Linear Flow Systems Research Articles

Implementasi Chatbot untuk Layanan Frequently Asked Question Akademik dengan Penggunaan Dialogflow

Academic Frequently Asked Questions (FAQ) service is a service designed to answer academic questions that are often asked by students. A survey conducted on April 12, 2022, to 33 students of the Ahmad Dahlan University Informatics study program showed that 39.4% of students rarely open the FAQ menu on the portal application. Students more often ask questions to administrators and lecturers, but 30.3% of students receive answers that last more than 10 minutes. Chatbot is an artificial intelligence system used to interact with users in real-time to provide information. The use of dialog flow in the system helps manage information and can provide an answer quickly and precisely to users. This research uses the waterfall method, which is a simple classic model with a linear flow system. The User Experience Questionnaire (UEQ) survey results get a score of 1,536 for attractiveness, 1,714 for clarity, 1,375 for efficiency, 1,357 for fixity, 1,536 for stimulation, and 0.964 for novelty. Based on these results, it shows that the application level is above average on the UEQ scale.

Impact of Polymer Rheology on Gel Treatment Performance of Horizontal Wells with Severe Channeling

Summary Gel treatment has been a cost-effective method to control the conformance of a reservoir with severe heterogeneity problems. The water channels in such reservoirs can be classified as open fractures or high permeability porous media with pore-throat network. Many simulation studies have been conducted to discuss gel treatment performance for conformance control. However, nobody considered the polymer rheology difference in open fractures and porous media in simulation. Previous simulation studies also ignored the residual resistance factor as a function of rock permeability rather than a constant parameter. In this study, a conceptual simulation model was established to simulate the linear flow system for the reservoir with horizontal wells considering the two factors mentioned above. The results demonstrate that the gel treatment always provides the better placement results in the open fracture type channel than pore-throat network type channel. Moreover, it is very necessary to consider residual resistance factor as a function of permeability, which is based on the experimental results and can provide much greater plugging efficiency in the higher permeable channels than constant residual resistance factor. Sensitivity analysis studies and multifactor analysis indicate that increasing oil viscosity and permeability ratio has a strong positive influence on conformance control results, which indicate in-situ gel treatment can be better applied in heavy or viscous oil reservoirs with fracture-like channels. Besides, the results also indicate that in reservoirs with severe channeling problem where channel velocity was high, the differences of gelant placement and profile improvement in models with two different types of channels could be enlarged greatly.

Matrix permeability and flow-derived DFN constrain reactivated natural fracture rupture area and stress drop — Marcellus Shale microseismic example

Microseismic events associated with shale reservoir hydraulic fracturing stimulation (HFS) are interpreted to be reactivations of ubiquitous natural fractures (NFs). Despite adoption of discrete fracture network (DFN) models, accounting for NFs in fluid flow within shale reservoirs has remained a challenge. For an explicit account of NFs, this study introduced the use of seismology-based relations linking seismic moment, moment magnitude, fault rupture area, and stress drop. Microseismic data from HFS monitoring of Marcellus Shale horizontal wells had been used to derive planar hydraulic fracture geometry and source properties. The former was integrated with associated well production data found to exhibit transient linear flow. Analytical solutions led to linear flow parameters (LFPs) and system permeability for scenarios depicting flow through infinite and finite conductivity hydraulic fractures. Published core plug permeability was stress-corrected for in-situ conditions to estimate average matrix permeability. For comparison, the burial and thermal history for the study area was used in 1D Darcy-based modeling of steady and episodic expulsion of petroleum to account for geologic timescale persistence of abnormal pore pressure. Both evaluations resulted in matrix permeability in the same picodarcy (pD) range. Coupled with LFPs, reactivated NF surface area for stochastic DFNs was estimated. Subsequently, the aforementioned seismology-based relations were used for determining average stress drops needed to estimate NF rupture area matching flow-based DFN surface areas. Stress drops, comparable to values for tectonic events, were excluded. One of the determined values matched stress drops for HFS operations in past and recent seismological studies. In addition, calculated changes in pore pressure matched estimates in the aforementioned studies. This study unlocked the full potential of microseismic data beyond extraction of planar geometry attributes and stimulated reservoir volume (SRV). Here, microseismic events were explicitly used in the quantitative account of NFs in fluid flow within shale reservoirs.

Moving boundary approach to forecast tight oil production

AbstractA novel semianalytical production predictive tool for tight reservoirs based on the application of material balance on a transient linear flow system is developed in this paper. This method considers two important regions during transient production of oil reservoirs: the saturated region where gas evolves and flows with oil, and the undersaturated region where only oil flows. A zonal moving boundary approach is used to evolve the two regions as the reservoir pressure gradually decreases. A semianalytical method is used to calculate pressures in the various regions and volumetric expansions. For both black oil and volatile oil scenarios, calculations from this analytical framework are able to match reservoir pressures, oil and gas rates, and cumulative gas–oil ratios determined using a reservoir simulator. The model was also applied to wells in tight reservoirs around the United States such as the Bakken (ND) and the Eagle Ford (TX) with reasonable success.

Analytical modeling and probabilistic evaluation of gas production from a hydraulically fractured shale reservoir using a quad-linear flow model

During hydraulic fracturing, secondary fractures are created around hydraulic fractures and serve as important channels connecting the shale matrix and the hydraulic fractures. We developed an analytical model to simulate shale gas production from a multi-stage fractured horizontal well. The analytical model is based on the trilinear flow model, but it is free from the assumption that the length of secondary fractures is equal to the half-distance between hydraulic fractures. This analytical model captures the fundamental characteristics of a hydraulically fractured shale reservoir by incorporating transient gas flow in the matrix, secondary fractures, and hydraulic fractures. Because this model describes four linear flow systems (unstimulated reservoir volume, matrix in the stimulated reservoir volume, secondary fracture, and hydraulic fracture), it is called the quad-linear flow model. Production data from two shale gas wells were used to validate the model. Moreover, using the variance-based method and quasi-Monte Carlo simulation, we developed a stochastic framework to perform a probabilistic assessment of shale gas production. We also conducted a global sensitivity study with nine uncertainty parameters to identify important parameters and their interactions that affect well productivity. The results indicate that the existence of dense secondary fractures (the distance between secondary fractures is small) results in higher initial production rate and ultimate recovery, but a sharper decline in production rate. Increasing the length of the secondary fractures can more effectively enhance gas production in the presence of dense secondary fractures. Moreover, the benefits of dense secondary fractures are mostly limited to a high porosity shale reservoir.

Groundwater Flow Determination Using an Interval Parameter Perturbation Method

Groundwater flow simulation often inevitably involves uncertainty, which has been quantified by a host of methods including stochastic methods and statistical methods. Stochastic methods and statistical methods face great difficulties in applications. One of such difficulties is that the statistical characteristics of random variables (such as mean, variance, covariance, etc.) must be firstly obtained before the stochastic methods can be applied. The dilemma is that one is often unclear about such statistical characteristics, given the limited available data. To overcome the problems met by stochastic methods, this study provides an innovative approach in which the hydrogeological parameters and sources and sinks of groundwater flow are represented by bounded but uncertain intervals of variables called interval of uncertainty variables (IUVs) and this approach is namely the interval uncertain method (IUM). IUM requires only the maximum and minimum values of the variable. By utilizing the natural interval expansion, an interval-based parametric groundwater flow equation is established, and the solution of that equation can be found. Using a hypothetical steady-state flow case as an example, one can see that when the rate of change is less than 0.2, the relative error of this method is generally limited to less than 5%; when the rate of change is less than 0.3, the relative error of this method can be kept within 10%. This research shows that the proposed method has smaller relative errors and higher computational efficiency than the Monte Carlo methods. It is possible to use this method to analyze the uncertainties of groundwater flow when it is difficult to obtain the statistical characteristics of the hydrogeological systems. The proposed method is applicable in linear groundwater flow system. Its validity in nonlinear flow systems such as variably saturated flow or unconfined flow with considerable variation of water table will be checked in the future.

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.

Integrated Linear-processing Ion-beam Sputtering System Using a Meter-scale Ribbon-beam

We present a system capable of performing linear PVD processing by DC ion beam sputtering, suitable for reactive or high-vacuum deposition of dielectrics, metals, or magnetic materials onto conductive, insulating, or magnetic substrates. This equipment can be installed on a single vacuum flange for mounting on a variety of vacuum systems, but linear flow systems are preferred. Our recently developed ion source can generate ribbon ion beams of high current and low divergence over a wide range of energies, but is optimized for about 1 to 5 keV, and high ion currents of up to 1A per meter breadth; breadths of several meters are possible. The current density is an order of magnitude higher than existing systems. Uniformity is intrinsically good and can be controlled in real-time. The ion source and the sputter target are mounted close to each other and to the target; the cross section of the equipment does not change as the equipment is scaled up to large dimensions. The ion beam impinges on the sputter target at the optimum angle and energy, in a field-free region, and in high vacuum. This combination of conditions is unique, and dramatically raises the sputter yield. Free choice of beam energy permits higher thermal efficiency. High vacuum means that the deposited atoms comprising the film retain the full energy of several eV that was produced in the sputtering process. The geometry further permits extremely simple and efficient jetting of reactive gases such as oxygen for the production of oxide films. The single broad-beam source has far higher current density and a far more compact layout than existing ion-beam sputtering systems, and can be installed in linear processing systems in a similar manner to linear magnetrons.

Analytical modeling dynamic drainage volume for transient flow towards multi-stage fractured wells in composite shale reservoirs

This paper presents an analytical solution to predict the expansion of drainage volume for a composite transient linear flow system consisting of stimulated-reservoir volume (SRV) and unstimulated reservoir volume. Correct prediction of dynamic drainage volume (DDV) is essential in production data analysis and well space evaluation. With the prediction of DDV, we can calculate the average pressure and average saturation with different time, which can assist designing different exploitation scenarios.The compound linear flow solution within both SRV and unstimulated matrix is derived under constant-flowing-bottomehole-pressure (FBHP) and constant-rate boundary conditions. Laplace transform and numerical inversion are implemented to obtain the analytical solution. The location of pressure front is calculated using the impulse response concept, which is the maximum rate of pressure response. A multi-variable regression method is applied to determine an empirical equation indicating the relationship between DDV and the square root of time; the empirical equation includes conductivities of both SRV and unstimulated matrix volume, fracture length, and fracture spacing.The results suggest that the DDV demonstrates a linear relationship with square-root-of-time for both linear flow regime within SRV and the compound linear flow in composite fractured reservoirs. The advancement of DDV within stimulated-reservoir volume is much faster than unstimulated matrix, which is approximately 100 times in general. To verify the accuracy of newly derived DDV equations, we analyze the synthetic production data from series of fine-grid numerical simulations. Finally, we make a sensitivity analysis of hydraulic fracture spacing with respect to DDV, which can be implemented to evaluate the fracturing design. In practice, the solution derived can be used to determine optimal fracture spacing.

Stormwater wetlands for the enhancement of environmental ecosystem services: case studies for two retrofit wetlands in Brisbane, Australia

Constructed stormwater wetlands are examples of ‘blue–green’ ecological engineering in the urban environment providing a range of ecosystem services. A study was undertaken in Brisbane, Australia to examine the enhancement of environmental ecosystem services in 2 retrofit wetlands. Originally concrete drainage channels in existing residential catchments, a series of wetlands and ponds were created i.e. green infrastructure in a brownfield setting. Boardwalks, pathways and interpretive signage were incorporated into the design.Golden Pond wetland was only 0.2% of the catchment whereas Bridgewater Creek – Bowie's Flat wetland was 0.4% of the catchment. The larger 0.8 ha Bridgewater Creek wetland had an overflow by-pass channel. Water quality (suspended solids and nutrients) and the diversity of aquatic macroinvertebrates were monitored for 2–4 years after construction.During storm events suspended solids increased at Golden Pond due to resuspension from the high velocities in this small linear flow system. Resuspension was minimised at Bridgewater Creek due to the by-pass channel. During dry weather suspended solids in both wetlands increased due to resuspension from the activity of waterbirds. Both wetlands were effective in reducing nutrient concentrations especially NOx–N and PO4–P, attributed to biological uptake; but during dry periods NH4–N increased within the system. The concept of irreducible background concentrations in wetland systems is discussed.Open water and aquatic vegetation provided habitats for macroinvertebrates. Species richness increased by more than 50% in both stormwater wetlands, compared to the concrete drains.Wetland sizing and design are essential parameters for water quality improvement and biodiversity.

Modified analytical equations of recovery factor for radial flow systems

Abstract Buckley–Leverett displacement equations have been derived strictly from linear flow systems, and have been verified by linear flow experiments only. This paper presents analytical algorithms to calculate recovery factors for radial flow systems, which is expected to be more accurate for peripheral water-flooding reservoirs. The proposed equations have been verified with field data. The original Buckley–Leverett equation generally results in much lower recovery factors that barely match the well cumulative production at interest. Consequently, the estimated ultimate recovery (EUR) by volumetric methods tends to be low. As a result, the production projection according to volumetric EUR is not reasonable in comparing to the historical performance. The proposed analytical model improves the prediction of reservoir performance.

Linear vs. Radial Boundary-Dominated Flow: Implications for Gas-Well-Decline Analysis

Summary Linear flow is a fundamental reservoir-flow geometry typically associated with production from unconventional resources stimulated by means of hydraulic fracturing. Recently, linear flow has been intensively studied following the fast pace of development of unconventional resources. Previous studies have mainly focused on early transient behavior and behavior of composite linear-flow systems. In this work, a density-based analysis method is extended to study decline behavior of the linear-flow system in boundary-dominated flow (BDF). In this study, we first discuss traditional approaches used to model linear flow in gas reservoirs. Second, we show the applicability of the density-based method for gas linear flow both analytically and numerically. Next, late-time solutions are discussed, and the analytical forecasting solution that best describes the BDF behavior is selected for long-term decline-behavior studies. Previously reported results on radial flow as well as early transient-flow effect are also incorporated to provide a more complete understanding of decline behavior and the impact of flow geometry. We show that boundary-dominated responses in linear-flow scenarios fully develop at much later stages of reservoir depletion compared with radial-flow scenarios. As a result, and in marked contrast with radial flow, purely hyperbolic decline behavior may be completely lost in linear-flow scenarios during boundary-dominated conditions. It is demonstrated that most of the recoverable hydrocarbons are produced during the early transient period for linear-flow conditions, whereas most of them are recovered during the BDF period for radial flow. These results suggest that the availability of accurate early transient models is much more critical for the formulation of linear-flow-decline models than had been traditionally necessary for radial-flow-decline models.

Analysis of waste hierarchy in the European waste directive 2008/98/EC

Loss of recoverable resources in linear resource flow systems is likely to contribute to the depletion of natural resources and environmental degradation. The ‘waste hierarchy’ in the European Commission’s latest Waste Framework Directive 2008/98/EC (WFD2008) makes recommendations on how to address this issue. The WFD2008 is analysed in this work for its adequacy in ensuring return of ‘recoverable waste’ as a ‘resource’ into the productive system. Despite the release of guidance documents by the DG Environment, DEFRA and WRAP UK on the interpretation of key provisions of the WFD2008, lack of clarity still exists around the WFD2008 ‘waste hierarchy’. There is also an overlap between measures such as ‘prevention’ and ‘reduction’, ‘preparing for reuse’ and ‘reuse’ and lack of clarity on why the measure of ‘reuse’ is included in the WFD2008 definition of ‘prevention’. Finally, absence of the measures of ‘recovery’ and ‘reuse’ from the WFD2008 ‘waste hierarchy’ reduces its effectiveness as a resource efficiency tool. Without clarity on the WFD2008 ‘waste hierarchy’, it is challenging for decision makers to take direct action to address inefficiencies existing within their operations or supply chains. This paper proposes the development of an alternative ‘hierarchy of resource use’ and alternative ‘definitions’ that attempt to fill identified gaps in the WFD2008 and bring clarity to the key measures of waste prevention, reduction and recovery. This would help the key stakeholders in driving resource effectiveness, which in turn would assist in conservation of natural resources and prevention of environmental degradation.

Non-Darcy displacement in linear composite and radial aquifer during CO<SUB align="right">2 sequestration

This paper presents Buckley-Leverett type analytical solutions for non-Darcy displacement of two immiscible fluids in linear and radial composite porous media. High velocity or non-Darcy flow commonly occurs in the vicinity of the wellbore because of smaller flowing cross-sectional areas. However, the effect of such non-Darcy flow has been traditionally ignored. To examine the physical behaviour of multiphase immiscible fluids in non-Darcy displacement, an extended Buckley-Leverett type of solution is discussed. There exists a Buckley-Leverett type solution for describing non-Darcy displacement in a linear homogeneous reservoir. This work extends the solution to flow in linear and radial composite flow systems. We present several new Buckley-Leverett type analytical solutions for non-Darcy flow in more complicated flow geometries of linear and radial composite reservoirs, based on non-Darcy flow models of Forchheimer and Barree-Conway. As application examples, we use the analytical solutions to verify numerical simulation results as well as to discuss non-Darcy displacement behaviour. This theory of non-Darcy flow displacement is applied to evaluate the flow behaviour near wellbore areas during CO2 sequestration. The results show how non-Darcy displacement during CO2 injection in linear and radial composite systems is controlled not only by relative permeability, but also by non-Darcy coefficients, characteristic length, injection rates, as well as discontinuities in the saturation profile across the interfaces between adjacent composite flow domains.

대류가 유도하는 중규모 흐름에 미치는 비정역학 효과

대류가 유도하는 중규모 흐름에 미치는 비정역학 효과를 조사하기 위하여 기존의 무차원화된 정역학 모형을 바탕으로 무차원화된 비정역학 모형을 개발하였다. 모형을 검증하기 위하여 정역학 방정식 계의 해석해와 비정역학성이 아주 작은 경우의 수치 실험 결과를 비교하였고, 두 결과가 거의 같음을 확인하였다. 무차원화된 비정역학 모형을 이용하여 선형 계와 비선형 계에서 대류가 유도하는 중규모 흐름에 미치는 비정역학 효과를 조사하였다. 선형 계와 비선형 계 모두에서 비정역학성 인자가 작은 경우 열원 꼭대기 위에서 연직 방향으로, 비정역학성 인자가 상대적으로 큰 경우 주 상승 기류의 풍하측에서 수평 방향으로 상승 운동과 하강 운동이 교대하는 파동 형태의 섭동장이 나타났다. 풍하측에서 나타나는 상승 운동과 하강 운동을 분석하기 위하여 선형, 정상 상태, 비점성 흐름에 대한 Taylor-Goldstein 방정식을 구하였다. 주 상승기류의 풍하측에서 교대로 나타나는 상승 하강 기류세포는 전파파의 수평 방향 전파 성분과 에바네센트파, 즉 비정역학성 인자에 의해 결정되는 임계 파장보다 파장이 짧아 연직 방향으로 전파되지 못하고 수평 방향으로만 전파되는 중력파의 중첩으로 설명할 수 있다. 선형 계에 대한 수치 실험 결과에서 나타난 상승 하강 기류 세포의 수평 방향 길이는 선형 계에 대한 방정식에서 얻은 에바네센트 파의 임계 파장 길이의 절반과 일치하였으나, 약한 비선형 계에 대한 수치 실험 결과에서 나타난 상승 하강 기류 세포의 수평 방향 길이는 선형 계에 대한 방정식에서 얻은 에바네센트 파의 임계 파장 길이의 절반보다 다소 길었다. 주 상승 기류 지역 내에서 최대 상승 기류의 위치는 비선형성과 비정역학성 정도에 따라 다르게 나타났다. Nonhydrostatic effects on convectively forced mesoscale flows in two dimensions are numerically investigated using a nondimensional model. An elevated heating that represents convective heating due to deep cumulus convection is specified in a uniform basic flow with constant stability, and numerical experiments are performed with different values of the nonlinearity factor and nonhydrostaticity factor. The simulation result in a linear system is first compared to the analytic solution. The simulated vertical velocity field is very similar to the analytic one, confirming the high accuracy of nondimensional model's solutions. When the nonhydrostaticity factor is small, alternating regions of upward and downward motion above the heating top appear. On the other hand, when the nonhydrostaticity factor is relatively large, alternating updraft and downdraft cells appear downwind of the main updraft region. These features according to the nonhydrostaticity factor appear in both linear and nonlinear flow systems. The location of the maximum vertical velocity in the main updraft region differs depending on the degrees of nonlinearity and nonhydrostaticity. Using the Taylor-Goldstein equation in a linear, steady-state, invscid system, it is analyzed that evanescent waves exist for a given nonhydrostaticity factor. The critical wavelength of an evanescent wave is given by <TEX>${\lambda}_c=2{\pi}{\beta}$</TEX>, where <TEX>${\beta}$</TEX> is the nonhydrostaticity factor. Waves whose wavelengths are smaller than the critical wavelength become evanescent. The alternating updraft and downdraft cells are formed by the superposition of evanescent waves and horizontally propagating parts of propagating waves. Simulation results show that the horizontal length of the updraft and downdraft cells is the half of the critical wavelength (<TEX>${\pi}{\beta}$</TEX>) in a linear flow system and larger than <TEX>${\pi}{\beta}$</TEX> in a weakly nonlinear flow system.

Modelling of formation damage due to mud filtrate invasion in a radial flow system

This paper is a sequel of our previous paper that has addressed on mud filtrate invasion into oil formation in a linear flow system. As a natural extension, here we present a mathematical model to estimate skin factor due to mud filtrate invasion into oil formation in a radial flow system. In the model, solid particle invasion and irreducible water saturation are taken into account. The present model consists of mud cake thickness model, flow rate of mud filtrate into oil formation, mud filtrate concentration, and penetration depth of mud filtrate. The estimation for reduction of oil effective permeability and skin factor near wellbore are also presented. The model is simulated and verified using three vertical well data cited from the literature. The estimation results of oil effective permeability reduction and skin factor from the model are in agreement with the data. Beside that, for the case of static filtration in radial flow, we find a critical mud cake thickness above which the rate change of thickness is increasing.

Modeling of mud filtrate invasion and damage zone formation

In this paper, a model to estimate the invasion depth of mud filtrate from water-based mud is presented. The model includes the presence of mud cake layer and irreducible water saturation. Here, a linear flow system is considered. The filtration velocity and mud cake thickness model is derived from Darcy law and mass conservation. The invasion depth is obtained from mud filtrate profile in formation. It is found that the filtration velocity in a linear flow system depends on overbalance pressure, formation permeability, mud cake characteristics (porosity, permeability and density), and invasion time. Furthermore, the model is verified using the experimental data from literature. The invasion depth predicted by the present model is in agreement with the experimental results.

Objective function design for robust optimality of linear control under state-constraints and uncertainty

We consider a model for the control of a linear network flow system with unknown but bounded demand and polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective function that makes robust optimal the policy represented by the so-called linear saturated feedback control. We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations. © 2009 EDP Sciences, SMAI.

Intercomparison of number concentration measurements by various aerosol particle counters

Total aerosol particle number concentrations, as measured by means of 16 different measurement systems, have been quantitatively compared during an international workshop at the Institute for Experimental Physics of the University of Vienna, Austria, which was coordinated within the Committee on Nucleation and Atmospheric Aerosols (ICCP-IUGG). The range of measuring instruments includes Pollak counters (PCO) in use already for several decades, presently available commercial particle counters, as well as laboratory prototypes. The operation of the instruments considered was based on different measurement principles: (1) adiabatic expansion condensation particle counter, (2) flow diffusion condensation particle counter, (3) turbulent mixing condensation particle counter, (4) laser optical particle counter, and (5) electrostatic particle measurement system. Well-defined test aerosols with various chemical compositions were considered: DEHS, sodium chloride, silver, hydrocarbons, and tungsten oxide. The test aerosols were nearly monodispersed with mean particle diameters between 4 and 520 nm, the particle number concentrations were varied over a range from about 4×10 1 to 7×10 6 cm −3. A few measurements were performed with two-component aerosol mixtures. For simultaneous concentration measurements, the various instruments considered were operated under steady state conditions in a linear flow system. A series of at least 10 single concentration measurements was performed by each individual instrument at each set of test aerosol parameters. The average of the concentration data measured by the various instruments was defined as a common reference. The number concentrations obtained from the various instruments typically agreed within a factor of about two over the entire concentration range considered. The agreement of the measured concentrations is notable considering the various different measurement principles applied in this study, and particularly in view of the broad range of measurement instruments used. Significant deviations and nonlinear response were observed only in a few cases and are possibly related to calibration errors. For certain conditions, a dependence of aerosol counter response on particle composition has been found. The scatter of the number concentrations obtained from each individual instrument during measurements with constant test aerosol typically did not exceed 20% to 25%. At concentrations below 10 3 cm −3, however, several of the instruments, including electrostatic particle measurement systems, tend to show increased experimental scatter.

A Generalized, Transient Flow Model For Linear, Compartmentalized Systems

Abstract Fluid flow in narrow reservoirs or aquifers is predominately linear. However, this linear-flow system may possess variations in rock and fluid properties and/or presence of faults due to a number of geological phenomena. Such systems are modelled as linear, compartmentalized systems. In this study, a new generalized transient-flow model has been developed analytically for an n-region compartmentalized system. Each compartment or region may have distinct rock and fluid properties. A time-dependent production rate from each compartment is modelled in a general way. The conditions at the extreme boundaries are taken as non-homogeneous, time-dependent, Cauchy-type that can be modified to Dirichlet- or Neumann-type as a special case. A possible situation of poor communication between neighboring compartments has been incorporated into the model by considering the presence of a thin skin at each interface. A generalized solution for the dimensionless pressure has been derived using an integral-transform technique. This solution deals directly with situations like production rates and extreme boundary conditions being time-dependent without the need for using the principle of superposition in time or Duhamel's principle. Some limiting cases of this new solution have been used for validation purposes. Several advantages and practical applications of this model are also discussed. Introduction The flow of fluids through narrow reservoirs or aquifers is predominantly linear. However, this linear-flow system may possess variations in rock and fluid properties and/or faults due to geological phenomena. Levorsen(1) mentioned that the extent of a reservoir boundary may be sharp or it may be gradationa, as is more often the case. This heterogeneous character of a reservoir makes it difficult to model. To alleviate the mathematical difficulties of modelling such a system, the concept of compartmentalization may be used. With this concept, a heterogeneous system is assumed to be comprised of a number of homogeneous compartments. The communication of fluid between adjoining compartments may be hindered due to the presence of faults or any other barriers. Ehlig-Economides and Economides(2) have pointed out that there are several depositional environments showing possible oil- and gas-reservoir geometries that result in predominantly linear flow. These formations, which generally have long, narrow shapes, may be the result of river meander point bars, oxbow lakes, river channels, or tectonic breccias. However, such systems may also be compartmentalized due to variations of rock and fluid properties and the presence of faults and, therefore, can be modelled as linear, compartmentalized systems. In the literature, a number of studies of linear, one-dimensional flow systems are related to homogeneous reservoirs or aquifers(3, 4, 5). Nutakki and Mattar(6) generated transient pressure responses using the line-source solution with the principle of superposition for an infinitely long, narrow, homogeneous channel. They also developed a method to determine the time to the end of the radialflow period and the beginning of the linear-flow period. Ehlig- Economides and Economides(2) have presented the techniques for interference, drawdown and buildup analysis for an elongated linear flow system.