Steady-State Multiphase Flow—Past, Present, and Future, with a

Article pubs.acs.org/EF

Steady-State Multiphase FlowPast, Present, and Future, with a Perspective on Flow Assurance Mack Shippen* Schlumberger SIS, Houston, Texas 77056, United States

William J. Bailey Downloaded via NAGOYA UNIV on June 25, 2018 at 13:00:50 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

Schlumberger−Doll Research, Cambridge, Massachusetts 02139, United States ABSTRACT: A monumental amount of research and development work has been invested in multiphase flow modeling over the past 50 years. Yet, many challenges remain as we incorporate additional phases, account for exotic fluids, and push our simulation tools to their limits in the desire to optimize even more-complex production systems fraught with difficult flow assurance issues. A visual history of the evolution of steady-state multiphase flow models will be presented, leading to the current “state-of-the-art”. Looking toward the future, it is important that the models be advanced to address areas of greatest uncertainty and align with trends in field development strategies. The authors’ views of the top five areas of reseearch and development (R&D) necessary for these purposes will be presented.

■

For systems in operation, multiphase flow studies provide insight into which parameters may be adjusted to maximize production, efficiency, and, ultimately, net revenue. Such operational parameters include gas lift injection rates, pump speeds, choke settings, and so on. More-advanced analysis of multiphase systems further explores the impact of specific multiphase flow characteristics such as flow pattern, liquid holdup, and slug properties. These characteristics are used for fluids management (pigging, slug characteristics),1 prediction of erosion and corrosion, prediction of solids deposition, and identification of unstable flow (heading or liquid loading in wells and severe slugging in risers). Collectively, these applications fall within the flow assurance domain, with steady-state simulation serving as the basis for analysis and often the precursor for moredetailed transient simulation. Recent advances in modern software tools now provide the means to extend the engineering concepts (particularly for subsea tiebacks) to a broader landscape which can now include the complete flowing system from reservoir through the surface facilities and even beyond to the fiscal meter. The present article aims to provide background and context on the development of the steady-state multiphase flow models in use today, capture the current “state-of-the-art” and recommends likely areas for future research and development work. Practical Dimensionality. Our article is restricted to onedimensional, steady-state, multiphase flow (MPF) models. At first glance, this may appear somewhat simplistic and even confining. Such a view, however, is not correct, because such

INTRODUCTION The petroleum industry has dealt with multiphase flow for well over a century, although attempts to characterize multiphase flow in a more rigorous mathematical context began in earnest about 60 years ago. Over the past 30 years, however, engineers have increasingly relied upon simulation software to model multiphase flow for a variety of applications ranging from the front-end design of production systems to real-time optimization of operations. Today, both steady-state and transient multiphase flow models are firmly embedded in simulation tools to allow study of the behavior of the entire production system from the reservoir to the separator and beyond. This article focuses on steady-state two-phase (gas and liquid) and three-phase (gas, oil, and water) flow, where a rich diversity of models and approaches exist in the literature. While the presence of solids, complex fluids, and flow with four (or more) phases is real, such flows are beyond the purview of this work. Nevertheless, complex fluids are the subject of ongoing research and is discussed later as one of the main research and development (R&D) challenges facing the industry today. The most basic role of a steady-state multiphase flow model is to provide a relationship between the flow rate and pressure change along a single conduit. Combined with inflow performance relationships from the reservoir, and models for downhole and field equipment, theoretical production (or injection) capacity for the system may be calculated. From this standpoint, a number of design workflows may be performed, including: • The behavior of the lower completion design (reservoir contact), • The response of the upper completion design (tubing and artificial lift systems), and • The impact and proper design of surface equipment and connecting flowlines. © 2012 American Chemical Society

Special Issue: Upstream Engineering and Flow Assurance (UEFA) Received: February 21, 2012 Revised: June 8, 2012 Published: June 8, 2012 4145

dx.doi.org/10.1021/ef300301s | Energy Fuels 2012, 26, 4145−4157

Energy & Fuels

Article

Figure 1. Annotated “scale plot” showing the time scale (in seconds) and length scale (in meters) with aspects relating to multiphase flow overlaid (source: G. Oddie, Schlumberger−Gould Research, Cambridge, U.K., private communication, 2011). Chemistry-related processes are also shown close to the “1 mm/s” contour. Detonation (in red) is located above the “1500 m/s” contour and cavitation is shown in orange. The blue region and text relates to the flowing petroleum system (up to the separator) are, quite notably, located roughly along the “1 m/s” contour. The term “Hyd. Slugs” denotes hydrodynamic slugs.

models have proven consistently reliable in the petroleum industry and will continue to do so for the foreseeable future. As we shall see, these models are by no means complete and there remains a need for further research and development to improve them. Naturally, one would ask how additional dimensions of space and time could be applied for the purposes of modeling petroleum production systems with applications in flow assurance. In short, the added dimension of time is of greater practical interest than the added spatial dimensions. Steady-state and transient modeling are generally complementary, rather than competitive, and are often used in tandem for flow assurance purposes. For example, hydrodynamic slug flow can be modeled using steady-state models while terrain-induced slugging requires transient modeling, as does the accurate portrayal of in situ conditions of shutdown and startup, which is essential for the purposes of flow assurance. Inclusion of additional spatial dimensions have trailed that of time, owing both to the complexity and computational power required as well as the utility of providing this additional information. Additional spatial dimensions require the solution of the fundamental transport equations governing fluid dynamics. Generally, this involves a numerical solution of the Navier− Stokes equations using computational fluid dynamics (CFD) software code. [See Darrigol2 for a good explanation and history of the Navier−Stokes equations.] In petroleum systems, CFD has only a specific, small-scale, application and has not been utilized for large-scale multiphase flow in pipes beyond academic studies. Nevertheless, CFD has provided insight into our understanding of fundamental physical mechanisms of multiphase flow behavior which may be applied in the development and validation of closure relationships. Putting Scale into Perspective. The topic of multiphase flow itself covers a much broader spectrum of applications than modeling petroleum production systems. These include:

chemistry, microfluidics (flow through membranes), combustion, cavitation, detonation, and general thermodynamic processes. To assist in distinguishing between various applications, we can consider their respective length and time scales and plot them accordingly, as shown in Figure 1, which has time on the x-axis and length on the y-axis. Linear contours for the various constant velocities can then be overlaid. By placing on this plot particular aspects of multiphase flow, it becomes evident that issues of interest pertaining to conduit flow lie roughly along the “1 m/s” velocity diagonal (in blue), along with various flow patterns located according to their own characteristic length and time scale. It is worth noting that slug flow occupies a wide range on both scales but remains roughly on the “1 m/s” velocity contour. The more dispersed (i.e., bubbly) flow patterns have typically shorter time scales and even smaller length scales, but these also fall on the “1 m/s” contour line. Issues related to chemistry, formation damage, and thermodynamics are located in a region somewhere below the “1 mm/s” line (as labeled). [The term “formation damage” refers to damage caused by the ingress of drilling fluid into the formation due to excessive downhole pressure as a result of having too-high mud weight.] Detonation, on the other hand, involves significantly shorter timeframes and much higher velocities. Figure 1 thus provides a means to visualize time- and length-scale aspects of any particular multiphase flow problem. This so-called “scale plot” is, of course, incomplete because other applications (e.g., combustion) can be added as necessary.

■

THE PAST: A BRIEF HISTORY OF MULTIPHASE FLOW MODELING In 1992, Brill and Arirachakaran3 presented a classification to distinguish multiphase flow models based on the level of physics used to derive them (the vertical axis in Figure 2). These authors also identified three general stages in the 4146

dx.doi.org/10.1021/ef300301s | Energy Fuels 2012, 26, 4145−4157

Energy & Fuels

Article

Figure 2. Evolution of multiphase flow modeling, showing a selection of the more widely used models. The timeline (x−axis) is associated with two criteria: Flow Equation Formulation (upper) and Engineering Application (lower). The vertical axis increases with model complexity and is subdivided into five general “categories”. The various models credited in this figure, from bottom-left (the earliest) to the top-right, are as follows: Single-Phase: Darcy4 (1857) and Weisbach5 (1845), Moody6 (1944) (see the work of Brown7 for historical development). Empirical “A”: Lockhart and Martinelli8 (1949); Poettmann and Carpenter9 (1952); Baxendell and Thomas10 (1961). Empirical “B”: Drift flux (Zuber and Findlay,11 1965; and Holmes,12 1977); Hagedorn and Brown13 (1965); Flanigan14 (1958), Eaton et al.15 (1967), and Dukler16 (1969); Gray17 (1974). Empirical “C”: Duns and Ros18 (1963); Orkiszewski19 (1967); Beggs and Brill20 (1973); Mukherjee and Brill21 (1985); SLB Drift-Flux22,23 (2005). Mechanistic: Aziz, Govier, and Forgarasi24 (1972); Taitel and Dukler25 (1976); Hasan and Kabir26 (1988); Xiao et al.27 (1994); Ansari et al.28 (1994); Petalas and Aziz29 (2000); TUFFP Unified30,31 (2003); Bendiksen et al.32 (1990); Danielson et al.33 (2005).

evolution of multiphase flow research, which are shown on the horizontal time scale in Figure 2, labeled “Flow Equation Formulation”, namely: • “The Empirical Period” (1950−1975): These models relied heavily on fitting experimental and/or field data and, therefore, were correlations in the true sense and were limited in terms of both accuracy and breadth of application. • “The Awakening Years” (1975−1985): In response to the growing realization of the shortcomings of the empirical approach, research started to focus on a more fundamental treatment of the underlying physics. • “The Modeling Years” (1980−present): The current era has seen the emergence of more-generalized multifluid models based on combined momentum equations and flow regime transitions incorporating fundamental physics such as force balances and stability analysis. Although more accurate overall, many closure relationships still, however, remain empirical in nature.

• Intuition: No rigorous solutions were available and experience and “engineering intuition” were commonly applied. • Graphical: Improved understanding of such flowing systems resulted in graphical methods such as nomographs to help solve some multiphase flow problems. • Steady-State: With the advent of more accessible computing and improved fundamental insight into multiphase flow, steady-state analysis has been applied to the modeling of wells (NODAL), pipelines and, eventually, large complex networks. This solution gained rapid acceptance in the industry and represented a step change in our ability to model system behavior. • Transient: This came about in the late 1980s, building heavily on advances in the nuclear industry, and realized a long-held need to model transient events such as shutdown, startup, and terrain-induced slugging. • Coupled: Around the mid-1990s, efforts to couple reservoir simulation and wellbore and network models were being realized. This coupling effort was later extended to consider more complex gathering networks, process facilities, export pipelines and, finally, the fiscal meter. Figure 2 illustrates the historical model development over these periods and shows the general trend of how models have

A second time-based scale has been added to Figure 2, labeled “Engineering Application”, which chronicles advancements in the methods applied to multiphase flow engineering solutions, namely, 4147

dx.doi.org/10.1021/ef300301s | Energy Fuels 2012, 26, 4145−4157

Energy & Fuels

Article

Table 1. Types and Examples of Closure Relationships (Adapted from Ellul et al.38)a Flow Regime closure relationship for:

stratified flow

annular flow

slug flow horiz./incl.

interfacial shear/friction factor wall−gas shear/friction factor wall−liquid shear/friction factor liquid droplet entrainment slug frequency slug velocity slug length bubble entrainment/slug holdup bubble diameter droplet diameter wetted wall fraction

A, B, P, Q A, B B, C, N, O

B, F, V

P, Q

D, N, O E, G

N, O G, J, T, Z G, K, M G, L H, I, R W W X, S

V, Y X, S

slug flow vertical

bubbly flow

N, O

N, O

M R

U W W

F

a

Key: A, Taitel and Dukler25 (1976); B, Laurinat and Hanratty39 (1984); C, Cheremisinoff and Davis40 (1979); D, Hewitt41 (1982); E, Oliemans et al.42 (1986); F, Wallis43 (1969), G, Creare, Inc.44,45 (1986); H, Gregory et al.46 (1978); I, Fabre et al.47 (1983); J, Gregory and Scott48 (1969); K, Zuber and Findlay11 (1965); L, Dukler and Hubbard49 (1975); M, Bendiksen50 (1984); N, Spedding and Hand51 (1997); O, Blasius52 (1913); P, Andritsos and Hanratty53 (1987); Q, Andreussi and Persen54 (1987); R, Zhang et al.30,31 (2003); S, Zhang and Sarica55 (2010); T, Al-Safran56 (2009); U, Nydal and Andreussi57 (1991); V, Ambrosini et al.58 (1991); W, Andreussi et al.59 (1999); X, Grolman60 (1994), Y, Al-Sarkhi and Hanratty61 (2002), Z, Hill and Wood62 (1994). Note: The terms “Horiz.” and “Incl.” refer to horizontal and inclined flow, respectively.

used. Once the flow pattern is established, the appropriate holdup and friction factor is applied. Acceleration pressure gradient may also depend on the flow pattern. • Mechanistic (or Phenomenological): This class of model solves the combined momentum balance equations for each phase and are sometimes referred to as “two-fluid” or “multi-fluid” models. Continuity is preserved within them by simultaneous mass balances on the fluids (sometimes referred to as “fields”), depending on how the phases are grouped. Flow patterns and their transition criteria are either decoupled from (are explicit), or solved with (are implicit), the solution of the momentum equations used. Mechanistic models vary in the degree of empiricism used to formulate their closure relationships and, as such, represent a spectrum of complexity. Some minimize their reliance on empiricism by employing as much from first principals as possible (for example, the Fernandez et al.36 vertical slug flow model), although some empiricism is unavoidable to enable closure. [The Fernandez et al model comprises some 22 simultaneous equations that describe, in detail, the hydrodynamic behavior of gas− liquid slugs in vertical pipes. Even a model as refined as this still possesses some empiricism to enable closure.] On the other hand, other such models (e.g., Xiao et al.1 and Ansari et al.28) have a greater reliance on empirical closure relationships. Seeking Closure. While the classification presented in Figure 2 captures models in a form complete enough to be commonly used in practical well and pipeline modeling applications (and, therefore, are most recognizable to the practicing engineer), some of the key contributions in recent years have been from researchers in the form of closure relationships that are embedded into the modern mechanistic modeling frameworks. This area also has evolved to accommodate broader ranges of flow conditions and move toward a more fundamental treatment of the basic physical mechanisms to characterize these phenomena. Table 1 lists some commonly used closure relationships that have been developed in recent years. A more complete treatment of

adopted more fundamental physics and influenced further work. The desire for models to generalize across broader conditions is reflected in the number of phases considered and the range of inclination angles that are valid. Other aspects of generalization not captured in this figure include the evolution of models to scale-up to larger pipe diameters and cope with broader ranges of fluid properties such as viscosity. Generally, these effects are incorporated into various closure relationships that comprise the overall model. The classifications stated on the vertical axis of Figure 2 are as follows: • Single-Phase Homogeneous: No-slip, no flow pattern. The friction factor is based only on the mixture Reynolds number34 with volume-weighted average density and viscosity for all phases. [Refer to Rott35 for an excellent review of the Reynolds number and its use in the power law.] This is often called the “no-slip” model. This approach is generally not used in practice, except with single-phase simulators to provide a quick approximation of multiphase flow effects (often with tuning factors). This approach may also be used to benchmark the improvements gained from considering slip effects of more-refined multiphase models. • Empirical Category “A”: No-slip, no flow pattern. The mixture density is calculated based on the input gas− liquid ratio and both phases are assumed to travel at the same velocity. These correlations adjust only the twophase no-slip friction factor to match limited sets of experimental and/or field data. No distinction is made for flow patterns. • Empirical Category “B”: Slip is considered; however, flow pattern is not considered. A correlation is required for both liquid holdup and the friction factor. Because the liquid and gas can travel at different velocities, a method must be provided to predict the fraction of pipe occupied by each phase. The same correlations used for liquid holdup are used for all flow patterns. • Empirical Category “C”: Slip between phases is considered and the flow pattern is considered. Correlations to predict liquid holdup and the friction factor as well as methods to predict the flow pattern are 4148

dx.doi.org/10.1021/ef300301s | Energy Fuels 2012, 26, 4145−4157

Energy & Fuels

Article

Table 2. Comparison of TUFFP, LedaFlow Point Model (Leda-PM), and OLGAS Three-Phase Flow Models Model Characteristic

TUFFP Three-Phase

Leda-PM Three-Phase

OLGAS Three-Phase

continuity equationsa

three mass equationsc − gas core − oil film − water film

nine mass equations − gas bulk + gas bubbles in oil and water − oil bulk + oil droplets in gas and water − water bulk + water droplets in gas and oil

five mass equationsc − gas − oil film and oil droplets − water film and water droplets

momentum equationsa

three momentum equations − gas pocket in slug − oil and water in film zone − oil and water in the slug body

three momentum equations − gas bulk + oil and water droplets − oil bulk + gas bubbles and water droplets − water bulk + gas bubbles and oil droplets

three momentum equations − gas and liquid droplets − hydrocarbon film − water film

μLiquid Modelb

Brinkman66

continuous phase

Pal and Rhodes67

gas−liquid flow regimes

− − − − −

stratified intermittent annular bubbly dispersed bubble

− − − − −

stratified smooth stratified wavy slug annular bubbly

− − − − −

stratified smooth stratified wavy slug annular bubbly

oil−water flow regimes

− − − − −

stratified annular dispersed oil in water dispersed water in oil fully mixed (emulsion)

− − − − −

stratified smooth stratified wavy dispersed oil in water dispersed water in oil fully mixed (emulsion)

− − − − −

stratified smooth stratified wavy dispersed oil in water dispersed water in oil fully mixed (emulsion)

The number of equations used may be reduced for certain flow patterns. bRefers to the default method; additional options may be configured. Fractions for gas bubbles/liquid entrainment explicitly considered with closure relationships.

a c

The key recommendations made from this activity are summarized as follows: (1) Improve understanding of flow pattern development and prediction for a broader parameter set (diameter, fluid properties, etc.). (2) Improve understanding of dispersed systemsparticularly the interaction between the continuous and discontinuous phases as a function of turbulence. (3) Leverage first principles (CFD) to better understand the fundamental physics. (4) Improve instrumentation for multiphase experiments to more accurately isolate and measure specific properties. (5) Improve the multifluid modelparticularly, the stability and closure relationshipsand optimize to best suit the practical application. Not surprisingly, as directors of two of the most prominent and accessible industry-supported research consortia in this field [Professor Brill is with TUFFP (the Tulsa University Fluid Flow Projects, University of Tulsa) and Prof. Hewitt is with TMF (Imperial College, Department of Chemical Engineering)], a series of research studies soon followed that concentrated specifically on these areas. While these lists are not mutually exclusive, each research program focused on addressing these problems. The result, combined with work from other research institutions, has significantly advanced our understanding of multiphase flow phenomena and resulted in greatly improved predictive models.

closure relationships for mechanistic models is provided by Shoham.37

■

FUTURE VISIONS: 20 YEARS AGO Before discussing the current “state-of-the-art” in multiphase flow and future needs, it is worth reflecting on the state of technology around 1992, as captured by two prominent figures in the field: Professor James Brill (University of Tulsa) and Professor Geoff Hewitt (Imperial College, University of London, U.K.). With the benefit of hindsight, each published, quite independently, what turned out to be prescient views of where research activities should focus to further improve our understanding of multiphase flow in conduits and their potential applications. In their 1992 paper, Brill and Arirachakaran3 identified several areas of research that they felt required further study, restated in condensed form as follows: (1) Improve treatment of inclination effects (particularly for deviated and horizontal wells and downward flow). (2) Improve models to account for terrain effects, particularly hilly terrain pipelines. (3) Improve our understanding and the modeling for 3phase (gas, oil, and water) flow, particularly for horizontal and near-horizontal flow. (4) Continue to develop and improve closure relationships. (5) Validate models under field-scale conditions. In June 1992, an international workshop on multiphase flow was held at Imperial College that attracted many notable figures in the field. Professor Hewitt summarized the results63 of several breakout sessions where independent groups of experts were asked to identify the most critical areas for future research.

■

THE PRESENT: ARE WE THERE YET? Steady-state multiphase flow simulation tools are commonplace today and the practitioners, the vast majority of whom have little in-depth exposure to multiphase flow theory, are often 4149

dx.doi.org/10.1021/ef300301s | Energy Fuels 2012, 26, 4145−4157

Energy & Fuels

Article

Leda-PM were commercialized along with the LedaFlow transient simulator in 2011. The model is the result of ∼10 years of research and has been developed based on experiments collected at the SINTEF Multiphase Flow Laboratory. The existing TILDA database used in the development of OLGA was augmented with additional experiments. In addition, the models have been validated with field data supplied by ConocoPhillips and Total. TUFFP Unified. The TUFFP Unified Mechanistic Model is the collective result of many research projects performed by the Tulsa University Fluid Flow Projects (TUFFP) research consortium, established in 1973. The Two-Phase Model30,31 was first published in 2003 and the Three-Phase model was published in 2006.68 The principal concept underlying the model is the premise that slug flow shares transition boundaries with all the other flow patterns. The flow pattern transition from slug flow to stratified and/or annular flow is predicted by solving the momentum equations for slug flow. The entire film zone is treated as the control volume and the momentum exchange between the slug body and the film zone is introduced into the combined momentum equation. This approach differs from traditional methods of using separate models for each transition. The advantage of a single hydrodynamic model is that the flow pattern transitions, slug characteristics, liquid holdup, and pressure gradient are implicitly related. The closure relationships included in the model are based on focused experimental research programs at University of Tulsa and elsewhere. As new and improved closure relationships become available, the TUFFP Unified Model is updated and validated. Accuracy and a “Rule of 10”. How accurate are these “state-of-the-art” steady-state models? This is one of the most frequently asked questionsboth in practice and in academiaand is ultimately the reason why this field of research remains lively. We introduce the “Rule of 10” as a rough guide to assessing the accuracy of these predictions. According to this “rule”, the current unified mechanistic models are generally quite reliable with an expectation of predictive accuracy of ±10% for holdup and pressure gradient when applied within these ranges: • stable flow < operational flow rate < erosional limits • deviation angles in the range of θ ± 10° upward (vertical) or horizontal • liquid holdup, hL ≳ 10% • water and oil holdups, hw.o ≲ 10% (relative to total liquid) for emulsion-forming fluids • internal pipe diameters, D ≲ 10 in. • oil viscosities, μo ≲ 10 cP Despite the fact that each of the aforementioned models incorporate research investments on the scale of tens of millions of dollars, when applied beyond these limits, confidence in the predictive accuracy suffers and the degree to which the inaccuracies manifest themselves depend both on the model’s framework and especially its underlying closure relationships, which are not always transparent and open to scrutiny. For systems in operation, it is possible to tune the models to match field data; however, this must be done with discretion to avoid absorbing discrepancies unrelated to multiphase flow: such as errors in fluid property estimates and measurement uncertainty. Adjustments in friction and holdup correction

faced with the increasingly daunting task of selecting a multiphase flow model from among many. Those who do not appreciate the historical context, limitations and applicability of the various choices are justifiably tempted to choose a model deemed to be the most universally applicable, which is generally one with a perception (correct or otherwise) of high development cost. Still others may choose older models that, from past experience, have a proven track record. Indeed, the Hagedorn and Brown13 vertical flow model, published in 1965 and subsequently revised, has been shown to perform well against modern mechanistic models in comparative studies.28,64,65 With experience, the general bias of such models are often better understood than the constantly evolving class of unified, mechanistic models. Nevertheless, among the plethora of models advanced, a select few have emerged that are capable of modeling such a broad range of flow conditions to be considered truly “state-ofthe-art” today. These models include the OLGA Steady-State Model (OLGAS), the LedaFlow Point Model (Leda-PM), and the TUFFP Unified Model. These models are applicable for both two-phase gas−liquid and three-phase gas−oil−water flow for all inclination angles, pipe diameters, and fluid properties. A brief description of the development of the models follows, along with some key characteristics that are presented in Table 2. OLGAS. The OLGAS mechanistic model is the steady-state version of the multiphase flow model incorporated in the widely used OLGA transient simulator, commercialized by SPT Group (Norway). [SPT Group was purchased by Schlumberger in 2012.] The model has evolved considerably since its introduction in the 1980s. The OLGAS Two-Phase model32 was first commercialized in 1989 and the OLGAS Three-Phase model was introduced in 2002. The OLGAS models are refined continuously and are released approximately annually. OLGAS is based, in large part, on data from the SINTEF multiphase flow laboratory at Tiller, near Trondheim, Norway. The test facilities were designed to operate at conditions that approximated field conditions with oil, gas, and water as test fluids. The test loop is 2600 ft long with pipes 8 and 12 inches in diameter. Operating pressures of 300−1320 psia were studied. Gas superficial velocities of up to 43 ft/s, and liquid superficial velocities of up to 13 ft/s were obtained. In order to simulate the range of viscosities and surface tensions experienced in field applications, different hydrocarbon liquids were used (naphtha, diesel, and lube oil). Nitrogen was used as the gas. Pipeline inclination angles in increments of 1° were studied in addition to flow up or down a hill section ahead of a 165-ft vertical riser. Over 10 000 data points comprising the TILDA database were collected on this test loop during a period of eight years. [TILDA is the name given to the database used to develop OLGA and includes all experiments conducted at SINTEF, Trondheim, Norway, and covers both small and large loops, two-phase, and three-phase flow.] The facility was run in both steady-state and transient modes. Additionally, the development of the OLGA model has benefited from a history of validation against field data through OVIP (OLGA Validation and Improvement Project). LedaFlow Point Model. The LedaFlow Point Model (Leda-PM)33 is the steady-state version of the transient LedaFlow simulator model developed by SINTEF in collaboration with Total and ConocoPhillips and commercialized by Kongsberg (Norway). Two- and three-phase versions of 4150

dx.doi.org/10.1021/ef300301s | Energy Fuels 2012, 26, 4145−4157

Energy & Fuels

Article

Figure 3. Photographic images of three-phase gas−oil−water slug flow in a horizontal pipe. Upper image shows the head of the liquid slug while the lower image shows its tail.

Figure 4. Oil−water flow experiments in 6-in.-diameter pipe (oil shown with red dye and water with blue dye). Each case has identical volumetric flow rates: 1500 bpd of each phase. The left-hand image shows upward flow inclined at θ = +2° (from the horizontal). The center image shows horizontal flow θ = 0°, while the right-hand image shows downward flow inclined at θ = −2° (from the horizontal). We observe that in the left-hand image, oil "slips" much faster over the water. In the center image, we have near-perfect stratified flow with no discernible slippage between phases, while in the right-hand image, we observe water rapidly slipping beneath the oil. These experiments clearly show how even a small inclination in pipe elevation can have a dramatic effect on slippage and associated flow regimes.

be “plugged-in” to broader simulation frameworks, shifting the burden of coding the models to the research institutions.

factors greater than 10% are not advised, except, perhaps, in cases of heavy oils where further adjustments in the friction correction factor may be warranted. For front-end design scenarios, in the absence of field data to benchmark against, one must rely upon the model itself in its raw form. Given the complexities and limitations of the models as constrained by assumptions and the data available to validate them, some notion of uncertainty can be gained by comparing the models against one another. This is quite easy to do within modern multiphase flow simulation programs, such as PIPESIM. Technology Transfer. The vast majority of the empirical and mechanistic models developed through the 1990s were published in complete form, allowing providers of multiphase flow simulation software to easily implement these models directly within commercially available products. However, in recent years, technology transfer from research institutions has become more independent as the aforementioned “state-of-theart” models are evolutionary in nature and either contain proprietary elements or are too complex to code and maintain for most software providers. Therefore, the model of technology transfer has become one of either reselling or acquisition of code through direct participation in a consortia. To accommodate this practice, simulation programs have become more extensible to allow multiphase flow technology to

■

FUTURE DIRECTIONS

Despite the investment and progress made in this field, much work remains to address the areas of greatest uncertainty and to align with trends in field development strategies. The authors’ view of the top five challenges toward better understanding and modeling of multiphase flow behavior follows. R&D Challenge 1: Three-Phase Flow Models. This past decade has seen increased attention on treating oil and water as separate phases, recognizing that slip between the oil and water phases not only affects the overall hydraulics, but also impacts flow assurance issues such as corrosion, wax, and hydrate prediction. Three-phase flow is considerably more complex to model than two-phase flow (see Figure 3). While the main drivers for slip between the phases remain the same (differences in density and viscosity), these properties for oil and water are much closer in magnitude than for gas and liquid. In addition, as a function of turbulence, oil and water may remain in distinct phases, may disperse into one another or may form emulsions. This introduces additional considerations in terms of phaseinversion behavior and in characterizing the rheology of the fluid mixture. Predictive models for both of these effects carry a 4151

dx.doi.org/10.1021/ef300301s | Energy Fuels 2012, 26, 4145−4157

Energy & Fuels

Article

lead to more optimal treatments of wells experiencing liquid loading. Additional Phases. The conventional two- and three-phase flow models discussed previously generally do not cope with additional phases, which may include immiscible phases, partitioning phases and solids. For example, under-balanced drilling may involve five coincident phases: gas, oil, brine, drilling mud, and solids. Glycols, most commonly MEG (monoethylene glycol), are routinely used to suppress hydrate formation temperature and inhibit CO2-induced corrosion. MEG partitions into both the hydrocarbon and aqueous phases and has been observed to alter flow patterns.73 Other field data suggests that MEG may promote emulsion formation.74 Incorporating the effects of MEG into multiphase flow models may improve multiphase flow characterization, particularly for flow with low liquid holdup, which is commonly associated with systems prone to hydrate formation. Many pipelines that operate near the hydrate formation region experience slurry flow, which involves the transport of solids and particulates. Improved models will help our understanding of conditions that promote hydrate transport and to avoid settling that may lead to the formation of large hydrate plugs. In particular, the effect of anti-agglomerate inhibitors on the transportability of hydrates may be better quantified. Sand production is another frequently encountered problem involving solids transport in the flow assurance domain. Better estimates of the critical velocity required to move sand through the pipeline will allow operators to avoid accumulations of sand in the pipeline and operate the systems more efficiently. R&D Challenge 3: Closure Relationships. The emergence of unified mechanistic models, as discussed above, depends heavily on a suite of closure relationships in order to capture a broad range of multiphase flow behavior. As studies have focused more toward characterizing specific phenomena, closure relationships have been developed for these purposes in a somewhat ad-hoc fashion. It is not uncommon for unified models to employ over a dozen independently derived closure relationships within the overall model framework (see Table 1). However, this complexity may cause discontinuities as different closure relationships are invoked when conditions change. Therefore, it is desirable to remove unnecessary empiricism and extend individual closure relationships to be applicable to a broader range of conditions (geometries, fluid properties, flow regimes, etc.) while maintaining mathematical continuity. In particular, steep downward flow, as encountered in steam injection wells, mountainous terrain, and offshore downcomers, has received less attention in research studies and remains poorly understood. This is particularly important for calculating the elevational pressure gradient, which is not simply the inverse of that for upward flow. Depending on the overall pipe geometry and flow regime, slack or open-channel flow may occur and the head of the fluid may be dissipated as frictional heat rather than recovered by increasing pressure.14,75,76 More work is required to clarify guidelines for recognizing these situations such that the proper treatment may be applied. Furthermore, it is becoming apparent that certain closure relationships have greater impact on the overall prediction of pressure gradient and liquid holdup. Recent studies by Chen77 and Posluszny et al.78 at the University of Tulsa have shown that for stratified and annular flow, the entrainment fraction is

high degree of uncertainty and the data required to build these models is difficult to obtain with good quality. To illustrate the impact of oil−water slip, the images shown in Figure 4 were taken from the Schlumberger multiphase flow loop at the Cambridge Research Center, U.K. The flow rates for each of the cases shown were identical: Qwater = 10 m3/h (equivalent to ∼1500 bpd for water) and Qoil = 10 m3/h (equivalent to ∼1500 bpd for oil). The pipe internal diameter (Di) was 6 inches. The left-hand image in Figure 4 shows oil and water flow for an upward inclination of just +2° (from the horizontal). The center image in Figure 4 shows the same flow for perfectly horizontal pipe and the right-hand image shows downward flow of −2° (from the horizontal). Because the oil viscosity (μoil) was quite low (∼1.5 cP), the main driver for the slip is the difference in densities caused by the change in the inclination angle. Obviously, the effect is quite significant. R&D Challenge 2: Exotic Fluids. There is an increasing trend toward transporting fluids whose properties deviate from what most multiphase flow models have focused on historically, a category we call “exotic fluids”. While such fluids may seem quite familiar to the practicing flow assurance engineer, they will remain “exotic” in the context of multiphase flow modeling until the reliability of characterizing the effects of these fluids may be systematically understood. While not comprehensive, the examples provided illustrate fluids that have complex rheological behavior or introduce additional phases. In practice, some flows may indeed experience a combination of these issues and, as such, their elaborate nature requires more detailed study and understanding. Fluids with Viscous or Complex Rheological Behavior. The most notable of these fluids is heavy (°API ≲ 22) and extraheavy (°API ≲ 10) oil, which together comprise ∼75% of the total world oil resources. Optimizing the design of these production systems involves modeling processes such as SAGD (Steam-Assisted Gravity Drainage), where condensed steam is produced with the oil, causing significant temperature changes. Prediction of the multiphase flow behavior is made difficult by a number of factors, including the formation of emulsions, complex heat transfer mechanisms, and the potential of the flow to be non-Newtonian in nature. Design of pumping units (ESPs, PCPs, surface pumps, etc.) to lift and transport the fluids is tightly dependent on the backpressure mainly caused by viscosity effects on the frictional pressure gradient. Evaluation of the benefits of measures such as active line heating and injection of diluents requires a good understanding of the relationship between the viscosity and the pressure gradient. Studies have shown70 that many of the current multiphase models lose considerable accuracy in predicting behavior of high-viscosity fluids in nearly every aspect: flow pattern, liquid holdup, pressure gradient and slug characteristics. More work is needed both experimentally and in the development of improved closure relationships to further improve accuracy. Foams, which are commonly encountered in drilling and completions operations, are also produced when surfactants are used to mitigate liquid loading in gas wells and also in some EOR production systems where the solvents used to treat immobile oil may cause foaming of wellstream fluids. Flow behavior with foams can be quite complex,71,72 requiring models to describe both the rheology of the fluid and the mechanics of bubble formation and transport. A better understanding of the mechanisms of foam production may 4152

dx.doi.org/10.1021/ef300301s | Energy Fuels 2012, 26, 4145−4157

Energy & Fuels

Article

the most critical closure relationship followed in order by interfacial friction factor and interfacial wetted perimeter. For slug flow, translational velocity and slug length closure relationships were found to have greater impact over slug liquid holdup or interfacial friction factor. Understanding the relative importance among multiple closure relationships that impact the overall solution should help to focus R&D in the most critical areas, thereby further reducing uncertainty with the added goal of promoting unification and continuity wherever possible. A means to provide some statistical analysis is also warranted, especially during the design stage (facility sizing, etc.), and should form part of any analysis workflow. Mechanisms to allow seamless and realizable inclusion of models and other uncertainties are necessary and now realistic. Such mechanisms may, for example, include the Efficient Frontier79,80 generated from an optimization of the flowing system that folds into it not only the stated uncertainties of models (closure relationships) but other system uncertainties as well. R&D Challenge 4: Numerical Discontinuities and Simplified Models. One of the downsides of the advanced and comprehensive mechanistic models is that such complexity introduces numerical discontinuities in the overall solution for liquid holdup and pressure gradient as a function of the input parameters. There are several sources for these discontinuities, and their manifestation varies for the different models, although none of the most advanced models are entirely immune from this problem. These include: • reliance of multiple and often independently derived closure relationships, • occurrence of multiple roots and methods to select the appropriate solution, • sudden transitions in flow regimes, particularly as a function of inclination angle, and • sudden transitions in phase inversions (continuous phase). An example of such a discontinuity is shown by the upper solution surface in Figure 5 which plots liquid holdup fraction (hL, as a percentage), on the z-axis, against superficial liquid, (usL), and superficial gas, (usG), velocities (the latter two parameters being commonly used to map flow regimes). This upper solution surface was generated using a mechanistic model that considers discrete flow regimes. The lower surface (which is partially obscured) was generated using the flow-regimeindependent Drift Flux model69 and is smooth throughout, with no discontinuities. It is evident from the upper surface in Figure 5 that a distinct “region” exists in which the liquid holdup fraction abruptly changes, appearing as a red plateau. This discontinuity corresponds to the slug flow regime. Such abrupt changes in liquid holdup fraction, hL, also results in equally abrupt changes in calculated pressure gradients that may create a number of problems for the higher-level simulations, particularly those coupled with reservoir and/or surface facility simulation packages. The smooth and continuous behavior of the lower surface in Figure 5 is, however, ideally suited for such high-level coupled simulations and especially suited in automated optimization where solution robustness is critical. While experimental observations may indeed indicate rather abrupt transitions as a function of measured input parameters, given the uncertainties surrounding these phenomena in the context of other factors, such precision is not justified. The

Figure 5. Liquid holdup (hL), solution surfaces against superficial gas (usG), and superficial liquid (usL) velocities. The upper surface was generated using a mechanistic model with discrete flow regimes. The lower surface (which is mostly hidden from view) is smooth (no discontinuities) and was generated using the Drift Flux69 model. The discontinuities observed correspond to the transitions to slug flow and is most visible in the approximate center of the upper surface.

current approach for dealing with these problems in practical applications is for the higher-level simulation framework to invoke its own and sometimes brutal means of suppressing this problem through techniques such as averaging, smoothing, and adaptive segmentation. While this approach will continue to be required for as long as well and pipeline systems are defined as discrete segments with defined lengths and step changes in inclination angle for adjacent segments, the consequences would be diminished significantly if the underlying multiphase flow model did not further exacerbate the problem by introducing additional discontinuities. This drawback is of particular consequence to optimization problems that require derivatives of the function to ascertain whether the relationship between the input and output parameters is direct or indirect and the degree to which this is so. Additionally, for cases where the multiphase flow model is directly or implicitly incorporated into the system of equations used to solve the larger problem (i.e., reservoir simulation with multisegment well models), not only does the multiphase flow model need to be continuous, but it also must be smooth and differentiable. For these reasons, simpler multiphase flow models are used for these problems and continue to evolve to better approximate more-advanced models. In fact, given the increased level of empiricism inherent in these simpler models, one approach that has been taken is to tune the simpler models (adjust their parameters) to emulate those that are more advanced.69 The obvious tradeoff is accuracy versus simplicity, and the objective is to correctly capture the trends and general behavior of the multiphase flow characteristics while settling for reduced accuracy. In this sense, the simpler models serve as “proxies” for more-advanced models. This approach is quite common in other areas of petroleum engineering such as upscaling three-dimensional (3D) geological models for reservoir simulation and 3D reservoir simulation models to onedimensional (1D) material balance tank models. R&D Challenge 5: Fully-Coupled Full-Field Models. The ability to seamlessly couple previously discrete simulation 4153

dx.doi.org/10.1021/ef300301s | Energy Fuels 2012, 26, 4145−4157

Energy & Fuels

Article

Figure 6. Scale plot showing the present state of application domains, shaded in blue (wells, pipelines, and facilities) and red (reservoir) and the likely (near- to midterm) future evolution into fully coupled (full-field) models, as shown by the larger green domain which encompasses both reservoir and wells, pipelines and facilities, and more.

components of a petroleum system began in the 1990s (see ‘Engineering Application’ in Figure 2). Figure 6 illustrates these components in the context of the length and time scales introduced in Figure 1 and suggests the future state of fully integrated system modeling capability. However, we need to resolve a number of challenges to achieve this, namely, • Stable coupling schemes between steady-state and transient models. This applies particularly to the connection between gathering networks and facility models. The issue of stability may require closer investigation of the potentially differing timescales involved. Simplified transient modeling is an area where such development may prove beneficial. • Stable and accurate coupling of reservoir simulators with complex wells (i.e., horizontal wells with complex completions and downhole equipment) and the steadystate multiphase flow model. While various methods exist to enable such coupling, developments into the next generation of reservoir simulators are extending the reservoir model to include complex wellbores and surface gathering networks. • Optimization of a fully coupled system with uncertainty (in the reservoir and/or in the flowing model) needs some development. While treating uncertainty in optimization utilizing the Efficient Frontier has been proposed,81,82 these concepts have, so far, only been applied to reservoir forecast simulation. Attempts at optimizing a full-field coupled reservoir-multiphase flow model exposed certain problems involving nonphysical solution and run-time stability.69 The source of these issues was found to involve numerical discontinuities the nature of which is addressed in R&D Challenge 4. • Benchmarking of a full-field system, and its associated optimization, is necessary in order to establish the suitability of such a deeply integrated problem.83,84 Therefore, benchmarks are crucial in determining the quality and reliability of such models, because their

■

underlying complexity increases as more aspects of the flowing system are incorporated into the analysis. Therefore, more open benchmarks should be developed to cover a broader range of reservoirs, facilities, fluids, and so on.

CONCLUSIONS

Much effort has been invested over the past half-century toward a better understanding and characterization of steady-state multiphase flow. The resulting models are now used routinely in the design and optimization of petroleum production systems. Increasing focus on flow assurance issues over the past couple decades has demanded that these models evolve and adapt to cope with ever more difficult situations. The course of development of these models, leading to the current "state-of-the-art," has been presented. Key future challenges have been identified to further advance the science and enable practicing engineers to maximize the efficiency of petroleum production operations. These challenges include the following: (1) Better characterization of three-phase (oil−water−gas) flow. (2) Expanded treatment of “exotic” fluids, namely those that are not currently modeled with sufficient accuracy. (3) More accurate and more generalized closure relationships. (4) Improved numerical behavior to eliminate mathematical discontinuities and better enable optimization and coupled system models. (5) Development of tighter integration of multiphase flow models with reservoir and process facility models for complete system optimization. Given the high level of ongoing research and development activity, continued advancements in this field are expected to address these challenges, and more. 4154

dx.doi.org/10.1021/ef300301s | Energy Fuels 2012, 26, 4145−4157

Energy & Fuels

■

Article

(12) Holmes, J. A. Description of the Drift Flux Model in the LOCA Code Relap-UK. Inst. Mech. End., 1977, 103−108 (Paper No. C206/ 77). (13) Hagedorn, A. R.; Brown, K. E. Experimental Study of Pressure Gradients Occurring During Continuous Two-Phase Flow in SmallDiameter Vertical Conduits. J. Pet. Technol. 1965, 17 (4), 475−484. (14) Flanigan, O. Effect of Uphill Flow on Pressure Drop in Design of Two-Phase Gathering Systems. Oil Gas J. 1958, (March 10). (15) Eaton, B. A.; Andrews, D.; Knowles, C.; Brown, K. The Prediction of Flow Patterns, Liquid Holdup and Pressure Losses Occurring During Continuous Two-Phase Flow in Horizontal Pipelines. J. Pet. Technol. 1967, 19 (6), 815−828 (SPE Paper 1525). (16) Dukler, A. E. Gas Liquid Flow in Pipelines: I. Research Results; AGA-API Project NX-28, May 1969. (17) Gray, H. E. Subsurface Controlled Safety Valve Sizing Computer Program, Appendix B. In Vertical Flow Correlation in Gas Wells, User Manual for API 14BM; API: Dallas, TX, 1974. (18) Duns, H., Jr.; Ros, N. C. J. Vertical Flow of Gas and Liquid Mixtures in Wells. In Proceedings of the Sixth World Petroleum Congress, Frankfurt, Germany, 1963; pp 451−465 (Section II, Paper 212.PD6). (19) Orkiszewski, J. Predicting Two-Phase Pressure Drops in Vertical Pipes. J. Pet. Technol., Trans. AIME 1967, 19 (6), 829−838 (SPE Paper 1546-PA). (20) Beggs, H. D.; Brill, J. P. A Study of Two-Phase Flow in Inclined Pipes. J. Pet. Technol., Trans., AIME 1973, 25 (5), 607−617. (21) Mukherjee, H.; Brill, J. P. Pressure Drop Correlations for Inclined Two-Phase Flow. J. Energy Resources Technol., Trans., ASME 1985, 107, (December), 549−468. (22) Shi, H.; Holmes, J. A.; Durlofsky, L. J.; Aziz, K.; Diaz, L. R.; Alkaya, B.; Oddie, G. Drift-Flux Modeling of Two-Phase Flow in Wellbores. SPE 84228-PA, SPE J. 2005, 10 (1), 24−33. (Originally presented as SPE Paper 84228, with the same authorship, at the 2003 SPE Annual Technical Conference and Exhibition, Denver, CO, October 5−8, 2003.) (23) Shi, H.; Holmes, J. A.; Durlofsky, L. J.; Aziz, K.; Diaz, L. R.; Alkaya, B.; Oddie, G. Drift-Flux Parameters for Three-Phase SteadyState Flow in Wellbores. SPE J. 2005, 10 (2), 130−137. (Originally presented as SPE Paper 89836 at the SPE Annual Technical Conference & Exhibition, Houston, TX, Sept. 26−29, 2004.) (24) Aziz, K.; Govier, G. W.; Forgarasi, M. Pressure Drop in Wells Producing Oil and Gas. J. Can. Pet. Technol. 1972, 11 (3), 38−48. (25) Taitel, Y.; Dukler, A. E. A Model for Predicting Flow Regime Transitions in Horizontal and Near Horizontal Gas−Liquid Flow. AIChE J. 1976, 22 (1), 47−55. (26) Hasan, A. R.; Kabir, S. H. A Study of Multiphase Flow Behavior in Vertical Wells. SPE Prod. Eng. 1988, 3 (2), 263−272 (SPE Paper 15138). (27) Xiao, J.-J.; Shoham, O.; Brill, J. P. A Comprehensive Mechanistic Model for Two-Phase Flow in Pipelines. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, LA, Sept. 23−25, 1994; SPE Paper 20631. (28) Ansari, A. M.; Sylvester, N. D.; Sarica, C.; Shoham, O.; Brill, J. P. A Comprehensive Mechanistic Model for Upward Two-Phase Flow in Wellbores. SPE Prod. Facil. J. 1994, 9 (2), 143−151. (Originally presented, with same authorship, as SPE Paper 20630, “A Comprehensive Mechanistic Model for Upward Two-Phase Flow in Wellbores,” at the Proceedings of the SPE Annual Technical Conference & Exhibition, New Orleans, LA, Sept. 23−26, 1990.) (29) Petalas, N.; Aziz., K. A Mechanistic Model for Multiphase Flow in Pipes. J. Can. Pet. Technol. 2000, 39 (6), 43−55. (Originally presented as Paper No. 98-39 at The Petroleum Society, Annual Technical Meeting, Calgary, Alberta, Canada, June 8−10, 1998.) (30) Zhang, H.-Q.; Wang, Q.; Brill, J. P. A Unified Mechanistic Model for Slug Liquid Holdup and Transition Between Slug and Dispersed Bubble Flows. Int. J. Multiphase Flow 2003, 29 (1), 97−107. (31) Zhang, H.-Q.; Wang, Q.; Sarica, C.; Brill, J. P. Unified Model for Gas−Liquid Pipe Flow Via Slug DynamicsPart 1: Model Development. J. Energy Resources Technol., Trans. ASME 2003, 125, 266−274.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. Biographies Mack Shippen is a Principal Petroleum Engineer with Schlumberger in Houston, where he is responsible for the global business of the PIPESIM multiphase flow simulation software. He has extensive experience in well and network simulation studies, ranging from flow assurance to dynamic coupling of reservoir and surface simulation models. He has served on several committees and chaired the SPE Reprint Series on Offshore Multiphase Production Operations. He holds B.S. and M.S. degrees from Texas A&M University, where his research focused on multiphase flow modelling. William Bailey is a Principal Reservoir Engineer with SchlumbergerDoll Research in Cambridge, MA. He has held various operational and research positions in Schlumberger (mainly in reservoir and production engineering) as well as other appointments during his 22 years in the industry. He holds a M.Eng. (Hons.) and Ph.D. degrees in Petroleum Engineering and an MBA degree from Warwick Business School, U.K. He has authored 20 peer-reviewed papers, contributed to 3 books and has over 23 conference articles. He was Chair of the New York and New England Petroleum Section of SPE for 8 years, a Review Chair for SPE Production & Facilities J. and remains a reviewer for numerous journals.

■

REFERENCES

(1) Xiao, J.-J.; Shoup, G. Sizing Wet-Gas Pipelines and Slug Catchers with Steady-State Multiphase Flow Simulations. J. Energy Resources Technology, Trans. ASME 1998, 120 (2), 106−111. (2) Darrigol, O. Worlds of Flow: A History of Hydrodynamics from the Bernoullis to Prandtl; Oxford University Press: New York, 2005; 376 pp (ISBN 0-19-856843-6). (3) Brill, J. P.; Arirachakaran, S. J. State-of-the-Art in Multiphase Flow. J. Pet. Technol. 1992, 44 (5), 538−541 (SPE Paper No. 23835). (4) Darcy, H. Recherches Experimentales Relatives au Mouvement de L’Eau dans les Tuyaux (Engl. Transl.: “Experimental Research Relating to the Movement of Water in Pipes”), Vol. 2; Mallet−Bachelier: Paris, 1857; 268 pp. (5) Weisbach, J. Lehrbuch der Ingenieur- und Maschinen-Mechanik, Vol. 1. Theoretische Mechanik (Engl. Transl.: “Textbook on Engineering Mechanics and Mechanics of Machines, Vol. 1. Theoretical Mechanics”); Vieweg und Sohn: Braunschwieg, Germany, 1845; 535 pp. (6) Moody, L. F. Friction Factors for Pipe Flow. Trans. ASME 1944, 66 (8), 671−684. (7) Brown, G. O. The History of the Darcy−Weisbach Equation for Pipe Flow Resistance. In Environmental and Water Resources History; Rogers, J. R., Fredrich, A. J., Eds.; Proceedings and Invited Papers for the ASCE 150th Anniversary (1852−2002) Conference on Environmental and Water Resources History; American Society of Civil Engineers: Reston, VA, 2002; pp 34−43. (8) Lockhart, R. W.; Martinelli, R. C. Proposed Correlation of Data for Isothermal Two-Phase, Two-Component Flow in Pipes. Chem. Eng. Progress 1949, 45 (1), 39−48. (9) Poettmann, F. H.; Carpenter, P. G. Multiphase Flow of Gas, Oil and Water Through Vertical Flow Strings. Drill. Prod. Pract. 1952, 257. (10) Baxendell, P. B.; Thomas, R. The Calculation of Pressure Gradients In High-Rate Flowing Wells. J. Pet. Technol. 1961, 13 (10), 1023−1028. (11) Zuber, N.; Findlay, J. Average Volumetric Concentration in Two-Phase Flow Systems. J. Heat Transfer, Trans. ASME, Ser. C 1965, 26 (3), 453−468. 4155

dx.doi.org/10.1021/ef300301s | Energy Fuels 2012, 26, 4145−4157

Energy & Fuels

Article

Transl.: “The Law of Similarity in Friction Processes in Liquids”). In Mitteilungen über Forschungs−Arbeit des Ingenieur-Wesens; Verein Deutscher Ingenieure (VDI) Verlag: Berlin, Germany, 1913; Vol. 131, 39 pp.) (53) Andritsos, N.; Hanratty, T. J. Influence of Interfacial Waves in Stratified Gas−Liquid Flows. AIChE J. 1987, 33 (3), 444−454. (54) Andreussi, P.; Persen, L. N. Stratified Gas−Liquid Flow in Downwardly Inclined Pipes. Int. J. Multiphase Flow 1987, 13 (4), 565− 575. (55) Zhang, H.-Q.; Sarica, C. A Model For Wetted Wall Fraction and Gravity Center of Liquid Film in Gas−Liquid Pipe Flow. In Proceedings of the 15th International Conference on Multiphase Technology, Banff, Canada, June 2−4, 2010; Smith, S. P., Ed.; BHR Group, Limited: Cranfield, Bedfordshire, U.K., 2010; pp 265−275. (56) Al-Safran, E. Investigation and Prediction of Slug Frequency in Horizontal Gas/Liquid Two-Phase Flow Pipeline. J. Pet. Sci. Eng. 2009, 69 (1−2), 143−155. (57) Nydal, O. J.; Andreussi, P. Gas Entrainment in a Long Liquid Slug Advancing in a Near Horizontal Pipe. Int. J. Multiphase Flow 1991, 17 (2), 179−189. (58) Ambrosini, W.; Andreussi, P.; Azzopardi, B. J. A Physically Based Correlation for Drop Size in Annular flow. Int. J. Multiphase Flow 1991, 17 (4), 497−507. (59) Andreussi, P.; Paglianti, A.; Silva, F. S. Dispersed Bubble Flow in Horizontal Pipes. Chem. Eng. Sci. 1999, 54 (8), 1101−1107. (60) Grolman, E. Gas−Liquid Flow with Low Liquid Loading in Slightly Inclined Pipes, Ph.D. Thesis, Faculty of Science, FNWI: Van’t Hoff Institute for Molecular Sciences, University of Amsterdam, Amsterdam, The Netherlands, 1994. (61) Al-Sarkhi, A.; Hanratty, T. J. Effect of Pipe Diameter on the Drop Size in a Horizontal Annular Gas−Liquid Flow. Int. J. Multiphase Flow 2002, 28 (10), 1617−1629. (62) Hill, T. J.; Wood, D. G. Slug Flow: Occurrence, Consequences and Prediction. Presented at the University of Tulsa Centennial Petroleum Engineering Symposium, Tulsa, OK, August 29−31, 1994, SPE Paper 27960. (63) Hewitt, G. F. Multiphase Flow: Views of the Future. A Report on Discussions at the Third International Workshop on Multiphase Flow, London, June 1992. Multiphase Sci. Technol. 1999, 11, 59−77. (64) Finlay, C. F. Multiphase Design Methods; Research Report, Baker Jardine & Associates: London, U.K., December 1995, 19 pp. (65) Pucknell, J. K.; Mason, J. N. E.; Vervest, E. G. An Evaluation of Recent “Mechanistic” Models of Multiphase Flow For Predicting Pressure Drops in Oil and Gas Wells. In Proceedings of SPE Offshore Europe, Aberdeen, U.K., Sept. 7−10, 1993, SPE Paper 26682. (66) Brinkman, H. C. The Viscosity of Concentrated Suspensions and Solutions. J. Chem. Phys. 1952, 20 (4), 571. (67) Pal, R.; Rhodes, E. Viscosity/Concentration Relationships for Emulsions. J. Rheol. 1989, 33 (7), 1021−1045. (68) Zhang, H.-Q.; Sarica, C. Unified Modeling of Gas/Oil/Water Pipe Flow-Basic Approaches and Preliminary Validation. SPE Proj., Facil. Construct. J. 2006, 1 (2), 1−7. (Originally presented as SPE Paper 95749 at the SPE Annual Technical Conference & Exhibition, Dallas, TX, Oct. 9−12, 2005.) (69) Li, Y.; Bailey, W. J.; Rashid, K.; Couët, B.; Shippen, M.; Holmes, J. Optimized Parameters and Extension of a 2-Phase Flow-RegimeIndependent Flow Model. In Proceedings of the 15th International Conference on Multiphase Technology, Cannes, France, June 15−17, 2011; Hunt, A. P., Ed.; BHR Group, Limited: Cranfield, Bedfordshire, U.K., 2011; pp 225−239 (ISBN 978-1-85598-125-6). (70) Gokcal, B.; Wang, Q.; Zhang, H. Q.; Sarica, C.; Al-Safran, E. Effects of High Oil Viscosity on Oil−Gas Flow Behavior in Horizontal Pipes. In Proceedings of the SPE Annual Technical Conference & Exhibition, San Antonio, TX, Sept. 24−27, 2006, SPE Paper SPE 102727. (71) Bogdanovic, M.; Gajbhiye, R.; Kam, S. I. Experimental Study of Foam Flow in Horizontal Pipes: Two Flow Regimes and its Implications. Colloids Surf. A 2009, 344 (1−3), 56−71.

(32) Bendiksen, K. H.; Malnes, D.; Moe, R.; Nuland, S. The Dynamic Two-Fluid Model OLGA: Theory and Application. SPE Prod. Eng. 1991, 6 (2), 171−180 (SPE Paper 19451). (33) Danielson, T. J.; Bansal, K. M.; Hansen, R.; Leporcher, E. LEDA: The Next Multiphase Flow Performance Simulator. In Proceedings of the 9th International Conference on Multiphase Technology, Barcelona, Spain, 2005; BHR Group Limited: Cranfield, Bedfordshire, U.K., 2005; pp 477−492. (34) Reynolds, O. An Experimental Investigation of the Circumstances Which Determine Whether the Motion of Water Shall Be Direct or Sinuous, and of the Law of Resistance in Parallel Channels. Philos. Trans. R. Soc. 1883, 174, 935−982. (35) Rott, N. Note on the History of the Reynolds Number. Ann. Rev. Fluid Mech. 1990, 22 (January), 1−11. (36) Fernandez, R. C.; Semiat, R.; Dukler, A. E. Hydrodynamic Model For Gas−Liquid Slug Flow In Vertical Tubes. AIChE J. 1983, 29 (6), 981−989. (37) Shoham, O. Mechanistic Modeling of Gas-Liquid Two-Phase Flow in Pipes; Society of Petroleum Engineers: Richardson, TX, 2006; 408 pp (ISBN: 978-1-55563-107-9). (38) Ellul, I.; Sæther, G.; Shippen, M. E. The Modeling of Multiphase Systems Under Steady State and Transient Conditions. In Proceedings of the Pipeline Simulation Interest Group (PSIG), 36th Annual Meeting, Palm Springs, CA, Oct. 20−22, 2004. (39) Laurinat, L. E.; Hanratty, T. J. Pressure Drop and Film Height Measurements for Annular Gas−Liquid Flow. Int. J. Multiphase Flow 1984, 10 (3), 341−356. (40) Cheremisinoff, N. P.; Davis, E. J. Stratified Turbulent− Turbulent Gas−Liquid Flow. AIChE J. 1979, 25 (1), 48−56. (41) Hewitt, G. F. Flow Regimes. In Handbook of Multiphase Systems; Hetsroni, G., Ed.; McGraw−Hill Book Co.: New York, 1982. (42) Oliemans, R. V. A.; Pots, B. F. M.; Trompé, N. Modelling of Annular Dispersed Two-Phase Flow in Vertical Pipes. Int. J. Multiphase Flow 1986, 12 (5), 711−732. (43) Wallis, G. B. One Dimensional Two-Phase Flow; McGraw−Hill Book Co.: New York, 1969. (44) Crowley, C. L.; Sam, R. G.; Rothe, P. H. Investigation of TwoPhase Flow in Horizontal and Inclined Pipes at Large Pipe Size and High Gas Density. Technical Note TN-399; Creare, Inc.: Hanover, NH, 1986. (45) Crowley, C. L.; Sam, R. G. Investigation of Two-Phase Flow in Horizontal and Inclined Pipes at Large Pipe Size and High Gas Density. Prepared for the Materials Committee of Pipeline Research Council International, Inc., Contract No. PR-172-507; Creare, Inc.: Hanover, NH, February 1986. (46) Gregory, G. A.; Nicholson, M. K.; Aziz, K. Correlation of the Liquid Volume Fraction in the Slug for Horizontal Gas−Liquid Slug Flow. Int. J. Multiphase Flow 1978, 4, (1), 33−39. (47) Fabre, J.; Ferschneider, G.; Masbernat, I. Intermittent Gas Liquid Flow modelling in Horizontal or Weakly Inclined Pipes. In Proceedings of the International Conference on the Physical Modelling of Multiphase Flow; BHRA: Cranfield, Coventry, U.K., April 19−21, 1983; pp 223−254. (48) Gregory, G. A.; Scott, D. S. Correlation of Liquid Slug Velocity and Frequency in Horizontal Cocurrent Gas−Liquid Slug Flow. AIChE J. 1969, 15 (6), 933−935. (49) Dukler, A. E.; Hubbard, M. G. A Model for Gas−Liquid Slug Flow in Horizontal and Near Horizontal Tubes. Ind. Eng. Chem. Fundam. 1975, 14 (4), 337−347. (50) Bendiksen, K. H. An Experimental Investigation of The Motion of Long Bubbles in Inclined Tubes. Int. J. Multiphase Flow 1984, 10 (4), 467−483. (51) Spedding, P. L.; Hand, N. P. Prediction in Stratified Gas−Liquid Co-Current Flow In Horizontal Pipelines. Int. J. Heat Mass Transfer 1997, 40 (8), 1923−1935. (52) Blasius, H. Das Ä hnlichkeitsgesetz bei Reibungsvorgängen (Engl. Transl.: “Similarity Laws for Friction”). VDI Z. 1912, 56, 639− 643. (A revised treatment was published in 1913 as Blasius, H. Das Ä hnlichkeitsgesetz bei Reibungsvorgängen in Flüssigkeiten (Engl. 4156

dx.doi.org/10.1021/ef300301s | Energy Fuels 2012, 26, 4145−4157

Energy & Fuels

Article

(72) Gregory, G. A. Foam Flow Modelling For UBD Applications. J. Can. Pet. Technol. 2003, 42 (3), 8−13. (73) Hart, J.; Hamersma, P. J.; Fortuin, J. M. H. Correlations Predicting Frictional Pressure Drop and Liquid Holdup During Horizontal Gas-Liquid Pipe Flow with a Small Holdup. Int. J. Multiphase Flow 1989, 15 (6), 947−964. (74) Manfield, P.; Nisbet, W.; Balius, J; Broze, G.; Vreenegoor, L. Wax-On, Wax-Off: Understanding and Mitigating Wax Deposition in a Deepwater Subsea Gas/Condensate Flowline. In Proceedings of the Offshore Technology Conference, Houston, TX, April 30−May 3, 2007, OTC Paper 18834. (75) Baker, A.; Nielsen, K.; Gabb, A. Pressure Loss, Liquid-Holdup Calculations Developed. Oil Gas J. 1988, 86 (11), 55−59. (76) Nicholas, E. Simulation of Slack Line Flow−A Tutorial. In Proceedings of the 27th Annual Pipeline Simulation Interest Group (PSIG) Conference, Albuquerque, NM, Oct. 18−20, 1995, PSIG Paper 0905. (77) Chen, X. Droplet-Homophase Interaction Study. University of Tulsa Fluid Flow Projects, University of Tulsa, Tulsa, OK, 2005, TUFFP Research Project No. 105. (78) Posluszny, D.; Klavetter, K.; Cremaschi, S.; Sarica, C.; Subramani, H. J. Uncertainty Analysis of Multiphase Flow Modeling: A Case Study for Vertical Flows. In Proceedings of the 14th International Conference on Multiphase Technology, Banff, Canada, June 2−4, 2010; Smith, S. P., Ed.; BHR Group, Limited: Cranfield, Bedfordshire, U.K., 2010; pp 397−407. (79) Markowitz, H. M. Portfolio Selection. J. Finance 1952, 7 (1), 77−91. (80) Markowitz, H. M. Portfolio Selection: Efficient Diversification of Investments; John Wiley & Sons: New York, 1959; 344 pp. (81) Raghuraman, B.; Couët, B.; Savundararaj, P.; Bailey, W. J.; Wilkinson, D. Valuation of Technology and Information for Reservoir Risk Management. SPE Reservoir Eng. J. 2003, 6 (5), 307−316 (SPE Paper 86568). (82) Bailey, W. J.; Couët, B.; Wilkinson, D. Framework for Field Optimization to Maximize Asset Value. SPE Reservoir Eng. J. 2005, 8 (1), 7−21 (SPE Paper 87026). (83) Juell, A.; Whitson, C. H.; Hoda, M. F. Model-Based Integration and OptimizationGas Cycling Benchmark. Presented at the SPE EUROPEC/EAGE Annual Conference & Exhibition, Amsterdam, The Netherlands, June 8−11, 2009 (SPE Paper 121252). (84) Rahmawati, S. D.; Whitson, C. H.; Foss, B.; Kuntadi, A. MultiField Asset Integrated Optimization Benchmark. In Proceedings of the SPE EUROPEC/EAGE Annual Conference & Exhibition, Barcelona, Spain, June 14−17, 2010 (SPE Paper 130768).

4157

dx.doi.org/10.1021/ef300301s | Energy Fuels 2012, 26, 4145−4157