Five-region Model Research Articles

Identifying the key atmospheric and economic drivers of global carbon monoxide emission transfers

ABSTRACT This paper proposes a structural decomposition analysis (SDA) augmented with cross-country atmospheric circulation and uncovers that changes in carbon monoxide (CO) levels are driven by atmospheric flows way more than by any of the traditional SDA components. Applied to a five-region model, our results show, among others, that South Korea has certainly been able to reduce the CO emissions in its own territory by 0.8Tg over 1990–2014 but up to 10.6Tg of CO flowing to its borders came from its upwind neighbor China. That amount was primarily driven by activities satisfying the growth of China's domestic demand, although changes in foreign demand and in the technology effect were not negligible. By quantifying the role of upwind countries in air pollution changes, our methodology allows us to identify more comprehensive global emission abatement policies than the consumer- or producer-focused approaches currently used.

Trade-off principle for standard shadowed sets and its generalization to five-regions

A shadowed set S interprets and makes decision with a fuzzy set F from its approximation regions and a tri-valued mapping μS:F⟶{0,0.5,1} on fuzzy membership grades. The original idea of shadowed sets is to balance the uncertainty of F in S by a principle of uncertainty relocation. This paper proposes a principle of making a trade-off between uncertainty for certainty to minimize the amount of unclassified data and maximize the number of items for which crisp decisions are made. We provide detailed derivations for determining the optimum partition threshold for a trade-off three-region shadowed set and generalized it to five-region model S5. We investigate the existence and uniqueness of the optimum partition threshold of S5. Also, we outline some application examples where five-region shadowed sets can be reasonably exploited, including fuzzy clustering, decision-making, etc. To deliver guidance on how to construct S5, several detailed numeric examples are also provided.

Production analysis of multifractured horizontal wells with composite models: Influence of complex heterogeneity

Multi-linear analytical models are of high computational convenience to simulate the fluid production out of low-permeability unconventional (tight and shale) reservoirs stimulated with multifractured horizontal wells (MFHWs). But multi-linear models cannot accurately describe the flow behavior in such reservoirs since the fluid flow around hydraulic fracture tips is not linear flow. This creates barriers for the multi-linear models to consider pressure/stress-dependent fracture and reservoir characteristics. In addition, multi-linear models in the literature cannot consider or fully consider heterogeneity conditions including the reservoir heterogeneity and well completion heterogeneity.In this study, a composite model is developed to model the fluid flow in unconventional reservoirs with MFHWs under various heterogeneity conditions. In the composite model, the reservoir is divided into sub-systems and each sub-system is further divided into flow regions. The fluid flow in one flow region can be simply linear, radial or source/sink flow. The composite model considers the pressure/rate distribution characteristics beyond fracture tips with fast calculations. The composite model is applicable to one or combinations of the following three heterogeneous conditions-fractured horizontal wells with heterogeneous completions, reservoir heterogeneity around the horizontal well and reservoir heterogeneity around a hydraulic fracture. The model’s applicability in heterogeneous reservoirs is demonstrated by the comparison with the trilinear-flow model, five-region model and numerical solutions. In this study solutions of the composite model are utilized to analyze two sets of production data from fractured horizontal wells in heterogeneous conditions.

A Model for Gate-Underlap-Dependent Short- Channel Effects in Junctionless MOSFET

In this paper, we investigate the impact of gate–source/drain underlap on short-channel behavior of junctionless (JL) transistor through a quasi-analytical model and 2-D numerical simulations. The proposed five-region model for potential is developed for the symmetric mode operation of double-gate (DG) JL MOSFET in the subthreshold regime, to predict and minimize short-channel effects (SCEs) using the optimum design of underlap regions. The five-region model can be transformed into four or three regions to incorporate the possible dependence of biases, doping, and gate workfunction with the underlap length. The parameters indicating SCEs can also be extracted using an analytical approximation for subthreshold drain current. The results from the proposed model are in reasonable agreement with simulation data. Analyses show that underlap length is a critical parameter to restrict the lateral extension of depletion region into the ungated portion. With increasing the underlap length, SCEs improve prominently for moderate doping concentration ( $10^{18}$ cm $^{-3}$ ). The improvement in SCEs ceases once the device achieves the maximum lateral extension of the depletion region. This paper provides the physical insights into the optimal use of underlap region in nanoscale JL devices for suppressing SCEs.

Unconventional multi-fractured analytical solution using dual porosity model

Five-region linear flow system proved to be a useful model to reproduce the flow behavior for multi-fractured horizontal wells in shale reservoirs. In earlier developments, the model was assumed single-porosity throughout all five regions. However, assumption of single porosity system for stimulated region may promote errors in pressure transient analysis. So by adopting the existing mathematical models for naturally fractured reservoirs (dual-porosity system), one can apply the dual-porosity nature of flow in the stimulated reservoir volume (SRV). In this study the analytical solution for single-porosity model is reproduced and compared with numerical solution. Then the five-region model of previous studies is modified by implementing the dual porosity behavior in Laplace domain and compared to single-porosity solution using the same reservoir properties. Furthermore, a series of type-curves is constructed in this study using dimensionless properties, such as matrix-fracture capacity ratio and storativity ratio, hydraulic fracture conductivity, and hydraulic fracture half-length. Theses curves could provide valuable information to characterize the multi-fractured complex systems.

Analytical Model for Multifractured Systems in Liquid-Rich Shales with Pressure-Dependent Properties

One of today’s challenges in reservoir management of liquid-rich shales is to accurately forecast production performance based on pressure/rate transient analyses. The need for large pressure gradients to produce from shale reservoirs through multifractured horizontal wells (MFHWs) may induce considerable changes in rock and fluid properties that can largely affect transient bottom-hole pressure response which can result in inaccurate predictions for well performance. Therefore, the assumption of constant properties in shale reservoirs may not be safe when modeling MFHW performance. This paper presents a nonlinear analytical MFHW performance model for single-phase systems based on the five-region model (Stalgorova and Mattar in SPE Reserv Eval Eng 16(03):246–256, 2013) that accounts for pressure-dependent rock and fluid properties in liquid-rich shales. Properties are assumed to vary exponentially with pressure. Because of this, the resulting nonlinear diffusivity equation is linearized by means of an exponential transformation. The nonlinear MFHW performance model is benchmarked against numerical simulation data for a number of case studies. The proposed analytical solution is able to accurately capture transient bottom-hole pressure response while delivering a highly accurate estimation of depletion time. In this study, it was found that nonlinear diffusion processes in liquid-rich shales, under the assumption of exponential changes in properties with pressure, are fully described by the porous medium equation (PME). The PME is presented along with a straightforward application to identify and forecast flow regimes in the reservoir (fast, normal or slow diffusion). Finally, a brief review on diagnostic plots for systems with pressure-dependent properties concludes this work.

A multi-linear flow model for multistage fractured horizontal wells in shale reservoirs

This paper presents an analytical multi-linear flow model for shale gas reservoirs with multistage fractured horizontal wells (MFHW). It has been proved that the hydraulic fractures are branched rather than simple bi-wing shape, and the seepage flow of shale gas reservoirs is more complicated than conventional gas reservoirs due to the gas occurrence characteristics and fracture networks. Based on the published trilinear flow models, a developed five-region model considering effective fractured volume and adsorption effect was established. Laplace transformation method and Stehfest numerical algorithm were used to obtain typical pressure response curves. In addition, the presented model was validated by the actual production data, different flow regimes were divided, and the prediction of presented model was compared with the results of Eclipse simulator. Effects of some factors such as stimulated reservoir volume, storativity ratio, and Langmuir volume on the performance were analyzed. The results showed that the presented model considering stimulated volume and adsorbed gas could predict the productivity of MFHW better. The linear flow of stimulated region was the main contribution to gas production, and the duration of formation linear flow was influenced by different parameters. So the selection of optimal combination is very important in the development of shale gas reservoirs.

A semi-analytical solution for multiple-trilinear-flow model with asymmetry configuration in multifractured horizontal well

Trilinear-flow model presented by Brown in 2009 are commonly used to simulate the pressure-transient and production behaviors of multiple fractured horizontal wells (MFHW) in unconventional reservoirs. Brown's model was established on the symmetry hypothesis of MFHW, i.e., single-fracture-based configuration. The principle focus of this work is on proposing a novel semi-analytical solution to fill the gap between trilinear-flow model on the symmetry hypothesis of MFHW and actual asymmetry multi-fractured configuration. The new solution is generated by incorporating the principle of pressure superposition, which could take the effect of fracture-production interaction and property heterogeneity of fractures into account. The results obtained from new solution are also validated by comparing with numerical simulation in two specific cases: identical properties of fractures in the unequally-spaced configuration and different properties of fractures in the equally-spaced configuration. Meanwhile, this paper provides approximated relationships to associate existing single-fracture-based solution with our multi-fractures-based solution. A synthetic sample is also presented to illustrate the improvement of new solution towards pressure transient analysis. The proposed model could provide a practical alternative to the solutions for MFHW model based on Green's function method, and also extend existing multilinear-flow (e.g., enhanced five-region model) and multi-porosity model (e.g., dual/triple porosity and adsorption effect) to multiple-fractured configuration.

A new analytical model for non-uniformly distributed multi-fractured system in shale gas reservoirs

Recently, many kinds of linear flow models, such as tri-linear flow model and five-region model, have been introduced to simulate the flow in shale gas reservoirs with multiple fractured horizontal wells (MFHWs) due to their conciseness and effectiveness. However, most of the existing linear flow models are based on many ideal assumptions that may not always be true in practice. Based on the five-region model, this paper establishes a new analytical model (enhanced five-region model) of MFHWs in shale gas reservoirs considering desorption, different models in stimulated reservoir volume (SRV) region, non-uniform distribution of fractures and stimulated or un-stimulated region, and distinct respective properties in each region. Laplace transformation and Duhamel's theorem are employed to solve this new model. The pseudo-pressure transient responses are inverted into time space using Stehfest algorithm. Type curves of pressure transients are plotted. The main flow regimes for two situations (homogenous and dual-porosity) in SRV region are identified. The sensitivity analysis in terms of the size of SRV region, property of SRV region, fracture number, fracture intervals, dimensionless fracture conductivity coefficient, inter-porosity flow coefficient, storativity ratio and adsorption coefficient on type curves are presented. Type curves calculated by the simplified present model and existing models match well. This also indicates the validity of the proposed new model. Compared with the existing linear flow models, more factors (different relevant parameters in non-uniformly or uniformly distributed multi-fractured systems) are considered in the new model. So the new model can be applied to interpret more complex cases.

Effect of flow mechanism with multi-nonlinearity on production of shale gas

Different from oil reservoirs, variations of gas properties (such as viscosity, Z-factor and gas compressibility) under different pressures is strongly nonlinear and non-Darcy effect is significant in fractures due to high rate. Shale gas reservoirs are extremely tight with nanopores, where Darcy's law breaks down and the flow behavior is significantly influenced by pore scale and pressure. 20%–80% of the shale gas in place (in-situ) is adsorbed to organic matters and the desorption is a nonlinear process varying with pressure. Furthermore, hydraulic fractures and natural fractures close gradually, as the production proceeds, resulting in a non-linear relationship between permeability and pressure. However, the multi-nonlinear flow mechanism, as well as its effect on gas production, in the process of shale gas development is always overlooked by both laboratories and industrial analyses.Based on the five-region model, finite difference method is applied to get numerical solution in this paper. Afterwards, the effect of nonlinear mechanism on production is analyzed, according to which, the enhanced ultimate recovery (EUR) schemes are proposed. The results show that the effects of compressibility, multi-scale flow, stress sensitivity and non-Darcy flow in fractures on production are significant during early stage and should be considered in well testing model. For middle and late production stages, the effects of compressibility, multi-scale flow, stress sensitivity in natural fractures should be considered in the Rate Transient Analysis (RTA) model and long-term production prediction model. The negative effect of stress sensitivity and non-Darcy flow can be reduced or mitigated by optimizing schedule and controlling early pressure drawdown. Furthermore, some nonlinear factors can be used positively by refracturing, which reduces formation pressure and consequently leading to the increase of gas compressibility, desorption compressibility and apparent permeability.

Analytical Model for Unconventional Multifractured Composite Systems

Summary This paper presents an analytical model for unconventional reservoirs with horizontal wells with multiple fractures. The model is an extension of the "trilinear flow" solution, but it subdivides the reservoir into five regions instead of three. This enables it to be used for more-complex reservoirs. Accordingly, the model can simulate a fracture that is surrounded by a stimulated region of limited extent (fracture branching), whereas the remaining reservoir is nonstimulated. In addition to modeling flow within the fracture and flow within the stimulated region, the model takes into account flow from the surrounding nonstimulated region, both parallel to and perpendicular to the fracture. The model can be used to simulate the flow in tight reservoirs with multifractured horizontal wells. In many cases, the fractures do not have a simple biwing shape, but are branched. This effectively creates regions of higher permeability around each fracture, which obviously affect the production performance significantly. However, in many tight reservoirs, in spite of their low permeability, the surrounding nonstimulated region can also be a significant contributor to long-term production. The five-region model accounts for this contribution. Thus, it is particularly valuable when generating production forecasts for reserves evaluation. The model was validated by comparing its results with numerical simulation. We found that analytical and numerical results are in good agreement only when the geometry of the system falls within certain limitations. However, these limitations are met in most cases of interest. Therefore, the model is useful for practical engineering purposes.

The Implications of Elections for Federalism in Iraq: Toward a Five-Region Model

For most observers, Iraq's recent elections were an important first step on the road to democratic normalcy. However, three related outcomes—the political marginalization of Sunni Arabs, the electoral gains made by Shi'a religious parties, and the triumphant performance of the Kurds—render the task of crafting Iraq's permanent constitution significantly more problematic. In this paper, we examine the implications of these election results for the design of Iraq's federal system. Our focus is on the character of the subunits in any future system, specifically on whether Iraq should adopt a form of territorial federalism based on the country's existing eighteen provinces (as most scholars argue) or whether a form of ethnic, or “plurinational,” federalism based on five regions would be better able to address the very significant problems created by the election results. After assessing the relative merits of the various proposals for a federal Iraq, we conclude that a system based on five broad regions, though not ideal, is the least bad of the options available. Copyright 2005, Oxford University Press.

One-dimensional model of detached plasmas in the scrape-off layer of a divertor tokamak

Numerical and analytical study of a detached divertor equilibrium is presented. The model uses one-dimensional equations for continuity, momentum and energy balance with radiation, ionization, charge-exchange, and recombination processes. A reasonably simple neutral model is also employed. Analytical calculation, using a simple five-region model for a case with negligible convective heat flux and constant sources/sinks, captures the essence of detailed numerical calculation for the same case. More general cases are handled numerically. The detachment is studied as a function of the ratio Q⊥/S⊥ [the ratio of power and particle volume source, coming from the core to the scrape-off layer (SOL) region]. For low values of Q⊥/S⊥ (detached state), at the midplane and at the target, the ion temperature (Ti) is almost equal to the electron temperature (Te). As this ratio increases (attached state), Ti is larger than Te at the midplane. However at the target, Te is found to be slightly larger than Ti. It is also observed that as Q⊥/S⊥ increases, the region of most intense radiation shifts progressively from closer to the X-point towards the target plate.

Use of a priori information in estimating tissue resistivities - application to measured data

A statistically constrained minimum mean squares error estimator (MiMSEE) has been shown to be useful in estimating internal resistivity distribution by the use of simulated data. In this study, the performance of the MiMSEE algorithm is tested by using measured data from resistor phantoms. The MiMSEE uses a priori information on body geometry, electrode position, statistical properties of tissue resistivities, instrumentation noise and linearization error to calculate the optimum inverse matrix which maps the surface potentials to unknown regional resistivities. In this study, the MiMSEE is also constrained with the variance-covariance of the modelling error to improve the estimation accuracy. The data are obtained from two different phantom geometries, namely five-region and thorax. Using the measured data, the estimations are realized and errors are calculated. Then, the results are compared with the results obtained by using a conventional least squares error estimator (LSEE). The five-region model results show similarity with the simulation study results of Baysal and Eyüboglu. On the thorax model, the total estimation error is 34.2% with the MiMSEE compared with 856% with the LSEE. It is concluded that the MiMSEE is more robust than the LSEE and applicable to measured data.

A characteristics model of transient friction in pipes

A quasi two-dimensional model of transient flows in pipes of circular cross-section is developed, using the one dimensional method of characteristics in concentric cylindrical annuli. Lateral velocity components are permitted between adjacent cylinders. The model can nominally incorporate any desired relationship between shear stresses and local velocities. In this paper, it is applied to laminar flows and to a five-region model of turbulent flows. The accuracy of Zielke's (1969) one-dimensional expression for transient wall-shear stresses in laminar flows is verified, and it is shown that his expression is also a reasonable approximation for smooth-wall, turbulent flows, at least at low Reynolds numbers. Quasi-steady relationships are shown to be highly inaccurate in transient laminar or turbulent flows.

A five-region model for the edge-guided mode ferrite-loaded stripline isolator

A five-region model for the inhomogeneously ferrite-loaded strip/microstrip isolator with loss loading on one side of the ferrite slab is presented. A ferrite slab between two infinite perfectly conducting planes is sided by a lossy sheet and a dielectric slab. The bias magnetization is taken to be perpendicular to the ground planes. The problem is solved approximately by replacing the lossy film by suitable impedance boundary conditions.

Time domain analysis of ultrasonic propagation in a five-region layered structure

This paper presents the results of a study of the propagation of ultrasonic waves incident normally on a five-region model consisting of water/ aluminium/adhesive/aluminium/water layers. The ultrasonic signal power reflected from various interfaces in the multi-layered structure was calculated using the energy partition principle; the ultrasonic attenuation in the various media was taken into account in the study. The phase relationship between the incident and reflected portions of each ultrasonic pulse was followed in detailed calculation. Results of the analysis show excellent correlation with experimental results obtained by pulsing ultrasound at a three-layered structure immersed in water.