Material Balance Equations Research Articles

Monte Carlo simulation of chemistry following radiolysis with TOPAS-nBio

Simulation of water radiolysis and the subsequent chemistry provides important information on the effect of ionizing radiation on biological material. The Geant4 Monte Carlo toolkit has added chemical processes via the Geant4-DNA project. The TOPAS tool simplifies the modeling of complex radiotherapy applications with Geant4 without requiring advanced computational skills, extending the pool of users. Thus, a new extension to TOPAS, TOPAS-nBio, is under development to facilitate the configuration of track-structure simulations as well as water radiolysis simulations with Geant4-DNA for radiobiological studies. In this work, radiolysis simulations were implemented in TOPAS-nBio. Users may now easily add chemical species and their reactions, and set parameters including branching ratios, dissociation schemes, diffusion coefficients, and reaction rates. In addition, parameters for the chemical stage were re-evaluated and updated from those used by default in Geant4-DNA to improve the accuracy of chemical yields. Simulation results of time-dependent and LET-dependent primary yields Gx (chemical species per 100 eV deposited) produced at neutral pH and 25 °C by short track-segments of charged particles were compared to published measurements. The LET range was 0.05–230 keV µm−1. The calculated Gx values for electrons satisfied the material balance equation within 0.3%, similar for protons albeit with long calculation time. A smaller geometry was used to speed up proton and alpha simulations, with an acceptable difference in the balance equation of 1.3%. Available experimental data of time-dependent G-values for agreed with simulated results within 7% ± 8% over the entire time range; for over the full time range within 3% ± 4%; for H2O2 from 49% ± 7% at earliest stages and 3% ± 12% at saturation. For the LET-dependent Gx, the mean ratios to the experimental data were 1.11 ± 0.98, 1.21 ± 1.11, 1.05 ± 0.52, 1.23 ± 0.59 and 1.49 ± 0.63 (1 standard deviation) for , , H2, H2O2 and , respectively. In conclusion, radiolysis and subsequent chemistry with Geant4-DNA has been successfully incorporated in TOPAS-nBio. Results are in reasonable agreement with published measured and simulated data.

Embedded Discrete Fracture Modeling With Artificial Intelligence in Permian Basin

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 187202, “Field Study: Embedded Discrete Fracture Modeling With Artificial Intelligence in Permian Basin for Shale Formation,” by Song Du, Baosheng Liang, and Lin Yuanbo, Chevron, prepared for the 2017 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 9–11 October. The paper has not been peer reviewed. Full-field models using unstructured grids can capture detailed geometric information such as fracture distribution. However, these are computationally expensive and often numerically unstable because of convergence issues. In the complete paper, the authors investigated embedded discrete fracture modeling (EDFM) using artificial intelligence (AI) to overcome challenges associated with unstructured modeling. Introduction It has been proved that EDFM enables flexible fracture geometry because the fracture domain is relatively independent of the matrix regions. EDFM has been widely accepted recently because of its simplicity and computational efficiency. The authors’ studies applied EDFM with AI optimization for fracture-network representation. The growth of computational power and the availability of large quantities of data have led to the widespread promotion of applications of AI technologies. AI has been used in the oil and gas industry in the areas of production optimization, operating-cost reduction, and efficiency improvement. Currently, almost all AI technologies are still limited to executing specific tasks, also known as specialized AI, an application that lacks the capability of generalized AI in adaptive learning. However, specialized AI still has advantages of high speed, superior consistency and unmatchable repeatability over human intelligence. In the complete paper, application of AI technology in processing the fracture network for successive simulation is described. Methodology EDFM. This method has drawn considerable attention because of its efficiency. EDFM minimizes the local grid resolution while preserving flow behavior between fracture and matrix by maintaining the original fracture orientation and distribution. The EDFM method is composed of two major elements: matrix and fracture. A long fracture is subdivided into small segments at the interconnecting points. A simple material-balance equation can show the flow behaviors at the cross sections. The fractures and matrix are modeled as two different domains. As de-scribed previously, fluid communication between fractures and the matrix uses mass-balance equations. Nonneighbor connection (NNC) must be calculated explicitly for a reservoir simulator. EDFM With Mangrove. Mangrove, an engineered stimulation design package, is a hydraulic-fracture simulator that links reservoir characterization and simulation and helps optimize completion designs in unconventional reservoirs. It has been of considerable use in unconventional-field development and has provided guidance for well-landing, completion-design, and well-/fracture-optimization decisions. However, the package creates unstructured simulation grids that can lead to convergence issues, and is also computationally expensive.

A semi-analytical method of production prediction for shale gas wells considering multi-nonlinearity of flow mechanisms

Unlike conventional reservoirs, production prediction for shale gas wells is not easy with analytical models for model nonlinearity caused by multi flow mechanisms of shale gas, such as desorption, slippage flow and diffusion. This paper presents a method to linearize the production prediction model based on the trilinear flow model. The nonlinearity of desorption and gas compressibility is linearized by defining a pseudo-pressure and pseudo-time, and the nonlinearity of apparent permeability is dealt with iterations. Average pressure in the investigation is applied to convert the pseudo-time to real time, which is calculated with material balance equation and Newton iteration. The results show that: (1) The production predicted with the semi-analytical method is accurate for the nonlinearity in the model being dealt properly; (2) Neglecting the compressability of gas has a great influence on precision of production prediction; slippage flow and diffusion of shale gas increase the productivity of shale gas wells, but they aggravate the decline of production; desorption in shale matrix can enhance middle and long term production, and alleviate production decline; (3) The field case shows the veracity of the semi-analytical model, and gas production and EUR can be evaluated with the model.

A mathematic model for characterizing the relationship between coal reservoir pressure and fluid saturation

At present, the research on the gas water two-phase flow during the development process of coalbed methane reservoirs (CMB) is still weak. Numerous production prediction models and transient production data analysis methods have been developed. However, part of these previous models assume the single water or gas phase within the coal seams, the other part overlook the gradient of fluid saturation and pressure and another part investigate the effect of fluid saturation distribution on productivity by utilizing the concept of average saturation, which is obtained through the derivation of material balance equation in CMB reservoirs. Notably, the average saturation cannot capture the feature of saturation distribution in the coal seams. Therefore, the existed models do not take into account the influence of fluid saturation distribution characteristics on gas well productivity, which result in relatively large error between the present productivity model and the actual CMB wells. In these regards, according to the gas and water two-phase seepage differential equation, considering the stress sensitivity, matrix shrinkage, gas adsorption/desorption effect, this research establishes a mathematical model characterizing the relationship between formation pressure and saturation. Combined with gas-water two-phase relative permeability curve, the model can be solved to obtain the saturation distribution on the basis of reservoir pressure distribution. Moreover, the reliability of the model is verified against commercial numerical simulation software with excellent agreements. The proposed model fills the gap of CMB development theory, and significantly contributes to the precise calculation of the gas-water two-phase pseudo pressure. In addition, it lays a theoretical foundation for accurate prediction of CMB productivity.

The modified gas-water two phase version flowing material balance equation for low permeability CBM reservoirs

The flowing material balance (FMB) equation is a frequently-utilized engineering tool to extract reservoir information according to production performance of producing wells. At present, it is still significantly challenging to adapt the FMB equation to CBM reservoirs due to the existence of gas-water two phase flow, stress dependence, matrix shrinkage and gas desorption. With all my respect to previous FMB equations for CBM reservoirs, a great deal of attention has been drawn to the single water/gas flow, which can only be applied for early production stage or cannot capture the gas-water two phase flow features of general CBM reservoirs. The most recent and comprehensive research effort of FMB equation for CBM reservoirs is performed by Clarkson and Salmachi (2017), which takes the aforementioned characteristics into account. However, suffering the limitation that the pressure-saturation relationship is not available, Clarkson and Salmachi (2017) assume the saturation and pressure gradients in coal seams are negligible, i.e., the relative permeability is not incorporated in the pseudo-pressure calculation, which will inevitably lead to large deviation compared with the precise results. Notably, during the depressurization development process of low-permeability CBM reservoirs, the pressure and saturation gradients are large enough and cannot be overlooked. Thus, a robust FMB equation for gas-water two phase flow in low-permeability CBM reservoirs is still lacking in the petroleum industry and is significantly necessary to be developed. In this study, the important pressure-saturation relationship is rigorously derived in terms of the conservation of mass and momentum equations, in which the gas desorption, matrix shrinkage and stress dependence are fully coupled. Next, the developed relationship is used to calculate the gas/water phase pseudo-pressure and subsequently the previous FMB equation for CBM reservoirs is modified. Finally, reliability of proposed FMB equation is successfully verified against the numerical simulation with excellent agreements compared with the input reservoir properties. In addition, with the intent of further solidifying the field applicability of the modified FMB equation, the production performance of an actual low-permeability CBM well in Hancheng field, China is analyzed through the proposed FMB equation and desirable interpretation results are achieved. Incorporating the pressure-saturation relationship for the first time, the modified FMB equation can serve as a practical and robust tool to extract valuable information regarding the low-permeability CBM reservoirs.

Treatment of Rate-Transient Analysis During Boundary-Dominated Flow

Summary Significant advances have been made in the development of analytical models for performing rate-transient analysis (RTA) for single-phase oil and gas reservoirs. The primary complication associated with the adaptation of these solutions to wells exhibiting multiphase flow is the single-phase assumption in the development of the material-balance time function. Despite some efforts in modifying existing dry-gas formulations for use with gas/condensate reservoirs, that approach is not practical for analyzing multiphase flow from oil wells with multiphase-flow characteristics. In this work, we present a simple yet semianalytical model that provides a solution for analyzing production data from wells exhibiting multiphase flow during boundary-dominated flow periods. The solution is obtained by combining the material-balance equation and the productivity index (PI) for all flowing phases. Appropriately defined total pseudopressure and total pseudotime are introduced to handle the associated multiphase nonlinearities in the governing flow equations of oil, gas, and water phases simultaneously. A generalized flowing-material-balance (FMB) equation is derived from the total pseudovariables to estimate original fluid in place and drainage area (given volumetric input). The presented model provides a theoretical framework for analyzing production data considering a wide variety of reservoir-fluid systems. The new method is validated against numerical simulation, covering a wide range of fluid properties and operating conditions. In all simulated cases, the new method matches simulation input acceptably. Two field examples are also analyzed to demonstrate the practical applicability of this approach. This work serves as a practical and simple engineering tool for production-data analysis on wells exhibiting single and multiphase flow during boundary-dominated flow.

Modeling and simulation of a fluidized bed gasifier

AbstractA mathematical model to simulate continuous gasification of coal particles in a bubbling fluidized bed reactor is presented. Material and energy balance equations have been formulated based on the 2‐phase theory. Well‐known correlations have been used to estimate the hydrodynamics. Devolatilization, heterogeneous reactions, and homogenous reactions have been included in the model. The model is used to simulate 29 experimental data sets from the published literature. The model predictions agree very well with the experimental data by adjusting the particle size. After establishing agreement with the data, the model was used to investigate influence of various operating parameters on overall performance (carbon conversion and the gross calorific value of generated gas). Thermodynamic analysis (using the minimization of the Gibbs free energy approach) has also been discussed. The presented model and results provide useful tool and insight on design and operation of fluidized bed gasifier.

Experimental and material balance equations analyses of cyclic solvent injection based on a large 3D physical model

A cyclic solvent injection (CSI) test is conducted in a large 3D physical model (80 × 40 × 20 cm3). 23.57 l heavy oil (2700 cp@21 °C) is saturated into this model. The test ran for 30 cycles achieving the recovery factor of 67.1%. Experimental results are compared with those of a cylindrical model (d = 15.24 cm, L = 30.48 cm) CSI test to investigate dominated driving mechanisms of CSI under different physical models. A linear form of material balance equation (MBE) of CSI is established for the first time to obtain the amount of diluted oil (Ndi) after the solvent injected into the model in each cycle, which could be used to evaluate the efficiency of oil dilution (Esd) and recovery factor of diluted oil (Rd). Esd is defined as the ratio of the Ndi to remaining oil. Rd is defined as the ratio of the cumulative oil production as per cycle to Ndi. In the MBE, since non-equilibrium phase behavior is presented in CSI, Rs and Bo measured by conventional PVT test under equilibrium state cannot be directly used in the MBE. In this study, Rs and Bo are first matched through the proposed MBE by using experimental data from large 3D test. With estimated Rs, Bo and other experimental data, Ndi of each cycle in large 3D test are obtained by liner regression. At last, to further verify the proposed MBE, the tuned Rs and Bo are used to obtain Ndi of the cylindrical model test.Comparison between two tests indicates that the gravity force still dominates the recovery factor rather than the model size. The model shape significantly affects the change of production rate, but not the average production which is mainly determined by the original oil in place (OOIP). The same behavior of minimum production pressure occurred in two tests with the same pressure decline rate. Ndi of each cycle in the large 3D test is successfully obtained through the established MBE. Then Ndi are used to obtain Esd and Rd. The results show that Esd first increases from 4.75% to 10.70% with the growth of solvent chamber. Then it keeps around 13.78% for main stage. During the very late stage, Esd decreases to 10.11%. Not as Esd dramatically varies, Rd in each cycle is in the range of 28%–34%, which indicates that recovery of CSI has much more potential. A higher recover factor could be expected if Esd and Rd would be both improved. By the tuned Rs and Bo in the large 3D case, Ndi of each cycle in the cylindrical model CSI test is matched with very good agreement (average R2 = 0.9899), which suggests that the established MBE is reliable to evaluate production performance of CSI.

A new fast approach for well production prediction in gas-condensate reservoirs

Prediction of gas-condensate well production is significant for sensible decision making for the reservoir development plan, infrastructure investment, and produced gas and condensate sales contract. Typically, time-consuming numerical simulation with fine grids or local grid refinement around the well is implemented in order to capture the effects of condensate blockage and predict gas-condensate well deliverability. In addition, in the commencement of the reservoir lifetime, the numerical simulation predicts erroneous results due to high uncertainty in reservoir data. A simple analytical model can estimate gas-condensate well production reasonable with a limited number of input data. On the other hand, uncertainty studies require repetitious usage of the analytical calculation. Therefore, a faster and more practical method for calculation of gas-condensates well flow rate has a precious value. In this paper, a fast analytical method is introduced for prediction of gas and condensate production profiles based on the two-phase pseudo-pressure integral and material balance equation. Proposed analytical model in contrast to previous ones, predicts the exact plateau time. As the result, it does not need iteration in each reservoir pressure step to compute the relevant flowing bottom-hole pressure during the constant gas production period. The model is expanded to take into account the high-velocity phenomena in near the wellbore region. It is also extended for the first time for different well geometries including vertical, deviated, horizontal, and hydraulic-fractured wells. Additionally, the analytical model is validated using fine grid numerical simulation for a wide range of rock and fluid properties. The developed analytical model can be used as a fast engineering tool for evaluating the uncertainty in well and reservoir data to choose the best strategy for reservoir development.

A phenomenological description of charge transfer within polaron-containing films with unramified polymer chains

According to the existing modified electrode theory, both radical-cations (polarons) and reduced quasi-particles of conducting polymer films include the same number of repeat units of polymer chains. As opposed to such supposition, any reduced repeat unit of polymer chains is assumed to be a separate quasiparticle in scope of the recently proposed approach to treating the conductance of polaron-containing films. To say nothing of the obtained new results of such approach, it is necessary to indicate that its applications have been restricted so far to the cases of either a homogeneous polaron population, which means the absence of any polaron transformations (for example, into bipolarons), or the presence of such transformations proceeding in equilibrium conditions. The main purpose of the presented communication is to derive charge carrier fluxes and material balance equations valid for non-equilibrium conditions and accounting for the above transformations and translocations of quasi-particles along polymer chains. Consecutive acts of any type of the indicated processes are treated as sequences of similar reactions proceeding in the film interior. This allows one to apply the Bronsted rule of linear correlation between activation energies of such reactions and their generalized heat effects, in order to express the reaction rate as a function of the local electric field. Using a lattice model of films formed by unramified polymer chains, non-stationary flux and material balance equations have been obtained. A comparison between the derived results and those conformed to the existing theory shows their significant difference. Some other inferences from the description carried out and possible prospects of its development are discussed.

Technique Blends Dimensionless Numbers and Data Mining To Predict Recovery Factors

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 181024, “Recovery-Factor Prediction for Deepwater Gulf of Mexico Oil Fields by Integration of Dimensionless Numbers With Data-Mining Techniques,” by Priyank Srivastava and Xingru Wu, SPE, University of Oklahoma, and Amin Amirlatifi, SPE, Mississippi State University, prepared for the 2016 SPE Intelligent Energy International Conference and Exhibition, Aberdeen, 6–8 September. The paper has not been peer reviewed. Using attributes from a database of 395 deepwater Gulf of Mexico oil fields, a set of dimensionless numbers is calculated that helps in scaling attributes for all the oil fields. On the basis of these dimensionless numbers, various data-mining techniques are used to classify the oil fields. Subsequently, partial-least-square (PLS) regression is used to relate the dimensionless numbers to the recovery factor. This study shows that dimensionless numbers, together with data-mining techniques, can predict field behavior in terms of recovery factor for sparse data sets. Introduction The digitization of information and the rise of inexpensive sensor technologies have ushered in a new era of computing in which acquired data are used to show hidden patterns and trends. This method of computing is very efficient in solving inverse problems where parameters affecting system characteristics are not completely known. Hydrocarbon reservoirs provide a classic case of a natural system where engineers have limited control on the design of the system that they work with; thus, they have to rely on indirect measurements to determine properties of the reservoir and use these properties for prediction of future trends. Performance prediction is usually accomplished with either analytical material-balance equations or numerical reservoir simulation. However, both methods use a bottom-up work flow, which suffers from a drawback: the need for accurate representation of subsurface geology. Data mining, on the other hand, provides an alternative top-down intelligent-reservoir-modeling approach, which uses measured reservoir properties as the basis for modeling. Using publicly available information—including information on geology, geophysics, reserves, production, and infrastructure—the complete paper applies various data-mining and predictive-analytics algorithms to estimate recovery factor. Classical reservoir engineering assumes that recovery factor is dependent on rock properties, fluid properties, geological structures, and mode of production. Instead of using traditional deterministic methods, such as material balance or numerical simulation, this study uses data-driven analytics to estimate the recovery factor.

Multiwell, Multiphase Flowing Material Balance

Summary Flowing-material-balance (FMB) analysis is a practical method for determining original hydrocarbon volumes in place. It is attractive because it enables performing material-balance calculations without shutting in wells to obtain estimates of reservoir pressure. However, with some exceptions, its application is limited to single-phase oil and/or gas reservoirs over limited pressure ranges during depletion. In unconventional reservoirs, reservoir and/or production complexities may further restrict FMB use. Among these complexities are significant production/injection of water, production resulting in higher gas/oil ratios (GORs) and pressure drawdowns, geomechanical effects, and multiwell-production effects. As a result, application of the conventional FMB to unconventional reservoirs may lead to significant errors in hydrocarbons-in-place estimation. This paper first discusses the application of conventional FMB to the analysis of single-phase or multiphase flow in single or multiwell scenarios, and then provides a new, comprehensive version of the FMB to address the previously mentioned complications. For the new FMB, pseudopressure is used to account for two-phase oil/gas flow. In addition, by use of a general material-balance equation, water production/injection and multiwell effects are included in the analysis. The new FMB-analysis approach is validated by comparing results with numerical simulation of multifractured horizontal wells (MFHWs). These comparisons demonstrate that, not only gas production, but also water production/injection can have a significant effect on the calculated original-in-place hydrocarbon volumes. The new FMB-analysis approach provided herein successfully accounts for all flowing phases in the reservoir, and is demonstrated to be applicable for multiwell scenarios. The methodology presented in this paper maintains the simplicity of FMB, yet accounts for multiphase flow and multiwell complications. The developed FMB and the presented approach can be used by reservoir engineers to reasonably determine the original volumes of hydrocarbons in place in both conventional and unconventional reservoirs.

Packed bed reactor modeling of the catalytic auto-thermal reforming of synthetic crude glycerol

Modeling and simulation studies of synthetic crude glycerol auto-thermal reforming were performed in a catalytic packed bed reactor over a 5wt% Ni/CeZrCa catalyst. The numerical model comprised of two-dimensional material and energy balance equations and an in-house developed power law kinetic rate model. The model was validated against experimental data and a close agreement between the predicted and experimentally measured values was obtained with an average absolute deviation of <9%. Also, it was found that for the set of conditions and reactor dimensions used for this study, the effect of the axial dispersion term on the glycerol conversion was negligible. This effect is expected to be more pronounced at a larger scale and under actual operating conditions and therefore should not be neglected.

Ion-transfer across a membrane in the presence of a preceding slow homogeneous chemical reaction in the diffusion layer

The theory of rotating disk electrode developed by Levich is being advanced further and adapted to electromembrane systems with a slow chemical reaction. In terms of the system of Nernst–Plank equations supplemented by the equation of material balance with the source of ions that appear due to the weak-electrolyte dissociation, an attempt is undertaken to describe theoretically the ion electrodiffusion in the diffusion layer of a membrane system complicated by a limiting homogeneous chemical reaction. It is shown that the kinetics in membrane systems with a preceding slow homogeneous chemical reaction has limiting cases in which the process is controlled by either the chemical reaction or electrodiffusion. Depending on the rate constant of dissociation, a kind of mixed kinetics is observed between these two limiting cases. The approximate equation for estimating the limiting kinetic current is derived. The ion concentration profiles and the reaction rate in the diffusion layer are calculated. The effect of the weak electrolyte concentration, the rate constant of dissociation, and the membrane disk rotation rate on the electrochemical characteristics of the system is studied. The theoretical fundamentals for determination of the rate of slow chemical reaction in electromembrane systems by the method of rotating membrane disk are developed.

Study of Non-Newtonian fluid flow in porous media at core scale using analytical approach

Characterizing in situ polymer rheology in porous media is critical before further implementation of polymer injection in oilfield. Polymer as non-Newtonian fluid has unique behavior whose viscosity changes over various shear rate. This behavior creates unsuitable conditions which can lead to ineffective sweep efficiency improvement. The challenging issue in characterizing the in situ polymer rheology is how to construct the in situ Power Law model since the in situ viscosity cannot be measured directly. In this study, we use an analytical model to construct the in situ Power Law model. The model combines material balance equation, modified Darcy equation for non-Newtonian fluid flow, and equation of state. The model is solved for early (transient) time and late (steady-state) time. Coreflooding results in Berea Sandstone with 2000 and 500 ppm HPAM polymer injection are used for model’s simulations. Rheometer measurements are also used for comparison. The overall simulation results show there is no difference in flow behavior index between rheometer and porous media. The same fluid definitely gives the same flow behavior index through different measurement methods. However, there is significant difference in flow consistency index. It is caused by the effect of porous media’s tortuosity. The quantity of the skin parameter also depicts the thinning and thickening phenomena.

Transport and Retention Modelling of Iron Oxide Nanoparticles in Core Scale Porous Media for Electromagnetic Heating Well-Stimulation Optimization

Understanding the transport and retention of iron oxide nanoparticles is critical in optimizing electromagnetic heating well stimulation. If the injected concentration or injection rate is too big, nanoparticles can build-up inside the pore throat, which can reduce the permeability of the reservoir. A numerical model has been created to describe the behavior of iron oxide nanoparticles in porous media. The model is coupling material balance equation and fluid flow in porous media equations. There are six parameters to be estimated through matching with experimental data: irreversible attachment rate, reversible attachment rate, irreversible attachment capacity, reversible attachment capacity, reversible detachment rate and permeability. All parameters were obtained directly through coreflooding result in previous study. We add Langmuir static isotherm test to limit the maximum adsorption capacity to provide a better estimation of concentration distribution. We use 1% NaCl solution as the base fluid and 45-50 mesh sand as the porous media. From the Langmuir static isotherm test, the maximum adsorption concentration is determined. Then, coreflooding is conducted using 10 ppm nanofluid and 12 cc/min injection rate. The proposed model is matched with the experimental data and its parameters are consistent with the maximum adsorption capacity provided from the test.

Application of material balance methods to CO 2 storage capacity estimation within selected depleted gas reservoirs

Depleted gas reservoirs are potential sites for CO 2 storage; therefore, it is important to evaluate their storage capacity. Historically, there have been difficulties in identifying the reservoir drive mechanism of gas reservoirs using traditional P / z plots, having direct impacts for the estimation of the original gas in place (OGIP) and dependent parameters for both theoretical and effective CO 2 storage capacity estimation. Cole plots have previously provided an alternative method of characterization, being derived from the gas material balance equation. We use production data to evaluate the reservoir drive mechanism in four depleted gas reservoirs (Hewett Lower Bunter, Hewett Upper Bunter, and North and South Morecambe) on the UK Continental Shelf. Cole plots suggest that the North Morecambe and Hewett Upper Bunter reservoirs experience moderate water drive. Accounting for cumulative water influx into these reservoirs, the OGIP decreases by up to 20% compared with estimates from P / z plots. The revised OGIP values increase recovery factors within these reservoirs; hence, geometrically based theoretical storage capacity estimates for the North Morecambe and Hewett Upper Bunter reservoirs increase by 4 and 30%, respectively. Material balance approaches yield more conservative estimates. Effective storage capacity estimates are between 64 and 86% of theoretical estimates within the depletion drive reservoirs, and are 53 – 79% within the water drive reservoirs. Supplementary material: A more detailed description of the aquifer modelling is available at https://doi.org/10.6084/m9.figshare.c.3803770.v1

A novel simplified multivariate PBE solution method for mass transfer problems

Interphase mass transfer estimation may require not only the accurate knowledge of the interfacial area, which depends on the information about the size of each dispersed element, but also on the driving force, that can be different if the elements of the disperse phase have different chemical composition. To take into account such polydispersity, bivariate (or multivariate) population balance model (PBM) are formulated according to physical phenomena occurring in the investigated mass transfer problem. This often includes aggregation, breakage, advection, mass transfer of the chemical species and chemical reactions of the transferring components. In this work we propose a novel and simplified method to solve the bivariate/multivariate population balance equation for a mass transfer problem, based on the high-order moment-conserving method of classes (HMMC) (Alopaeus et al., 2006). The proposed method is based on the idea of deriving additional material balance equations for the concentration of the droplets belonging to each size class, reducing significantly the total number of unknown variables with respect to true bivariate/multivariate method of classes. This modeling approach is compared with two other possible solution methods for a test case in which mass transfer and chemical reactions occur in a system with two immiscible liquid phases. In the first the traditional approach is used, where a single material balance is formulated for the disperse phase along with PBM, while in the second a true bivariate/multivariate solution method is used. The results of this comparison show that the proposed method is robust and accurate, capable of properly describing the multidimensional droplet size-composition distribution needed to evaluate the mass transfer rates, in a fraction of the computational time compared with more accurate methods.

A method to calculate reasonable water injection rate for M oilfield

In recent years, M oilfield has entered into high water cut stage. Two main problems are imposed in the process of development including sharp water cut rising rate and rapid oil production decline. These problems are difficult to solve, which may bring other problems. In order to slow down production decline rate and control the rising rate of water cut, it is necessary to control water injection rate. However, oil production rate can be affected if water injection rate is too low to provide enough water volume for maintaining reservoir pressure. A method to calculate reasonable injection–production ratio and predict water cut is provided in this paper. Its main mechanism is to resolve above contradictions by calculating reasonable water injection rate. Firstly, an equation to calculate reasonable injection–production ratio is deduced by material balance equation. It considers several parameters including rate of pressure recovery, water cut and other production indexes. Secondly, reasonable oil production rates and water cut of future 10 years are predicted. Oil production is predicted by the law of production decline, and water cut is predicted by regression equation of water drive characteristic curve. Lastly, reasonable water injection rates of next 10 years are calculated through predicted injection–production ratios and liquid production rates. Taking M oilfield as an example, this paper presents a method to determine reasonable water injection rate of multilayer sandstone water drive reservoir.

A STATIC MODEL OF THE REACTOR OXIDATION OF AMMONIA IN THE MANUFACTURE OF NITRIC ACID

Nitric acid is one of the dangerous types of production of highly potent acids. At one stage of the process of oxidation of ammonia to yield nitric oxide. The oxidation occurs under the action of the platinum catalyst also may be possible to use other catalysts such as chromium oxide. To get nitric oxide use of the three layer oxidation reactor, in which alternately pass through the catalyst layers, the ammonia mixed with air. Under the action of a catalyst increases the reaction rate, which further affects the temperature change in the catalyst and the pressure change in the object. To study the temperature mode of operation of the oxidation reactor, namely the static characteristics of the proposed model to build static that will display the state of the object when the temperature of the input flow and temperature in the reactor. To do this, make an equation of material balance. From the total range of tasks of production of nitric acid, in which there is a need to identify the change in the properties of transients, select the most important, in our opinion is the task of control and regulation in automated control systems of these technological processes. One of the requirements to the automatic control systems is the requirement to maintain a current value regulowane values specified value at any given point in time and compliance with the regulated value of the process parameters. Therefore, the modeling of objects for automatic control systems are important. In addition to the objectives of the study parameters of the process, there is also a more difficult problem study of the changes of non-stationary modes of the reactor oxidation of ammonia.