Production forecasting in shale (ultra-low permeability) gas reservoirs is of great interest due to the advent of multi-stage fracturing and horizontal drilling. The well renowned production forecasting model, Arps? Hyperbolic Decline Model, is widely used in industry to forecast shale gas wells. Left unconstrained, the model often overestimates reserves by a great deal. A minimum decline rate is imposed to prevent overestimation of reserves but with less than ten years of production history available to analyze, an accurate minimum decline rate is currently unknown; an educated guess of 5% minimum decline is often imposed. Other decline curve models have been proposed with the theoretical advantage of being able to match linear flow followed by a transition to boundary dominated flow. This thesis investigates the applicability of the Stretched Exponential Production Decline Model (SEPD) and compares it to the industry standard, Arps' with a minimum decline rate. When possible, we investigate an SEPD type curve. Simulated data is analyzed to show advantages of the SEPD model and provide a comparison to Arps' model with an imposed minimum decline rate of 5% where the full production history is known. Long-term production behavior is provided by an analytical solution for a homogenous reservoir with homogenous hydraulic fractures. Various simulations from short-term linear flow (~1 year) to long-term linear flow (~20 years) show the ability of the models to handle onset of boundary dominated flow at various times during production history. SEPD provides more accurate reserves estimates when linear flow ends at 5 years or earlier. Both models provide sufficient reserves estimates for longer-term linear flow scenarios. Barnett Shale production data demonstrates the ability of the models to forecast field data. Denton and Tarrant County wells are analyzed as groups and individually. SEPD type curves generated with 2004 well groups provide forecasts for wells drilled in subsequent years. This study suggests a type curve is most useful when 24 months or less is available to forecast. The SEPD model generally provides more conservative forecasts and EUR estimates than Arps' model with a minimum decline rate of 5%.

The paper presents a posteriori error estimators for the stationary Stokes problem. We consider anisotropic finite element discretizations (i.e. elements with very large aspect ratio) where conventional, isotropic error estimators fail. Our analysis covers two- and three-dimensional domains, conforming and nonconforming discretizations as well as different elements. This large variety of settings requires different approaches and results in different estimators. Furthermore many examples of finite element pairs that are covered by the analysis are presented. Lower and upper error bounds form the main result with minimal assumptions on the elements. The lower error bound is uniform with respect to the mesh anisotropy with the exception of nonconforming 3D discretizations made of pentahedra or hexahedra. The upper error bound depends on a proper alignment of the anisotropy of the mesh which is a common feature of anisotropic error estimation. In the special case of isotropic meshes, the results simplify, and upper and lower error bounds hold unconditionally. Some of the corresponding results seem to be novel (in particular for 3D domains), and cover element pairs of practical importance. The numerical experiments confirm the theoretical predictions and show the usefulness of the anisotropic error estimators.

Reserves estimation in an unconventional-reservoir setting is a daunting task because of geologic uncertainty and complex flow patterns evolving in a long-stimulated horizontal well, among other variables. To tackle this complex problem, we present a reserves-evaluation workflow that couples the traditional decline-curve analysis with a probabilistic forecasting frame. The stretched-exponential production decline model (SEPD) underpins the production behavior. Our recovery appraisal workflow has two different applications: forecasting probabilistic future performance of wells that have production history; and forecasting production from new wells without production data. For the new field case, numerical model runs are made in accord with the statistical design of experiments for a range of design variables pertinent to the field of interest. In contrast, for the producing wells the early-time data often need adjustments owing to restimulation, installation of artificial-lift, etc. to focus on the decline trend. Thereafter, production data of either new or existing wells are grouped in accord with initial rates to obtain common SEPD parameters for similar wells. After determining the distribution of model parameters using well grouping, the methodology establishes a probabilistic forecast for individual wells. We present a probabilistic performance forecasting methodology in unconventional reservoirs for wells with and without production history. Unlike other probabilistic forecasting tools, grouping wells with similar production character allows estimation of self-consistent SEPD parameters and alleviates the burden of having to define uncertainties associated with reservoir and well-completion parameters.

Title: Syntactic specialities of stretched verb s in the german journalism Summary: This work interprets the meaning and use of stretched verb constructions. Every element of this construction is described. The practical part analyses the use of these verbs in newspapers. It shows that their use depends on the newspaper and even on the region. The last Chapter offers some grammatical exercises. Keywords: stretched verb, syntax, newspaper analyse, exercises

Title: Syntactic characteristics (features) of stretched verb constructions in the language of german journalism Summary: This thesis interprets the meaning and the use of stretched verb constructions. The german newspapers "Frankfurter Allgemeine Zeitung", "Mannheimer Morgen" and "Bild" were chosen as the research objects. The thesis is devided in three chapters. The first chapter explains the theory in general and describes the newspapers and the research method in detail. The practical part analyses the use of these verbs in newspapers and shows that their use depends not only on the newspaper but on the region. The last chapter offers some grammar exercises for the practical use of this construction. Keywords: stretched verb constructions, syntax, newspaper analyse, exercises

O presente estudo teve por finalidade avaliar os efeitos da contagem de células somáticas (CCS) no leite cru (nos níveis de 100-200.000, 400-500.000 e >800.000 céls./mL) sobre as características físicas, químicas, microbiológicas, sensoriais e funcionais dos queijos Minas Frescal e tipo Mussarela. Utilizou-se um delineamento experimental em parcelas subdivididas em blocos, considerando-se a contagem de células somáticas como efeito principal, os dias de análise como subparcelas e os processamentos como blocos. Cada tipo de leite foi obtido da ordenha de animais previamente selecionados de acordo com o nível de células somáticas. As etapas de elaboração dos queijos incluíram a pasteurização do leite (65º C, 30 minutos), adição de cloreto de cálcio, fermento (para a Mussarela) e coalho, coagulação e obtenção do coágulo, dessoragem, salga na massa, filagem, moldagem, salga na salmoura (para a Mussarela), e embalagem dos produtos. Os queijos foram mantidos em B.O.D. a 4 ºC e avaliados nos dias 2, 9, 16, 23 e 30 após a fabricação. A seqüência de elaboração dos queijos Minas e tipo Mussarela foi repetida 5 e 3 vezes, respectivamente, para cada tratamento. As análises realizadas nos queijos foram: pH, acidez, percentuais de gordura, matéria seca (MS), cinzas, nitrogênio total (NT), nitrogênio não protéico (NNP), nitrogênio não caseinoso (NNC), índice de proteólise, ácidos graxos livres (AGL), textura, avaliação sensorial, propriedades funcionais (capacidade de derretimento a 107 ºC e percentual de óleo livre - somente no queijo tipo Mussarela), contagem de mesófilos, psicrotróficos e número mais provável a 35 e 45 ºC. No queijo Minas Frescal, não houve interação entre CCS e dias de armazenamentos nas avaliações físico-químicas, microbiológicas, funcionais e índice de lipólise, porém houve efeito significativo (P<0,05) para índices de proteólise e profundidade da proteólise. Já para mesófilos, psicrotróficos, acidez, matéria seca, firmeza e ácidos graxos livres houve efeito significativo (P<0,05) ao avaliar dias de armazenamento. A avaliação sensorial, no primeiro dia de análise, não apresentou diferença significativa nos atributos, porém o queijo de alta CCS (> 800.000 céls./mL) diferiu dos demais no dia 30, em que recebeu menor nota em todas as características. No queijo tipo Mussarela, houve interação entre CCS e dias de armazenamento apenas para a capacidade de derretimento, resultando em aumento do derretimento no decorrer do tempo. Para as características de pH, ácidos graxos livres, índices de proteólise, extensão e profundidade da proteólise, mastigabilidade e elasticidade houve efeito significativo (P<0,05) para dias de armazenamento. Entre os atributos avaliados na sensorial, apenas a aparência apresentou diferença entre tratamentos. O rendimento dos queijos, Minas frescal e tipo Mussarela, não foram influenciados pela quantidade de células somáticas dos leites. Os resultados do trabalho indicaram que o leite destinado à fabricação dos queijos Minas e tipo Mussarela deve apresentar CCS até 400-500.000 céls./mL, de maneira a evitar alterações na qualidade dos produtos ao longo do período de armazenagem. / The aim of the present study was to evaluate the effect of somatic cells counts (SCC) in raw milk (at levels of 100-200,000, 400-500,000 and 800,000 cells./mL) on physical, chemical, microbiological, sensorial and functional characteristics of Minas frescal and Mozzarella type cheeses. A completely randomized block design was used, considering SCC as the main effect, the days of analysis as sub parcels and the processing batches as the blocks. Each type of milk was obtained from cows previously selected according to its individual SCC. The manufacture of cheeses included: pasteurization of milk (65ºC, 30 minutes), addition of calcium chloride, starter culture (for Mozzarella) and rennet, coagulation and separation of the curd, whey drainage, salting (for Minas cheese), stretching of the curd, kneading and salting in brine (for Mozzarella), and packing the products. The cheeses were stored in a B.O.D. oven at 4ºC and evaluated on days 2, 9, 16 23 and 30 after the manufacture. The sequence of elaboration of the Minas frescal and Mozzarella cheeses was repeated 5 and 3 times, respectively, for each treatment. The analyses carried out in the cheeses were: pH, acidity, percentages of fat, dry matter (DM), ashes, total nitrogen (NT), non-protein-nitrogen (NPN), non-casein nitrogen (NCN), proteolysis, free fatty acids (FFA), texture, sensorial evaluation, functional properties (melting capacity the 107 ºC and percentage of free oil - only in the cheese Mozzarella), mesophile and psychrotrophic counts and the most probable number at 30 and 45ºC. For Minas frescal cheese, no interaction was found between SCC and days of storage when considering the data on chemical, physical, microbiological, functional and lipolysis index. However, a significant effect (P<0.05) was observed for proteolysis and depth of proteolysis. For mesophiles, psychrotrophics, acidity, dry matter, firmness and free fatty acids, there was a significant effect (P<0.05) for days of storage. The sensorial evaluation made on the first day of analysis did not present significant differences for all attributes. However, the Minas cheese made with high SCC (800,000 cells/mL) differed on day 30, when it received worse grades for all the attributes. For the Mozzarella cheese, an interaction between SCC and days of storage was observed only for the melting capacity, which resulted in an increment of the melting along the time of storage. The parameters of pH, free fatty acid, proteolysis, extension and depth of proteolysis, springiness and elasticity had significant effect (P<0.05) for days of storage. Amongst the attributes evaluated in the sensorial, only the appearance presented difference between treatments. The yield of Minas frescal and Mozzarella cheese was not influenced by the amount of somatic cells in the original milk. Results indicated that milk used for the manufacture of Minas frescal and Mozzarella cheeses should present SCC up to 400-500,000 cells/mL, in order to avoid quality changes in those products during storage.

Today everyone seems to agree that ultra-low permeability and shale reservoirs have become the potentials to transform North America's oil and gas industry to a new phase. Unfortunately, transient flow is of long duration (perhaps life of the well) in ultra-low permeability reservoirs, and traditional decline curve analysis (DCA) models can lead to significantly over-optimistic production forecasts without additional safeguards. Stretched Exponential decline model (SEDM) gives considerably more stabilized production forecast than traditional DCA models and in this work it is shown that it produces unchanging EUR forecasts after only two-three years of production data are available in selected reservoirs, notably the Barnett Shale. For an individual well, the SEDM model parameters, can be determined by the method of least squares in various ways, but the inherent nonlinear character of the least squares problem cannot be bypassed. To assure a unique solution to the parameter estimation problem, this work suggests a physics-based regularization approach, based on critical velocity concept. Applied to selected Barnett Shale gas wells, the suggested method leads to reliable and consistent EURs. To further understand the interaction of the different fracture properties on reservoir response and production decline curve behavior, a series of Discrete Fracture Network (DFN) simulations were performed. Results show that at least a 3-layer model is required to reproduce the decline behavior as captured in the published SEDM parameters for Barnett Shale. Further, DFN modeling implies a large number of parameters like fracture density and fracture length are in such a way that their effect can be compensated by the other one. The results of DFN modeling of several Barnett Shale horizontal wells, with numerous fracture stages, showed a very good agreement with the estimated SEDM model for the same wells. Estimation of P90 reserves that meet SEC criteria is required by law for all companies that raise capital in the United States. Estimation of P50 and P10 reserves that meet SPE/WPC/AAPG/SPEE Petroleum Resources Management System (PRMS) criteria is important for internal resource inventories for most companies. In this work a systematic methodology was developed to quantify the range of uncertainty in production forecast using SEDM. This methodology can be used as a probabilistic tool to quantify P90, P50, and P10 reserves and hence might provide one possible way to satisfy the various legal and technical-society-suggested criteria.

Abstract: Background: At present, device closure of interatrial communication has become a well established technique in order to adequately treat severe left-to-right shunt associated with ASDs. During the traditional procedure, fluoroscopy with the waist of a compliant balloon is used to determine the appropriate size of the closure device and defect sizing. Choice of adequate closure device using transthoracic echocardiography (TTE) has been hitherto unreported. Methods & Materials: Between December 2002 and October 2004, 40 patients (15 males, 25 females, mean age; 11.7 ¡Ó 7.8 years ) with secundum ASDs underwent transcatheter closure at our institution. In group 1, 30 patients had the procedure by balloon sizing and TTE sizing. In 10 patients (group 2), TTE sizing was used as the sole too l for selecting device size and the device size was chosen to be based on the Amplatzer septal occluder ( ASO ) size and TTE size ratio in group 1. The procedure was performed under continuous transoesophageal echocardiographic monitor with general anesthesia. Results: The correlation was found between TTE and stretched balloon sizing diameter SBD ( y= 1.2645x-1.4465; R&#x00B2;=0.9861 ), and between TTE size and ASO size ( y = 1.3412x-1.2864; R&#x00B2;=0.9929 ) in group 1. In group 2, statistical correlation between TTE and ASO ( y=1.3419x-0.1172; R&#x00B2;=0.9934 ) was also found. Good linear regression between TTE size and ASO chosen size was noted in group 1 and group 2 (R&#x00B2;=0.99).In group 2, successful device implantation was accomplished in all patients whose device size was chosen to be based on the ASO and TTE ratio in group 1. Conclusions: TTE sizing is a safe and ideal method to measure interatrial defect and choose the occluding device respectively. With our experience, the sizing based on the TTE is generally easier than measurement from the balloon sizing.

We consider a singularly perturbed reaction-diffusion problem and derive and rigorously analyse an a posteriori residual error estimator that can be applied to anisotropic finite element meshes. The quotient of the upper and lower error bounds is the so-called matching function which depends on the anisotropy (of the mesh and the solution) but not on the small perturbation parameter. This matching function measures how well the anisotropic finite element mesh corresponds to the anisotropic problem. Provided this correspondence is sufficiently good, the matching function is O(1). Hence one obtains tight error bounds, i.e. the error estimator is reliable and efficient as well as robust with respect to the small perturbation parameter. A numerical example supports the anisotropic error analysis.

Singularly perturbed problems often yield solutions ith strong directional features, e.g. with boundary layers. Such anisotropic solutions lend themselves to adapted, anisotropic discretizations. The quality of the corresponding numerical solution is a key issue in any computational simulation. To this end we present a new robust error estimator for a singularly perturbed reaction-diffusion problem. In contrast to conventional estimators, our proposal is suitable for anisotropic finite element meshes. The estimator is based on the solution of a local problem, and yields error bounds uniformly in the small perturbation parameter. The error estimation is efficient, i.e. a lower error bound holds. The error estimator is also reliable, i.e. an upper error bound holds, provided that the anisotropic mesh discretizes the problem sufficiently well. A numerical example supports the analysis of our anisotropic error estimator.