to estimate oil solubility parameters, it can also linearly be related to DFA-measured density.24 With all of the parameters obtained, in the second step, the asphaltene concentration gradient is calculated by the FHZ EOS with one tightly constrained parameter, the size of asphaltene or heavy resin. Furthermore, for low-GOR fluids (conventional black and mobile heavy oil), the FHZ EOS reduces to a very simple form, consisting only of the gravitational term, because the solubility and entropy terms have opposite effects on asphaltene concentration gradients and can approximately be canceled out. These treatments make the FHZ EOS simple and easy to use and, in particular, perfectly suited for DFA integration. Therefore, it can be applied downhole in real time to reduce the biggest risk factors in formation evaluation in a cost-effective manner, while the tool is still in the well. Reservoir crude oils can typically be divided into volatile oil, black oil, and mobile heavy oil. In general, the volatile oil has a GOR of 350−750 (m3 m−3) and an American Petroleum Institute (API) gravity of 40−50° API. The black oil has a GOR of 20−350 (m3 m−3) and an API gravity of 25−40° API. The

gradients are frequently small;2,3 however, asphaltene concentration gradients in these fluids can be quite large.4,5 In particular, if the fluid gradients are used for reservoir evaluation, then measurement and analysis of asphaltene (heavy end) gradients in crude oils is mandated because the variations of bulk fluid properties, such as GOR and density, with depth are often not sensitive enough for formation evaluation. Nevertheless, the enormous viscosity dependence upon the asphaltene content, among other reasons, mandates analysis of asphaltene gradients. Pressure gradient analysis is widely used to determine reservoir connectivity in the oil and gas industry. If two permeable zones are not in pressure communication, they are not in flow communication. The presumption that pressure communication implies flow communication has repeatedly been proven to be incorrect. Pressure equilibration requires relatively little fluid flow and can be more than 7 orders of magnitude faster than fluid compositional equilibration,6 even in the presence of leaky flow barriers. Continuous pressure gradients are a necessary but insufficient condition for reservoir connectivity.1 Therefore, the DFA measurement of asphaltene concentration gradients provides an excellent method to delineate the complexity of oil columns. The massive fluid flow in the reservoir that is required to equilibrate the oil column needs good reservoir connectivity. As a result, the measurement of fluid compositional equilibration indicates reservoir connectivity.6 Moreover, asphaltene gradients are frequently more useful than GOR gradients to assess fluid equilibration, particularly for low-GOR fluids. DFA OD (fluid color) measurements are very robust and linearly related to the asphaltene content.4 Using the Flory− Huggins−Zuo equation of state (FHZ EOS), it can be determined whether or not asphaltenes or resins are in thermodynamic equilibrium in the reservoir. In particular, if the asphaltenes are observed to have equilibrated distributions across the reservoir laterally and vertically, this suggests strong connectivity because (1) asphaltenes necessarily charge into the reservoir in an ultimate non-equilibrated state and (2) to equilibrate the component of crude oil with by far the least mobility necessitates substantial permeability and considerable fluid flow. Therefore, asphaltene (OD) and/or resin (fluorescence intensity) grading analysis in oil columns becomes useful to discern reservoir complexities. Recent advances in the understanding of the molecular and colloidal structure of asphaltenes in crude oils are codified in the Yen−Mullins model.7 The Yen−Mullins model enables the development of the industry’s first simple physical model, referred to as the FHZ EOS in ref 8 to model concentration gradients of asphaltenes and heavy ends of reservoir crude oils for evaluation of reservoir connectivity. In the book Molecular Thermodynamics of Fluid-Phase Equilibria written by Prausnitz and co-workers,9 an equation of state (EOS) is defined as the mathematical relation between pressure, volume, temperature, and composition, and most forms of EOS are pressure-explicit. Because the FHZ EOS is derived from the Helmholtz freeenergy approach using temperature and volume as independent variables10 for the asphaltene and maltene two-pseudocomponent system, the required parameters (variables) are associated with an EOS for a bulk reservoir fluid and a function of pressure, volume, temperature, and compositions.11 Therefore, it is the mathematical relation between pressure, volume, temperature, and composition, although it is not pressureexplicit (or volume-explicit). Hence, it is referred to as the FHZ EOS in ref 8. Because a large vertical depth interval is often 1723

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mobile heavy oil has a GOR of 0−20 (m3 m−3), an API gravity of 10−25° API, and a viscosity of 8 wt %).29,30 The FHZ EOS can identify at least two types of tar mats: one with a large discontinuous increase in the asphaltene content versus depth typically at the base of an oil column (corresponding to asphaltene phase transition) and one with a continuous increase in the asphaltene content at the base of a heavy oil column simply by extending the oil column in the downdip direction because of an exponential increase in viscosity with the asphaltene content.31 This paper reviews the FHZ EOS and its applications in oil field formation evaluation for the entire range of crude oils from high-GOR volatile oils to black oils to mobile heavy oils [GOR range from 10 to 720 (m3 m−3)].

Figure 1. Yen−Mullins model, the new first-principles paradigm of asphaltenes.8 Asphaltene molecules have an average molar mass of ∼750 g mol−1. Nanoaggregates have ∼6 molecules, and clusters have ∼8 nanoaggregates. Condensates have a molecular dispersion of heavy ends. Stable black oils have asphaltenes in nanoaggregates. Unstable black oils and heavy oils have asphaltenes in clusters of nanoaggregates.

of these asphaltene species can be present. Coupling the Yen− Mullins model and FHZ EOS with the new generation of DFA technology provides a new powerful approach for delineating reservoir connectivity, tar mat formation, non-equilibrium with a late gas charge, and asphaltene destabilization through asphaltene concentration gradient analysis.

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FHZ EOS FOR ASPHALTENE CONCENTRATION GRADIENTS AND TAR MAT FORMATION The FHZ EOS was developed by Freed et al.10 and Zuo et al.11,22,23 It is assumed that a reservoir fluid is treated as a mixture with two pseudo-components: a solvent (nonasphaltene component or maltene) and a solute (asphaltene). The solvent is also a mixture whose properties are calculated by the cubic EOS; the details are given in refs 18−23. As noted previously, the Flory−Huggins equation has been used to analyze asphaltene precipitation with similar assumptions.12−15 Hirschberg17 proposed the idea of using the Flory−Huggins formalism for understanding asphaltene gradients. However, asphaltene dispersions in crude oil were not understood at that time nor was there a thorough understanding of the solubility of asphaltenes in crude oils. As such, the original treatments ignored variations of fluid properties with depth, such as GOR and density gradients, which have been shown to play an important role for asphaltene concentration gradients. Moreover, the new, simple form of the FHZ EOS allows for practical application of this model to oil reservoirs using various measurements of reservoir fluid properties, in particular by employing asphaltene concentration ratios or OD ratios at two different depths in the reservoir. It is assumed that there are nm(h) maltene molecules and na(h) asphaltene molecules at each depth h. The free energy at depth h for the asphaltene and solvent oil is given by

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YEN−MULLINS MODEL OF ASPHALTENES Asphaltenes herein are defined as the heaviest fraction of crude oil that is soluble in toluene but insoluble in n-heptane. To model concentration distributions (gradients) of asphaltenes in oil columns, gravitational forces must be taken into account because of routinely large vertical reliefs in oil fields. The driving forces for gravity depend upon the size (molar volume) of asphaltenes and density difference between asphaltenes and oil. Moreover, other terms, such as the entropy term and the solubility term, also depend upon the particle size. Therefore, without understanding the molecular and colloidal structures of asphaltenes in crude oil, modeling asphaltene concentration distributions in oil columns is largely precluded. In the past decade, fortunately, enormous progress has been made in relation to all areas of asphaltene science.32 In particular, the molecular and colloidal structures of asphaltenes have largely been resolved and are now codified in the Yen−Mullins model.7 The Yen−Mullins model provides a framework/ foundation for understanding the dispersion of asphaltenes in crude oil. In the Yen−Mullins model,7,8 asphaltenes are dispersed and/ or suspended in crude oils and/or in solvents in three forms, as depicted in Figure 1: molecules, nanoaggregates, and clusters of nanoaggregates. Asphaltene molecules have an average molar mass of ∼750 g mol−1 in a range of 400−1000 g mol−1. The number of fused aromatic rings (FARs) per asphaltene polycyclic aromatic hydrocarbon (PAH) is ∼7. The critical nanoaggregate concentration (CNAC) of asphaltenes is 50− 150 mg L−1. The aggregation number of nanoaggregates is ∼6. The concentration of asphaltene cluster formation is 2−5 g L−1. Clusters have ∼8 nanoaggregates. Laboratory and field data have proven the Yen−Mullins model.8 Asphaltene molecules are dissolved in condensates. Nanoaggregates are dispersed in stable black oil. Clusters are stably suspended in mobile heavy oil and destabilized in black oil. In some cases, more than one

ΔA(h) = ΔAentropy (h) + ΔA sol (h) + ΔAgrav (h)

(1)

where ΔAentropy(h), ΔAsol(h), and ΔAgrav(h) are the Helmholtz free energy because of the entropy of mixing, the solubility of the asphaltene in the maltene, and gravity, respectively. When the difference in sizes between the solute and solvent is taken into account, the entropy of mixing is given by the Flory− Huggins expression ΔAentropy (h) = kT ∑ ni ln φi i

(2)

where k, T, and ϕ are the Boltzmann constant, temperature, and volume fraction, respectively. 1724

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∼3000 carbon atoms in clusters, the gravity effects are increasingly large, creating large gradients. Gravity impacts GOR gradients in a sense indirectly through fluid compressibility. However, for compressible (high-GOR) fluids, the hydrostatic head pressure of the oil column causes a density gradient. This density gradient in effect squeezes out the light components, such as methane, from the base of the column. Thus, fluid compressibility (with gravity) enables a fluid density gradient to produce a compositional (or GOR) gradient. However, for incompressible fluids, such as low-GOR crude oils, the hydrostatic head pressure of the oil column does not create a density gradient (because of incompressibility). Consequently, there is no thermodynamic drive to create a compositional gradient, and the GOR is relatively uniform. The solubility term in the FHZ EOS treats the chemical heuristic “like dissolves like”. This heuristic is treated in the regular solution equation in terms of the solubility parameters; similar magnitudes of the solubility parameter indicate good solvency. In a more detailed approach, the Hansen solubility parameter can be considered with its components, polarizability, polarity, and hydrogen bonding. For asphaltenes and crude oils, it has been found that the polarizability component of the solubility parameter dominates, and one can successfully treat asphaltenes and crude oils with the simple regular solution formalism.33 The solubility parameter of the asphaltenes is relatively high, δa = ∼22 MPa0.5. High-GOR fluids have small solubility parameters and low solvation power for dissolving asphaltenes. For example, it is well-known that miscible gas flood or even gas lift can induce asphaltene flocculation. In contrast, low-GOR fluids have high (solubility parameter) solvation power for dissolving asphaltenes (e.g., heavy oil contains high asphaltene content without asphaltene flocculation). For high-GOR fluids, the GOR gradient creates a large solubility gradient and enhances the asphaltene gradient. The entropy term has an opposite effect; it attempts to randomize the asphaltene distribution. This decreases the asphaltene gradient, and the Flory−Huggins entropy term yields this because the oil molar volume at h2 is greater than that at h1. Consequently, to understand the asphaltene concentration gradient in the oil column, it is crucial to measure the asphaltene (coloration and OD), GOR, and density gradients in the column, as well as to understand the molecular and colloidal structures of asphaltenes in crude oils. The former can be measured by DFA at downhole conditions, while the latter is known from the Yen−Mullins model. If it is assumed that the crude oil solution is an ideal solution (it should be noted that the entropy of ideal mixing yields the mole fraction ratio at two depths because the free energy of ideal mixing can be expressed by eq 2 but ϕi must be replaced by xi), then eq 5 is rewritten as

The part of the free energy because of the solubility of the asphaltenes is given by the regular solution model. ΔA sol (h) = nm(h)φa(h)vm(h)[δa − δm(h)]2

(3)

The gravity term is expressed as ΔAgrav (h) = g[nm(h)vm(h)

∫0

h

ρm (h′)dh′ + na(h)vaρa h] (4)

where ρa and ρm are the densities of the asphaltene and maltene, respectively. The chemical potential of the asphaltene at depth h is then the derivative of ΔA(h) with respect to na with VT(h) (total volume) held fixed at each depth. The condition for equilibrium is that the chemical potentials for the asphaltene are the same at all depths. Finally, the FHZ EOS is derived and given by φ (h 2 ) OD(h2) = a φa(h1) OD(h1) ⎧ ⎪ vag (ρ − ρ )(h 2 − h1) a = exp⎨ ⎪ RT ⎩ v + a [(δa − δ)h12 − (δa − δ)h2 2 ] RT ⎫ ⎡⎛ v ⎞ ⎛ v ⎞ ⎤⎪ ⎬ + ⎢⎜ a ⎟ − ⎜ a ⎟ ⎥⎪ ⎢⎣⎝ v ⎠h2 ⎝ v ⎠h1⎥⎦⎭

(5)

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 depths h1 and h2, respectively. The solubility parameter, molar volume, density of bulk fluids, temperature, pressure, and compositions are dependent upon depth. Therefore, the FHZ EOS is a mathematical relation between pressure, volume, temperature, and compositions. The concentration (volume fraction) variations of asphaltenes with depth depend upon three terms: gravity, solubility (enthalpy), and entropy. In particular, the addition of the gravity term to the Flory−Huggins equation is key to enabling this formalism to apply to the oilfield reservoir with a large vertical relief. As described below, the recognition of the pivotal role of GOR to enabling useful application of this formalism to reservoir fluids is now proven in numerous oilfield case studies. This modified formalism in use globally for oilfield formation evaluation is now known as the FHZ EOS in ref 8. The gravitational term increases the asphaltene gradient because (ρ − ρa) < 0 and (h2 − h1) < 0 (owing to negative values of h, true vertical depth subsea). If an oil column has a small-GOR gradient, such as low-GOR black oil (ρ and δ are slightly dependent upon depth), then the gravity term dominates asphaltene distributions in the oil column. The gravity term consisting of the buoyancy force makes light components move toward the top of the oil column and heavy components go toward the bottom of the oil column. For small species, such as methane, the gravity forces are small (similar to the components of the Earth’s atmosphere); therefore, the gradients are not large. For asphaltene species with ∼70 carbon atoms in molecules, ∼400 carbon atoms in nanoaggregates, and

⎧ vag (ρ − ρ )(h2 − h1) ⎫ xa(h2) a ⎬ = exp⎨ xa(h1) RT ⎩ ⎭

(6)

where x is the mole fraction. Equation 6 is the same as Hirschberg’s expression.17 In Hirschberg’s work, the variations of oil properties, such as GOR and oil solubility parameters, with depth were ignored; these variations play an important role in high-GOR oil columns. For low-GOR fluids, the solubility and entropy terms can approximately be canceled out because of the opposite influence on the asphaltene concentration gradient. Thus, eq 5 becomes 1725

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

Review

that the solubility parameters of liquids and solids are not significantly affected by changes in the pressure.37 The oil molar volume and solubility parameter are obtained as follows. The cubic EOS approach is applied to calculate compositional grading without taking into consideration asphaltenes separately. The method described by Zuo et al.20,21 is used for this purpose. The bulk fluid properties, such as molar volume, composition, molar mass, etc., are then calculated by the cubic EOS at different depths. Because the cubic EOS is usually tuned to match pressure/volume/ temperature (PVT) properties of the fluids in question, the properties calculated by the cubic EOS are the bulk properties, including the maltene and asphaltene contributions. Therefore, the values estimated in this way represent properties of bulk fluids (maltenes + asphaltenes), such as v, ρ, and δ, which are required in eq 5. Densities are usually measured by DFA and/ or laboratories at different depths. Because the solubility term in eq 5 is sensitive to oil solubility parameters, a simple relationship has also been developed to estimate the solubility parameter for live oil [GOR of 0−890 (m3 m−3)] based on DFA-measured live-fluid density alternatively24

(7)

The first application of eq 7 to an oilfield column was for a highly undersaturated low-GOR black oil, with incorporation of nanoaggregates from the Yen−Mullins model, shown in Figure 1.4,5 The resulting connectivity analysis based on eq 7 has been proven correct in production from the oilfield.34 It should be noted that the asphaltene mole fraction ratio in eq 6 is quite different from the asphaltene volume fraction ratio in eq 7 because of the size difference between asphaltenes and maltenes. In eq 5, the ratio of molar volumes at two depths is originally derived from the free energy and then replaced by the ratio of the OD values measured by DFA because the OD measured by DFA is linearly related to asphaltene weight percentage (or volume percentage), as confirmed by dozens of field case studies. Figure 2 shows the results for two typical black oils

δ = 17.347ρ + 2.904

(9) −3

where ρ and δ are in g cm and MPa . Once we obtain the properties (parameters in the FHZ EOS) mentioned above, the only adjustable parameter is the size (molar volume or diameter) of asphaltenes or heavy ends, which is determined in two ways. The first way is to tune the size of asphaltenes to match DFA OD (or fluorescence intensity) measurements at different depths. The obtained size is then compared to the Yen−Mullins model to check whether the results are consistent. If not, the fitted size of asphaltenes is not physically meaningful and cannot be used for reservoir connectivity and asphaltene phase instability. The second way is to assume the size of asphaltenes (or heavy ends) to be either one of three asphaltene forms in the Yen−Mullins model (asphaltene molecules, nanoaggregates, or clusters) or perylene-like resins for high-GOR volatile oil with virtually no asphaltenes, and then OD (which correlates with the asphaltene concentration) or fluorescence intensity gradients can be predicted by the FHZ EOS. The asphaltene or heavy end hard spherical diameter is typically within ∼10% uncertainty of these values based on 1 nm for perylene-like resins, 1.3 nm for asphaltene molecules (heavy asphaltene-like resins), 1.8 nm for asphaltene nanoaggregates, and 5 nm for asphaltene clusters. In some cases, a combination of the colloidal and molecular asphaltenes can be present. DFA asphaltene (OD) logs can be predicted by the FHZ EOS. The real DFA logs are then compared to the DFA OD log predictions to check whether the DFA logs are consistent. If the FHZ EOS applies among (DFA) data from different wells, then a laterally equilibrated oil column is suggested. If so, reservoir connectivity is suggested. Otherwise, more DFA stations are required to uncover a source for the discrepancy. The lack of agreement between the FHZ EOS and measured data can be determined while the DFA tool is still in the well, thereby enabling additional measurements to identify the specific complexity causing the mismatch. The formation can be evaluated in a cost-effective manner to reduce the biggest risk factors. For a reservoir under active late gas charging and/or large thermal diffusion, the reservoir fluid is not equilibrated. To deal with such a non-equilibrium oil column, the cubic EOS is first used to describe the non-equilibrium compositional gradient of

Figure 2. Correlation between ODs measured by DFA and asphaltene content from laboratory SARA analysis for two typical black oils with a GOR of 180 and 90 (m3 m−3).4,28

with a GOR of 180 and 90 (m3 m−3), respectively.4,28 In addition, the measurements of relative asphaltene content have exceedingly small error (∼ ±1%) using optical measurements, such as DFA. These errors are at least an order of magnitude better than standard laboratory separation [saturates, aromatics, resins, and asphaltenes (SARA) analysis] measurements.1 In eq 5, OD, T, ρ, and h are known from DFA and other measurements. The remaining five unknowns are the asphaltene density as well as the molar volumes (v) and solubility parameters (δ) of both oil and asphaltenes, respectively. The five parameters can be determined as follows. As a solubility class, asphaltenes have a solubility parameter with estimates varying between 19 and 24 MPa0.5 and a density between 1.13 and 1.20 g/cm3 at ambient conditions. Therefore, densities (ρa) of asphaltenes, asphaltene-like heavy resins, and bulk resins are set to 1.2, 1.15, and 1.05 g/m3, respectively. Solubility parameters (δa) of asphaltenes, asphaltene-like heavy resins, and bulk resins are treated as a function of the temperature, as proposed by Mohammadi and Richon35 δa(T ) = δa(T0)[1 − 1.07 × 10−3(T − T0)]

(8)

where T0 is the temperature at a reference state (e.g., T0 = 298.15 K) and δa(T0) = 21.85 MPa0.5 for asphaltenes and heavy resins,36 while δa(T0) = 20.5 MPa0.5 for bulk resins.35 These values can be adjusted on the basis of new findings in asphaltene science. The impact of pressure on the asphaltene solubility parameter is often small and can be ignored. These results are consistent with a number of observations showing 1726

0.5

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Figure 3. Resin and asphaltene gradients in five different oil reservoirs (from left to right): high-GOR volatile oil with virtually no asphaltenes (Shell case study25) and a true molecular solution of perylene-like resin molecules, condensate with a true molecular solution of asphaltene (or asphaltenelike) molecules (Statoil case study26), intermediate-GOR (Marathon case study28) and low-GOR black oil (Chevron case study4,5) with asphaltene nanoaggregates, and mobile heavy oil with asphaltene clusters (Petroecuador case study29,31). Note that the larger clusters produce a gravitational gradient 50× larger than the low-GOR black oil. For the volatile oil, condensate, and intermediate-GOR oil, the GOR gradient helps create the asphaltene gradient. The solid curves are calculated by the FHZ EOS, and the symbols are all of the measured values.

the reservoir fluid. For example, when gas charges into an oil column, the gaseous charge often rises to the top of the reservoir through high mobility streaks, and then the gas can diffuse slowly downward into the oil column. The cubic EOS coupled with a diffusion term can account for the composition versus depth. Then, the FHZ EOS is used to calculate the asphaltene concentration gradient with the assumption of local asphaltenes equilibrated with a local fluid (local GOR and composition) at each small vertical depth interval. The asphaltene concentration gradient in the non-equilibrium hydrocarbon reservoir column is thus obtained, and this can also be used for the analysis of reservoir connectivity and asphaltene phase instability.38 After asphaltene concentrations are obtained at different depths, phase equilibrium calculations can be performed at all depths to check whether the asphaltenes can be stably dispersed or suspended in crude oils using the FHZ EOS with the same set of parameters in the asphaltene concentration gradient calculations. If asphaltenes are unstable, a first type of tar mat (discontinuously increasing asphaltene content versus depth) may be formed at that depth.31 To conduct this analysis, the following equilibrium criteria must be satisfied for both asphaltene and maltene components at that depth: xioil(h)γioil(h) = xiasph(h)γiasph(h)

Flory−Huggins regular solution model. Hence, the activity coefficients in eq 10 are calculated by the Flory−Huggins regular solution model that has widely been used for asphaltene phase instability calculations. In some cases, there is only slight asphaltene instability. In these cases, the asphaltenes can migrate and accumulate at the base of the oil column. This process can create a heavy oil column and tar mat immediately below at the lower portion of the reservoir. For heavy oil, if asphaltenes are stable but their content is as high as tens of percentages, asphaltene clusters are formed on the basis of the Yen−Mullins model and viscosity should be checked because viscosity increases exponentially with the asphaltene content.30,31 Extremely high viscosity may yield immobile extra heavy oil, and the second kind of tar mat may be formed at the base of a heavy oil column.30,31

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APPLICATION OF THE FHZ EOS TO DIFFERENT TYPES OF OIL RESERVOIRS The FHZ EOS has been applied to different types of oils. Figure 3 summarizes the recent application of the FHZ EOS to five different types of oils, which cover an entire range of oils worldwide: high-GOR volatile oil with virtually no asphaltenes, condensates with very low asphaltene content, black oils with a few weight percentages of asphaltenes, and mobile heavy oil with high asphaltene content up to tens of weight percentages. These field studies show that asphaltenes or heavy ends are in different forms in different reservoir fluids, depending upon fluid types (GOR) and asphaltene or heavy end concentrations. The perylene-like resins are molecularly dispersed in the highGOR volatile oil with virtually no asphaltenes (almost colorless) but sufficiently high fluorescence intensity, as

(10)

where superscripts oil and asph represent the oil- and asphaltene-rich phases and xi and γi are the mole fraction and activity coefficient, respectively, of component i (asphaltene and maltene). Because the equilibrium criteria are used at the same depth for both phases, the gravitational term can be canceled out in the FHZ EOS. The FHZ EOS reduces to the 1727

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Figure 4. (Left panel) Light blue crude oil from deep water, Gulf of Mexico.39 Its unusual blue color is due to fluorescence from a specific component perylene (molecular structure shown). (Center and right panels) Two-dimensional fluorescence spectra identifying perylene as dominating the blue fluorescence emission from this crude oil. The long axis of perylene is ∼1 nm.

shown in a case study with Shell.25 The colored condensate possesses a true molecular solution of asphaltene (or asphaltene-like) molecules, as shown in a case study with Statoil.26 Asphaltene nanoaggregates are dispersed in intermediate-GOR oil, as shown in a case study with Marathon,28 and low-GOR black oil, in a Chevron oilfield.4,5 Asphaltene clusters are found in the mobile heavy oil, as shown, for example, in case studies with Petroecuador29,31 and in the Saudi Arabian oilfield.30 For the low-GOR fluids, the simplified FHZ EOS of eq 7 is suitable. The larger asphaltene clusters produce a gravitational gradient 50× larger than the highly undersaturated low-GOR black oil. For the volatile oil, condensate, and intermediate-GOR oil, the GOR gradient helps create the asphaltene gradients. It should be noted that the equilibrium resin or asphaltene distribution versus depth calculated by the FHZ EOS strongly suggests the reservoir connectivity in all of the oilfield reservoirs. The subsequent production proved the analysis. The more detailed discussions are given below. Perylene-Like Resin Molecules in High-GOR Volatile Oil. Juyal et al.39 observed a notable blue crude oil with only traces of asphaltenes from the SARA analysis. A five-ring PAH perylene was identified as the source of the blue color, as shown in Figure 4. Elshahawi et al.25 showed a volatile oil whose GOR decreases from 720 to 463 (m3 m−3) in a 134 m true vertical depth (TVD) oil column in the downdip direction. The optical absorption measurement by DFA is low and not sufficiently robust for such high-GOR oil samples (especially for the shallowest two DFA stations). The difference between colorless (100% light transmission) and almost colorless (99% light transmission) is very difficult to determine. Nevertheless, the fluorescence intensity is much more robust than the OD for this high-GOR volatile oil column. That is, the difference between no fluorescence (0%) versus some fluorescence (1%) is much easier to determine than the OD reduction. In particular, OD baseline issues can become problematic at low OD. The volatile oil has virtually no asphaltene; the heaviest end in this oil is heavy resin. The fluorescence intensity for this oil is linearly related to a fraction of the heavy resin25 because, in the low concentration limit, the fluorescence intensity is linearly related to the OD,40 as shown in Figure 5.

Figure 5. Linear relation between the OD and fluorescence intensity for the high-GOR volatile oil having virtually no asphaltenes. This is expected in the dilute limit.40 Nevertheless, higher in the oil column, the fluorescence measurement remains robust, while the OD measurement becomes uncertain (cf. Figure 6).

To apply the FHZ EOS to this volatile oil column with the large compositional and GOR gradients, the cubic EOS is employed to match the fluid property gradients. The variations of the live-fluid density, molar volume, and solubility parameters with depth have been calculated by the cubic EOS with volume translation. Therefore, all of the parameters, except size of the heavy resin, are obtained for the FHZ EOS. The size of the heavy resin is then determined by matching the DFA-measured fluorescence intensity data. The fitted size is 1 nm, corresponding to the molar mass of 280 g mol−1, which is close to but slightly bigger than that of perylene (250 g mol−1). Perylene is ∼1 nm on its long axis but smaller in other dimensions. It should be noted that the FHZ EOS with the same size of the heavy resin can also predict the OD gradient, as shown in Figure 6. The obtained results indicate that the fluorescence intensity in this high-GOR volatile oil predominantly comes from the heavy resin−perylene-like aromatics. The results also show that the heavy resin is molecularly dispersed in this volatile oil column. The heavy resin molecules are somewhat smaller than the asphaltene sizes stated in the Yen−Mullins model; thus, the gravity term in the FHZ EOS is also smaller, whereas the GOR contrast (the solubility term in the FHZ EOS) dominates the fluorescence intensity (heavy resin) gradient. The equilibrium heavy resin concentration distribution suggests that this highGOR volatile oil column is connected, which is also proven by the other log and production data, with the latter indicating a 1728

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GOCs could be explained by two very different reservoir descriptions: either the reservoir is compartmentalized or there is a single compartment with a small lateral disequilibrium in solution gas. Because asphaltenes partition only to the liquid, they are relatively insensitive to the exact depth of the gas cap. Equilibrated asphaltenes across the reservoir would be a good indication of connectivity, independent of the two different GOCs. The FHZ EOS was applied to this reservoir. The cubic EOS was first used to calculate the fluid property variations, including GOR, molar volume, density, and solubility parameter. Then, the FHZ EOS was used to estimate the OD variation. The results are shown in the right panel of Figure 7 with the adjusted diameter of ∼1.5 nm of the asphaltene molecules (or the asphaltene-like heavy resins). Indeed, the heaviest resins have been shown to be comparable in size to asphaltene molecules.41 At these concentrations, the asphaltene molecules or asphaltene-like resin molecules are dissolved in the condensate as molecules instead of nanoaggregates. It should be noticed that, if we only used the gravity term to model the OD gradient, a very big diameter of asphaltenes (4.6 nm) was obtained, which corresponds to clusters of asphaltene nanoaggregates. This contradicts laboratory and field data. At such a low asphaltene concentration, it is impossible to form asphaltene clusters. In any event, there is no question that the variations in GOR (oil solubility parameter) with depth must be taken into account. The OD at 647 nm follows a consistent trend calculated by the FHZ EOS, except for the deepest points for wells A and B. A bit more OD is usually found near the oil/water contact (OWC) or even at low points in single wells. This topic is currently under investigation. The OD data from the third well, referred to as well C, are also on the same trend curve calculated by the FHZ EOS. The continuous equilibrium distribution of heavy ends in this reservoir indicates that the oil leg is indeed connected. The subsequent production data have proven the connectivity of the reservoir. Therefore, the unexpected 18 m GOC difference is likely caused only by a subtle lateral non-equilibrium. In a normal burial sequence, gas would be the last fluid to come out of the source rock. If gas enters a reservoir with two structural maxima, as depicted in the left panel of Figure 7, there is no way that the gas would fill each maximum equally; thus, unequal GOCs are expected. The process of equilibrating the two GOCs by dissolving gas, diffusively transporting it, and releasing gas is extremely slow even on the scale of geologic time. Consequently, evaluation of this reservoir using the FHZ EOS for heavy end distribution is superior to the use of the cubic EOS for solution gas analysis. Asphaltene Nanoaggregates in Stable Black Oil. Dong et al.28 presented the Marathon field case for a black oil column with GOR of about 180 (m3 m−3). The pressure gradients from two wells are illustrated in the left panel of Figure 8. The subtle difference in the pressure gradients of the two wells made it inconclusive as to whether or not the sand in well 1 is disconnected with the sand in well 2. The FHZ EOS was used to analyze this oil column. Because the fluids have some GOR variations with depth, the cubic EOS is used to perform compositional gradient calculations to obtain the parameters in the FHZ EOS. The result of the asphaltene distribution calculated by the FHZ EOS is shown in the right panel of Figure 8. The asphaltene nanoaggregates with a hard spherical diameter of 2 nm from the Yen−Mullins model were employed in the FHZ EOS predictions. The results from the FHZ EOS

Figure 6. DFA-measured fluorescence intensity and OD gradients for high-GOR volatile oil in a Shell oilfield.25 FL1 means DFA fluorescence at channel 1.

variable mix of the end members. It should be noted that ignoring the GOR contrast in this volatile oil column results in a large heavy end diameter (∼5 nm, corresponding to asphaltene clusters), which contradicts the size of the heavy resin in the volatile oil, and the large size is not physically meaningful. Therefore, the GOR contrast must be taken into consideration. Asphaltene-Like Heavy Resins in Condensate. Condensates with gas caps have very small concentrations of asphaltenes because high concentrations of dissolved gas and light hydrocarbons make them very poor solvents for asphaltenes. In addition, mechanisms of forming condensate reservoirs do not tend to generate asphaltenes. Therefore, there is very little crude oil OD, as determined by DFA in the nearinfrared light. In the Statoil case study,26 the condensate reservoir has a large GOR gradient varying from 445 to 267 (m3 m−3) in the downdip direction and two separate gas caps, as shown in the left panel of Figure 7. Both separate gas caps

Figure 7. (Left panel) Statoil oilfield with two gas caps.26 The two GOCs differ by 18 m TVD. Either there is lateral non-equilibrium or compartmentalization. (Right panel) Variations of OD with depth for the fluids for wells A, B, and C. The fit is consistent with a molecular distribution of asphaltene-like resin molecules. The large 4× gradient of OD in 40 m is dominated by the large GOR gradient, whereas the gravity term yields a secondary contribution. The heavy ends are continuous and equilibrated across the oilfield. Connectivity is indicated. There are redundant DFA measurements increasing reliability of the data with the compositional fluid analyzer (CFA) and live-fluid analyzer (LFA).

are thought to share a common oil leg. However, the two gas/ oil contacts (GOCs) differ by 18 m TVD. If the oil sand is continuous, then the reservoir fluid cannot be in equilibrium because there cannot be two different saturation pressures at one depth (saturation pressure should be equal to formation pressure at GOC). The unexpected 18 m TVD difference of 1729

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Figure 8. (Left panel) In a Marathon case study, pressure data versus relative TVD for a black oilfield with GOR of ∼180 (m3 m−3).28 Pressure gradient analysis is inconclusive with regard to whether or not the formation in the updip well is disconnected with the formation of the downdip well. (Right panel) FHZ EOS suggests that the updip and downdip formations are connected. The subsequent production data confirmed that the FHZ EOS prediction is correct.

Figure 9. (Left panel) Chevron reservoir along with exploration and appraisal wells and the first development well.4,5 The Chevron oilfield consists of two stacked sands (M21A and M21B) that are not in pressure communication; both the “red” sand and “green” sand contain a low-GOR black oil. (Right panel) Variations of OD with depth for the Chevron fluids. The theoretical fit is consistent with an equilibrium distribution of asphaltene nanoaggregates of ∼2 nm in diameter. The gravitational term dominates the OD variation. The “blue sand” also contains an equilibrated asphaltene distribution; however, with half of the color as the other two sands, the blue sand is not connected to either the red or green sand.

suggest that the two wells are connected. The subsequent production data confirmed the results of the FHZ EOS. It should be noted that, if the gravity term is used, only the asphaltene size is ∼3 nm, which is not physically meaningful compared to the Yen−Mullins model. Therefore, the GOR contrast must be taken into account. For low-GOR undersaturated black oil, compositional gradients are usually small because they are less compressible according to Høier and Whitson.2,3 Therefore, variations of oil solubility parameters and properties with depth are small. On the other hand, asphaltenes with relatively low concentrations in black oil have very small influence on density and solubility parameters but have a large influence on fluid viscosity. As mentioned previously, the solubility term in eq 5 enhances the asphaltene gradient, whereas the entropy term reduces the asphaltene gradient. Nevertheless, the combination of the enthalpy (solubility) and entropy terms in eq 5 has a small influence on the asphaltene gradient for low-GOR black oils [typically GOR < 125 (m3 m−3)], and thus, the gravitational term dominates the asphaltene gradient for the low-GOR black oils with relatively low concentrations of asphaltenes. Therefore, the cubic EOS part can be ignored. The Chevron case4,5

shows that the asphaltene gradient can be successfully used to discern the reservoir connectivity using the simplified FHZ EOS of eq 7. This Chevron reservoir, as illustrated in the left panel of Figure 9, has two primary sands (M21A and M21B) that are in different pressure regimes (compartments). The OD gradient results calculated by the FHZ EOS are shown in the right panel of Figure 9. The fitted asphaltene diameter is ∼2 nm by the FHZ EOS. The results indicate that asphaltenes are dispersed as nanoaggregates in this black oil column. In Figure 9, each of the reservoir sands has the same asphaltene gradient using the same asphaltene size; the asphaltene distribution is continuous and equilibrated. Consequently, reservoir connectivity in each reservoir is predicted. This prediction is now known to be correct because the oilfield has gone into production, providing the ultimate test. Betancourt et al.27 reported that a black oil in a 200 m TVD column was analyzed by the DFA and advanced laboratory analytical chemistry methods. The oil samples were taken from two wells with low and similar GOR of ∼125 (m3 m−3); the shallower sample PER-1 is from a depth of 674 m, the deeper sample PER-2 is from 874 m. This is also highly undersaturated 1730

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black oil, whose critical point and bubble point are far away from the formation conditions. The asphaltene content in stock tank oil was analyzed by a standard n-heptane precipitation method. It is impossible to conclude whether or not the oil column is connected in terms of the traditional compositional grading method. Again, coupling the simplified FHZ EOS for asphaltene gradient analysis using the asphaltene diameter of ∼2 nm with the other advanced chemical analyses could give a conclusion that they are connected. Asphaltene Nanoaggregates in Non-equilibrium Oil Columns with Late Gas Charging. Another major success of the FHZ EOS is the capability to account for the gigantic asphaltene gradient in a single near-critical oil column in deepwater, Gulf of Mexico.38 The field map with GOR contour lines is given in Figure 10.

Figure 11. Asphaltene and color gradients calculated by the FHZ EOS in a Shell oil field.38 The GOR gradient is grossly out of equilibrium because of current charging of biogenic methane. The asphaltenes are assumed to be locally equilibrated with the local solution gas content. This simple theory matches the measurements. Moreover, this continuous gradient is consistent with connectivity, as observed in production.

The color variation of 24 bottles of the flashed dead-oil samples from this reservoir is shown in the top panel of Figure 12. The huge color variation is because of a gigantic asphaltene gradient, and the corresponding asphaltene content varies from 0 to 5 wt % over 122 m of vertical relief. The FHZ EOS can reproduce the large asphaltene gradient. It is the large lateral dimension coupled to methane diffusion that helps create this giant asphaltene gradient. Excessive gas (light hydrocarbons) charging into the reservoir can destabilize the asphaltenes, thereby causing the first type of tar mat formation, which is characterized by a discontinuous increase of the asphaltene concentration versus in the hydrocarbon column. A field case was shown, where the excessive gas charge is confirmed by compositional and isotopic analyses of mud gas, thus yielding disequilibrium.31,42 Flow assurance issues were encountered in production streams in this field. Additionally, phase instability of asphaltenes for fluids in well 1 is indicated in Figure 13. Fluids combined from wells 1 and 2 are shown in the picture to the left, while globules precipitated from the well 1 gas stream are shown in the picture to the right. The late gas charge was also taken into consideration by the cubic EOS for this disequilibrium reservoir. The FHZ EOS was then used to estimate the asphaltene concentration gradients by extending to the oil rim and presuming that local asphaltenes are equilibrated with local fluids. Figure 14 shows the asphaltene gradient with depth estimated by the FHZ EOS with the asphaltene diameter of 2 nm. It can be seen that asphaltenes are concentrated at the base of the oil rim. The estimated asphaltenes were checked by the FHZ EOS for phase instability at each depth (solving eq 10). It was found that the asphaltenes at the base of the oil column were destabilized to form a tar mat (a large and discontinuous increase in asphaltene content versus depth). A tar mat was discovered in the core samples downdip, as shown in Figure 15, thus confirming the analysis. Clusters of Asphaltene Nanoaggregates in Mobile Heavy Oil. For heavy oil with little compressibility, GOR is very small and, thus, a GOR gradient is negligible. The maltene concentration hardly changes with depth. However, because of the high concentration of asphaltenes, clusters of asphaltene nanoaggregates can be stably suspended in heavy oil, and because of the gravity term in eq 5, a large asphaltene concentration gradient can be observed in the oil column even

Figure 10. Field map with superposed GOR contour lines exhibiting a large-GOR gradient in a Shell oil field.38 The critical fluid line shows GOR of about 392 (m3 m−3).

Carbon isotope analyses were conducted on the flashed gases from the live-fluid samples. The analysis of the samples collected from the three exploration and appraisal wells and one of the production wells shows that both methane concentrations in the reservoir gas and the ratio of biogenic/ thermogenic gas (by carbon isotope analysis) increase toward the top of the structure. The increase in the methane concentration and the carbon isotope 12C toward the updip can be attributed to active charging of biogenic gas. This active methane charge creates a state of disequilibrium of GOR in the column. To apply the FHZ EOS to this disequilibrium reservoir, first of all, the cubic EOS was used to reproduce the fluid property gradients assuming that the methane influx is 0.78 STD m3 m−2 MY−1 in the downdip direction and that the effective methane diffusion coefficient is approximately 8 × 10−8 m2 s−1, thus yielding a large GOR gradient. All of the parameters in FHZ EOS were then obtained, and the asphaltene size was taken from the Yen−Mullins model with 2 nm. The reservoir was divided into small grid blocks vertically using the onedimension model. Finally, it was assumed that local asphaltenes are equilibrated with local fluids in each small vertical interval, so that the FHZ EOS can be used. The results of the FHZ EOS with methane diffusion are compared to the measured data in Figure 11. The FHZ EOS predictions are in good agreement with the measured data, relating to the large asphaltene variation in this oil column. The local equilibrium asphaltene distribution implies that the reservoir connected, and it was proven by the subsequent production. 1731

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Figure 12. Well-known array of dead-oil samples from this reservoir. The color variation is due to a gigantic asphaltene variation. The FHZ EOS has enabled modeling this asphaltene content for the first time (courtesy of Elshahawi, Shell).

The correlated viscosity results for this live mobile heavy oil at reservoir conditions are shown in Figure 17.29,31 The correlated results are in good agreement with the measured data. The viscosity increases exponentially with an increase in the asphaltene content. This is the important observation in mobile heavy oil. Typically, uniform fluid properties are presumed for simulating mobile heavy oil reservoirs in the oil industry because traditional cubic EOS and viscosity models cannot handle such large asphaltene and viscosity gradients in mobile heavy oil. Viscosity is the key parameter for heavy oil recovery, and how to deal with large asphaltene and viscosity gradients in heavy oil is still challenging for conventional reservoir simulators. Seifert et al.30 show the example of mobile heavy oil in a Jurassic oil field in Saudi Arabia. The conventional black oil is at the crest of the anticline. The mobile heavy oil is along the rim of the anticline. A thick tar mat is below the mobile heavy oil at the OWC. A giant asphaltene concentration gradient was observed in the mobile heavy oil zone, and the asphaltene content changes from 5 to 32 wt %. The simplified FHZ EOS of eq 7 matches the asphaltene concentration gradient for the three wells, which are ∼8 km apart, as shown in the left panel of Figure 18. The fitted asphaltene size is 5.2 nm (clusters) and very close to that in the Yen−Mullins model. In turn, this giant asphaltene gradient produces an enormous viscosity gradient, as illustrated in the right panel of Figure 18. It can be seen that viscosity increases significantly at the base of the heavy oil column. Therefore, the second type of tar mat can form at the base of a heavy oil column simply by a gravitationally induced continuous increase of the asphaltene content in the heavy oil column over geologic time, leading to a huge viscosity at the base of the column. Because viscosity increases exponentially with an increase in the asphaltene content as depth increases, below the mobile heavy oil column, a very thick immobile tar (tar mat) was observed in the oil field. The FHZ EOS and viscosity model were able to describe this oil column in a good agreement with the laboratory measurements. The equilibrium asphaltene distributions imply the reservoir connectivity. In addition, asphaltene destabilization may also occur at the base of this heavy oil column to form the tar mat. Further investigation is under way. Coexisting Asphaltene Nanoaggregates and Clusters of Asphaltene Nanoaggregates in Unstable Black Oil. In stable black oil, asphaltenes are dispersed as nanoaggregates, whereas in mobile heavy oil, asphaltenes are stably suspended as clusters of asphaltene nanoaggregates, as shown previously. If asphaltenes are destabilized in black oil, some nanoaggregates can form clusters, and thus, nanoaggregates and clusters coexist in unstable black oil.

Figure 13. Evidence of asphaltene destabilization is shown in this photograph:31,42 (left) commingled fluid from wells 1 and 2 and (right) precipitated asphaltenes in the well 1 gas stream.

Figure 14. Asphaltene phase instability (tar mat formation) at the base of the gas condensate column caused by a late stage of gas charge, which is confirmed by methane carbon isotope analysis in a Shell case study.31,42

with a small maltene gradient. For mobile heavy oil, the FHZ EOS reduces to the simplified FHZ EOS − gravity term only because the solubility and entropy terms have opposite effects and can be canceled out. A case study with mobile heavy oil was described by the FHZ EOS.29,31 The mobile heavy oil (which is defined as having viscosity less than ∼1000 cP at reservoir conditions) with very low GOR [12 (m3 m−3)] has a significant asphaltene gradient (10−20 wt %) in ∼20 m TVD. The corresponding viscosity gradient is about a factor of 30; hence, this gradient is extremely important for production. Note that, in the relevant sand, the pressure gradient is continuous. The simplified FHZ EOS of eq 7 was used to represent the asphaltene gradient in this oil zone. The results are illustrated in Figure 16. The fitted asphaltene size is 5 nm in diameter (the same as the Yen−Mullins model). The equilibrium distribution of clusters of asphaltene nanoaggregates indicates that the oil zone is connected, which is in accordance with the pressure depletion. 1732

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Figure 15. (Left panel) Tar was observed in the core samples downdip. (Right panel) Thin section showing the presence of tar (black) just above the cemented (pink) section of the sandstone (white). The blue is pore space and not water. Water had no role on the formation of this tar mat.

charge proven by geochemistry analysis. A huge OD gradient was found, ∼10× in ∼80 m. The continuous pressure gradient data show that the oil zone is in pressure communication. The simplified FHZ EOS was used to estimate the asphaltene gradient, as shown in Figure 19. The simplified FHZ EOS matches the DFA data using 90% nanoaggregates (2 nm) and 10% clusters (5 nm). This reservoir pressure is comparable to the asphaltene onset pressure, proving that some asphaltenes were destabilized and consistent with some cluster formation.43 Classical Cubic EOS for Low-GOR Fluids. Zuo et al.44 applied the classical cubic EOS to calculate asphaltene gradients in low-GOR black oil columns. The critical properties of asphaltene components were estimated by the empirical property correlations. The molar mass of asphaltene nanoaggregates (1600−2100 g mol−1) was tuned to match the laboratory and DFA data. Recently, Zuo et al.45 extended the method to mobile heavy oil. The large molar mass of asphaltene clusters was obtained (60 000 g mol−1, corresponding 5.4 nm in diameter). Although the method has worked well for the low-GOR fluids in question, it has the following disadvantages: (1) SARA and compositional analysis data are required as inputs. (2) It cannot be used in real time because of the lack of SARA data. (3) It cannot be used for higher GOR fluids with large GOR gradients because the cubic EOS cannot handle asphaltene gradients in such systems with a reasonable molar mass of asphaltenes or heavy ends. For instance, to model asphaltene/heavy resin gradients for the same high-GOR systems mentioned previously,25,26 a very large size (molar mass = 50 000 g mol−1) of asphaltenes/resins is required to match the measured data. This is not physically meaningful because there are no asphaltene clusters in such high-GOR fluids. Therefore, the cubic EOS can be used only for the lowGOR fluids, which have asphaltene gradients predominantly induced by the gravitational force. For such systems, the simplified FHZ EOS (eq 7) can be applicable and is much simpler and easier to use. It should be mentioned that the statistical associating fluid theory (SAFT) EOS was also employed to model asphaltene gradients for black oil reservoirs with success.46

Figure 16. Significant asphaltene gradient in a mobile heavy oil column of a Petroecuador oilfield.29,31 The asphaltene gradient is in accordance with an equilibrium distribution of clusters of asphaltene nanoaggregates with the diameter of 5 nm. The continuous, equilibrium distribution implies the formation connectivity, which is consistent with but not proven by the continuous pressure gradient.

Figure 17. Significant viscosity gradient in a heavy oil column. A continuous asphaltene gradient with depth results in an exponential increase of heavy oil viscosity.29,31

A black oil has a GOR of ∼140 (m3 m−3).43 The oil column has some GOR gradient and density gradient with depth. A fraction of asphaltenes is destabilized by a late stage of gas 1733

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Figure 18. Huge asphaltene gradients and gigantic viscosity gradients shown in three wells in a Saudi Arabian oilfield.30 (2) Høier, L. Miscibility variations in compositionally grading petroleum reservoirs. Ph.D. Thesis, Norwegian University of Science and Technology, Trondheim, Norway, 1997. (3) Høier, L.; Whitson, C. H. Compositional grading−Theory and practice. SPE Reservoir Eval. Eng. 2001, 525−535. (4) Betancourt, S. S.; Dubost, F. X.; Mullins, O. C.; Cribbs, M. E.; Creek, J. L.; Mathews, S. G. Predicting downhole fluid analysis logs to investigate reservoir connectivity. Proceedings of the International Petroleum Technology Conference; Dubai, United Arab Emirates, Dec 4−6, 2007; SPE 11488. (5) Mullins, O. C.; Betancourt, S. S.; Cribbs, M. E.; Creek, J. L.; Dubost, F. X.; Andrews, A. B.; Venkataramanan, L. Asphaltene gravitational gradient in a deepwater reservoir as determined by downhole fluid analysis. Proceedings of the SPE International Symposium on Oilfield Chemistry; Houston, TX, Feb 28−March 2, 2007; SPE 106375. (6) Pfeiffer, T.; Reza, Z.; Schechter, D. S.; McCain, W. D.; Mullins, O. C. Determination of fluid composition equilibrium under consideration of asphaltenesA substantially superior way to assess reservoir connectivity than formation pressure surveys. Proceedings of the SPE Annual Technical Conference and Exhibition; Denver, CO, Oct 30−Nov 2, 2011; SPE 145609. (7) Mullins, O. C. The modified Yen model. Energy Fuels 2010, 24 (4), 2179−2207. (8) Mullins, O. C.; Sabbah, H.; Eyssautier, J.; Pomerantz, A. E.; Barré, L.; Andrews, A. B.; Ruiz-Morales, Y.; Mostowfi, F.; McFarlane, R.; Goual, L.; Lepkowicz, R.; Cooper, T.; Orbulescu, J.; Leblanc, R. M.; Edwards, J.; Zare, R. N. Advances in asphaltene science and the Yen− Mullins model. Energy Fuels 2012, 26 (7), 3986−4003. (9) Prausnitz, J. M.; Lichtenthaler, R. N.; de Azevedo, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria, 3rd ed.; Prentice Hall PTR: Upper Saddle River, NJ, 1999; p 124. (10) 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. (11) 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. (12) Buckley, J. S.; Wang, X.; Creek, J. L. Solubility of the least soluble asphaltenes. In Asphaltenes, Heavy Oils and Petroleomics; Mullins, O. C., Sheu, E. Y., Hammami, A., Marshall, A. G., Eds.; Springer: New York, 2007; Chapter 16, pp 401−438. (13) 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. (14) Wang, J. X.; Creek, J. L.; Buckley, J. S. Screening for potential asphaltene problems. Proceedings of the 2006 SPE Annual Technical Conference and Exhibition; San Antonio, TX, Sept 24−27, 2006; SPE 103137.

Figure 19. Significant asphaltene gradient.43 The results show 90% nanoaggregates + 10% clusters by the simplified FHZ EOS.

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CONCLUSION The paper reviews recent advances in the FHZ EOS for asphaltene concentration gradients and its applications in oil fields. The FHZ EOS has been developed to integrate recent advances in asphaltene science with DFA technology to address the biggest concerns today with oil reservoirs. This powerful combination of the FHZ EOS, Yen−Mullins model, and DFA technology has been applied successfully to indicate reservoir connectivity from condensates to black oils to mobile heavy oils. In addition, the method has also been used to address nonequilibrium reservoirs with a late gas charge. Two types of tar mats have been successfully described by the FHZ EOS. This novel approach has proven successful in field cases around the world in all manners of reservoirs. The combination of new asphaltene science and new fluid measurement technology is yielding an enormous improvement in reservoir evaluation, with expectations of many varied new applications.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Mullins, O. C. The Physics of Reservoir Fluids: Discovery through Downhole Fluid Analysis; Schlumberger: Sugar Land, TX, 2008. 1734

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Energy & Fuels

Review

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dx.doi.org/10.1021/ef301239h | Energy Fuels 2013, 27, 1722−1735