Journal articles on the topic 'Formation damage (Petroleum engineering) – Mathematical models'

Summary Two offshore, wedge-shaped reservoirs in south Louisiana were interpreted with pressure-buildup responses by comparing the results from simulated finite-element model studies. The importance of knowing the correct reservoir shape, and how it is used to interpret the generated boundary-pressure responses, is briefly discussed. Two different 3D computer models incorporating different wedge-shaped geometries simulated the test pressure-buildup response patterns. Variations in the two configurations are topologically expressed as a constant thickness and a nonconstant thickness, with smooth-surface, wedged-shaped reservoir models. The variable-thickness models are pinched-out updip at one end and faulted at the other end. Numerical well-test results demonstrated changes in the relationships between the pressure-derivative profile, the wellbore location, and the extent of partial penetration in the reservoir models. The wells were placed along the perpendicular bisector (top view) at distances starting from the apex at 5, 10, 20, 40, 50, 60, 80, and 90% of the reservoir length. Results demonstrate that boundary distance identification (such as distance, number, and type) based solely on the log-log derivative profile in rectangular and triangular wedge-shaped reservoirs should be strongly discouraged. Partial-penetration effects (PPE's) in wedge-shaped reservoirs are highly dependent on the wellbore location relative to the wedge, and the well-test-data analysis becomes more complex. Introduction The interpretation of the effect of reservoir shape on pressure-transient well-test data needs improvement. It is economically imperative to be able to generate an accurate estimate of reserves and producing potential. This is especially critical for independent operators who wish to participate in deepwater opportunities in the Gulf of Mexico. Proper interpretation of data extracted from cost-effective well tests is an integral part of describing, evaluating, and managing such reservoirs. Well-test information such as average reservoir pressure, transmissivity, pore volume, storativity, formation damage, deliverability, distance to the boundary, and completion efficiency are some of the technical inputs into economic and operational decisions. Several key economic decisions that operators have to make are:Should the reservoir be exploited?How many wells are needed to develop the reservoir?Is artificial lift necessary (and if so, when)? The identification of morphological demarcation components such as impermeable barriers (faults, intersecting faults, facies changes, erosional unconformities, and structural generated depositional pinchouts) and constant-pressure boundaries (aquifer or gas-cap) from well testing help to establish the reservoir boundaries, shape, and volume. One must remember that the geological entrapment structure or sedimentological body does not always define the reservoir's limits. Our present study provides insight into wedge-shaped reservoirs in the Gulf of Mexico. Seismic exploration can define geological shapes in either two or three dimensions in the subsurface. These shapes are expressions of the preserved structural history and depositional environments and are verified by observations of such structures in outcrops and present-day depositional environments. From a sedimentological viewpoint, the following sedimentary deposits can exhibit wedge-shaped geometries. Preserved barchan sand dunes, reworked transgressive sands, barrier-island sands, offshore bars, alluvial fan deposits, delta-front sheet sands, and lenticular channel sands form the more plausible pinchout, wedge-shaped geological models recognized in the Gulf of Mexico sedimentary sequence. Wedge-Shaped Reservoirs Reviewing the petroleum engineering literature, we found very few technical papers addressing wedge-shaped reservoir geometries and their effects on reservoir performance. Their detailed analytical results are discussed and applied to the interpretations of our model results. An overview of the conceptual models is presented as a quick orientation to emphasize some model issues. Horne and Temeng1 were the first to address the problem of recognizing, discriminating, and locating reservoir pinchouts with the Green's functions method proposed by Gringarten and Ramey2 in pressure-transient analysis. The analytical solution considered a dimensionless penetration depth of the well. Their results showed that pinchout boundaries appear similar to constant-pressure boundaries with respect to pressure-drawdown behavior and not as a perpendicular sealing boundary. Yaxley3 presented a set of simple equations for calculating the stabilized inflow performance of a well in infinite rectangular and wedge-shaped drainage systems. The basis for Yaxley's mathematical model is the application of transient linear flow (as opposed to radial flow conditions assumed for the reservoir) and the mathematical difference between a plane source and a line source in linear-flow drainage systems for various rectangular drainage shapes. The equations were derived from transient linear-flow relationships for a well located between parallel no-flow boundaries. This concept was applied to intersecting no-flow boundaries and an outer circular, no-flow, constant-pressure boundary. His approach involved a constant ßr that is interpreted as an extra pressure drop relative to a well of radius ro (radial distance to the well location), which is a result of the distortion of the radial streamline pattern. Chen and Raghavan4 developed a solution to compute pressure distributions in wedge-shaped drainage systems using Laplace transforms. Their mathematical approach overcame existing limitations in some of the previous solutions, which were mentioned earlier. By applying the inversion theorem to the Laplace transformation, they verified that the slope of the pressure profile is inversely proportional to the wedge angle of the drainage system. An examination of their results is important to the interpretation of our own simulated pressure-response issues. Generally, their model solutions showed three radial-flow periods in the absence of wellbore-storage effects. The radial-flow periods showed that:During an initial radial-flow period, neither of the impermeable boundaries registered either singly or jointly.In the second phase, one or two boundaries became evident on the pressure signature.A third radial-flow period exhibited a semi logarithmic slope proportional to p/?o, where ?o=the angle of the wedge.

Lithology identification is an indispensable part in geological research and petroleum engineering study. In recent years, several mathematical approaches have been used to improve the accuracy of lithology classification. Based on our earlier work that assessed machine learning models on formation lithology classification, we optimize the boosting approaches to improve the classification ability of our boosting models with the data collected from the Daniudi gas field and Hangjinqi gas field. Three boosting models, namely, AdaBoost, Gradient Tree Boosting, and eXtreme Gradient Boosting, are evaluated with 5-fold cross validation. Regularization is applied to the Gradient Tree Boosting and eXtreme Gradient Boosting to avoid overfitting. After adapting the hyperparameter tuning approach on each boosting model to optimize the parameter set, we use stacking to combine the three optimized models to improve the classification accuracy. Results suggest that the optimized stacked boosting model has better performance concerning the evaluation matrix such as precision, recall, and f1 score compared with the single optimized boosting model. Confusion matrix also shows that the stacked model has better performance in distinguishing sandstone classes.

The process of paraffin formation has been considered, including the peculiarities of the paraffin structure as a result of phase transitions with a decreasing temperature. Mathematical models for thermodynamic and kinetic calculations of the "solid-liquid" system phase equilibrium have been developed. To shift the "fuel oil-paraffin" balance towards the liquid, it is necessary to reduce the activity ratio of solid and liquid phases by introducing into the system a substance with a lower solubility parameter. To increase the stability, as well as structural and mechanical characteristics of fuel oil, the additive of plant origin was synthesized. The phase transitions in fuel oil depending on the temperature when adding different amounts of additives have been studied.

Summary Drill-in fluid loss is the most important cause of formation damage during the drill-in process in fractured tight reservoirs. The addition of lost-circulation material (LCM) into drill-in fluid is the most popular technique for loss control. However, traditional LCM selection is mainly performed by use of the trial-and-error method because of the lack of mathematical models. The present work aims at filling this gap by developing a new mathematical model to characterize the performance of drill-in fluid-loss control by use of LCM during the drill-in process of fractured tight reservoirs. Plugging-zone strength and fracture-propagation pressure are the two main factors affecting drill-in fluid-loss control. The developed mathematical model consists of two submodels: the plugging-zone-strength model and the fracture-propagation-pressure model. Explicit formulae are obtained for LCM selection dependent on the proposed model to control drill-in fluid loss and prevent formation damage. Effects of LCM mechanical and geometrical properties on loss-control performance are analyzed for optimal fracture plugging and propagation control. Laboratory tests on loss-control effect by use of different types and concentrations of LCMs are performed. Different combinations of acid-soluble rigid particles, fibers, and elastic particles are tested to generate a synergy effect for drill-in fluid-loss control. The derived model is validated by laboratory data and successfully applied to the field case study in Sichuan Basin, China.

AbstractHydraulic fracturing is a key measure to increase production and transform oil and gas reservoirs, which plays an important role in oil and gas field development. Common hydraulic fracturing is of inevitable bottlenecks such as difficulty in sand adding, sand plugging, equipment wearing and fracturing fluid damage. To solve these problems, a new type of fracturing technology, i.e., the self-propping fracturing technology is currently under development. Technically, the principle is to inject a self-propping fracturing liquid system constituting a self-propping fracturing liquid and a channel fracturing liquid into the formation. Self-propping fracturing liquid changes from liquid to solid through phase transition under the formation temperature, replacing proppants such as ceramic particles and quartz sand to achieve the purpose of propping hydraulic fractures. The flow pattern, effective distance and filling ratio of the self-propping fracturing liquid system in the hydraulic fracture are greatly affected by the parameters such as the fluid leak-off rate, surface tension and injection velocity. In this paper, a set of mathematical models for the flow distribution of self-propping fracturing liquid system considering fluid leak-off was established to simulate the flow pattern, effective distance, as well as filling ratio under different leak-off rates, surface tensions and injection velocities. The mathematical model was verified by physical experiments, proving that the mathematical model established herein could simulate the flow of self-propping fracturing liquid systems in hydraulic fractures. In the meantime, these results have positive impacts on the research of interface distribution of liquid–liquid two-phase flow.

The inter-salt argillaceous dolomite reservoirs in the central region of China contain large abundance of oil resources with ultra-low permeability and porosity. However, the oil wells in this area show a very quick reduction with the decline of formation pressure. This article aims to investigate the main possible reasons that affect oil well productivity in the target oilfield. This study begins with analysis of capillary microscopic model, core stress sensitivity experiments, and non-Darcy percolation experiments. The impact of effective stress on permeability and porosity of the reservoir was revealed in this article. The novel productivity model and productivity evaluation model which couples stress sensitivity and threshold pressure gradient were proposed. The analysis of capillary microscopic model shows stress sensitivity of permeability to be much greater than that of porosity during the process of depressurization. The core stress sensitivity experiments results indicate that permeability and effective stress show index relationship while porosity and effective stress show binomial relationship. Damage rate and recovery rate of permeability and porosity were put forward to describe the degree of influence of stress sensitivity on permeability and porosity. The models were used to investigate the factors that affect single well productivity for the target oilfield. Application of the proposed model to this tight oilfield indicates that, the degree of influence of stress sensitivity is much greater than that of threshold pressure gradient. In addition, the greater the stress sensitivity coefficient and threshold pressure gradient are, the greater the productivity reduction will be.

Summary Sulfate scaling in offshore waterflood projects, in which sulfate from the injected seawater (SW) reacts with metals from the formation water (FW), forming salt deposit that reduces permeability and well productivity, is a well known phenomenon. Its reliable prediction is based on mathematical models with well-known parameters. Previous research presents methods for laboratory determination of model coefficients using breakthrough concentration during coreflooding. The concentration measurements are complex and cumbersome, while the pressure measurements are simple and require standard laboratory equipment. In the present work, a new laboratory method is developed for determination of the model coefficients from pressure measurements. Several laboratory corefloods have been performed. The tests show that the proposed method is more precise for artificial cores than for the natural reservoir cores. Further development of the method is required to determine parameters of formation damage caused by sulfate scaling for reservoir core samples.

There are numerous engineering applications where Glass Fiber Reinforced Polymer (GFRP) composite tubes are utilized, such as desalination plants, power transmission systems, and paper mill, as well as marine, industries. Some type of machining is required for those various applications either for joining or fitting procedures. Machining of GFRP has certain difficulties that may damage the tube itself because of fiber delamination and pull out, as well as matrix deboning. Additionally, short machining tool life may be encountered while the formation of powder like chips maybe relatively hazardous. The present paper investigates the effect of process parameters for surface roughness of glass fiber-reinforced polymer composite pipes manufactured using the filament winding process. Experiments were conducted based on the high-speed turning Computer Numerical Control (CNC) machine using Poly-Crystalline Diamond (PCD) tool. The process parameters considered were cutting speed, feed, and depth of cut. Mathematical models for the surface roughness were developed based on the experimental results, and Analysis of Variance (ANOVA) has been performed with a confidence level of 95% for validation of the models.

Ultrasonic techniques are widely used for the detection of defects in solid structures. They are mainly based on estimating the impulse response of the system and most often refer to linear models. High-stress conditions of the structures may reveal non-linear aspects of their behavior caused by even small defects due to ageing or previous severe loading: consequently, models suitable to identify the existence of a non-linear input-output characteristic of the system allow to improve the sensitivity of the detection procedure, making it possible to observe the onset of fatigue-induced cracks and/or defects by highlighting the early stages of their formation. This paper starts from an analysis of the characteristics of a damage index that has proved effective for the early detection of defects based on their non-linear behavior: it is based on the Hammerstein model of the non-linear physical system. The availability of this mathematical model makes it possible to derive from it a number of different global parameters, all of which are suitable for highlighting the onset of defects in the structure under examination, but whose characteristics can be very different from each other. In this work, an original damage index based on the same Hammerstein model is proposed. We report the results of several experiments showing that our proposed damage index has a much higher sensitivity even for small defects. Moreover, extensive tests conducted in the presence of different levels of additive noise show that the new proposed estimator adds to this sensitivity feature a better estimation stability in the presence of additive noise.

Summary Designing matrix-acid stimulation treatments in vuggy and naturally fractured carbonate reservoirs is a challenging problem in the petroleum industry. It is often difficult to physically model this process, and current mathematical models do not consider vugs or fractures. There is a significant gap in the literature for models that design and evaluate matrix-acid stimulation in vuggy and naturally fractured carbonate reservoirs. The objective of this work is to develop a new model to simulate matrix acidizing under field conditions in vuggy and naturally fractured carbonates. To obtain accurate and reliable simulation parameters, acidizing coreflood experiments were modeled using a reactive-flow simulator. A 3D radial field-scale model was used to study the flow of acid in the presence of vugs (pore spaces that are significantly larger than grains) and natural fractures (breaks in the reservoir that were formed naturally by tectonic events). The vugs’ size and distribution effects on acid propagation were studied under field conditions. The fracture length, conductivity, and orientation, and the number of fractures in the formation, were studied by the radial model. The results of the numerical simulation were used to construct Gaussian-process (GP)-based surrogate models for predicting acid propagation in vuggy and naturally fractured carbonates. Finally, the acid propagation in vuggy/naturally fractured carbonates was evaluated, as well.The simulation results of vuggy carbonates show that the presence of vugs in carbonates results in faster and deeper acid propagation in the formation when compared with homogeneous reservoirs at injection velocities lower than 8×10–4 m/s. Results also revealed that the size and density of the vugs have a significant impact on acid consumption and the overall performance of the acid treatment. The output of the fracture model illustrates that under field conditions, fracture orientations do not affect the acid-propagation velocity. The acid does not touch all of the fractures around the well. The GP model predictions have an accuracy of approximately 90% for both vuggy and naturally fractured cases. The vuggy/naturally fractured model simulations reveal that fractures are the main reason behind the fast acid propagation in these highly heterogeneous reservoirs.

Summary Formation damage mechanisms in general lower the quality of the near wellbore, often manifested in the form of permeability reduction, and thus reducing the productivity of production wells and injectivity of injection wells. Asphaltene deposition, as one of the important causes, can trigger serious formation damage issues and significantly restrict the production capacity of oil wells. Several mechanisms acting simultaneously contribute to the complexity associated with prediction of permeability impairment owing to asphaltene deposition; thus, integration of modeling efforts for asphaltene aggregation and deposition mechanisms seems inevitable for improved predictability. In this work, an integrated simulation approach is proposed to predict permeability impairment in porous medium. The proposed approach is novel because it integrates various mathematical models to study permeability impairment considering porosity reduction, particle aggregation, and pore connectivity loss caused by asphaltene deposition. To improve the accuracy of simulation results, porous media is considered as a bundle (different size) of capillary tubes with dynamic interconnectivity. The total volume change of interconnected tubes will directly represent permeability reduction realized in porous media. The prediction of asphaltene deposition in porous media is improved in this paper via integration of the particle aggregation model into calculation. The simulation results were verified by comparing with existing experimental data sets. After that, a sensitivity analysis was performed to study parameters that affect permeability impairment. The simulation results show that our permeability impairment model—considering asphaltene deposition, aggregation, and pore connectivity loss—can accurately reproduce the experimental results with fewer fitting or empirical parameters needed. The sensitivity analysis shows that longer aggregation time, higher flow velocity, and bigger precipitation concentration will lead to a faster permeability reduction. The findings of this study can help provide better understanding of the permeability impairment caused by asphaltene deposition and pore blockage, which provides useful insights for prediction of production performance of oil wells.

Summary Wellbore storage effects have been identified to significantly smear the accuracy of evaluating reservoir productivity through the fluid outflow rate from the annulus during underbalanced drilling. Such effects have continuously introduced considerable errors in characterizing the reservoir during underbalanced drilling. Conceptually, because of the ready volume-changing ability of the gas, wellbore storage becomes a determining factor during underbalanced drilling of a gas reservoir. Wellbore storage could either cause decrease (unloading effects) or increase (loading effects) in the annular gas density, depending on the choke opening procedures. Correspondingly, annular fluid outflow rate is considerably affected. Because it is practically difficult to deduct the fluid-flow rate attributable to the wellbore storage from the total fluid outflow rate, reducing the influence of wellbore effects on the evaluation of gas-reservoir productivity is presented in this study. Volumetric production analysis at the wellbore-sand face is introduced through a mathematical modeling of inflow of gas bubbles into the wellbore. This mathematical modeling utilizes forces such as the viscous force, drilling fluid ejecting forces from the bit nozzles, buoyancy, interfacial tension, and gas-reservoir forces for its analyses. Some analytical results that are overshadowed by wellbore storage are presented and supported by extensive experimental studies. Introduction One of the derivable benefits from underbalanced drilling is the ability to evaluate the productivity of a reservoir during drilling operations (Beiseman amd Emeh 2002). Other benefits include little to no invasive formation damage; higher penetration rate, especially in hard rocks; and lower cost of drilling operations if underbalanced drilling could consistently be maintained (Bennion et al. 2002). However, from the real-time bottomhole pressure measurements taken while drilling, it is obvious that continuous maintenance of underbalanced conditions at the bottomhole is difficult. Pressure surges that occur during some subsidiary operations such as pipe connections and surveys tend to jeopardize the avoidance of invasive formation damage (Yurkiw et al. 2002). From the recent literature, reservoir evaluation has been approached through the estimation of the reservoir fluids flow rates into the wellbore. Assumption of the reservoir fluid inflow rate being the difference in the drilling fluid surface injection rate and the fluid outflow rate from the annulus has consistently been used (Kardolus and van Kruijsdijk 1997; Larsen and Nilsen 1999; Hunt and Rester 2000; Kneissl 200l; Lorentzen et al. 2001; Vefring et al. 2002; Biswas et al. 2003). So far, efforts in modeling reservoir fluid inflow have been concentrated on the oil inflow (Kardolus and van Kruijsdijk 1997; Larson and Nilsen 1999; Hunt and Rester 2000; Kneissl 200l; Lorentzen et al. 2001; Vefring et al. 2002; Biswas et al. 2003). These present approaches to production evaluation and characterization of gas formation recognize the important effects of wellbore phenomena, but have not been able to provide adequate means of reducing the influences. These wellbore phenomena include the gas-bubble coalescence and breakage, and bubble expansion and compression that are not possible to practically quantify during bubble annular upward flow. Because the present approaches involve the comparison of the surface fluid injection rate with the annular outflow rate, the influence of these phenomena on the gas formation evaluation is inevitable. Unfortunately, all of these wellbore phenomena cause additional annular flow rates that cannot be individually and practically measured, and thus the reservoir fluid inflow rate at the bottomhole cannot be practically modified for their influences. Not recognizing the impact of such additional annular flow rates could cause misjudgment of the inflow capabilities of the gas reservoir. In order to properly alleviate these effects on gas-inflow analyses, a volumetric production analysis at the wellbore-sand face contact is presented in this study. The conduction of gas-inflow analyses have been similarly performed as the liquid inflow in the petroleum engineering sectors. Practically speaking, gas inflow into a denser fluid system is bubbly in character, while liquid inflow is streaky. It is, therefore, proper to mathematically couple the forces of the viscosity, surface tension, inertia, and buoyancy that are responsible for gas-bubble formation or development to the drilling-fluid-ejecting forces from the bit nozzles and the reservoir forces in modeling gas-inflow scenarios. Therefore, with the existence of underbalanced pressure conditions at the bottomhole, the modeling procedures presented in this study could be used for predicting the total volume of gas inflow with significantly reduced wellbore effects while drilling. This is possible as long as an underbalanced condition is maintained at the bottomhole. This is a computer-simulation approach that utilizes real-time surface measurable underbalanced drilling data to predict quantitative gas volumes at the wellbore-sand face during drilling. As an additional advantage, the analyses do not involve knowing the gas inflow rate at the sand face, which could be difficult to accurately measure during underbalanced drilling operations. Standard engineering concepts are used to estimate downhole conditions for the analyses. Among the benefits from this study are reduced influences of the wellbore effects on the evaluation of gas-reservoir volumetric productivity during underbalanced drilling, the revealing of possible greater near-wellbore damage in some gas reservoirs, and possible in-situ permeability impairment through pore space compression.

When analyzing the fire safety of building structures, in addition to considering their fire resistance, the limits of flame expansion and other fire-safety engineering features, there should be considered also the probability of their progressive collapse in case of a damage caused to some their elements. In case of progressive collapse of the building structures, socio-economic losses become the worst possible. The article proposes a method of calculation for the estimation of the possibility of progressive destruction. The method is based on the assumption that one or several compressed elements are damaged and must be removed from the system, which ensures the rigidity and geometric immutability. The basic point of the method is the hypothesis of formation of the line of plastic hinge joints in the ceiling plate. The estimation of the possibility of progressive destruction is made according to the energy criterion on the basis of a comparison of the work of internal and external forces on the possible movements of the system, which, under these conditions, is geometrically variable. The proposed method is productive and economical comparing to the existing methods which involve complex mathematical models and software complexes.

Introduction. The work is devoted to the results of many years of research to ensure the fire and explosion safety of tanks for liquefied petroleum gases, conducted by the Moscow state University of Railways (MIIT), together with other organizations.Methods. On the basis of statistical data, the main scenarios of emergency situations were determined.Experimental and theoretical studies of the behavior of tanks under emergency conditions associated with dynamic and thermal effects were carried out. Numerous experiments were carried out both on full-scale samples and on models using the theory of similarity. The results of the ex¬periments are used both for verification of theoretical models and for specification of parameters of the calculation schemes.The mathematical models developed in the framework of theoretical research were implemented in the form of a package of computer programs and used later to select the parameters of the means of protection.Results. In terms of protection against thermal effects, the following were proposed: safety valves, fire-retardant coatings, upgraded versions of control, drain and safety valves using design solutions adopted in nuclear engineering. In particular, the use of fire-resistant coatings SGKprovides an increase of 2.5-3.5 times the time of the accident-free stay of the tank in the fire.A new layout of the drain-filling pipes is recommended, which significantly reduces the proba¬bility of breakage of the elements of the drain-filling fittings. The design of safety arcs and nodes for connection of arc elements with the shell is proposed.Conclusion. On the basis of the whole complex of the conducted researches the family of tanks for the transportation of liquefied hydrocarbon gases was developed, the production of which was carried out at the enterprises of Russia, Ukraine, Japan, Poland.However, there is a problem of contradictions in the regulatory documentation on the issues of fire and explosion safety of tanks, which requires the formation of a unified technical policy in this area.

Summary The importance of pressure/volume/temperature (PVT) properties, such as the bubblepoint pressure, solution gas-oil ratio, and oil formation volume factor, makes their accurate determination necessary for reservoir performance calculations. An enormous amount of PVT data has been collected and correlated over many years for different types of hydrocarbon systems. Almost all of these correlations were developed with linear or nonlinear multiple regression or graphical techniques. Artificial neural networks, once successfully trained, offer an alternative way to obtain reliable results for the determination of crude oil PVT properties. In this study, we present neural-network-based models for the prediction of PVT properties of crude oils from the Middle East. The data on which the network was trained represent the largest data set ever collected to be used in developing PVT models for Middle East crude oils. The neural-network model is able to predict the bubblepoint pressure and the oil formation volume factor as a function of the solution gas-oil ratio, the gas specific gravity, the oil specific gravity, and the temperature. A detailed comparison between the results predicted by the neural-network models and those predicted by other correlations are presented for these Middle East crude-oil samples. Introduction In absence of experimentally measured pressure/volume/temperature (PVT) properties, two methods are widely used. These methods are equation of state (EOS) and PVT correlations. The equation of state is based on knowing the detailed compositions of the reservoir fluids. The determination of such quantities is expensive and time consuming. The equation of state involves numerous numerical computations. On the other hand, PVT correlations are based on easily measured field data: reservoir pressure, reservoir temperature, oil, and gas specific gravity. In the petroleum process industries, reliable experimental data are always to be preferred over data obtained from correlations. However, very often reliable experimental data are not available, and the advantage of a correlation is that it may be used to predict properties for which very little experimental information is available. The importance of accurate PVT data for material-balance calculations is well understood. It is crucial that all calculations in reservoir performance, in production operations and design, and in formation evaluation be as good as the PVT properties used in these calculations. The economics of the process also depends on the accuracy of such properties. The development of correlations for PVT calculations has been the subject of extensive research, resulting in a large volume of publications.1–10 Several graphical and mathematical correlations for determining the bubblepoint pressure (Pb) and the oil formation volume factor (Bob) have been proposed during the last five decades. These correlations are essentially based on the assumption that P b and Bob are strong functions of the solution gas-oil ratio (Rs) the reservoir temperature (T), the gas specific gravity (?g) and the oil specific gravity (?o) or P b = f 1 ( R s , T , γ g , γ o ) , ( 1 ) B o b = f 2 ( R s , T , γ g , γ o ) . ( 2 ) In 1947, Standing1 presented graphical correlations for the determination of bubblepoint pressure (Pb) and the oil formation volume factor (Bob) In developing these correlations, Standing used 105 experimentally measured data points from 22 different crude-oil and gas mixtures from California oil fields. Average relative errors of 4.8% and of 1.17% were reported for Pb and Bob respectively. Later, in 1958, Lasater9 developed an empirical equation based on Henry's law for estimating the bubblepoint pressure. He correlated the mole fraction of gas in solution to a bubblepoint pressure factor. A total of 137 crude-oil and gas mixtures from North and South America was used for developing this correlation. An average error of 3.8% was reported. Lasater did not present a correlation for Bob In 1980, two sets of correlations were reported, one by Vasquez and Beggs10 and the other by Glasø.7 Vasquez and Beggs used 600 data points from various locations all over the world to develop correlations for Pb and Bob. Two different types of correlations were presented, one for crudes with °API>30 and the other for crudes with °API 30. An average error of 4.7% was reported for their correlation of Bob Glasø used a total of 45 oil samples from the North Sea to develop his correlations for calculating Pb and Bob. He reported an average error of 1.28% for the bubblepoint pressure and ?0.43% for the formation volume factor. Recently, Al-Marhoun4 used 160 experimentally determined data points from the PVT analysis of 69 Middle Eastern hydrocarbon mixtures to develop his correlations. Average errors of 0.03% and ?0.01% were reported for Pb and Bob respectively. Dokla and Osman6 used a total of 50 data points from reservoirs in the United Arab Emirates to develop correlations for Pb and Bob. They reported an average error of 0.45% for the bubblepoint pressure and 0.023% for the formation volume factor. The conventional approach to develop PVT correlations is based on multiple-regression techniques. An alternative approach will be to use an artificial neural network (ANN). PVT models based on a successfully trained ANN can be excellent, reliable tools for the prediction of crude-oil PVT properties. The massive interconnections in the ANN produces a large number of degrees of freedom, or fitting parameters, and thus may allow it to capture the system's nonlinearity better than conventional regression techniques. Recently, artificial neural networks have found use in a number of areas in petroleum engineering.11–20 The objective of this study is to use ANNs to develop accurate PVT correlations for Middle East crude oil to estimate Pb and Bob as functions of Rs, T, ?g, ?o. With additional experimental data, the neural-network model can be further refined to incorporate these new data. In addition, in this article we evaluate the accuracy of the ANN models developed in this study compared to other PVT correlations.

Summary This work presents a new computational model for the non-isothermal gravitational compositional equilibrium. The works of Bedrikovetsky [Mathemathical Theory of Oil and Gas Recovery, Kluwer Academic Publishers, London, (1993)] (gravity and temperature) and of Whitson and Belery ("Compositional Gradients in Petroleum Reservoirs," paper SPE 28000, presented at the 1994 University of Tulsa Centennal Petroleum Engineering Symposium, Tulsa, 29-31 August) (algorithm) are the basis of the mathematical formulation. Published data and previous simplified models validate the computational procedure. A large deep-water field in Campos Basin, Brazil, exemplifies the practical application of the model. The field has an unusual temperature gradient opposite to the Earth's thermal gradient. The results indicate the increase of oil segregation with temperature decrease. The application to field data suggests the reservoir could be partially connected. Fluid composition and property variation are extrapolated to different depths with its respective temperatures. The work is an example of the application of thermodynamic data to the evaluation of reservoir connectivity and fluid properties distribution. Problem Compositional variations along the hydrocarbon column are observed in many reservoirs around the world.1–4 They may affect reservoir/fluid characteristics considerably leading to different field development strategies.5 These variations are caused by many factors, such as gravity, temperature gradient, rock heterogeneity, hydrocarbon genesis and accumulation processes.6 In cases where thermodynamic associated factors (gravity and temperature) are dominant (mixing process in the secondary migration), existing gravitational compositional equilibrium (GCE) models7,8 provide an explanation of most observed variations. However, in some cases8,9 the thermal effect could have the same order of magnitude as the gravity effect. The formulation for calculating compositional variation under the force of gravity for an isothermal system was first given by Gibbs10 $$\mu {ci}(p, Z, T)=\mu {i}(p {{\rm ref}}, Z {{\rm ref}}, T {{\rm ref}}) - m {i}g(h - h {{\rm ref}}),\eqno ({\rm 1})$$ $$\mu {ci}=\delta [nRT\,{\rm ln}(f {i})]/\delta x,\eqno ({\rm 2})$$ $$f {i}=f({\rm EOS}),\eqno ({\rm 3})$$where p =pressure, T=temperature, Z=fluid composition, m=mass, ? c=chemical potential, h=depth, ref=reference, EOS=equation of state, i=component indices, R=real gas constant, n=number of moles, f=fugacity, ln=natural logarithm, x=component concentration, and g=gravitational acceleration. In 1930 Muskat11 provided an exact solution to Eq. (1), assuming a simplified equation of state and ideal mixing. Because of the oversimplified assumptions, the results suggest that gravity has a negligible effect on the compositional variation in reservoir systems. In 1938, Sage and Lacey12 used a more realistic equation of state (EOS), Eq. (3), to evaluate Eq. (2). At that time, the results showed significant composition variations with depth and greater ones for systems close to critical conditions. Schulte13 solved Eq. (1) using a cubic equation of state (3) in 1980. The results showed significant compositional variations. They also suggested a significant effect of the interaction coefficients and the aromatic content of the oil as well as a negligible effect of the EOS type (Peng-Robinson and Soave-Redlich-Kwong) on the final results. A simplified formulation that included gravity and temperature separately was presented by Holt et al.9 in 1983. Example calculations, limited to binary systems, suggest that thermal effects can be of the same magnitude as gravity effects. In 1988, Hirschberg5 discussed the influence of asphaltenes on compositional grading using a simplified two component model (asphaltenes and non-asphaltenes). He concluded, that for oils with oil gravity <35°API, the compositional variations are mainly caused by asphalt segregation and the most important consequences are the large variations in oil viscosity and the possible formation of tar mats. Montel and Gouel7 presented an algorithm in 1985 for solving the GCE problem using an incremental hydrostatic term instead of solving for pressure directly. Field case applications of GCE models were presented by Riemens et al.2 in 1985, and by Creek et al.1 in 1988. They reported some difficulties in matching observed and calculated data but, in the end, it was shown that most compositional variations could be explained by the effect of gravity. Wheaton14 and Lee6 presented GCE models that included capillary forces in 1988 and 1989, respectively. Lee concluded that the effect of capillarity can become appreciable in the neighborhood of 1 ?m pore radius. In 1990, an attempt to combine the effects of gravity and temperature for a system of zero net mass flux was presented by Belery and Silva.15 The multicomponent model was an extension of earlier work by Dougherty and Drickamer16 that was originally developed in 1955 for binary liquid systems. The comparison of calculated and observed data from Ekofisk field in the North Sea is, however, not quantitatively accurate (with or without thermal effect). An extensive discussion and the formal mathematical treatment of compositional grading using irreversible thermodynamics, including gravitational and thermal fields, was presented by Bedrikovetsky17 in 1993. Due to the lack of necessary information on the values of thermal diffusion coefficients, which in general are obtained experimentally only for certain mixtures in narrow ranges of pressure and temperature, simplified models were proposed. In 1994, Hamoodi and Abed3 presented a field case of a giant Middle East reservoir with areal and vertical variations in its composition.

Abstract This paper presents short-time interpretation methods for radial-spherical (or radial-hemispherical) flow in homogeneous and isotropic reservoirs inclusive of wellbore storage, wellbore phase redistribution, and damage skin effects. New dimensionless groups are introduced to facilitate the classic transformation from radial flow in the sphere to linear flow in the rod. Analytical expressions, type curves (in log-log and semilog format), and tabulated solutions are presented, both in terms of pressure and rate, for all flow problems considered. A new empirical equation to estimate the duration of wellbore and near-wellbore effects under spherical flow is also proposed. Introduction The majority of the reported research on unsteady-state flow theory applicable to well testing usually assumes a cylindrical (typically a radial-cylindrical) flow profile because this condition is valid for many test situations. Certain well tests, however, are better modeled by assuming a spherical flow symmetry (e.g., wireline formation testing, vertical interference testing, and perhaps even some tests conducted in wellbores that do not fully penetrate the productive horizon or are selectively penetrate the productive horizon or are selectively completed). Plugged perforations or blockage of a large part of an openhole interval may also promote spherical flow. Numerous solutions are available in the literature for almost every conceivable cylindrical flow problem; unfortunately, the companion spherical problem has not received as much attention, and comparatively few papers have been published on this topic. papers have been published on this topic. The most common inner boundary condition in well test analysis is that of a constant production rate. But with the advent of downhole tools capable of the simultaneous measurement of pressures and flow rates, this idealized inner boundary condition has been refined and more sophisticated models have been proposed. Therefore, similar methods must be developed for spherical flow analysis, especially for short-time interpretations. This general problem has recently been addressed elsewhere. Theory The fundamental linear partial differential equation (PDE) describing fluid flow in an infinite medium characterized by a radial-spherical symmetry is (1) The assumptions incorporated into this diffusion equation are similar to those imposed on the radial-cylindrical diffusivity equation and are discussed at length in Ref. 9. In solving Eq. 1, the classic approach is illustrated by Carslaw and Jaeger (later used by Chatas, and Brigham et al.). According to Carslaw and Jaeger, mapping b=pr will always reduce the problem of radial flow in the sphere (Eq. 1) to an equivalent problem of linear flow in the rod for which general solutions are usually known. (For example, see Ref. 17 for particular solutions in petroleum applications.) Note that in this study, we assumed that the medium is spherically isotropic; hence k in Eq. 1 is the constant spherical permeability. This assumption, however, does not preclude analysis in systems possessing simple anisotropy (i.e., uniform but unequal horizontal and vertical permeability components). In this case, k as used in this paper should be replaced by k, an equivalent or average (but constant) spherical permeability. Chatas presented a suitable expression (his Eq. 10) obtained presented a suitable expression (his Eq. 10) obtained from a volume integral. It is desirable to transform Eq. 1 to a nondimensional form, thereby rendering its applicability universal. The following new, dimensionless groups accomplish this and have the added feature that solutions are obtained directly in terms of the dimensionless pressure drop, PD, not the usual b (or bD) groups. ......................(2) .......................(3) .........................(4) The quantity rsw is an equivalent or pseudospherical wellbore radius used to represent the actual cylindrical sink (or source) of radius rw. SPEJ p. 804

<p>A Análise de Testes de Poços é um ramo da Engenharia de Reservatórios no qual<br />empregamos dados de pressão de poço a partir de testes de produção/injeção de fluido em conjunto com modelos físico-matemáticos para caracterizar o sistema poço-reservatório, usando problemas inversos. Nessas situações, aplicamos amplamente soluções analíticas e semianalíticas do modelo físico-matemático que descreve o fluxo. Nesse contexto, o objetivo do presente estudo é 1) realizar uma revisão bibliográfica sobre algumas das soluções analíticas clássicas para determinação da pressão no poço produtor e 2) implementar os códigos numéricos para a criação de uma biblioteca computacional, proporcionando as soluções analíticas voltadas para a determinação da pressão em poços produtores de petróleo. Os sistemas poço-reservatório estudados possuem um poço vertical e levam em consideração os efeitos de condições de contorno, a estocagem na coluna de produção do poço, dano à formação, períodos de fluxo e estática, bem como a presença de fraturas naturais. Obtivemos as soluções analíticas usando a transformada de Laplace e uma inversão numérica, utilizando o algoritmo Stehfest, para calcular a variação de pressão ao longo do tempo.</p><p><br /><strong>Palavras-chave</strong>: Soluções Analíticas, Transformada de Laplace Inversa, Tranformada de Laplace, Algoritmo de Stehfest, Análise de Teste de Poço.</p><p>===================================================================</p><p>Well Testing Analysis is a branch of Reservoir Engineering, in which we<br />employ well pressure data from production tests/fluid injection in conjunction with physical-mathematical models to characterize the well-reservoir system, using inverse problems. In these situations, we widely used analytical and semi-analytical solutions of the physical-mathematical model that describes the flow. In this context, the objective of this work is to 1) carry out a bibliographic review on some of the classic analytical solutions for determining the pressure in the producing well and 2) implement the numerical codes for the creation of a computational library, providing the analytical solutions aimed at determining pressure in oil-producing wells. The well-reservoir systems with a vertical well take into account the boundary effects, wellbore storage, formation damage, drawdown and buildup test analysis, and the presence of natural fractures. We obtain the analytical solutions using the Laplace transform and a numerical inversion, using the Stehfest algorithm, to calculate the pressure variation in the time domain.</p><p><br /><strong>Key words</strong>: Analytical Solutions, Inverve Laplace Transform, Laplace Transform, Stehfest Algorithm, Well Testing Analysis.</p>

Summary A new log-calibration technique presented in this paper determines how much core-sample variance should be reproduced by a calibrated log. The linear calibration parameters are then calculated from this variance and the log and core-sample means. The method relies on the idea that the correlation structure of core data and a calibrated log should be the same for distances longer than the log resolution, after the variance reduction due to log averaging is accounted for. The procedure is illustrated by using synthetic data, followed by example applications that use real data. Introduction The quantification of subsurface rock properties is essential for modeling petroleum-reservoir flow processes. Because most reservoirs have a limited amount of core, well logs are a basic source of petrophysical data. The accuracy of well logs is usually improved by calibration to cores in the same reservoir, but traditional calibration methods ignore inherent differences in measurement volume between the two data types. The calibrations are typically linear correlations with two free parameters, giving independent control of the predicted mean and variance of log measurements. Clearly the calibrated logs should reproduce the core-sample mean if the core sampling is unbiased. However, calibrated logs should usually produce smaller variances than core data because the logging tools measure averages over larger volumes, and most reservoirs have significant variance below the log resolution. The traditional calibration methods all reproduce the core-sample mean, but they represent different choices for predicted variance. Choosing an appropriate calibration amounts to determining an appropriate variance for the prediction. A natural approach to this problem is to calibrate the log after averaging the core data to the log measurement scale, which has been done successfully by means of closely spaced minipermeametry1and "strip samples" analysis.2 However, core samples are generally not spaced closely enough for the averaging to eliminate much of the smoothing-effect scatter; there are not enough samples within the log-measurement volume to compute an accurate average. Williams and Sharma 3 outlined a procedure that uses high-frequency information from a formation microscatter (FMS) to estimate the required sample density for a given accuracy in averaging. Greder et al.4 described a method involving the construction of a "core log," an estimate of a core-sample scale property at close spacing, constructed by kriging the primary core data with conditioning to some additional secondary data. The closely spaced estimate can then be smoothed, giving an estimated core property at the log scale for use in calibration. To be helpful the secondary data must be closely spaced (for example, minipermeametry or acoustic measurements on the whole core). In this paper a new technique is presented for calibrating logs to core data when only the usual core data are available. No additional finely spaced measurements are required. A Mathematical Model for Log Calibration Well log models are commonly calibrated by fitting a line to a crossplot of the log measurement and the corresponding core data. An example using synthetic data is shown in Fig. 1. An appropriate mathematical model for this problem is5 (1) x = x t + d x , (2) y = y t + d y , and (3) y t = m x t + b , where m and b are constants determined by the calibration, x and y are the (possibly transformed) log and core data, and dx and d y are deviations of those data from the "true" but unknown rock properties, xt and yt The calibration is used to estimate yt in wells that have no core as follows: (4)yt≈ye=mx+b. In this paper, log measurements will be associated with the x axis and core measurements with the y axis, emphasizing that the log data x is the "independent" variable being used to predict the "dependent" core property yt. The opposite convention can be used as well, leading to an equivalent development wherein the meanings of x and y are interchanged. Although the measurements x and y are not perfectly correlated, perfect correlation of xt and yt can be enforced by choosing dx and dy to represent the uncorrelated components of x and y Linearity of the relationship between xt and yt can be enforced by using appropriate transformations of x and y. The transformations may be nonlinear (a common example is the logarithmic transformation for permeability). They may also involve more than one basic core or log measurement. Much of the art and science of well log interpretation involves the determination of appropriate combinations and transformations for the raw log and core measurements, but the details will not be discussed further in this paper. It is assumed that x and y have already been transformed as required, and all that remains is to determine the linear calibration. Different Scales of Measurement It is well known that well log and core-sample measurements occur at different scales.6–8 The core measurements typically represent effective properties within 1-in. plugs sampled every foot along a 4-in.-diameter core. There are a wide variety of well log tools, each with different properties, but the measurements generally represent averages over a much larger volume both radially and vertically (with the rock of the wellbore itself removed). Carefully calibrated logs may therefore provide a better estimate of an average property within the log-measurement volume than would a single core plug taken at the same depth. The log data are sampled from a continuous measurement, commonly at a spacing finer than that of the core data, but for many logs the vertical averaging length is larger than both the log and core-sample spacing. Although logs may offer more raw data than core and, perhaps, better estimates of local averages, they therefore have less information about short-range variability.

Summary Evaluation of reservoir parameters through well-test and decline-curve analysis is a current practice used to estimate formation parameters and to forecast production decline identifying different flow regimes, respectively. From practical experience, it has been observed that certain cases exhibit different wellbore pressure and production behavior from those presented in previous studies. The reason for this difference is not understood completely, but it can be found in the distribution of fractures within a naturally fractured reservoir (NFR). Currently, most of these reservoirs are studied by means of Euclidean models, which implicitly assume a uniform distribution of fractures and that all fractures are interconnected. However, evidence from outcrops, well logging, production-behavior studies, and the dynamic behavior observed in these systems, in general, indicate the above assumptions are not representative of these systems. Thus, the fractal theory can contribute to explain the above. The objective of this paper is to investigate the production-decline behavior in an NFR exhibiting single and double porosity with fractal networks of fractures. The diffusion equations used in this work are a fractal-continuity expression presented in previous studies in the literature and a more recent generalization of this equation, which includes a temporal fractional derivative. The second objective is to present a combined analysis methodology, which uses transient-well-test and boundary-dominated-decline production data to characterize an NFR exhibiting fractures, depending on scale. Several analytical solutions for different diffusion equations in fractal systems are presented in Laplace space for both constant-wellbore-pressure and pressure-variable-rate inner-boundary conditions. Both single- and dual-porosity systems are considered. For the case of single-porosity reservoirs, analytical solutions for different diffusion equations in fractal systems are presented. For the dual-porosity case, an approximate analytical solution, which uses a pseudosteady-state matrix-to-fractal fracture-transfer function, is introduced. This solution is compared with a finite-difference solution, and good agreement is found for both rate and cumulative production. Short- and long-time approximations are used to obtain practical procedures in time for determining some fractal parameters. Thus, this paper demonstrates the importance of analyzing both transient and boundary-dominated flow-rate data for a single-well situation to fully characterize an NFR exhibiting fractal geometry. Synthetic and field examples are presented to illustrate the methodology proposed in this work and to demonstrate that the fractal formulation consistently explains the peculiar behavior observed in some real production-decline curves. Introduction Evaluation of reservoir parameters through decline-curve analysis has become a common current practice (Fetkovich 1980; Fetkovich et al. 1987). The main objectives of the application of decline analysis are to estimate formation parameters and to forecast production decline by identifying different flow regimes. Different solutions have been proposed during both transient (Ehlig-Economides and Ramey 1981; Uraiet and Raghavan 1980) and boundary-dominated (Fetkovich 1980; Fetkovich et al. 1987; Ehlig-Economides and Ramey 1981; Arps 1945) flow periods. Both single- and double-porosity (Da Prat et al. 1981; Sageev et al. 1985) systems have been addressed. During the boundary-dominated-flow period, in homogeneous systems, there is a single production decline, but for NFRs in which the matrix participates, there are two decline periods, with an intermediate constant-flow period (Da Prat et al. 1981; Sageev et al. 1985). Carbonate reservoirs contain more than 60% of the world's remaining oil. Yet, the very nature of the rock makes these reservoirs unpredictable. Formations are heterogeneous, with irregular flow paths and circulation traps. In spite of this complexity, at present, all studies on constant-bottomhole-pressure tests found in petroleum literature assume Euclidean or standard geometry is applicable to both single-porosity reservoirs and NFRs (Fetkovich 1980; Fetkovich et al. 1987; Ehlig-Economides and Ramey 1981; Uraiet and Raghavan 1980; Arps 1945; Da Prat et al. 1981; Sageev et al. 1985), even though real reservoirs exhibit a higher level of complexity. Specifically, natural fractures are heterogeneities that are present in carbonate reservoirs on a wide range of spatial scales. It is well known that flow distribution within the reservoir is controlled mostly by the distribution of fractures (i.e., geometrical complexity). There could be regions in the reservoir with clusters of fractures and others without the presence of fractures. The presence of fractures at different scales represents a relevant element of uncertainty in the construction of a reservoir model. Thus, highly heterogeneous media constitute the basic components of an NFR, so Euclidean flow models have appeared powerless in some of these cases. Alternatively, fractal theory provides a method to describe the complex network of fractures (Sahimi and Yortsos 1970). The power-law behavior of fracture-size distributions, characteristic of fractal systems, has been found by Laubach and Gale (2006) and Ortega et al. (2006). Distributions of attributes such as length, height, or aperture can frequently be expressed as power laws. Scaling analysis is important because it enables us to infer fracture attributes such as fracture strike, number of fracture sets, and fracture intensity for larger fractures from the analysis of microfractures found in oriented sidewall cores. This approach offers a method to overcome fracture-sampling limitations, with microfractures as proxies for related macrofractures in the same rock volume (Laubach and Gale 2006; Ortega et al. 2006). The first fractal model applied to pressure-transient analysis was presented by Chang and Yortsos (1990). Their model describes an NFR that has, at different scales, poor fracture connectivity and disorderly spatial distribution in a proper fashion. Acuña et al. (1995) applied this model and found the wellbore pressure is a power-law function of time. Flamenco-Lopez and Camacho-Velazquez (2003) demonstrated that to characterize a NFR fully with a fractal geometry, it is necessary to analyze both transient- and pseudosteady-state-flow well pressure tests or to determine the fractal-model parameters from porosity well logs or another type of source. Regarding the generation of fracture networks, Acuña et al. (1995) used a mathematical method for this purpose, while Philip et al. (2005) used a fracture-mechanics-based crack-growth simulator, instead of a purely stochastic method, for the same objective. In spite of all the work done on decline-curve analysis, the problem of fully characterizing an NFR exhibiting fractal geometry by means of production data has not been addressed in the literature. Thus, the purpose of this work is to present analytical solutions during both transient- and boundary-dominated-flow periods and to show that it is possible to characterize an NFR having a fractal network of fractures with production-decline data.

Abstract Pressure–volume–temperature (PVT) properties of crude oil are considered the most important properties in petroleum engineering applications as they are virtually used in every reservoir and production engineering calculation. Determination of these properties in the laboratory is the most accurate way to obtain a representative value, at the same time, it is very expensive. However, in the absence of such facilities, other approaches such as analytical solutions and empirical correlations are used to estimate the PVT properties. This study demonstrates the combined use of two machine learning (ML) technique, viz., functional network (FN) coupled with particle swarm optimization (PSO) in predicting the black oil PVT properties such as bubble point pressure (Pb), oil formation volume factor at Pb, and oil viscosity at Pb. This study also proposes new mathematical models derived from the coupled FN-PSO model to estimate these properties. The use of proposed mathematical models does not need any ML engine for the execution. A total of 760 data points collected from the different sources were preprocessed and utilized to build and train the machine learning models. The data utilized covered a wide range of values that are quite reasonable in petroleum engineering applications. The performances of the developed models were tested against the most used empirical correlations. The results showed that the proposed PVT models outperformed previous models by demonstrating an error of up to 2%. The proposed FN-PSO models were also compared with other ML techniques such as an artificial neural network, support vector regression, and adaptive neuro-fuzzy inference system, and the results showed that proposed FN-PSO models outperformed other ML techniques.

Cyclic and low-magnitude loading promotes osteogenesis (i.e. new bone formation). Normal strain, strain energy density and fatigue damage accumulation are typically considered as osteogenic stimuli in computer models to predict site-specific new bone formation. These models however had limited success in explaining osteogenesis near the sites of minimal normal strain, for example, neutral axis of bending. Other stimuli such as fluid motion or strain gradient also stimulate bone formation. In silico studies modeled the new bone formation as a function of fluid motion, however, computation of fluid motion involves complex mathematical calculations. Strain gradients drive fluid flow and thus can also be established as the stimulus. Osteogenic potential of strain gradients is however not well established. The present study establishes strain gradients as osteogenic stimuli. Bending-induced strain gradients are computed at cortical bone cross-sections reported in animal loading in vivo studies. Correlation analysis between strain gradients and site of osteogenesis is analyzed. In silico model is also developed to test the osteogenic potential of strain gradients. The model closely predicts in vivo new bone distribution as a function of strain gradients. The outcome establishes strain gradient as computationally easy and robust stimuli to predict site-specific osteogenesis. The present study may be useful in the development of biomechanical approaches to mitigate bone loss.

Despite the increasing reliance on alternative and renewable energy sources in recent years, coal is set to continue being the most vital element of the global energy sector. The world coal supply (1,070 billion tons) shall last for 130 years with the current mining levels. In contrast to some large countries (such as the USA and Germany) reducing their coal production and consumption, Russia plans to increase the coal production levels as part of its strategy regarding the future of the coal mining industry. The annual volume of coal output is more than 440 million tons, 1/3 of which is extracted underground. The current and projected levels of underground coal mining present a set of issues pertaining to elevated dust concentration in the air and increased dust dispersion. High dust concentration in the air leads to damage to the skin, mucous membranes and respiratory organs of workers. Also, with high dust content, visibility in the longwalls decreases, the risk of injury and accidents increases. The present article deals with the formation of detrimental dust conditions that happen in the course of cleaning and preparatory mining operations in coal mines. The article reviews the international practices on dust reduction in coal mining operations and provides an overview of studies on dustiness levels and airborne dust composition in longwall faces of coal mines. It also presents mathematical models dealing with projections on dust composition, including projections on most hazardous dust particles the size of 0.1-10 and 0.1-35 μm. The article also presents a newly developed wetting method showing increased effectiveness.

Purpose: To compare radiation responses of yeast and mammalian cells to combined actions of various agents and on this basis to draw
 a conclusion about the possibility of synergy ideas application in medical radiology.
 Material and methods: The yeast cells of Saccharomyces cerevisiae were exposed to the combined action of hyperthermia (22–58 °C,
 exposure time 0–9 hrs) with ionizing radiation (25 MeV bremsstrahlung 5 and 25 Gy/min or γ-rays 60Co, 2, 10, and 80 Gy/min, acute
 irradiation) or anti-tumor drug cisplatin (0,05 or 0,25 mg/ml, exposure time 0–3 hrs). The result of synergistic interaction for yeast cells
 was assessed by the survival curves obtained by the authors after separate exposure to hyperthermia, ionizing radiation, cisplatin and after
 combined action of hyperthermia with ionizing radiation or cisplatin. To quantify the synergistic interaction of similar combined actions
 on mammalian cells, the data published by other authors have been used who did not evaluate the synergistic effect themselves.
 Results: The synergistic interaction of hyperthermia with ionizing radiation or cisplatin was established for yeast and mammalian
 cells. It is shown that the synergistic effect of the simultaneous action of these agents is observed only within a certain temperature range,
 within which there is an optimal temperature at which the greatest synergism occurs. This optimal temperature is shifted to lower values
 with a decrease in the dose rate of ionizing radiation or concentration of cisplatin. For sequential application of hyperthermia and ionizing
 radiation the effect of combined action increases with an increase in acting temperature up to a certain limit, after which it remains
 constant. These results are interpreted using the mathematical models previously proposed, in accordance with which the synergism is
 determined by the formation of additional damage due to the interaction of sub-damage that are not effective after separate application of
 agents.
 Despite the fact that all of the data presented were obtained at temperatures far beyond the ambient temperature, it is not excluded that
 there could be optimal intensities of harmful agents existing in the biosphere and capable of interacting with physiological heat of animals
 and man in a synergistic manner. Hence, the assessment of health or environmental risks from numerous natural and man-made agents at
 the level of intensities found in environmental and occupational settings should take into account synergistic interaction between harmful
 agents.
 Conclusion: The general regularities of synergistic effects of combined action of hyperthermia with ionizing radiation or with cisplatin
 for yeast and mammalian cells have been established – the existence of optimal parameters for acting agents providing the highest synergy
 and its dependence on the intensity of agents applied.