Pseudo-steady State Research Articles

Optimal integration of vacuum UV with granular biofiltration for advanced wastewater treatment: Impact of process sequence on CECs removal and microbial ecology

This study explored process synergies attainable by integrating a vacuum ultraviolet-based advanced oxidation process with biofiltration. A comparison using granular activated carbon or granular zeolite as filtration media were examined in context of advanced wastewater treatment for potable reuse. Six biofiltration columns, three with granular activated carbon and three with granular zeolite, were operated in parallel and batch-fed daily with nitrified secondary effluent. After achieving a pseudo-steady state through the filter columns, vacuum ultraviolet treatment was applied as pre-treatment or as post-treatment, at two different applied energies (i.e., VUV-E1=1 kWh/m3 and VUV-E10=10 kWh/m3). Once granular activated carbon had transitioned to biologically activated carbon, as determined based on soluble chemical oxygen demand removal, adsorption was still observed as the main mechanism for contaminants of emerging concern and nitrate removal. Vacuum ultraviolet pre-treatment markedly improved contaminants of emerging concern removal through the integrated system, achieving 40% at VUV-E1 and 90% at VUV-E10. When applied as post-treatment to zeolite column effluents, VUV-E1 and VUV-E10 further increased contaminants of emerging concern removal by 20% and 90%, respectively. In the zeolite system, vacuum ultraviolet pre-treatment also increased soluble chemical oxygen demand removal efficiency, indicating that higher energy vacuum ultraviolet increased biodegradability. Total prokaryotes were two-fold more abundant in biologically activated carbon than in zeolite, with vacuum ultraviolet pretreatment markedly affecting microbial diversity, both in terms of richness and composition. Media type only marginally affected microbial richness in the biofilters but showed a marked impact on structural composition. No clear relationship between compositional structure and depth was observed.

The optimal semi-analytical modeling for the infinite-conductivity horizontal well performance under rectangular bounded reservoir based on a new instantaneous source function

The main objective of this study is to develop the optimal semi-analytical modeling for the infinite-conductivity horizontal well performance under rectangular bounded reservoir based on a new instantaneous source function. The available semi-analytical infinite-conductivity models (ICMs) for horizontal well under rectangular bounded reservoir in literature were developed by applying superposition of pressures in space (SPS). A new instantaneous source function (i.e., instantaneous uniform-flux segmentary source function under bounded reservoir) is derived to be used instead of SPS to develop the optimal semi-analytical ICM. The new semi-analytical ICM is verified with ICM of Schlumberger [1] and with previous semi-analytical ICMs in terms of bottom hole pressure (BHP) profile and inflow rate distribution along the wellbore. The model is also validated with real horizontal wells in terms of inflow rate distribution along the wellbore. The results show that the developed model gives the optimal semi-analytical modeling for the infinite-conductivity horizontal well performance under rectangular bounded reservoir. Besides that, high computational-efficiency and high-resolution of wellbore discretization have been achieved (i.e., wellbore segment number could be tens of hundreds depending on solution requirement). The results also show that at pseudo-steady state (PSS) flow regime, inflow rate distribution along the wellbore by previous semi-analytical ICMs is stabilized U-shaped as performance of inflow rate distribution at late radial flow regime. Therefore, the previous semi-analytical ICMs are incorrectly modeling inflow rate distribution at PSS flow regime due to the negative influence of applying SPS. The optimal semi-analytical ICM is in a general form and real time domain, and can be applicable for 3D horizontal well and 2D vertical fracture well under infinite and rectangular bounded reservoirs, of uniform-flux and infinite-conductivity wellbore conditions at any time of well life.The novelties in this study are as follows:1. At PSS flow regime:(1) Inflow rate distribution along the wellbore is stabilized uniform-flux which was verified mathematically.(2) Primary pressure derivative (PPD) (i.e., PPD = ∂PDt/∂tDA) is equal to (2π/mt) for any well and reservoir configurations and depends only on half-length wellbore segments number (mt).2. The new ICM gives different trend of Bourdet derivative for the first three flow regimes (i.e., early radial, early linear, late radial) and gives the same trend of Bourdet derivative for PSS flow regime, to their counterparts by uniform-flux model (UFM). The trend of pressure derivatives by UFM for any flow regime is well studied in literature, while the counterparts by ICM are new and need detailed study.

Transient Interporosity Flow in Shale/Tight Oil Reservoirs: Model and Application.

The dual-porosity model has been used widely to describe the fracture network in well test or numerical simulation due to the high computational efficiency. The shape factor, which can be used to determine the capability of mass transfer between the matrix and fracture, is the core of the dual-porosity model. However, the conventional shape factor, which is usually obtained under pseudo-steady state assumption, has certain limitation in characterization of the mass transfer efficiency in a shale/tight reservoir. In this study, a new transient interporosity flow model has been established by considering the influence of nonlinear flow, stress sensitivity, and fracture pressure depletion. To solve this new model, a finite difference and Newton iteration method was applied. According to the Duhamel principle, the solution for time-dependent fracture pressure boundary condition has been obtained. The solution has been verified by using the fine-grid finite element method. Then, the influence of nonlinear flow, stress sensitivity, and fracture pressure depletion on shape factor and interporosity flow rate has been studied. The study results show that constant shape factors are not suitable for unconventional reservoirs, and the interporosity flow in the shale/tight reservoir is controlled by multiple factors. The new model can be used in test interpretation and numerical simulation, and also provides a new approach for the optimization of the perforation cluster number.

Study on the local heat transfer behaviour in a flat plate pulsating heat pipe

A closed-loop Flat Plate Pulsating Heat Pipe, filled with a water-ethanol mixture (filling ratio = 50% vol.), is tested in horizontal orientation at different heat loads to assess local wall-to-fluid heat fluxes exchanged within its adiabatic section. In addition, the thermal interactions between adjacent channels are investigated since they could be responsible for poorer thermal performances in such kinds of cooling systems. The studied device is obtained from a copper plate (width: 80 mm, length: 200 mm, thickness: 3.5 mm) machined with a single square shaped groove (3 x 3 mm2) forming a series of 8 turns in the evaporator zone and covered with a second copper plate having same length and width, and thickness equal to 0.5 mm. During the Flat Plate Pulsating Heat Pipe operation, the temperature of the external wall, coated with a high-emissivity paint, is monitored within the whole adiabatic section by an InfraRed camera during the pseudo-steady state. The thermographic measurements are post-processed by adopting the Inverse Heat Conduction Problem resolution approach, adequately validated by numerical simulations. The resulting wall-to-fluid heat fluxes are studied in terms of amplitude and oscillation, thus providing novel pieces of information regarding the working behaviour of Flat Plate Pulsating Heat Pipes in terms of oscillatory flow and thermal interactions by conduction between adjacent channels.

Advanced HRT-Controller Aimed at Optimising Nitrogen Recovery by Microalgae: Application in an Outdoor Flat-Panel Membrane Photobioreactor

A fuzzy knowledge-based controller of hydraulic retention time (HRT) was designed and tested in an outdoor membrane photobioreactor (MPBR) to improve nitrogen recovery from a microalgae cultivation system, maintaining the algae as photosynthetically active as possible and limiting their competition with other microorganisms. The hourly flow of the MPBR system was optimised by adjusting the influent flow rate to the outdoor environmental conditions which microalgae were exposed to at any moment and to the nitrogen uptake capacity of the culture. A semi-empirical photosynthetically active radiation (PAR) prediction model was calibrated using total cloud cover (TCC) forecast. Dissolved oxygen, standardised to 25 °C (DO25), was used as an on-line indicator of microalgae photosynthetic activity. Different indexes, based on suspended solids (SS), DO25, and predicted and real PAR, were used as input variables, while the initial HRT of each operating day (HRT0) and the variation of HRT (ΔHRT) served as output variables. The nitrogen recovery efficiency, measured as nitrogen recovery rate (NRR) per nitrogen loading rate (NLR) in pseudo-steady state conditions, was improved by 45% when the HRT-controller was set in comparison to fixed 1.25-d HRT. Consequently, the average effluent total soluble nitrogen (TSN) concentration in the MPBR was reduced by 47%, accomplishing the discharge requirements of the EU Directive 91/271/EEC.

Experimental and Numerical Validation of the One-Process Modeling Approach for the Hydration of K2CO3 Particles

Potassium carbonate (K2CO3) is a promising material for the long-term storage of renewable energy. A reactor vessel filled with K2CO3 can potentially be used as a domestic heat battery. The hydration and dehydration reactions of salt hydrates in a reactor vessel are generally described using a one-process model, such as the ‘Arrhenius-f(α)’ model. However, this modeling approach cannot always be applied correctly. If the reaction does not proceed in a pseudo-steady state, and/or when nucleation and growth processes are simultaneously active during the transformation from an anhydrous to a hydrated state, the one-process modeling approach should not be applied. In this paper, it is investigated using simultaneous thermal analysis (STA) experiments whether the pseudo-steady state approximation is valid during the hydration reaction of K2CO3. Additionally, ‘jump experiments’ using STA are employed to investigate the rate-determining step (RDS) of the hydration reaction by applying step-wise changes in partial water vapor pressure. The presence of nucleation and growth processes during the hydration reaction is investigated by fitting isotropic models to STA data. The STA results showed that indeed the hydration of K2CO3 happens in a pseudo-steady state, and the reaction can be described using a RDS. An isotropic nucleation and growth model shows that the hydration reaction can be described by assuming instantaneous nucleation followed by diffusion-limited growth. This leads to the general conclusion that the one-process modeling approach, such as the Arrhenius-f(α) model, is valid to describe the hydration reaction of K2CO3 particles.

Distributed economic model predictive control with pseudo-steady state modifier adaptation for an industrial fluid catalytic cracking unit

The fluid catalytic cracking (FCC) unit is a typical multi-timescale system. Its operational performance will make a significant difference in the overall economic benefits of the oil refining factory. Classical model-based optimization approaches may not always be completely satisfied due to unmeasurable disturbances and model-plant structure mismatch. A distributed economic MPC with pseudo-steady state modifier adaptation (DEMPC-MA) is proposed to cope with the difficulties. The strategy divides the plant into two parts, i.e., the slow dynamic part and pseudo-steady state part. The output modifier adaption is adopted to modify the model function according to the pseudo-steady state characteristics of the riser. Lyapunov stable constraints are added to the EMPC problem to guarantee a safe operation, while the feasibility of the algorithm is ensured by a set of auxiliary controllers, which are constructed offline based on the multi-model approach. The overall control optimization problem is solved in a distributed formulation through the alternating direction method of multipliers (ADMM) to improve the calculation performance. The proposed algorithm was applied to an industrial FCC unit model based on a refinery factory in Jiujiang, China. The results showed that the method obtained better economic benefits and finally reached the optimal steady-state operating point even if the model structure and parameter of the prediction model were mismatched.

Performance of a horizontal well in a bounded anisotropic reservoir: Part I: Mathematical analysis

Abstract To enhance the productivity of horizontal wells, it is of necessity to ensure that they perform optimally. This requires an understanding of how the reservoir’s geometry, anisotropy and well design affect the pressure response. Mathematical formulations can be used to simulate pressure response in the wellbore and the data obtained can be analysed to obtain well and reservoir parameters that can aid performance and evaluation. In this study, a mathematical model that can be used to approximate pressure response in a horizontal well is formulated, and a detailed mathematical analysis that can be used to obtain well and reservoir parameters are provided. A horizontal well inside a rectangular drainage volume with sealed boundaries is considered and the effect of each boundary on pressure throughout its productive life is studied. In the analysis, investigations on how the reservoir parameters can be approximated over a given period of production are conducted. This is achieved by identification of the appropriate source and Green’s functions. These source functions allow us to formulate a mathematical model for dimensionless pressure. Considering the diagnostic plots for both dimensionless pressure and dimensionless pressure derivative, mathematical analysis studies the possible behaviour of the plots. Analysis indicates that the reservoir anisotropy can be approximated during the infinite-acting flow at early times when other parameters are known. Further, when the first boundary is felt, in this case the vertical boundary, the horizontal permeability can be approximated during the transition flow periods at middle times. Finally, at late times when all the boundaries have been felt and a pseudosteady state flow is evident, reservoir dimensions can be approximated. These results can significantly improve well test analysis and enhance the performance evaluation of a horizontal well.

Pressure transient analysis of a multi-horizontal-well pad by a semi-analytical model: Methodology and case study

Drilling more infill multi-fractured horizontal wells (MFHWs) is one of the most direct oil and gas production methods in unconventional reservoirs with high recovery. MFHWs in the multi-horizontal-well pad can be easily interfered by the adjacent wells during well testing. Unfortunately, most of the existing well testing models for MFHWs are limited to a single well. A semi-analytical well testing model for transient pressure analysis in a multi-horizontal-well pad is presented in this work. In the proposed model, the entire formation is divided into three domains, namely matrix, natural fracture, and hydraulic fracture, to describe unconventional reservoirs comprehensively. With Laplace transform and Stehfest numerical inversion techniques, the reservoir models with matrix and natural fracture systems are solved analytically. The solutions of the hydraulic fracture model for multiple MFHWs are obtained by the finite difference method. The pressure superposition method and production rate relationship are used to characterize the impact from the adjacent wells. The general solutions of the multi-well reservoir model and hydraulic fracture model are then coupled to obtain the tested well's bottom-hole pressure. The results of the proposed model are in good agreement with the commercial numerical software. The multi-horizontal-well pad's integrated flow regimes can be divided into a bilinear flow, linear formation flow, the pseudo radial flow of hydraulic fracture, multi-MFHW effect, cross-flow between matrix and natural fracture, and formation pseudo radial flow. The pseudo radial flow of hydraulic fracture, the multi-MFHW effect, cross flow, and formation pseudo radial flow have unique characteristics in the multi-horizontal-well pad, and these flow regimes are highly affected by the adjacent MFHWs properties and well-spacing. With the change of well-spacing, the multi-MFHW effect is characterized by the linear flow inside the multi-horizontal-well pad or the multi-well pad's biradial flow. The comparison of pseudo-steady-state (PSS) flow and transient flow indicates that different cross-flow conditions from the matrix to natural fracture will only affect the derivative curve's cross-flow behavior. The case study shows that the proposed model can obtain a more accurate interpretation result of the tested well under the adjacent well's effect.

A modified shrinking core model for microwave-assisted leaching of aluminum from peat clay

Aluminum oxide in peat clay has the potential to be used as a catalyst, coagulant, and adsorbent for the water treatment process. The usefulness of aluminum oxide in peat clay is enhanced by the leaching process. Aluminum was leached from peat clay in a variety of microwave power, HCl concentrations, and particle size. The effect of the microwave leaching parameters on the aluminum leaching rate was observed. The shrinking core (SC) model used in microwave-assisted leaching was assumed a pseudo steady state with chemical reactions. Effective diffusivity (De), mass transfer coefficient (kc), and reaction rate constants (k) are used as fitting parameters. The best fitting parameters De, kc , and k obtained 0.0049 cm2/s, 2.49 cm/s, and 10.5 cm/s, respectively. The comparison of experimental data and model calculations shown that the SC model can describe experimental data well for all microwave-assisted leaching conditions. Precious information on the results of this research can be given for the goal of the scaling-up and design of the microwave assisted leaching process.

Production Calculation Model of Thermal Recovery after Hydraulic Fracturing and Packing in Tight Reservoir

It was deemed important to calculate the thermal recovery production model of tight oil reservoirs after fracturing and packing based on the field data of an oilfield in Bohai Sea, China. The thermal recovery production of a tight oil reservoir after fracturing is demonstrated through theoretical calculation and practical field data on the premise of five hypotheses. Fractures change the fluid flow capacity of the reservoir. Combined with the relevant theories of reservoir thermal production, the dual porosity system in the fractured zone and the single porosity system in the unfractured zone were established. The calculation models of heat loss in the fractured and unfractured zones were derived to determine the thermal recovery heating radius of the reservoir after fracturing and packing. Combined with the pseudo-steady state productivity formula of the composite reservoir, a production calculation model of thermal recovery after fracturing and packing in the tight oil reservoir was established. The results showed that the heating radius of the reservoir after fracturing and packing is smaller than that of the unfractured reservoir, and the additional heat absorption of the fracture system generated by fracturing and packing reduces the thermal recovery effect. The thermal recovery productivity of heavy oil reservoirs is mainly affected by the heating radius. With the increase of fracture density, the heating radius decreases and production decreases. The increase of fracture porosity also leads to the decrease of the heating radius and the production. The calculation result of this model is improved after tight oil reservoir fracturing during the production period, which indicates that the model has a better prediction effect of the production of the tight reservoir after fracturing and packing.

Assessing the effect of well completion types on productivity in a class 1G gas hydrate reservoir under pseudo steady state

This work focuses on the assessment of the effect of well completion types on gas productivity in subsea gas hydrate reservoirs of class 1G type where the gas hydrates have decomposed into gas and water. Three types of vertical well completions are considered: frac-packed well with vertical hydraulic fracture; frac-packed well with horizontal hydraulic fracture, and a cased-hole gravel-packed well. Sensitivity analysis was conducted with analytical well inflow models to determine factors that affect the gas well productivity. The results of the analyses indicated that proppant mass pumped during fracture treatment slightly improves well productivity for frac-packed natural gas hydrate wells. Well productivity increases nonlinearly with fracture productivity up to a threshold value of 50,000 md for frac-packed well with horizontal fracture, above which further increase in fracture conductivity would create no benefit. With a proppant mass of 50,000 Ibm and a corresponding proppant volume of 504 ft 3 , commercial gas production rates of 14.9 MMscf/d, 5.621 MMscf/d, and 11.35 MMscf/d are possible for frac-packed well with vertical fracture, frac-packed well with horizontal fracture, and cased-hole gravel-packed well, respectively. Because hydraulic fracture orientation depends on the in-situ formation stress, whether a well should be hydraulic-fractured or not depends on in-situ formation stress.

Estimate Gas Initially in Place of Tight Gas Reservoirs Based on Developed Methodology of Dynamic Material Balance Technique

With growing global demand for hydrocarbons and decreasing conventional reserves, the gas industry is shifting its focus in the direction of unconventional reservoirs. Tight gas reservoirs have typically been deemed uneconomical due to their low permeability which is understood to be below 0.1mD, requiring advanced drilling techniques and stimulation to enhance hydrocarbons. However, the first step in determining the economic viability of the reservoir is to see how much gas is initially in place. Numerical simulation has been regarded across the industry as the most accurate form of gas estimation, however, is extremely costly and time consuming. The aim of this study is to provide a framework for a simple analytical method to estimate gas. Usually during production three variables are readily accessible: production rate, production time, and pressure-volume-temperature properties. This paper develops an analytical approach derived from the dynamic material balance proposing a new methodology to calculate pseudo time, with an interactive technique. This model encompasses pseudo functions accounting for pressure dependent fluid and rock variables. With the dynamic material balance yielding weak results in the linear flow regimes, an additional methodology derived from the volumetric tank model has been taken into consideration whereby equivalent drainage area is linked to total reservoir area. It has been shown even with short production data this volumetric approach yields accurate results. This proposed methodology has been validated against previous literature and additional cases considered to determine the sensitivity of each of it to reservoir parameters. Finally, it is shown that this method works for both fractured and unfractured wells in tight gas reservoirs, however, it is sensitive to the quantity of data based within the pseudo steady state flow period.

Approach to shape factor determination in estimating horizontal wells productivity for pressure transient model of Mutalik et al.

Horizontal well productivity (Jh) equation at pseudo-steady state (PSS) of Mutalik et al. (in: Presented at SPE 63rd annual technical conference and exhibition, Houston, Texas, 1988) has long and widely been known to estimate well performance. One key parameter of that equation is the so-called shape factor (CA) that characterizes the effect of the pressure transient behavior at PSS depending on well and reservoir configuration. For limited well and reservoir configurations, CA tables had been generated decades ago, but at unknown accuracy they are still used widely via tedious correlation or interpolation from those reported CA tables to estimate Jh for different configurations even today. The innovation points in this study are as follows: (1) The pressure transient model of Mutalik et al. (in: Presented at SPE 63rd annual technical conference and exhibition, Houston, Texas, 1988) (PTM) is improved to generalized pressure transient model (GPTM) and verified by converting several dimensional parameters to dimensionless forms. (2) An efficient algorithm is developed, and accurate CA and Jh are obtained for any well and reservoir configuration. (3) The accuracy of the reported CA tables is quantified, and the consequences are determined when they are used to estimate Jh. (4) New CA tables and their correspondence dimensionless time based on drainage area at PSS ((TDA)PSS) tables are generated for a wider range of well and reservoir configurations. Although horizontal wells usually have been drilled with high dimensionless well length (LD) industrially (i.e., LD > 10), it is still a significant error in Jh by (< 7%) that has been determined when using the reported CA of PTM for rectangular reservoir aspect ratio (xe/ye) = (1) and (2) in the both assumed input data, while for (xe/ye = 5), significant error in Jh starts from (46.43%) to (1037%) for LD = (10) to (100), respectively, in the first assumed input data [variable, dimensionless wellbore radius (rWD)] and expected the same in the second assumed input data (constant rWD).

Effectiveness and comparison of physical barriers on seawater intrusion and nitrate accumulation in upstream aquifers

Physical barrier is a coastal engineering widely used to prevent seawater intrusion. However, previous studies have not evaluated the combined influence of type and structure of the physical barrier on nitrate accumulation in upstream aquifers. Furthermore, the mechanisms of nitrate accumulation caused by the physical barriers are still unclear. In this study, numerical simulations were conducted to investigate the mechanisms and influence of the physical barrier on seawater intrusion and NO3− accumulation. The results show that constructing physical barrier can result in the reduction of nitrate discharge to the sea and accumulation of nitrate in upstream aquifers. The accumulation degree is significant if the barrier height is large; the barrier location is near the sea; the nitrate infiltration rate is large; the infiltration nitrate concentration is large; the inflow is weak, and the inflow DOC concentration is low. A cut-off wall is more likely to cause nitrate accumulation than a subsurface dam. It can result in mean nitrate concentration in groundwater upstream increasing by more than 30 %. Because a nitrate accumulation zone is formed behind the cut-off wall where the flow is slow and dissolved oxygen carbon is difficult to be replenished so that the denitrification is weak. Despite the subsurface dam may not result in a significant increase in nitrate concentration, it cannot be applied to the areas where SI has occurred due to the residual seawater problem. The nitrate accumulation in the upstream aquifer is a long-term process that lasts for more than three years to reach a pseudo-steady state. Seasonal variations of inflow and infiltration lead to fluctuation of mean nitrate concentration, thereby the nitrate accumulation rate increased after April and weakened between July and December.

Time-frequency analysis of Li solid-phase diffusion in spherical active particles under typical discharge modes

Li transient concentration distribution in spherical active material particles can affect the maximum power density and the safe operating regime of the electric vehicles (EVs). On one hand, the quasi-exact/exact solution obtained in the time/frequency domain is time-consuming and just as a reference value for approximate solutions; on the other hand, calculation errors and application range of approximate solutions not only rely on approximate algorithms but also on discharge modes. For the purpose to track the transient dynamics for Li solid-phase diffusion in spherical active particles with a tolerable error range and for a wide applicable range, it is necessary to choose optimal approximate algorithms in terms of discharge modes and the nature of active material particles. In this study, approximation methods, such as diffusion length method, polynomial profile approximation method, Padé approximation method, pseudo steady state method, eigenfunction-based Galerkin collocation method, and separation of variables method for solving Li solid-phase diffusion in spherical active particles are compared from calculation fundamentals to algorithm implementation. Furthermore, these approximate solutions are quantitatively compared to the quasi-exact/exact solution in the time/frequency domain under typical discharge modes, i.e., start-up, slow-down, and speed-up. The results obtained from the viewpoint of time-frequency analysis offer a theoretical foundation on how to track Li transient concentration profile in spherical active particles with a high precision and for a wide application range. In turn, optimal solutions of Li solid diffusion equations for spherical active particles can improve the reliability in predicting safe operating regime and estimating maximum power for automotive batteries.

Permeability, solubility, and diffusivity of aniline in poly(ether-b-amide) membranes pertaining to aniline removal from aqueous solutions by pervaporation and sorption

This work dealt with the fundamental aspects of solubility, diffusivity, and permeability of aniline in PEBA 2533 pertaining to aniline removal from water via pervaporation and sorption, with an emphasis on membrane permeability determined via different approaches: (1) pervaporation experiments, (2) sorption experiments, and (3) direct measurements from pseudo steady state liquid permeation. The membrane exhibited high permselectivity for aniline separation via pervaporation, which was derived from the high solubility selectivity to aniline. The permeability of aniline in the membrane for pervaporative mass transfer was on the order of 105 Barrer, with a solubility and diffusivity of 105 mol/(m3∙Pa) and 8.3 × 10−12 m2/s, respectively, at 23 °C as determined from sorption experiments. Although it has been largely overlooked, caution should be exercised in determining or characterizing the membrane permeability based on different measurement techniques, and proper conversions are needed to rationalize and reconcile the permeability data. The sorption-desorption reversibility was investigated as well, which was relevant to aniline removal from water by cyclic sorption/desorption and steady state pervaporative separation.

A New Model for Predicting Flow in Fractured-Vuggy Carbonate Reservoirs under Pseudosteady State Condition

For constant rate production of a single well in a closed boundary fractured-vuggy carbonate reservoir, when the pressure wave propagates to the reservoir boundaries, boundary-dominated flow occurs, and the transient flow period ends, the reservoir will be in a state of pseudoequilibrium (i.e., pseudosteady state flow occurs, and the pressure at any point in the reservoir declines at the same constant rate over time). The characterization of fluid flow in the fractured-vuggy carbonate reservoir under pseudosteady state condition is of significance in describing the productivity index (PI) of the well. However, due to complex mechanisms (e.g., stress dependency of reservoir properties and crossflow between different systems of the reservoirs) during flow in fractured-vuggy carbonate reservoirs, researches on productivity prediction in fractured-vuggy carbonate reservoirs under pseudosteady state are very limited. The present work is aimed at developing a new analytical model for predicting flow in fractured-vuggy carbonate reservoirs under pseudosteady state condition. In the derived model, the crossflow between different systems (i.e., matrix, fracture, and vug) of the reservoirs was taken into account. In addition, based on Hooke’s law, a quantitative model was proposed to study stress-dependent permeability of the fracture system, which connects the reserve spaces. Moreover, the roughness morphology characteristics of fracture surface were taken into account with fractal theory. Finally, with our derived model, influences caused by various related factors on productivity were analyzed. The results show that well productivity during pseudosteady flow will be significantly affected by the morphology of fracture surface (e.g., fracture microstructure parameters) and effective stress. Specifically, due to effective stress, the fracture system in the fractured-vuggy reservoirs will be deformed, and the corresponding properties (e.g., permeability, porosity, and conductivity) will change, leading to the change of well productivity. In addition, there exists a negative relationship between the elastic storage capacity ratio of vugs and well productivity during pseudosteady flow. Moreover, a larger value of matrix-fracture interporosity flow coefficient or vug-fracture interporosity flow coefficient corresponds to a larger value of well productivity during the pseudosteady period. The new derived model is beneficial to improve the productivity prediction accuracy and reduce uncertainty. What is more, the findings of this study can help for providing theoretical reference for the design of efficient development of fractured-vuggy carbonate reservoirs.

Phosphorus removal from wastewater through struvite crystallization in a continuous fluidized-bed reactor: An improved comprehensive model

Promoting a wider application of struvite precipitation for nutrient recovery from wastewaters requires more efficient reactor designs, supported by models that integrate thermodynamic, kinetic and hydrodynamic behavior. The present work addresses the modeling of phosphorus recovery by struvite crystallization in fluidized-bed reactors, revealing discrepancies and errors in the literature and proposing corrections and improvements. A reduced thermodynamic model is presented. The potential of the struvite solubility constant was estimated to be 13.12 < pK < 13.30. Furthermore, a new strategy for a simple and quick estimation of the surface-area specific rate constant ka (1.70 dm/h ≤ ka ≤ 2.19 dm/h) was implemented. The technique involves operating the reactor with liquid in the transient regime as a completely stirred tank and solid-mixed bed in the pseudosteady state. Size distribution simulation results were obtained for different operational conditions using a one-dimensional perfect size classification model for the solid phase and a plug-flow model for the liquid phase.

Analytical solutions of advection-dispersion-reaction equation with first decay under constant and time-dependent boundary conditions: Mass transfer shape factor effects

To describe the combined dispersion and convection mechanisms of solute transport through porous media, one may typically refer to the advection-dispersion equation (ADE). In this study, a generalized analytical solution to the ADE combined with first order decay term is derived for the problem of solute transport through porous media in one-dimensional finite region considering transient boundary conditions. First, the addressed convection-dispersion-reaction equation is simplified into a diffusion equation. Subsequently, an analytical solution is generated for a general fractured porous medium for a case where a fracture is viewed as the transient boundary condition. To verify the proposed analytical solution, experimental data acquired from literature as well as numerical techniques of finite difference and element are utilized. Previous studies have utilized fixed values for mass transfer shaper factor which is deployed in dual porosity modeling approach of fractured reservoirs, while in reality this parameter changes over time. In this regard, an attempt is made to attain mass transfer shape factor while considering the impacts of important parameters such as Péclet number, and decay coefficient during both pseudo steady state (PSS) and transient periods. Moreover, for two circumstances of linearly ascending and constant concentration boundary conditions, a correlation is developed to compute PSS mass transfer shape factor as a function of Péclet number, dimensionless time, and decay coefficient. The results illustrated the dependency of PSS shape factor on the decay coefficient, Péclet number, and time while transient shape factor solely depended on time. In addition, the findings showed that the larger the Péclet number, the larger the PSS matrix-fracture mass transfer shape factor. The obtained analytical solution is helpful when validating the numerical simulation results and for performing fast sensitivity analysis. The developed mass transfer shape factor can be applied in the dual porosity modeling part of the commercial reservoir simulation software packages for more accurately modeling the solute transport in the fractured reservoirs.