Sideways Expansion Research Articles

Analytical model of steam-assisted gravity drainage (SAGD) process in relation to constant injection rate

Steam-Assisted Gravity Drainage or SAGD is a widely tested method for producing bitumen from oil sands (tar sands). Several analytical treatments of the basic process have been reported. In a typical model, the focus is on bitumen drainage ahead of an advancing steam-oil interface with no recourse to the steam injection rate – which is worked out after the fact.In this study, a comprehensive analytical model of the SAGD process in relation to constant injection rate, for the first time, was developed encompassing steam chamber rise, sideways expansion, and the confinement phases to evaluate the SAGD performance. The model is called Comprehensive Constant Heat Injection (CCHI). The accumulated heat ahead of the front plays a crucial role in SAGD modeling in order to find the advancing front velocity. There is a reciprocal relation between the advancing front velocity and the amount of stored heat ahead of the front. Considering the equilibrium situation for thermal recovery methods with dominant gravity drainage driving force, the advancing front velocity is responsible for heat accumulation ahead of the front, and in turn, the heated oil drains down to the production well and advances the front. Therefore, the key point in the modeling is to determine the advancing front movement that satisfies heat and mass balances over the system under equilibrium. In the CCHI model, after the rising chamber reaches the reservoir top, steam is injected at a constant rate into the system which is the case in the most field applications, and it provides heat for the growing steam chamber size, increasing heat loss, and heat flow by conduction ahead of the front. Unlike previous works, the steam chamber growth is maximum at the beginning of the sideways expansion phase with growth and oil production rate decreasing with time. It is believed that the inclusion of increasing heat loss and interface extension with time, ignored in previous works, into energy and mass balances results in decreasing steam chamber velocity. In this model, it is the first time that the SAGD oil rate is directly related to the steam injection rate. Some interesting analysis of a SAGD process can be extracted from the model. Also, the approach provides a tool for quick field-scale optimization and performance predictions instead of using extremely time-consuming thermal numerical simulators.

A new comprehensive model to estimate the steam chamber expansion and recovery performance of entire SAGD process

Steam-Assisted gravity drainage (SAGD) technique has been successfully applied to unlock the oilsands resources in Canada. But to accurately estimate the steam chamber expansion and productivity of the entire lifetime of a SAGD well pair is still challenging. In this paper, a new comprehensive model is proposed encompassing the different stages of SAGD. Firstly, for the rising stage, based on the theory of volumetric displacement, an analytical model is developed for the rise speed and oil rate. Thereafter, based on Butler's theory, a 2D numerical approach is modelled for predicting the lateral spreading and confinement stage of steam chamber. Thus, combining the two different mathematical models, the steam chamber shape and recovery performance of a SAGD process can be calculated. The calculation results are also compared against 3D experimental results and field data to confirm the accuracy of this model. Then, a sensitivity analysis is performed to discuss the effects of operation parameters on steam chamber expansion and recovery performance of SAGD process. Results indicate that the calculated results can match the experiment results and field date very well. The calculated peak oil production rate causes a large error and the plateau time of SAGD process obviously is shortened if the preheating stage is neglected. A higher steam chamber pressure results in a narrower inverted triangle interface shape in the rising stage and a more concave-like interface in the sideways expansion stage. In addition, the oil rate increases with steam chamber pressure allowing for varying steam injection rate, whereas the increasing trend of ultimate recovery decreases with the steam chamber pressure increases, which indicates that a proper steam chamber pressure to be chosen can not only achieve a preferable ultimate recovery but also benefit for project economics.

The Mechanical Role of the Radial Fiber Network Within the Annulus Fibrosus of the Lumbar Intervertebral Disc: A Finite Elements Study.

The annulus fibrosus (AF) of the intervertebral disc (IVD) consists of a set of concentric layers composed of a primary circumferential collagen fibers arranged in an alternating oblique orientation. Moreover, there exists an additional secondary set of radial translamellar collagen fibers which connects the concentric layers, creating an interconnected fiber network. The aim of this study was to investigate the mechanical role of the radial fiber network. Toward that goal, a three-dimensional (3D) finite element model of the L3-L4 spinal segment was generated and calibrated to axial compression and pure moment loading. The AF model explicitly recognizes the two heterogeneous networks of fibers. The presence of radial fibers demonstrated a pronounced effect on the local disc responses under lateral bending, flexion, and extension modes. In these modes, the radial fibers were in a tensile state in the disc region that subjected to compression. In addition, the circumferential fibers, on the opposite side of the IVD, were also under tension. The local stress in the matrix was decreased in up to 9% in the radial fibers presence. This implies an active fiber network acting collectively to reduce the stresses and strains in the AF lamellae. Moreover, a reduction of 26.6% in the matrix sideways expansion was seen in the presence of the radial fibers near the neutral bending axis of the disc. The proposed biomechanical model provided a new insight into the mechanical role of the radial collagen fibers in the AF structure. This model can assist in the design of future IVD substitutes.

Numerical simulations of mass loading in the tails of bow-shock pulsar-wind nebulae

When a pulsar is moving through a partially ionized medium, a fraction of neutral Hydrogen atoms penetrate inside the pulsar wind and can be photo-ionized by the nebula UV radiation. The resulting protons remains attached to the magnetic field of the light leptonic pulsar wind enhancing its inertia and changing the flow dynamics of the wind. We present here the first numerical simulations of such effect in the tails of bow shock nebulae. We produce a set of different models representative of pulsars moving in the interstellar medium with different velocities, from highly subsonic to supersonic, by means of 2D hydrodynamic relativistic simulations. We compare the different tail morphologies with results from theoretical models of mass loading in bow shocks. As predicted by analytical models we observe a fast sideways expansion of the tail with the formation of secondary shocks in the ISM. This effect could be at the origin of the head-and-shoulder morphology observed in many BSPWNe.

Small-scale Magnetic Flux Emergence in the Quiet Sun

Abstract Small bipolar magnetic features are observed to appear in the interior of individual granules in the quiet Sun, signaling the emergence of tiny magnetic loops from the solar interior. We study the origin of those features as part of the magnetoconvection process in the top layers of the convection zone. Two quiet-Sun magnetoconvection models, calculated with the radiation-magnetohydrodynamic (MHD) Bifrost code and with domain stretching from the top layers of the convection zone to the corona, are analyzed. Using 3D visualization as well as a posteriori spectral synthesis of Stokes parameters, we detect the repeated emergence of small magnetic elements in the interior of granules, as in the observations. Additionally, we identify the formation of organized horizontal magnetic sheets covering whole granules. Our approach is twofold, calculating statistical properties of the system, like joint probability density functions (JPDFs), and pursuing individual events via visualization tools. We conclude that the small magnetic loops surfacing within individual granules in the observations may originate from sites at or near the downflows in the granular and mesogranular levels, probably in the first 1 or 1.5 Mm below the surface. We also document the creation of granule-covering magnetic sheet-like structures through the sideways expansion of a small subphotospheric magnetic concentration picked up and pulled out of the interior by a nascent granule. The sheet-like structures that we found in the models may match the recent observations of Centeno et al.

Gamma-Ray Burst Jets and their Radio Observations

AbstractRadio observations play a key role in studying the jets that power GRBs, the most luminous cosmic explosions. They are crucial for determining the GRB jet energy, the external density, and the microphysical parameters of relativistic collisionless shocks, from afterglow broadband modeling. Radio image size measurements are rare, but provide extremely useful information. The “radio flare” peaking after ~1 day helps constrain the magnetisation and magnetic-field structure of GRB outflows. This review discusses the current observational and modeling status, focusing on the afterglow and outlining prompt radio emission searches, along with recent theoretical progress in GRB jet dynamics, focusing on magnetic acceleration, jet propagation inside a massive star progenitor (for long GRBs), the reverse shock, and the late afterglow. Great progress has been made in our understanding of magnetic acceleration, collimation and later sideways expansion of GRB jets, with interesting implications for the prompt, reverse shock, and afterglow emission. We outline how theory and observations were combined to study GRB jet physics and their immediate environment. Finally, potential paths are suggested for combining theory and observations to achieve greater progress, and some prospects for the future are discussed in light of the expected improvements in observational capabilities and theoretical advances.

Rarefaction acceleration in magnetized gamma-ray burst jets

Relativistic jets associated with long/soft gamma-ray bursts are formed and initially propagate in the interior of the progenitor star. Because of the subsequent loss of their external pressure support after they cross the stellar surface, these flows can be modeled as moving around a corner. A strong steady-state rarefaction wave is formed, and the sideways expansion is accompanied by a rarefaction acceleration. We investigate the efficiency and the general characteristics of this mechanism by integrating the steady-state, special relativistic, magnetohydrodynamic equations, using a special set of partial exact solutions in planar geometry (r self-similar with respect to the "corner"). We also derive analytical approximate scalings in the ultrarelativistic cold/magnetized, and hydrodynamic limits. The mechanism is more effective in magnetized than in purely hydrodynamic flows. It substantially increases the Lorentz factor without much affecting the opening of the jet; the resulting values of their product can be much grater than unity, allowing for possible breaks in the afterglow light curves. These findings are similar to the ones from numerical simulations of axisymmetric jets by Komissarov et al and Tchekhovskoy et al, although in our approach we describe the rarefaction as a steady-state simple wave and self-consistently calculate the opening of the jet that corresponds to zero external pressure.

OBSERVATIONAL IMPLICATIONS OF GAMMA-RAY BURST AFTERGLOW JET SIMULATIONS AND NUMERICAL LIGHT CURVE CALCULATIONS

We discuss jet dynamics for narrow and wide gamma-ray burst (GRB) afterglow jets and the observational implications of numerical simulations of relativistic jets in two dimensions. We confirm earlier numerical results that sideways expansion of relativistic jets during the bulk of the afterglow emission phase is logarithmic in time and find that this also applies to narrow jets with half opening angle of 0.05 radians. As a result, afterglow jets remain highly nonspherical until after they have become nonrelativistic. Although sideways expansion steepens the afterglow light curve after the jet break, the jet edges becoming visible dominates the jet break, which means that the jet break is sensitive to the observer angle even for narrow jets. Failure to take the observer angle into account can lead to an overestimation of the jet energy by up to a factor 4. This weakens the challenge posed to the magneter energy limit by extreme events such as GRB090926A. Late time radio calorimetry based on a spherical nonrelativistic outflow model remains relevant when the observer is approximately on-axis and where differences of a few in flux level between the model and the simulation are acceptable. However, this does not imply sphericity of the outflow and therefore does not translate to high observer angles relevant to orphan afterglows. For more accurate calorimetry and in order to model significant late time features such as the rise of the counterjet, detailed jet simulations remain indispensable.

On the sideways expansion of relativistic non-spherical shocks and gamma-ray burst afterglows

Expansion of non-spherical relativistic blast waves is considered in the Kompaneets (the thin shell) approximation. We find that the relativistic motion effectively "freezes out" the lateral dynamics of the shock front: only extremely strongly collimated shocks, with the opening angles $\Delta \theta \leq 1/\Gamma^2$, show appreciable modification of profiles due to sideways expansion. For less collimated profiles the propagation is nearly ballistic; the sideways expansion of relativistic shock becomes important only when they become mildly relativistic.

On the lateral expansion of gamma-ray burst jets

The dynamics of GRB jets during the afterglow phase have an important effect on the interpretation of their observations and for inferring key physical parameters such as their true energy and event rate. Semi-analytic models generally predict a fast lateral expansion, where the jet opening angle asymptotically grows exponentially with its radius. Numerical simulations, however, show a much more modest lateral expansion, where the jet retains memory of its initial opening angle for a very long time, and the flow remains non-spherical until it becomes sub-relativistic, and only then gradually approaches spherical symmetry. Here we suggest a new analytic model based on a new physically derived recipe for the lateral expansion. We also generalize the model by relaxing the common approximations of ultra-relativistic motion and a narrow jet opening angle. We find that the new analytic model fits much better the results of numerical simulations, mainly because it remains valid also in the mildly relativistic, quasi spherical regime. This model shows that for modest initial jet half-opening angles, \theta_0, the outflow is not sufficiently ultra-relativistic when its Lorentz factor reaches \Gamma = 1/\theta_0 and therefore the sideways expansion is rather slow, showing no rapid, exponential phase. On the other hand, we find that jets with an extremely narrow initial half-opening angle, of about \theta_0 << 10^{-1.5} or so, which are still sufficiently ultra-relativistic at \Gamma = 1/\theta_0, do show a phase of rapid, exponential lateral expansion. However, even such jets that expand sideways exponentially are still not spherical when they become sub-relativistic.

RELATIVISTIC JET DYNAMICS AND CALORIMETRY OF GAMMA-RAY BURSTS

We present numerical solutions of the 2D relativistic hydrodynamics equations describing the deceleration and expansion of highly relativistic conical jets, of opening angles 0.05<theta<0.2, propagating into a medium of uniform density. Jet evolution is followed from a collimated relativistic outflow through to the quasi-spherical non-relativistic phase. We show that relativistic sideways expansion becomes significant beyond the radius R at which the expansion Lorentz factor drops to 1/theta. This is consistent with simple analytic estimates, which predict faster sideways expansion than has been claimed based on earlier numerical modeling. For t>R/c the emission of radiation from the jet blast wave is similar to that of a spherical blast wave carrying the same energy. Thus, the total (calorimetric) energy of GRB blast waves may be estimated with only a small fractional error based on t>R/c observations.

Rarefaction acceleration of ultrarelativistic magnetized jets in gamma-ray burst sources

When a magnetically-dominated super-fast magnetosonic GRB jet leaves the progenitor star the external pressure support may drop and the jet may enter the regime of ballistic expansion during which its magnetic acceleration becomes highly ineffective. However, recent numerical simulations suggested that the transition to this regime is accompanied by a sudden "burst" of acceleration. We confirm this finding and attribute the acceleration to the sideways expansion of the jet - the magnetic energy is converted into the kinetic one in the strong magnetosonic rarefaction wave, which is launched when the jet loses its external support. This type of acceleration, the rarefaction acceleration, is specific to relativistic jets because their energy budget can still be dominated by magnetic energy even in highly super-fast magnetosonic regime. Just like the collimation acceleration of externally confined magnetized jets, it is connected with the geometry of magnetic flux sufaces. In both cases, in the acceleration zone the poloidal field lines diverge faster than in the monopolar configuration. On the other hand, whereas the collimation acceleration keeps the product of jet opening angle and Lorentz factor somewhat below unity, the rarefaction acceleration allows to make it significantly larger, in agreement with the standard model of jet breaks in afterglow light curves.

Decay of the toroidal field in magnetically driven jets

A 3D simulation of a non-relativistic, magnetically driven jet propagating in a stratified atmosphere is presented, covering about three decades in distance and two decades in sideways expansion. The simulation captures the jet acceleration through the critical surfaces and the development of (kink-)instabilities driven by the free energy in the toroidal magnetic field component. The instabilities destroy the ordered helical structure of the magnetic field, dissipating the toroidal field energy on a length scale of about 2-15 times the Alfven distance. We compare the results with a 2.5D (axisymmetric) simulation, which does not become unstable. The acceleration of the flow is found to be quite similar in both cases, but the mechanisms of acceleration differ. In the 2.5D case approximately 20% of the Poynting flux remains in the flow, in the 3D case this fraction is largely dissipated internally. Half of the dissipated energy is available for light emission; the resulting radiation would produce structures resembling those seen in protostellar jets.

THE DYNAMICS AND AFTERGLOW RADIATION OF GAMMA-RAY BURSTS. I. CONSTANT DENSITY MEDIUM

Direct multidimensional numerical simulation is the most reliable approach for calculating the fluid dynamics and observational signatures of relativistic jets in gamma-ray bursts (GRBs). We present a two-dimensional relativistic hydrodynamic simulation of a GRB outflow during the afterglow phase, which uses the fifth-order weighted essentially nonoscillatory scheme and adaptive mesh refinement. Initially, the jet has a Lorentz factor of 20. We have followed its evolution up to 150 years. Using the hydrodynamic data, we calculate synchrotron radiation based upon standard afterglow models and compare our results with previous analytic work. We find that the sideways expansion of a relativistic GRB jet is a very slow process and previous analytic works have overestimated its rate. In our computed light curves, a very sharp jet break is seen and the postbreak light curves are steeper than analytic predictions. We find that the jet break in GRB afterglow light curves is mainly caused by the missing flux when the edge of the jet is observed. The outflow becomes nonrelativistic at the end of the Blandford–McKee phase. But it is still highly nonspherical, and it takes a rather long time for it to become a spherical Sedov–von Neumann–Taylor blast wave. We find that the late-time afterglows become increasingly flatter over time. But we disagree with the common notion that there is a sudden flattening in light curves due to the transition into the Sedov–von Neumann–Taylor solution. We have also found that there is a bump in light curves at very late times (∼1000 days) due to radiation from the counter jet. We speculate that such a counter jet bump might have already been observed in GRB 980703.

Thermal activation of ferroelectric switching

By applying the theory of thermally activated nucleation to the switching of ferroelectric domains, a method is developed to experimentally obtain the value of both the activation enthalpy, ΔH, and activation volume, V*, for the thermally activated process involved in ferroelectric switching. The method was applied to the switching of a soft lead zirconate titanate and values of ΔH=(0.16±0.02) eV and V*=(1.62±0.16)×10−25 m3 were obtained at the coercive field. These values imply that the energy, ΔU, required for the formation of switching nuclei is mainly supplied by the work done by the electric field. A comparison of these values with those obtained from theoretical considerations suggests that the switching is achieved by the sideways expansion of nuclei formed at the domain boundaries in the form of low amplitude and long wavelength fluctuations of the domain walls.

GRB Energies and E γ - E peak Correlation with the Jet Expanding Laterally at the Sound Speed

A Gamma-ray burst (GRB) is generally believed to be a jet with a small opening angle, this opening angle is usually derived with the afterglow light curve break time using an analytical method. Here we show that the method is not accurate. Using the set of equations of hydrodynamic evolution with the sideways expansion at the local sound speed derived by previous authors and the observed light curve break times, we numerically derive the initial opening angles. Then the collimation-corrected energies (E-gamma) for a sample of GRBs are calculated. They are found to show a wide spread, suggesting that the previously declared clustering by some authors may not exist. Also, the E-peak - E-gamma relation, claimed by some other authors (E-peak is the spectral peak energy), is found still to hold, with a slightly stronger correlation.

Jet Sideways Expansion Effect on Estimating the Gamma-Ray Burst Efficiency

The high efficiency of converting kinetic energy into gamma rays estimated with late-time afterglows in gammaray burst (GRB) phenomenon challenges the commonly accepted internal-shock model. However, the efficiency is still highly uncertain because it is sensitive to many effects. In this Letter we study the sideways expansion effect of jets on estimating the efficiency. We find that this effect is considerable, reducing the efficiency by a factor of similar to 0.5 for typical parameters, when the afterglow data similar to 10 hr after the GRB trigger are used to derive the kinetic energy. For a more dense circumburst medium, this effect is more significant. As samples, taking this effect into account, we specifically calculate the efficiency of two bursts whose parameters were well constrained. Almost the same results are derived. This suggests that the sideways expansion effect should be considered when the GRB efficiency is estimated with the late afterglow data.

Estimation of the detectability of optical orphan afterglows

Aims. By neglecting sideways expansion of gamma-ray burst (GRB) jets and assuming their half-opening angle distribution, we estimate the detectability of orphan optical afterglows. Methods. This estimation is carried out by calculating the durations of off-axis optical afterglows whose flux density exceeds a certain observational limit. Results. We show that the former assumption leads to more detectable orphans, while the latter suppresses the detectability strongly compared with the model with half-opening angle θ j = 0.1. We also considered the effects of other parameters, and find that the effects of the ejecta energy E j and post-jet-break temporal index -α 2 are important but that the effects of the electron-energy distribution index p, electron energy equipartition factor ∈ e , and environment density n are insignificant. If E j and α 2 are determined by other methods, one can constrain the half-opening angle distribution of jets by observing orphan afterglows. Adopting a set of standard parameters, the detectable rate of orphan afterglows is about 1.3 x 10 -2 deg -2 yr -1 , it the observed limiting magnitude is 20 in R-band.

Jet Break Time–Flux Density Relationship and Constraints on Physical Parameters of Gamma‐Ray Burst Afterglows

We derive a relation between the flux density F(nu,j) at the light-curve break of a gamma-ray burst (GRB) afterglow and the break time t(j). The break is due to the transition from the spherical-like to jet-like evolution of the afterglow, when the Lorentz factor of the jet equals the inverse of the initial half-opening angle, i.e., gamma=1=theta(0). We show that this relation indeed behaves as F(nu,j) proportional to t(j)(-p) among GRBs for the slow-cooling case, where p is the power-law index of electron distribution. A statistical analysis of the optical jet breaks of nine GRBs gives p=2.10+/-0.21, which is consistent with the shock acceleration theory. The value of p derived in this way is different from the observed temporal index alpha(2) (F(nu) proportional to t(-alpha 2)) of the late-time light curve after t(j), which suffers several uncertainties from the unclear hydrodynamics of the sideways expansion and exhibits a large dispersion. Our results not only confirm that the remnants of GRBs are standard candles, but also provide the first evidence that the physical parameters of relativistic shocks are universal, with the favored values epsilon(e)similar to0.1 and epsilon(B)similar to10(-3).

No time for bugs [motor racing software

Motor-sport teams expect a fast turnaround when they tune the software that goes into the electronic controllers that manage the highly tuned engines used in their cars. Subtle changes to the way the embedded computer controls the engine can make the difference between winning and being stuck in the pits. And it means that the developers at one specialist company can have just two hours to make critical changes to their code. Life Racing is a tiny company tucked away in an industrial estate on the outskirts of the Essex town Basildon. It was formed as an offshoot of the specialist engine builder Advanced Engine Research (AER). Systems designer Mark Colby and a colleague moved over from another company when AER looked at a sideways expansion into electronic control units (ECUs) for motor racing. An important factor in software design for ECUs is to restrict sharing of code between different parts of the system. If a control strategy needs to be altered it is important that a change in one place does not cause problem anywhere.