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Ind. Eng. Chem. Res. 2008, 47, 7094–7103
Mathematical Modeling of the Destabilization of Crude Oil Emulsions Using Population Balance Equation Roberto E. P. Cunha,†,§ Montserrat Fortuny,†,‡ Claudio Dariva,†,‡ and Alexandre F. Santos*,†,‡ Programa de Engenharia de Processos, UniVersidade Tiradentes, Aracaju 49032-490 SE, Brazil, Laborato´rio de Engenharia de Petro´leo, Instituto de Tecnologia e Pesquisa, AV. Murilo Dantas 300, Aracaju 49032-490 SE, Brazil, and PETROBRAS/ENGP/EIPA, R. Acre 2504, Aracaju 49080-010 SE, Brazil
In this work, the stability of water-in-crude oil emulsions generated in laboratory was investigated using a phenomenological mathematical model based on the population balance equation, considering different phenomena such as the binary coalescence of water droplets, the interfacial coalescence with the resolved water phase, the diffusion of the dispersed phase, and droplet settling. The resulting population balance equation (PBE) was a nonlinear hyperbolic integro-partial differential equation, which for our particular case required numerical techniques for resolution. The PBE was converted into a system of partial differential equations using Kumar’s fixed-pivot technique. The spatial coordinate was discretized using the finite volume method and a first order upwind scheme, while the discretization of the time coordinate was based on a semi-implicit approach. On the basis of this algorithm, the mathematical model was solved against experimental results of water-in-crude oil emulsion destabilization runs, providing suited predictions of droplet size distribution profiles, and of both emulsified water and free-water volumes. 1. Introduction In the petroleum industry, the crude oil production is often associated with high salinity produced water, gas, sediments, and other contaminants. To achieve refinery specification, all these oil contaminants must be segregated and removed. The water hindered in the petroleum can be either under the free or emulsified form with the oil. The emulsified water can represent about 60% of the total water and, therefore, should be separated in the production gravitational separators and coalescing treaters, to achieve a maximum of 1% water content.1 Depending upon the crude oil source and on the production scheme, very tight water-in-crude oil emulsions can be formed during the crude oil production, making the breakup of these emulsions a difficult task. The stability of water-in-crude oil emulsions has been viewed as one of the greatest challenge problems in the primary separation of crude oils.2 The comprehension of the demulsification mechanisms involved in these systems is very complicated due to several factors such as the complex composition of the natural emulsifiers, the not well-known stabilization mechanisms, and the strong influence of the experimental conditions (water content, aqueous phase composition, droplet size distribution, temperature, emulsion age, etc.) on the stability of the water-in-crude oil emulsions.3 The general demulsification procedure found in the petroleum production facilities to resolve a water-in-crude oil emulsion into bulk phases of oil and water can be viewed as a three stage process involving, (i) destabilization, (ii) coalescence, and (iii) gravity separation. In short, the destabilization stage involves the weakening of the stabilizing effect of the natural emulsifiers that form a film surrounding the dispersed water droplets. This is usually accomplished by adding heat and/or a properly selected interfacially active chemical compound to the emulsion. The coalescence stage occurs when the film surrounding the * To whom correspondence should be addressed. Tel.: +55 79 32182115. Fax: +55 79 32182190. E-mail:
[email protected]. † Universidade Tiradentes. ‡ Instituto de Tecnologia e Pesquisa. § PETROBRAS/ENGP/EIPA.
water droplets is drained, allowing the contact between droplets that coalesce into larger droplets. This is generally accomplished by imposing a period of moderate agitation or by subjecting the destabilized emulsion to an alternating electric field, yielding high rates of contact of dispersed water droplets. The gravity separation stage requires sufficient residence time and a favorable flow pattern in a tank or vessel that will allow the coalesced droplets of water to separate from the oil.1 As a consequence, demulsification plants depend on the treating temperature, chemical usage and physical size of treating equipment. The design of a system for treating crude oil emulsions has been traditionally relied on experience and empirical data from other wells or fields in the area and on laboratory experiments.4,5 Numerous experimental and theoretical studies have also been presented in the literature in order to improve the understanding of mechanisms that may influence the crude oil emulsion destabilization. Traditional laboratory techniques based on droplet size distribution analyses and the so-called “bottle test”, which consists of determining by inspection the amount of water that separates from a quiescent emulsion sample with time, are among the main experimental techniques used in laboratoryscale investigations to evaluate the demulsification process. Due to their simplicity, these laboratory techniques have been also employed in the petroleum field to tune the operation conditions of the separation facilities, including the temperature, the amount of demulsifier, and the residence time. Nevertheless, these experimental approaches are unable to provide information on the desestabilization mechanisms. For instance, “bottle tests” provide a means for estimating ranges of treating temperature and retention time for design purposes. However, these tests are static in nature and do not model closely the dynamic effects of dispersed water droplets and the coalescence that occur during actual flow of crude oil emulsions.1,4 On the other hand, theoretical studies based on the joint use of mass balance and Stokes law have been proposed in the literature to simulate the destabilization of petroleum emulsions or to design separation vessels.4,6 In fact, the main phenomenon taken into account in these models is the droplet settling, which can be easily probed by experimental measurements of average droplet sizes and
10.1021/ie800391v CCC: $40.75 2008 American Chemical Society Published on Web 08/06/2008
Ind. Eng. Chem. Res., Vol. 47, No. 18, 2008 7095 Table 1. Crude Oil Characteristics property/component
units
value
density WC salinity TAN viscosity
(deg API) wt % mg NaCl/L of crude oil mg KOH/g crude oil cP
22.8 0.6 451.4 0.74 246.4 at 38 °C 134.0 at 50 °C 92.2 at 60 °C
SARA analysis saturated aromatics resins asphaltenes
wt wt wt wt
47.4 21.7 25.5 5.4
% % % %
retention times. Despite interesting pieces of information concerning the demulsification process can be obtained by either “bottle tests” or mass balance combined with Stokes law, much work remains to be done in terms of generating robust mathematical descriptions of the water-in-crude oil destabilization process. Useful mathematical models based on population balance equations (PBE) have been developed and implemented to describe the evolution of dispersed systems, taking into account their dynamics as a result of a set of events such as coalescence, breakage, nucleation, settling, and growth of particles or flocs, droplets, bubbles, crystals, etc.7-15 Each particular event should be described in accordance with the dispersed phase properties, for instance, the rate of coalescence between particles and the settling rate of one particle depend on a set of parameters including the diameter of the involved particle, and the physical properties of the continuous phase (e.g., viscosity, density, temperature). As a consequence, PBE models usually consider two types of coordinate systems: internal coordinate, which represents quantitative properties of the dispersed phase (e.g., volume, mass, density, age, etc.), and the external coordinate which stands for the particle position in the physical space. The resolution of the PBE model has allowed for predicting the entire particle size distribution in a number of systems.15 However, in this class of models, the number of works published dealing with crude oil emulsions is rather limited. In the current work, a general mathematical model based on population balance equations is proposed to describe water-incrude oil destabilization processes. This model includes binary coalescence of water droplets, interfacial coalescence with the resolved water phase, the diffusion of the dispersed phase and droplet settling. The solution techniques for solving the model are outlined, and simulation results are presented for a typical case of crude oil emulsion destabilization, as well as comparisons with experimental results. 2. Experimental Details 2.1. Crude Oil Characterization. An experimental study was conducted to evaluate the destabilization performance of water-in-crude oil emulsions prepared in the laboratory. A Brazilian crude oil was sampled in the petroleum field and used in this study. The characteristics of this crude oil are summarized in Table 1, and the techniques used in its characterization are described as follows. The dynamic viscosity of the crude oil was determined using a rotational rheometer (Physica Rheolab MC1, from Anton Paar) equipped with a heating jacket. The analysis consisted of measuring the shear stress as a function of the shear rate keeping the sample at the desired temperature ((0.3 °C). The water content (WC) of the crude oil was determined by the Karl Fischer (KF) reagent method, in accordance with
ASTM D-1744 procedures.16 The solvent used during the analysis was a mixture of dry methanol and chloroform (20%, v/v). For standardization of the KF reagent, distilled water was solubilized into the solvent cited before. A Metrohm KF titrator (model 836 Titrando) equipped with a double platinum electrode was employed during the water content determination tests. The salinity of the crude oil was determined using the electrometric method according to ASTM D-3230 procedures.17 The total acid number (TAN) was determined by potentiometric titration of the crude oil with alcoholic potassium hydroxide (KOH) solution, in accordance with the ASTM D-664 test method.18 Prior to each titration, crude oil samples were dissolved in a 50% v/v toluene/isopropanol solution. The same automatic titrator used for Karl Fischer analysis (Metrohm 836 Titrando) was employed for the acid number determination, however, equipped with a combination electrode suitable for nonaqueous titrations. Such an electrode consisted of a glass electrode combined with a silver/silver chloride (Ag/AgCl) reference electrode built in the same electrode body. The acid number is then described by the mass of KOH used to titrate sample per weight of crude oil (mgKOH/g oil). SARA analysis was performed at Petrobras R&D Centre, where a standard chromatographic procedure has earlier been developed for the semipreparative separation of crude oils and related materials into the four SARA fractions. 2.2. Emulsion Preparation and Characterization. The emulsions were produced according to a standard protocol considering a pre-emulsification stage and an emulsification stage. Prior to the pre-emulsification stage, the crude oil was shaken vigorously to ensure homogeneity before sampling and heated (
