An experimental investigation of the effects of nozzle ellipticity on the flow structure of co-flow jet diffusion flames

The flow structure of cold and ignited jets issuing into a co-flowing air stream was experimentally studied using a laser Doppler velocimeter. Methane was employed as the jet fluid discharging from circular and elliptic nozzles with aspect ratios varying from 1.29 to 1.60. The diameter of the circular nozzle was 4.6 mm and the elliptic nozzles had approximately the same exit area as that of the circular nozzle. These non-circular nozzles were employed in order to increase the stability of attached jet diffusion flames. The time-averaged velocity and r.m.s. value of the velocity fluctuation in the streamwise and transverse directions were measured over the range of co-flowing stream velocities corresponding to different modes of flame blowout that are identified as either lifted or attached flames. On the basis of these measurements, attempts were made to explain the existence of an apparent optimum aspect ratio for the blowout of attached flames observed at higher values of co-flowing stream velocities. The insensitivity of the blowout limits of lifted flames to nozzle geometry observed in our previous work at low co-flowing stream velocities was also explained. Measurements of the fuel concentration at the jet centerline indicated that the mixing process was enhanced with the 1.38 aspect ratio jet compared with the 1.60 aspect ratio jet. On the basis of the obtained experimental data, it was suggested that the higher blowout limits of attached flames for an elliptic jet of 1.38 aspect ratio was due to higher entrainment rates.

Morphological characterization with image analysis of cocoa beverage powder agglomerated with steam

In this study, the morphological characteristics of cocoa beverage powder granules under minimal, average, and maximal process conditions of a steam agglomerator were studied. a stereoscopic microscope coupled to a digital camera was used for the morphological analysis. The images were analyzed to obtain shape and size descriptors. aiming to evaluate the descriptors, 150 particles were analyzed. The results showed that there was no difference between the shape descriptors - compacity, circularity, roughness, and aspect ratio - in the operating conditions evaluated. It was observed that the cocoa beverage powder granules are elongated in shape. The size descriptors, area, perimeter, perimeter of convex bounding polygon, minimal and maximal Feret diameter, were different in the process conditions for the granules of size above 600 μm. as for the minimal process conditions, especially due to low solid feed rates, there is an increase in the size descriptor values. In addition, under the minimum process conditions, in which there is low solid feed rate (400g/min) for a steam pressure of 1.0 bar, it was obtained a good granular condition with retention of 81.1% of granules on sieves with aperture size between 300 and 1190 μm.

On the Growth Mechanism of Nickel and Cobalt Nanowires and Comparison of Their Magnetic Properties

Magnetic nanowires (NWs) are ideal materials for the fabrication of various multifunctional nanostructures which can be manipulated by an external magnetic fi eld. Highly crystalline and textured nanowires of nickel (Ni NWs) and cobalt (Co NWs) with high aspect ratio (~330) and high coercivity have been synthesized by electrodeposition using nickel sulphate hexahydrate (NiSO4·6H2O) and cobalt sulphate heptahydrate (CoSO4·7H2O) respectively on nanoporous alumina membranes. They exhibit a preferential growth along〈110〉. A general mobility assisted growth mechanism for the formation of Ni and Co NWs is proposed. The role of the hydration layer on the resulting one-dimensional geometry in the case of potentiostatic electrodeposition is verified. A very high interwire interaction resulting from magnetostatic dipolar interactions between the nanowires is observed. An unusual low-temperature magnetisation switching for fi eld parallel to the wire axis is evident from the peculiar high fi eld M(T) curve

Strain induced anomalous red shift in mesoscopic iron oxide prepared by a novel technique

Nano magnetic oxides are promising candidates for high density magnetic storage and other applications. Nonspherical mesoscopic iron oxide particles are also candidate materials for studying the shape, size and strain induced modifications of various physical properties viz. optical, magnetic and structural. Spherical and nonspherical iron oxides having an aspect ratio, ~2, are synthesized by employing starch and ethylene glycol and starch and water, respectively by a novel technique. Their optical, structural, thermal and magnetic properties are evaluated. A red shift of 0⋅24 eV is observed in the case of nonspherical particles when compared to spherical ones. The red shift is attributed to strain induced changes in internal pressure inside the elongated iron oxide particles. Pressure induced effects are due to the increased overlap of wave functions. Magnetic measurements reveal that particles are superparamagnetic. The marked increase in coercivity in the case of elongated particles is a clear evidence for shape induced anisotropy. The decreased specific saturation magnetization of the samples is explained on the basis of weight percentage of starch, a nonmagnetic component and is verified by TGA and FTIR studies. This technique can be modified for tailoring the aspect ratio and these particles are promising candidates for drug delivery and contrast enhancement agents in magnetic resonance imaging

Lithography-free micro- and nanostructuring based on conventional plasma etching

In now-a-days semiconductor and MEMS technologies the photolithography is the working horse for fabrication of functional devices. The conventional way (so called Top-Down approach) of microstructuring starts with photolithography, followed by patterning the structures using etching, especially dry etching. The requirements for smaller and hence faster devices lead to decrease of the feature size to the range of several nanometers. However, the production of devices in this scale range needs photolithography equipment, which must overcome the diffraction limit. Therefore, new photolithography techniques have been recently developed, but they are rather expensive and restricted to plane surfaces. Recently a new route has been presented - so-called Bottom-Up approach - where from a single atom or a molecule it is possible to obtain functional devices. This creates new field - Nanotechnology - where one speaks about structures with dimensions 1 - 100 nm, and which has the possibility to replace the conventional photolithography concerning its integral part - the self-assembly. However, this technique requires additional and special equipment and therefore is not yet widely applicable. This work presents a general scheme for the fabrication of silicon and silicon dioxide structures with lateral dimensions of less than 100 nm that avoids high-resolution photolithography processes. For the self-aligned formation of extremely small openings in silicon dioxide layers at in depth sharpened surface structures, the angle dependent etching rate distribution of silicon dioxide against plasma etching with a fluorocarbon gas (CHF3) was exploited. Subsequent anisotropic plasma etching of the silicon substrate material through the perforated silicon dioxide masking layer results in high aspect ratio trenches of approximately the same lateral dimensions. The latter can be reduced and precisely adjusted between 0 and 200 nm by thermal oxidation of the silicon structures owing to the volume expansion of silicon during the oxidation. On the basis of this a technology for the fabrication of SNOM calibration standards is presented. Additionally so-formed trenches were used as a template for CVD deposition of diamond resulting in high aspect ratio diamond knife. A lithography-free method for production of periodic and nonperiodic surface structures using the angular dependence of the etching rate is also presented. It combines the self-assembly of masking particles with the conventional plasma etching techniques known from microelectromechanical system technology. The method is generally applicable to bulk as well as layered materials. In this work, layers of glass spheres of different diameters were assembled on the sample surface forming a mask against plasma etching. Silicon surface structures with periodicity of 500 nm and feature dimensions of 20 nm were produced in this way. Thermal oxidation of the so structured silicon substrate offers the capability to vary the fill factor of the periodic structure owing to the volume expansion during oxidation but also to define silicon dioxide surface structures by selective plasma etching. Similar structures can be simply obtained by structuring silicon dioxide layers on silicon. The method offers a simple route for bridging the Nano- and Microtechnology and moreover, an uncomplicated way for photonic crystal fabrication.

Wechselwirkung von im NANOJET erzeugten Teilchen mit Polymeren und biologischen Objekten

Am Institut für Mikrostrukturtechnologie und Analytik wurde eine neue Technik entwickelt, die neue Anwendungen und Methoden der Mikro- und Nanostrukturierung auf Basis eines neuen Verfahrens erschlossen hat. NANOJET führt über die passive Rastersondenmikroskopie hinaus zu einem vielseitigen, aktiven Bearbeitungswerkzeug auf der Mikro- und Nanometerskala. NANOJET (NANOstructuring Downstream PlasmaJET) ist eine aktive Rasterkraft-Mikroskopie-Sonde. Radikale (chemisch aktive Teilchen, die ein ungepaartes Valenzelektron besitzen) strömen aus dem Ende einer ultradünnen, hohlen Rasterkraftmikroskop-Spitze. Dadurch wird es möglich, über die übliche passive Abtastung einer Probenoberfläche hinausgehend, diese simultan und in-situ durch chemische Reaktionen zu verändern. Die Abtragung von Material wird durch eine chemische Ätzreaktion erreicht. In dieser Arbeit wurde zum größten Teil Photoresist als Substrat für die Ätzexperimente verwendet. Für das Ätzen des Resists wurden die Atome des Fluors und des Sauerstoffs im Grundzustand als verantwortlich identifiziert. Durch Experimente und durch Ergänzung von Literaturdaten wurde die Annahme bestätigt, dass Sauerstoffradikale mit Unterstützung von Fluorradikalen für die hohen erzielten Ätzraten verantwortlich sind. Die Beimischung von Fluor in einem Sauerstoffplasma führt zu einer Verringerung der Aktivierungsenergie für die Ätzreaktion gegenüber Verwendung reinen Sauerstoffs. In weiterer Folge wurde ein Strukturierungsverfahren dargestellt. Hierbei wurden "geformte Kapillaren" (mikrostrukturierte Aperturen) eingesetzt. Die Herstellung der Aperturen erfolgte durch einen elektrochemischen Ätzstop-Prozess. Die typische Größe der unter Verwendung der "geformten Kapillaren" geätzten Strukturen entsprach den Kapillarenöffnungen. Es wurde ein Monte-Carlo Simulationsprogramm entwickelt, welches den Transport der reaktiven Teilchen in der langen Transportröhre simulierte. Es wurde sowohl die Transmission der Teilchen in der Transportröhre und der Kapillare als auch ihre Winkelverteilung nach dem Verlassen der Kapillare berechnet. Das Aspektverhältnis der Röhren hat dabei einen sehr starken Einfluss. Mit einem steigenden Aspektverhältnis nahm die Transmission exponentiell ab. Die geschaffene experimentelle Infrastruktur wurde genutzt, um auch biologische Objekte zu behandeln und zu untersuchen. Hierfür wurde eine neue Methodik entwickelt, die eine dreidimensionale Darstellung des Zellinneren erlaubt. Dies wurde durch die kontrollierte Abtragung von Material aus der Zellmembran durchgeführt. Die Abtragung der Zellmembran erfolgte mittels Sauerstoffradikalen, die durch eine hohle Spitze lokalisiert zum Ort der Reaktion transportiert wurden. Ein piezoresistiver Cantilever diente als Sensor in dem zur Bildgebung eingesetzten RKM. Das entwickelte Verfahren ermöglicht es nun erstmals, schonend Zellen zu öffnen und die innen liegenden Organellen weiter zu untersuchen. Als Nachweis für weitere Verwendungsmöglichkeiten des NANOJET-Verfahrens wurde auch Knochenmaterial behandelt. Die Ergebnisse dieser Experimente zeigen klar, dass das Verfahren für vielfältige biologische Materialien verwendbar ist und somit nun ein weiter Anwendungskreis in der Biologie und Medizin offen steht.

Profile simulations of gas chopping etching processes : model development and comparison with experiments

The progress in microsystem technology or nano technology places extended requirements to the fabrication processes. The trend is moving towards structuring within the nanometer scale on the one hand, and towards fabrication of structures with high aspect ratio (ratio of vertical vs. lateral dimensions) and large depths in the 100 µm scale on the other hand. Current procedures for the microstructuring of silicon are wet chemical etching and dry or plasma etching. A modern plasma etching technique for the structuring of silicon is the so-called "gas chopping" etching technique (also called "time-multiplexed etching"). In this etching technique, passivation cycles, which prevent lateral underetching of sidewalls, and etching cycles, which etch preferably in the vertical direction because of the sidewall passivation, are constantly alternated during the complete etching process. To do this, a CHF3/CH4 plasma, which generates CF monomeres is employed during the passivation cycle, and a SF6/Ar, which generates fluorine radicals and ions plasma is employed during the etching cycle. Depending on the requirements on the etched profile, the durations of the individual passivation and etching cycles are in the range of a few seconds up to several minutes. The profiles achieved with this etching process crucially depend on the flow of reactants, i.e. CF monomeres during the passivation cycle, and ions and fluorine radicals during the etching cycle, to the bottom of the profile, especially for profiles with high aspect ratio. With regard to the predictability of the etching processes, knowledge of the fundamental effects taking place during a gas chopping etching process, and their impact onto the resulting profile is required. For this purpose in the context of this work, a model for the description of the profile evolution of such etching processes is proposed, which considers the reactions (etching or deposition) at the sample surface on a phenomenological basis. Furthermore, the reactant transport inside the etching trench is modelled, based on angular distribution functions and on absorption probabilities at the sidewalls and bottom of the trench. A comparison of the simulated profiles with corresponding experimental profiles reveals that the proposed model reproduces the experimental profiles, if the angular distribution functions and absorption probabilities employed in the model is in agreement with data found in the literature. Therefor the model developed in the context of this work is an adequate description of the effects taking place during a gas chopping plasma etching process.

Preparation and applications of periodical gold nanoparticle arrays

Diese Arbeit beschäftigt sich mit der Herstellung und Anwendungen von periodischen Goldnanopartikel-Arrays (PPAs), die mit Hilfe von Nanosphären-Lithografie hergestellt wurden. In Abhängigkeit der verwendeten Nanosphären-Größe wurden dabei entweder kleine dreieckige Nanopartikel (NP) (bei Verwendung von Nanosphären mit einem Durchmesser von 330 nm) oder große dreieckige NPD sowie leicht gestreckte NP (bei Verwendung von Nanosphären mit einem Durchmesser von 1390 nm) hergestellt. Die Charakterisierung der PPAs erfolgte mit Hilfe von Rasterkraftmikroskopie, Rasterelektronenmikroskopie und optischer Spektroskopie. Die kleinen NP besitzen ein Achsverhältnis (AV) von 2,47 (Kantenlänge des NPs: (74+/-6) nm, Höhe: (30+/-4) nm. Die großen dreieckigen NP haben ein AV von 3 (Kantenlänge des NPs:(465+/-27) nm, Höhe: (1530+/-10) nm) und die leicht gestreckten NP (die aufgrund der Ausbildung von Doppelschichten ebenfalls auf der gleichen Probe erzeugt wurden) haben eine Länge von (364+/-16)nm, eine Breite von (150+/-20) nm und eine Höhe von (150+/-10)nm. Die optischen Eigenschaften dieser NP werden durch lokalisierte Oberflächenplasmon-Polariton Resonanzen (LPPRs) dominiert, d.h. von einem eingestrahlten elektromagnetischen Feld angeregte kollektive Schwingungen der Leitungsbandelektronen. In dieser Arbeit wurden drei signifikante Herausforderungen für Plasmonik-Anwendungen bearbeitet, welche die einzigartigen optischen Eigenschaften dieser NP ausnutzen. Erstens wurden Ergebnisse der selektiven und präzisen Größenmanipulation und damit einer Kontrolle der interpartikulären Abstände von den dreieckigen Goldnanopartikel mit Hilfe von ns-gepulstem Laserlicht präsentiert. Die verwendete Methode basiert hierbei auf der Größen- und Formabhängigkeit der LPPRs der NP. Zweitens wurde die sensorischen Fähigkeiten von Gold-NP ausgenutzt, um die Bildung von molekularen Drähten auf den PPAs durch schrittweise Zugabe von unterschiedlichen molekularen Spezies zu untersuchen. Hierbei wurde die Verschiebung der LSPPR in den optischen Spektren dazu ausgenutzt, die Bildung der Nanodrähte zu überwachen. Drittens wurden Experimente vorgestellt, die sich die lokale Feldverstärkung von NP zu nutze machen, um eine hochgeordnete Nanostrukturierung von Oberflächen mittels fs-gepulstem Laserlicht zu bewerkstelligen. Dabei zeigt sich, dass neben der verwendeten Fluenz die Polarisationsrichtung des eingestrahlten Laserlichts in Bezug zu der NP-Orientierung sowie die Größe der NP äußerst wichtige Parameter für die Nanostrukturierung darstellen. So konnten z.B. Nanolöcher erzeugt werden, die bei höheren Fluenzen zu Nanogräben und Nanokanälen zusammen wuchsen. Zusammengefasst lässt sich sagen, dass die in dieser Arbeit gewonnen Ergebnisse von enormer Wichtigkeit für weitere Anwendungen sind.

Development of directly modulated high speed telecommunication lasers based on surface defined feedback gratings

High-speed semiconductor lasers are an integral part in the implemen- tation of high-bit-rate optical communications systems. They are com- pact, rugged, reliable, long-lived, and relatively inexpensive sources of coherent light. Due to the very low attenuation window that exists in the silica based optical fiber at 1.55 μm and the zero dispersion point at 1.3 μm, they have become the mainstay of optical fiber com- munication systems. For the fabrication of lasers with gratings such as, distributed bragg reflector or distributed feedback lasers, etching is the most critical step. Etching defines the lateral dimmensions of the structure which determines the performance of optoelectronic devices. In this thesis studies and experiments were carried out about the exist- ing etching processes for InP and a novel dry etching process was de- veloped. The newly developed process was based on Cl2/CH4/H2/Ar chemistry and resulted in very smooth surfaces and vertical side walls. With this process the grating definition was significantly improved as compared to other technological developments in the respective field. A surface defined grating definition approach is used in this thesis work which does not require any re-growth steps and makes the whole fabrication process simpler and cost effective. Moreover, this grating fabrication process is fully compatible with nano-imprint lithography and can be used for high throughput low-cost manufacturing. With usual etching techniques reported before it is not possible to etch very deep because of aspect ratio dependent etching phenomenon where with increasing etch depth the etch rate slows down resulting in non-vertical side walls and footing effects. Although with our de- veloped process quite vertical side walls were achieved but footing was still a problem. To overcome the challenges related to grating defini- tion and deep etching, a completely new three step gas chopping dry etching process was developed. This was the very first time that a time multiplexed etching process for an InP based material system was demonstrated. The developed gas chopping process showed extra ordinary results including high mask selectivity of 15, moderate etch- ing rate, very vertical side walls and a record high aspect ratio of 41. Both the developed etching processes are completely compatible with nano imprint lithography and can be used for low-cost high-throughput fabrication. A large number of broad area laser, ridge waveguide laser, distributed feedback laser, distributed bragg reflector laser and coupled cavity in- jection grating lasers were fabricated using the developed one step etch- ing process. Very extensive characterization was done to optimize all the important design and fabrication parameters. The devices devel- oped have shown excellent performance with a very high side mode suppression ratio of more than 52 dB, an output power of 17 mW per facet, high efficiency of 0.15 W/A, stable operation over temperature and injected currents and a threshold current as low as 30 mA for almost 1 mm long device. A record high modulation bandwidth of 15 GHz with electron-photon resonance and open eye diagrams for 10 Gbps data transmission were also shown.

Growth of ZnO Nanorods on GaN Using Aqueous Solution Method

Uniformly distributed ZnO nanorods with diameter 80-120 nm and 1-2µm long have been successfully grown at low temperatures on GaN by using the inexpensive aqueous solution method. The formation of the ZnO nanorods and the growth parameters are controlled by reactant concentration, temperature and pH. No catalyst is required. The XRD studies show that the ZnO nanorods are single crystals and that they grow along the c axis of the crystal plane. The room temperature photoluminescence measurements have shown ultraviolet peaks at 388nm with high intensity, which are comparable to those found in high quality ZnO films. The mechanism of the nanorod growth in the aqueous solution is proposed. The dependence of the ZnO nanorods on the growth parameters was also investigated. While changing the growth temperature from 60°C to 150°C, the morphology of the ZnO nanorods changed from sharp tip with high aspect ratio to flat tip with smaller aspect ratio. These kinds of structure are useful in laser and field emission application.

A Two-level Prediction Model for Deep Reactive Ion Etch (DRIE)

We contribute a quantitative and systematic model to capture etch non-uniformity in deep reactive ion etch of microelectromechanical systems (MEMS) devices. Deep reactive ion etch is commonly used in MEMS fabrication where high-aspect ratio features are to be produced in silicon. It is typical for many supposedly identical devices, perhaps of diameter 10 mm, to be etched simultaneously into one silicon wafer of diameter 150 mm. Etch non-uniformity depends on uneven distributions of ion and neutral species at the wafer level, and on local consumption of those species at the device, or die, level. An ion–neutral synergism model is constructed from data obtained from etching several layouts of differing pattern opening densities. Such a model is used to predict wafer-level variation with an r.m.s. error below 3%. This model is combined with a die-level model, which we have reported previously, on a MEMS layout. The two-level model is shown to enable prediction of both within-die and wafer-scale etch rate variation for arbitrary wafer loadings.

Behavioral Measures and their Correlation with IPM Iteration Counts on Semi-Definite Programming Problems

We study four measures of problem instance behavior that might account for the observed differences in interior-point method (IPM) iterations when these methods are used to solve semidefinite programming (SDP) problem instances: (i) an aggregate geometry measure related to the primal and dual feasible regions (aspect ratios) and norms of the optimal solutions, (ii) the (Renegar-) condition measure C(d) of the data instance, (iii) a measure of the near-absence of strict complementarity of the optimal solution, and (iv) the level of degeneracy of the optimal solution. We compute these measures for the SDPLIB suite problem instances and measure the correlation between these measures and IPM iteration counts (solved using the software SDPT3) when the measures have finite values. Our conclusions are roughly as follows: the aggregate geometry measure is highly correlated with IPM iterations (CORR = 0.896), and is a very good predictor of IPM iterations, particularly for problem instances with solutions of small norm and aspect ratio. The condition measure C(d) is also correlated with IPM iterations, but less so than the aggregate geometry measure (CORR = 0.630). The near-absence of strict complementarity is weakly correlated with IPM iterations (CORR = 0.423). The level of degeneracy of the optimal solution is essentially uncorrelated with IPM iterations.

Velocities of compressional and shear waves in limestones

Carbonate rocks are important hydrocarbon reservoir rocks with complex textures and petrophysical properties (porosity and permeability) mainly resulting from various diagenetic processes (compaction, dissolution, precipitation, cementation, etc.). These complexities make prediction of reservoir characteristics (e.g. porosity and permeability) from their seismic properties very difficult. To explore the relationship between the seismic, petrophysical and geological properties, ultrasonic compressional- and shear-wave velocity measurements were made under a simulated in situ condition of pressure (50 MPa hydrostatic effective pressure) at frequencies of approximately 0.85 MHz and 0.7 MHz, respectively, using a pulse-echo method. The measurements were made both in vacuum-dry and fully saturated conditions in oolitic limestones of the Great Oolite Formation of southern England. Some of the rocks were fully saturated with oil. The acoustic measurements were supplemented by porosity and permeability measurements, petrological and pore geometry studies of resin-impregnated polished thin sections, X-ray diffraction analyses and scanning electron microscope studies to investigate submicroscopic textures and micropores. It is shown that the compressional- and shear-wave velocities (V-p and V-s, respectively) decrease with increasing porosity and that V-p decreases approximately twice as fast as V-s. The systematic differences in pore structures (e.g. the aspect ratio) of the limestones produce large residuals in the velocity versus porosity relationship. It is demonstrated that the velocity versus porosity relationship can be improved by removing the pore-structure-dependent variations from the residuals. The introduction of water into the pore space decreases the shear moduli of the rocks by about 2 GPa, suggesting that there exists a fluid/matrix interaction at grain contacts, which reduces the rigidity. The predicted Biot-Gassmann velocity values are greater than the measured velocity values due to the rock-fluid interaction. This is not accounted for in the Biot-Gassmann velocity models and velocity dispersion due to a local flow mechanism. The velocities predicted by the Raymer and time-average relationships overestimated the measured velocities even more than the Biot model.

The Effects of Stratification on Flow Separation

Separation of stratified flow over a two-dimensional hill is inhibited or facilitated by acceleration or deceleration of the flow just outside the attached boundary layer. In this note, an expression is derived for this acceleration or deceleration in terms of streamline curvature and stratification. The expression is valid for linear as well as nonlinear deformation of the flow. For hills of vanishing aspect ratio a linear theory can be derived and a full regime diagram for separation can be constructed. For hills of finite aspect ratio scaling relationships can be derived that indicate the presence of a critical aspect ratio, proportional to the stratification, above which separation will occur as well as a second critical aspect ratio above which separation will always occur irrespective of stratification.

The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a two-dimensional reservoir in an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting or extracting fluid. Numerical solution of this problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l. This is a situation which occurs frequently in the application to oil reservoir recovery. Under the assumption that epsilon=h/l<<1, we show that the pressure field varies only in the horizontal direction away from the wells (the outer region). We construct two-term asymptotic expansions in epsilon in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive analytical expressions for all significant process quantities. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the reservoir, epsilon, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighborhood of wells and away from wells.