Material Balance Equations Research Articles

DEVELOPMENT OF AN AUTOMATIC REFLUX RATIO REGULATION SYSTEM FOR THE RECTIFICATION COLUMN

This article provides an overview of the methods of managing the primary petroleum refining. To improve separation efficiency was proposed to stabilize the reflux ratio in the rectifying column. Purpose of work. To develop a system for automatic regulation of the reflux ratio of diesel fuel sec-tions in an atmospheric column of the refinery oil. To study the operating modes of an atmospheric column with the participation of the obtained automatic control system. Materials and methods. The article presented the features of the oil rectification process at the atmospheric unit of a small capacity refinery. The features of heat dissipation with intermediate circulation flash compared to a large-capacity unit will be shown in this article. The parameters of the facility were selected and divided into groups. A dynamic model of the section of shell-and-tube heat exchangers for heating oil with diesel fuel at a low-power refinery unit in the form of differential equations of heat balance has been developed to achieve the goal set work. An electrode dehydrator material balance equation has been compiled to find desalted oil consumption and saltwater consumption. The dependence of the reflux ratio of diesel fuel sections of the atmospheric column on the inlet and outlet temperatures of the atmospheric column circulation flash, the acute fractionation con-sumption, circulation flash, and oil fraction selection was obtained. The resulting model of the facili-ty consists of two parts: the linear part of the electric dehydrator and heat exchanger section, which determines the temperatures of the coolants, and the nonlinear output part, which determines the re-flux ratio depending on technological parameters. The proposed model makes it possible to investi-gate the effect of disturbances on the controlled parameters. The MATLAB/Simulink software prod-uct has been chosen as a tool to implement the model. A system of automatic regulation of the re-flux ratio in MATLAB/Simulink has been built with the participation of the developed model of the study object. Conclusion. The results of modeling a system for automatic regulation of the reflux ratio of diesel fuel sections in the atmospheric column of a low-power refinery unit has been ob-tained, taking into account the peculiarities of the process under disturbance conditions.

Operation Control of In Situ Combustion Based on the Material Balance Equation

The stability of combustion in the process of fire flooding requires not only a reasonable gas injection rate but also a matching exhaust rate. A reasonable injection-production balance system is very important. Based on the material balance of injection-production, the expression of injection-production ratio suitable for normal fire flooding production is established. The air injection rate of fire flooding combustion and oxygen consumption of formation pressurization is analyzed by this formula to calculate the gas production and liquid production in combustion. The reasonable injection and production parameters for the oilfield are calculated by using the oilfield parameters. It can be seen that the calculated value of injection-production ratio is consistent with the actual value, which shows that the injection-production ratio is reasonable and can guide the adjustment of production parameters in the oilfield.

To What Extent Is Manure Produced, Distributed, and Potentially Available for Bioenergy? A Step toward Stimulating Circular Bio-Economy in Poland

Bioenergy production from animal waste can be a key driver to achieving bio-economy goals. Developing a bio-economy sector could help to create opportunities for a circular system where not only people and the planet will be benefited, but it will also provide economic profitability to farmers, especially in the post-Covid period. To this end, manure production, its nutrient content, and bioenergy potential were estimated, along with their spatial distribution in the Lubelskie province, Poland. Farm-level data were processed and aggregated at the municipality level. Material balance equations were used to calculate the theoretical potential of livestock manure and bioenergy for different use scenarios: (1) Baseline (BC): direct manure application to land, which was compared against (2) Anaerobic Digestion (AD): anaerobic digestion to biogas with digestate returned to the fields (3) AD + Separation (AD + Sep): mechanical separation followed by anaerobic digestion, and (4) Surplus + AD: surplus manure (after application to the fields) is sent to anaerobic digestion. Manure, biogas, electricity, and thermal energy production of the AD scenario were estimated to be 7.5 Mt y−1, 378 Mm3 y−1, 907 GWe y−1, and 997.8 GWth y−1, respectively. The scenario, including mechanical separation followed by anaerobic digestion (AD + Sep), contributed to avoiding emissions to the largest extent (1 Mt CO2 eq), whereas AD outperformed the others in avoiding costs of fertilization. According to the estimated potential and the environmental cost-effectiveness of AD, new plants can be established that will recycle manure through bioenergy production, and, subsequently, the digestate can be applied as organic fertilizer, closing the nutrients cycle.

Analysis of early-time production data from multi-fractured shale gas wells by considering multiple transport mechanisms through nanopores

Analysis of early-time production and flowback data from multi-fractured shale gas wells is of critical importance in the characterization of hydraulic fractures (HF). However, the accurate estimation of HF properties in the current models is challenged by the complexity in multiple transport mechanisms and two-phase flow of shale gas reservoir. This study presents a new semi-analytical method to estimate HF attributes for shale gas wells exhibiting two-phase flow based on straight line analysis. The proposed method considers two-phase infinite acting linear flow (IALF) and boundary dominated flow (BDF) for both HF and matrix domains. In addition, matrix flow considers desorption, diffusion, slip flow, continuum flow, stress dependence rock, and adsorbed water film in the nanopores. A modified material balance equation is proposed to calculate average pressure in the fracture and distance of investigation (DOI) in the matrix by considering gas desorption and diffusion in the matrix domain. The accuracy of the proposed method is tested against numerical results obtained from commercial software (IMEX-CMG). The validation results confirm that the developed method can closely estimate initial fracture volume, permeability, and permeability modulus from early-time production data exhibiting two-phase IALF and BDF regimes. Furthermore, the results indicate that the consideration of desorption, diffusion, and slip flow plays an important role in the modeling of gas transport in shale matrix. The impact of these transport mechanisms on production modeling as well as characterization of HF properties becomes significant when the matrix experiences substantial pressure drops. For the purpose of field application, the proposed method is used to analyze flowback data from a multi-fractured horizontal well. The field results reveal that the calculated fracture properties are consistent between the proposed method and the long-term production data analysis method.

Effect of Blending Ratio and Temperature on CO2 Solubility in Blended Aqueous Solution of Monoethanolamine and 2-Amino-2-methyl-propanol: Experimental and Modeling Study Using the Electrolyte Nonrandom Two-Liquid Model.

This paper reports the newly measured experimental data for CO2 solubility in a blended aqueous solution of monoethanolamine (MEA) and 2-amino-2-methyl-propanol (AMP) at different amine mixing ratios (MEA/AMP/H2O = 9:21:70, 15:15:70, and 21:9:70 wt %) and working temperatures (323.15, 373.15, and 383.15 K). The successive substitution method was used for calculating the mole fractions of all molecules (four molecules) and electrolytes (three cations and four anions) from the equilibrium along with the material and charge balance equations (11 equations). The electrolyte nonrandom two-liquid (e-NRTL) model was used to investigate nonideality in the liquid phase. Using the abovementioned thermodynamic models, the partial pressures of CO2 in the gas phase, mole fractions of all components in the liquid phase, pH variations, heats of absorption, and cyclic capacities of CO2 according to the absorption/desorption temperature and the blending ratio of MEA/AMP were estimated.

Observations on and use of curves of current dimensionless potential versus recovery factor calculated from models of hydrocarbon production systems

In this work, curves of current dimensionless potential versus recovery factor are computed with models of hydrocarbon production systems. Additionally, a method to estimate production profiles using curves of current dimensionless potential versus recovery factor is presented. The author introduces three definitions, (1) the “production potential” is the maximum rate of hydrocarbon delivery for a production system at a given recovery factor. (2) The “maximum production potential” is defined as the maximum rate of hydrocarbon delivery at initial recovery factor. (3) The “current dimensionless potential” is defined as the production potential normalized by the maximum production potential. Several cases and modeling approaches, using coupled models of reservoir, well and gathering network are used. The reservoir was modeled using two approaches: a tank model (material balance equation) and a three-dimensional (3D) simulator. This work studies the effect of changes to the production system on the curve of current dimensionless potential, and how to handle such changes over the lifetime of the field when computing production profiles. It also discusses production scheduling using multiple curves of current dimensionless potential. Expressions and curves of current dimensionless potential versus recovery factor were derived using Arps decline equations and production data of a Norwegian offshore dry gas field.Results show that the curve of current dimensionless potential is not affected significantly by (1) changes in number of wells, (2) initial surface volume in place, (3) layout of gathering system, (4) pipe and tubing diameter, (5) artificial lift and (6) formation permeability. However, the curve is strongly dependent on (1) reservoir drive mechanism, (2) model components considered in the flow-path from reservoir to separator and (3) model upstream and downstream boundary pressures. Curves of current dimensionless potential derived with the Arps exponential decline equation are similar to the results of the dry gas study case.

An Intelligent prediction model for UCG state based on dual-source LSTM

Underground coal gasification (UCG) is a serious attempt to clean and efficient use of coal, but it has not been able to solve the problem of stable production. Predicting UCG can provide effective guidance for control, which effectively solves this problem. Existing UCG prediction models are not accurate, and most of them can only predict a single variable, and cannot adequately predict the UCG state. The paper proposes the concept of combustible gas equivalents that can characterize the concentration of mixed gas through stoichiometry and material balance equations. The equivalent gradient is introduced to characterize the trends in equivalent, and the UCG state discrimination standard is established to evaluate the UCG state. Eventually, a dual-source long short-term memory (LSTM) prediction model is proposed for predicting UCG state. The experimental results show that compared with Support Vector Machine (SVM) and Back Propagation Neural Network (BPNN) prediction model, the model can make a better prediction of equivalent value and the accuracy of predicting trends in equivalent reaches 90.99%.

Mathematical Model for Li-S Cell with Shuttling-Induced Capacity Loss Approximation

Lithium sulfur (Li-S) batteries have the potential to outperform the current lithium ion batteries and transform the technology of the future. However, dissolution, diffusion, and shuttling of the dissolved polysulfides result in parasitic reactions and substantial capacity loss. To provide a better understanding of the shuttling process, a 1D porous electrode mathematical model has been developed in this paper. An approximation method is used to account for the shuttling-induced capacity loss by adding an extra source/sink term in the material balance equations for the species involved in the parasitic reactions. Shuttling constants used in the source terms can be determined by fitting the model predictions to the experimental measurements. The results showed that by including the approximation method, the model was able to predict the active material loss and the continuous decrease of volume fractions of Li2S on the cathode surface. The model sheds light on the capacity loss mechanism occurring inside the cell as a result of the shuttling of polysulfides.

A new straight-line reserve evaluation method for water bearing gas reservoirs with high water production rate

A material balance equation (MBE) is usually used to estimate hydrocarbon reserves, to judge driving mechanism, and to predict the dynamic performance of oil and gas reservoirs. Few straight-line methods have been proposed for estimating original gas in place (OGIP) of water bearing gas reservoirs with high water production until now. For this type of gas reservoir, gas and mobile water mostly coexist in the same formation because of low permeability. Lots of water is produced even though there is no bottom or edge aquifer. Thus, the effect of water production on average pressure should not be ignored.In this work, an MBE for water bearing gas reservoirs considering the effects of water compressibility, pore compressibility, and water production, is derived step by step from the basic material balance principle, and the corresponding straight-line reserve evaluation method is developed. Then the proposed reserve evaluation method is validated against a computer modelling group (CMG) simulation case and two field cases using pressure transient analysis (PTA) method in the dynamic data analysis software KAPPA Ecrin. Finally, the necessity and importance of the proposed reserve evaluation method in water bearing gas reservoirs are discussed.Validation cases prove that the proposed straight-line reserve evaluation method for water bearing reservoirs is reliable and rational. The OGIP of water bearing reservoirs can be evaluated directly using the y-intercept divided by the minus slope of the straight line. If ignoring the effect of water production, the OGIP of water bearing gas reservoirs will be underestimated, especially for gas wells with high water production rate and short producing time.

The mathematical modeling of changes in grain moisture and heat loss on adsorption drying from parameters of grain dryer

The literary review has established that to reduce the heat loss of a dryer, the heat insulation of the dryer design, heat recovery and suction air flow are used. However, the use of prospective suction airflow is not fully disclosed. In the article, based on the equations of mass transfer, thermal and material balance, the dependences of grain moisture and heat consumption on drying from the regime parameters of the dryer, grain properties, and air flow used during drying are found. Analytical dependencies are illustrated by the corresponding schedules. Analysis of the analytical and graphical dependences of grain moisture and heat consumption on the corn grain sample has established that reducing the heat consumption when drying the grain, possibly reducing the pressure in the dryer, while simultaneously draining the air stream before it is fed to the drying chamber.

Short-Range Order Evolution in Nanocrystalline Mechanically Activated Fe–Cr Alloys in the Process of Annealing

Nanocrystalline Fe–Cr alloys synthesized from pure components in a planetary ball mill with a chromium content of 20–48 at % were annealed for 4 h at temperatures of Tan = 400–700°C. Short-range order (SRO) evolution and phase separation dependent on Tan were studied using Mossbauer spectroscopy and X-ray diffraction. The precipitation of the σ-FeCr phase was observed only in the samples with 48 at % of Cr at Tan = 600 and 700°C. For all the samples, the grain growth began most intensively from 400°C, and the higher the Cr content in an alloy, the smaller the final size of grains after Tan = 700°C. The analysis of behavior of the mean hyperfine field on Fe nuclei and distribution of the hyperfine field width depending on Tan, as well as fitting of Mossbauer spectra with spectral components corresponding to the α (Cr depleted) and α' (Cr rich) phases, demonstrated that the mechanically alloyed Fe-Cr samples were characterized by weak short-range separation passing at Tan = 400°C to a nearly statistically uniform distribution of atoms. Heterogeneous short-range order with the α and α' regions was formed in the alloys with 30 at % of Cr and more after annealing at 500–700°C. An analysis with the material balance equation led to our conclusion about the existence of the grain boundary segregations of Cr atoms.

Reasonable Degree of Formation Pressure Maintenance in Low Permeability Reservoirs

Due to the decline of formation pressure in the middle and late periods of low permeability reservoir development, the development effect deteriorates. Therefore, it is essential to restore and maintain reasonable formation pressure. Based on the two-phase fractional flow equation in low permeability porous media, we consider the flow characteristics in reservoirs with threshold pressure gradient and the influence of formation pressure on oil viscosity. By applying the material balance equation, we deduce the theoretical formula of future cumulative oil production with different formation pressures. In view of the contradictory relationship between cumulative oil production and water cut increasing rate, and we construct a bi-objective function to evaluate the reasonable formation pressure. Results show that during transition process from current formation pressure to reasonable formation pressure, when the reservoir formation pressure maintenance degree is 0.88, it can ensure that future cumulative oil production is relatively large and water cut increasing rate is relatively low. Under the condition of the same formation pressure maintenance degree, as threshold pressure gradient grows, the impact on cumulative oil production gradually increases. In order to provide a good development result, the formation pressure should be recovered as early as possible before it drops significantly. This method can be used to calculate reasonable formation pressure quantitatively and provide a reference for high efficiency development in low permeability reservoirs.

A Semianalytical Method for Two-Phase Flowback Rate-Transient Analysis in Shale Gas Reservoirs

Summary We propose a new semianalytical method for analyzing flowback water and gas production data to estimate hydraulic fracture (HF) properties and to quantify HF dynamics. The method includes a semianalytical flowback model, a set of two-phase diagnostic plots, and a workflow to evaluate initial fracture volume and permeability, as well as fracture compressibility and permeability modulus. The flowback model incorporates two-phase water and gas flow in both HF and matrix domains and considers variations of fluid and rock properties with pressure. The HF domain is modeled by boundary-dominated flow, whereas an infinite-acting linear flow is assumed for the matrix domain. The flowback model is developed by assigning the variable average pressure in the fracture as the inner boundary condition for matrix according to Duhamel's principle. The average pressure in the fracture and distance of investigation (DOI) in the matrix are calculated from a modified material-balance equation by updating the matrix DOI as well as phase saturation and relative permeability in both the fracture and matrix domains. A modified DOI equation is used for two-phase flow in the matrix, which considers the pressure-dependent fluid and rock properties in pseudotime. The diagnostic plots shed light on the identification of flow regimes during the coupled two-phase flow in both fracture and matrix. The proposed workflow quantifies the HF dynamics through the loss of both fracture volume and fracture permeability by reconciling flowback and long-term production data. The accuracy of the new method is tested against numerical simulations conducted by a commercial numerical simulator. The validation results confirm that the proposed method accurately predicts initial fracture volume, permeability, and permeability modulus. Further, we use production data from a multifractured horizontal well (MFHW) drilled in Marcellus Shale to test the practicality of the proposed method. The results show a significant reduction in fracture volume and permeability during production attributable to the HF closure.

Material balance equation of shale gas reservoir considering stress sensitivity and matrix shrinkage

As the formation pressure drops during the development process of shale gas reservoir, the effects of stress sensitivity and matrix shrinkage occur. Stress sensitivity effect decreases the porosity of reservoir formation, while matrix shrinkage effect increases the porosity. Therefore, the porosity will be influenced by the combined effect of both stress sensitivity and matrix shrinkage, which need to be considered in the material balance equation of shale gas reservoir. In this work, based on the material balance theory of shale gas reservoir, a material balance equation considering the influences of stress sensitivity and matrix shrinkage on shale gas reservoir that the porosity varies as formation pressure changes is established. Then, the material balance equation is linearized, and the original gas in-place (the controlled reserve) of single well can be calculated by the intercept and the slope of the straight line of the linearized material balance equation, which is convenient for field application. Production data of three gas wells of a certain shale gas reservoir are calculated with the proposed material balance equation in this work. The calculation results indicate that the stress sensitivity effect has the dominant influence on the porosity at the early stage of formation pressure dropping, while the matrix shrinkage effect dominates the influence on the porosity at the late stage of formation pressure dropping. Furthermore, the controlled reserves of the three gas wells have decreased by considering the effects of stress sensitivity and matrix shrinkage in the material balance equation.

Pressure-Predicting Model for Ultralow-Permeability Reservoirs considering the Water Absorption Characteristics of Mudstone Formations

The injection-production ratio of ultralow-permeability reservoirs is generally higher in the early stage of development because of the water absorption characteristics of transition layers and mudstone formations. In this paper, the water absorption characteristics of mudstone are experimentally studied, and the empirical function of the water absorption process is established. A new mathematical model of the whole lithology is established by applying the research results of mudstone water absorption characteristics. Combining the material balance method and finite difference method, the space terms in the basic differential equation are replaced by the material balance equation, and the finite difference in the time term is obtained. Then, the analytical solutions of the average pressures of the reservoir oil well area, reservoir water well area, transition layers, and mudstone formations are solved. Based on the static parameters of the reservoir in the Chaoyang Gou Oilfield of the ultralow-permeability reservoir in China, the new pressure prediction model is verified by the ideal model of numerical simulation and production data of the oil field. The experimental results show that the saturation water absorption rate of mudstone is 1.54-2.55%, and the water absorption process of mudstone cannot be described by the seepage equation of sandstone. The verification results of the numerical simulation show that the pressure of the transition layers and mudstone at the end of the water well gradually increases, while the pressure at the end of the oil well basically remains unchanged, which is consistent with the assumptions of the model. The verification results of the oilfield production data show that the water well static pressure and oil well static pressure calculated by the new model are highly consistent with the actual values, which well explains the phenomenon of the low reservoir pressure level under the condition of a high injection production ratio in an ultralow-permeability reservoir.

Micromorphic balance equations in mass transport and mass production

The balance equations for micromorphic materials with mass flux and mass production are determined based on the phenomenon of self-diffusion. In this study, the self-diffusive flux is the flux of mass of a single micromorphic species within itself which is captured by defining the relative macro-element spatial velocity vector and the relative micro-gyration tensor. By use of a binary micromorphic mixture theory, the self-diffusion of a single micromorphic species within itself results in an extra diffusive momentum field, an extra diffusive moment of momentum and their respective non-compliant terms. The concepts of the macro- and micro-mass flux are studied in the framework of the micromorphic theory. Furthermore, based on the Clausius-Duhem principle, admissible constitutive equations are presented for the diffusive and non-compliant quantities.

Comprehensive Studies on Production Data Analysis of Hydrocarbon Reservoirs

A review of field production data reveals that usually, it is very difficult to apply available decline models because of poor quality and often noisy character of initial data and also unrealistic assumptions of the models. This paper tries to introduce applicable procedures to correct initial data and reproduce missed data. Corrected data are analyzed and finally, the results for permeability and skin factor estimations are compared to results of transient well test analysis. Estimations for Initial Hydrocarbon In Place (IHIP) and reserve are also compared to the results of Material Balance Equation (MBE) and static model through field case studies. It is proved that the analysis can present acceptable estimations for radial permeability and skin values in naturally fractured reservoirs (NFR). Flowing material balance and Buba and Blasingame plotting function model give the best estimations for Original Gas In Place (OGIP) and gas reserve respectively. A simple but useful and applicable method is presented to determine reservoir fracture distribution mapping. It is also showed that the analysis can be used to distinguish water influx successfully.

Production data analysis of gas reservoirs with edge aquifer drive: A semi-analytical approach

Production data analysis is proved to be an efficient reservoir engineering tool that can be utilized to estimate some important reservoir parameters including fluid in place and, average reservoir pressure. Among the available production data methods, flowing material balance is more popular. In spite of the development of this method for volumetric gas and, oil reservoirs over the past years, non-volumetric effect doesn't feature the equations. In this paper, modified flowing material balance equations are proposed for production data analysis of gas reservoirs subjected to finite-extended edge aquifer. The validity of the presented equations is performed using analytical solutions. For the development of analytical solutions, special simplifying assumptions are considered. To evaluate these assumptions, a comparison is performed using a commercial numerical reservoir simulator for some models with different rock and, fluid properties. Moreover, the introduced flowing material balance equation is combined with material balance equation in order to find a simple equation to calculate average reservoir pressure. Detailed steps are presented to determine gas in place of and, average reservoir pressure of this kind of reservoirs. Furthermore, for a better match between analytical and numerical outputs of gas flow rates, a correction coefficient is recommended which depends on the strength of aquifer.

New Calculation Method and Application of Gas Loss From Coring Shale Gas Well

Abstract Gas content is one of the most important parameters of shale reservoir evaluation and productivity evaluation. In order to obtain gas content accurately, based on the first law of Fick and material balance equation, mathematical model of gas dispersion flow in shale reservoir is established, analytical solution is obtained, and evaluation method of gas dispersion in shale reservoir is formed. On the basis of this study, the onsite desorption gas measuring device and testing process for coring shale gas wells are designed, the time-varying shale desorption gas is obtained, and the residual gas of shale is measured by the crushing method. The calculation formula of shale gas content is obtained by fitting the test data, the shale gas loss, and total gas content are calculated, and then analyzed the influences of the shale gas-bearing properties and gas content on single well production and geological reserves by combining the data of shale absorbed gas. The results show that the gas content calculated by the new method is about 6.54% more than that of log interpretation, and about 7.57% on average more than that obtained by traditional empirical method. The gas content proportion of long Yi1 subsegmental small layers 1 and 2 is smaller than that of long Yi1 subsegmental small layers 3 and 4 and long Yi2 subsegmental. It is considered that the amount of shale gas lost is large, because of the pressure release during the coring, and the comparative error of gas content obtained by several methods is within the acceptable range. So the new method can be used as an important mean to obtain shale gas content. The most direct factors affecting gas content are complex: Buried depth, porosity, total organic carbon content, water saturation, and formation temperature. Shale gas content is the material basis of single well production and geological reserves of shale gas, and it is also the decisive factor. Therefore, the accurate evaluation of shale gas content is one of the key techniques to evaluate shale gas well productivity and shale gas resources, which is of great significance.

Equations of working lines in packed columns with regard to longitudinal diffusion

The analysis of differential equations of material balance with mass transfer taking into account longitudinal diffusion on both phases in a packed absorber and a distillation column is carried out. It is proposed according to the known algorithms for the calculation of absorption processes to calculate the working lines separately for two cases: 1) solid phase moves in the mode with longitudinal diffusion and dispersion in the ideal displacement mode; 2) continuous phase moves in the ideal displacement mode and dispersion mode with longitudinal diffusion, and then by summing the ordinates of the resulting working lines, to its overall significance to him and the equilibrium line on a standard methodology to calculate the height and diameter of the column.