Previous Formulas Research Articles

Prediction of Surface Oil Rates for Volatile Oil and Gas Condensate Reservoirs Using Artificial Intelligence Techniques

AbstractAllocated well production rates are crucial to evaluate the well performance. Test separators and flowmeters were replaced with choke formulas due to economic and technical issues special for high gas–oil ratio (GOR) reservoirs. This study implements Adaptive network-based fuzzy logic (ANFIS), and functional networks (FN) techniques to predict the oil rate through wellhead chokes. A set of data containing 1200 wells were obtained from actual oil fields in the Middle East. The data set included GOR, upstream and downstream pressure, choke size, and actual oil and gas rates based on the well test. GOR varied from 1000 to 9265 scf/stb, while oil rates ranged between 1156 and 7982 stb/d. Around 650 wells were flowing under critical flow conditions, while the rest were subcritical. Seventy percent of the data were used to train the artificial intelligence (AI) models, while thirty percent of the data were used to test and validate these models. The developed AI models were then compared against the previous formulas. For subcritical flow conditions, rate prediction was correlated to both upstream and downstream pressures, while at critical flow conditions, changes in the downstream pressure did not affect the prediction of the production rates. For each AI method, two models were developed for subcritical flow and critical flow conditions. The average absolute percent error (AAPE) in the case of subcritical flow for ANFIS and FN were 0.88, and 1.01%, respectively. While in the case of critical flow, the AAPE values were 1.07, and 1.3% for ANFIS and FN models, respectively. All developed AI models outperform the published formulas, where the AAPE values for published formulas were higher than 34%. The results from this study will greatly assist petroleum engineers to predict the oil and gas rates based on available data from wellhead chokes in real-time with no need for additional operational costs or field intervention.

A statistical methodology to identify imbalance-induced capacity wastes for LV networks

Phase imbalance (i.e., load imbalance among the three phases) causes inefficient use of three-phase distribution assets, resulting in additional reinforcement costs (ARCs) compared to if the three phases were balanced. However, two problems remain unresolved when calculating the ARC: 1) previous ARC formulas assume that the three-phase total peak and the single-phase peak current occur simultaneously, thus causing an underestimation of the ARC; and 2) previous formulas calculate ARC as a point value, using one year's peak load. However, the point value is not credible in supporting making investment decisions on phase balancing. This is because the growth of the yearly peak load is inconsistent over the years – the growth could be positive or negative over the years for low voltage (415 V, LV) networks. To address the above problems, this paper originally develops 1) an updated ARC formula; and 2) a customised approach, named as the cluster-wise probability assessment, to deliver a distribution and confidence range of ARCs for any given LV network. This approach only requires the yearly average current and single-phase peak current, making it applicable to the majority of the LV networks that have a minimal amount of data. Case studies also identify a counterintuitive finding of how the yearly single-phase peak current and the yearly average phase current impact the ARCs.

The effect of heart rate and pulse pressure on mean arterial pressure: the combined formula for calculation of mean arterial pressure.

We demonstrate a new formula to predict mean arterial pressure (MAP) using corrections of the key factors associated with the inaccuracy of the standard formula: heart rate (HR) and pulse pressure (PP). A total of 99 patients (50 men, 49 women; mean age 52.5 ± 10.3 years), who underwent elective coronary angiography, were enrolled in our study. The arterial pressure was measured in the aortic root. MAP was measured digitally by the area-under-the-pressure-time curve method. We evaluated the accuracy of four different formulas: the standard formula, the formula of Razminia et al., the formula of Meaney et al. and the combined formula. PP coefficient deviation of the standard formula was negatively correlated with PP (R = -0,561, P < 0.001), and positively correlated with HR (R = 0,298, P = 0.003). Both R and R2 values of the combined formula were higher than previous formulas. Accuracy parameters of the combined formula [root mean square error (RMSE): 1.801 mmHg, mean square residuals (MSR): 3.244 mmHg2, Akaike information criterion (AIC): 401.4] were superior to the standard formula (RMSE: 1.902 mmHg, MSR: 3.620 mmHg2, AIC: 412.3), the formula of Razminia et al. (RMSE: 2.022 mmHg, MSR: 4.089 mmHg2, AIC: 424.3) and the formula of Meaney et al. (RMSE: 2.137 mmHg, MSR: 4.568 mmHg2, AIC: 435.3). In the multivariate linear regression analysis, the combined formula was the only method that independently predicts the measured MAP (beta = 0,990, P < 0.001). The combined formula is superior to previous formulas for accurately predicting MAP.

Disentangling a deep learned volume formula

We present a simple phenomenological formula which approximates the hyperbolic volume of a knot using only a single evaluation of its Jones polynomial at a root of unity. The average error is just 2.86% on the first 1.7 million knots, which represents a large improvement over previous formulas of this kind. To find the approximation formula, we use layer-wise relevance propagation to reverse engineer a black box neural network which achieves a similar average error for the same approximation task when trained on 10% of the total dataset. The particular roots of unity which appear in our analysis cannot be written as e2πi/(k+2) with integer k; therefore, the relevant Jones polynomial evaluations are not given by unknot-normalized expectation values of Wilson loop operators in conventional SU(2) Chern-Simons theory with level k. Instead, they correspond to an analytic continuation of such expectation values to fractional level. We briefly review the continuation procedure and comment on the presence of certain Lefschetz thimbles, to which our approximation formula is sensitive, in the analytically continued Chern-Simons integration cycle.

Array Gain of a Linear Array in an Ocean Waveguide

Array gain is investigated based on the acoustic channel characteristics manifested by the fluctuant transmission loss and decrease in the acoustic channel spatial coherence. An analytical expression is derived as the summation of the products of the acoustic channel correlation coefficients and root-mean-square pressures. The formula provides insight into the physical mechanisms of the gain degradation in the ocean waveguide. Furthermore, this formula provides a new method to study array gain in the ocean waveguide from underwater acoustic field. The obtained expression is a more general formula that is applicable to shallow water, deep sea, and continental slope, with the traditional methods as a special case. Numerical results show that the array gain calculated by previous formulas are generally overestimated, caused by ignoring the effect of transmission loss fluctuation.

An approximate point-based alternative for the estimation of variance under big BAF sampling

BackgroundA new variance estimator is derived and tested for big BAF (Basal Area Factor) sampling which is a forest inventory system that utilizes Bitterlich sampling (point sampling) with two BAF sizes, a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation.MethodsThe new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means. The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula.ResultsSeveral computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature. In simulations the new estimator performed well and comparably to existing variance formulas.ConclusionsA possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees, an assumption required by all previous big BAF variance estimation formulas. Although this correlation was negligible on the simulation stands used in this study, it is conceivable that the correlation could be significant in some forest types, such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition. We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area. We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of frac {1}{n} where n is the number of sample points.

Experimental Investigation on the Static Performance of Stud Connectors in Steel-HSFRC Composite Beams.

In this research, high strength fiber reinforced concrete (HSFRC) was used to replace the normal strength concrete (NSC) in steel-concrete composite beams to improve their working performance, which might change the static performance of stud connectors. Firstly, push-out tests were conducted to investigation on the static performance of stud connectors in steel-HSFRC composite beams and compared with steel-NSC composite beams. Studs of 8 sizes, 13 mm, 16 mm, 19 mm and 22 mm in diameter and 80 mm and 120 mm in height were adopted to study the influence of stud dimension. The test phenomenon shown that the crack resistance of HSFRC was better than that of NSC, and there were some splitting cracks on NSC slabs whereas no visible cracks on HSFRC slabs when specimens failed. Next, the load-slip curves of studs were analyzed and a typical load-slip curve was proposed which was divided into four stages. In addition, the effects of test parameters were analyzed according to the characteristic points of load-slip curve. Compared with NSC slab, HSFRC slab could provide greater restraining force to the studs, which improved the shear capacity and stiffness of studs while suppressed the ductility of studs. The shear capacity, stiffness and ductility of studs would significantly increase with the increasement of stud diameter and the studs with large diameter were more suitable for steel-HSFRC composite beams. The stud height had no obvious influence on the static performance of studs. Finally, based on the test results, the empirical formulas for load-slip curve and shear capacity of stud connectors embedded in HSFRC were developed which considered the influence factors more comprehensively and had better accuracy and applicability than previous formulas.

Investigation on temperature distribution under the coupling action of transverse position and fire sealing of linear fire in tunnel

By sealing the portal at one end of tunnel and changing the transverse location of linear fire source in tunnel, the hot smoke layer, longitudinal temperature distribution and maximum temperature of linear fire source were investigated. It is found that the flame will bend under the influence of curved ceiling and hot smoke layer will be thicker when the linear fire source approaches to the side wall. The variation law of heat release rate is analyzed by considering the limiting effect of side wall and thermal feedback. By modifying the previous formula of effective ceiling height, an empirical formula for predicting longitudinal temperature distribution of linear fire sources with different aspect ratios is proposed, and the ventilation coefficient is obtained to characterized the temperature under sealing and without sealing. Moreover, the accuracy of predicted temperature under sealing is verified by using the ventilation coefficient. Based on dimensional analysis, it's concluded that the maximum temperature mainly depends on the heat release rate, and an empirical formula is proposed to predict the maximum temperature rise of linear fire sources with different aspect ratios in several transverse positions. The error of predicted values and actual values is within 13%.

Behavior of Box Concrete-Filled Steel Tube Columns Considering Confinement Effect

In recent years considerable attention has been given to estimating the strength of box concrete-filled steel tube (CFST) stub columns. The effect of confining pressures is one of the complexities in determining the ultimate strength of the CFST columns. An experimental database of 188 tested columns has been used to produce two types of formulae: modified and simplified, that can help to predict the ultimate strength of box CFST columns with a wide range of geometrical and material properties. Different code procedures and previous formulae given by other authors were used for verification purposes and to show reliability. The axial load-shortening behaviors of composite columns were plotted using a proposed model of confined concrete adopted in a finite element analysis and compared with the experimental results. It has been found that the present formulae and concrete model have given results that agree quite well with the results of the experimental tests.

Proposing new breaking wave height prediction formulae using gene expression programming

Wave breaking occurs when waves reach a critical level of amplitude, which results in releasing a significant amount of energy. Predicting the wave heights, locations and other characteristics of breaking waves in shallow water is an important area of research. The breaking wave height, which is the most important characteristic, depends on various parameters such as deepwater wavelength, breaking water depth and seabed slope. In this study, new formulae are proposed for predicting the breaking wave height focusing on two types of breaking waves, namely spilling and plunging. The breaking wave types can be classified by using the Iribarren number. A comprehensive set of laboratory and field observations is utilized to develop new formulae based on the Gene Expression Programming (GEP) numerical method. The datapoints representing individual waves whose breaking types have been determined to be different according to different wave breaking classification criteria have been ignored. In comparison with previous formulae, the new formulae proposed based on different breaking types have almost higher accuracy, especially in the plunging case. Therefore, it might be concluded that developing different formulae based on different breaking types, rather than a general one for all types, would lead to more accurate results.

Evaluation of Key Performance of Aircraft Fabric Rubber Seal During Flight

In this Paper, the mechanic properties and sealing performance of the aircraft fabric rubber seal during flight are studied. First, the mechanic parameters, geometric structure, loading method of different aircraft cabin door fabric rubber seals, and gas conditions are analyzed. Second, the modified gas leakage rate formula of fabric rubber seal within wide ranges of temperature and gas pressure is derived based on the previous gas leakage rate formula of fabric rubber seal and the gas leakage rate experimental results. Then, the gas leakage rate prediction method of multicontact sealing surfaces is established. Finally, the variation law of the aircraft gas leakage rate with the altitude are determined based on the configuration number of the aircraft fuselage doors and the finite element results of the aircraft door seals. The research results will provide reliable scientific guidance for the mechanical performance evaluation and sealing performance prediction of fabric rubber seals.

Modeling the quantitative effect of alloying elements on the Ms temperature of high carbon steel by artificial neural networks

Chemical composition affects the properties and the martensite start (Ms) temperature of steels. This study predicts the Ms temperature of high carbon steel via artificial neural networks. Meanwhile, it enables us to estimate the quantitative effect of alloying elements on the Ms temperature on a sizeable selectable scale, which is the first time to release such results exactly. Compared to the previous formulas, this one is simple, visual, with high accuracy.

Semiclassical regime for dark matter self-interactions

Many particle physics models for dark matter self-interactions - motivated to address long-standing challenges to the collisionless cold dark matter paradigm - fall within the semi-classical regime, with interaction potentials that are long-range compared to the de Broglie wavelength for dark matter particles. In this work, we present a quantum mechanical derivation and new analytic formulas for the semi-classical momentum transfer and viscosity cross sections for self-interactions mediated by a Yukawa potential. Our results include the leading quantum corrections beyond the classical limit and allow for both distinguishable and identical dark matter particles. Our formulas supersede the well-known formulas for the momentum transfer cross section obtained from the classical scattering problem, which are often used in phenomenological studies of self-interacting dark matter. Together with previous approximation formulas for the cross section in the quantum regime, our new results allow for nearly complete analytic coverage of the parameter space for self-interactions with a Yukawa potential. We also discuss the phenomenological implications of our results and provide a new velocity-averaging procedure for constraining velocity-dependent self-interactions. Our results have been implemented in the newly released code CLASSICS.

Numerical analysis of CFRP-confined concrete-filled stainless steel tubular stub columns under axial compression

The carbon fiber-reinforced polymer (CFRP)-confined concrete-filled stainless steel tubular (CFRP-CFSST) column has the superiority in outstanding mechanical properties, corrosion resistance, and low maintenance cost needed throughout its life cycle, and therefore it has a wide application prospect. In order to study the axial compression behavior of CFRP-CFSST stub column, a numerical simulation study based on the previous test was conducted. A finite element model of CFRP-CFSST was developed and the accuracy of the model was verified by the test results of typical failure modes and load-compression curves of specimens. the stress–strain responses and the interaction between different materials, which were difficult to obtain directly during tests, were disclosed through the finite model. The parametric analyses were also conducted for the sake of the effects of stainless steel, CFRP, concrete, diameter-to-thickness ratio, and cross-section area on the mechanical behavior of CFRP-CFSST. Compared the existing ultimate bearing capacity prediction formula, and a reduction factor ϕ = 0.9 was adopted to the previous formula proposed by Ref. [1].

A precise splice-length model for reinforced concrete structures

Various mathematical expressions have been proposed to evaluate or check the lapped length in spliced bars subjected to tension in reinforced concrete members. In this work, 284 tests on spliced bars were assessed in an attempt to improve the previous formulas, with the aim of proposing a new model to predict the lapped length, the transverse reinforcement spacing and the bond stress distribution in concrete beams with different compressive strengths. A genetic algorithm was used to optimise the proposed formulation. For both normal- and high-strength concrete, different bond-stress profiles were developed to predict the resistance provided by bonded embedment. The results clearly show that the proposed bond stress profiles lead to a more accurate evaluation of the lapped length in spliced bars than the expression proposed by the American Concrete Institute.

Modification of Anti-acne Bawang Dayak (Eleutherine bulbosa (Mill.)Urb.) Cream to Propionibacterium acnes.

Bawang dayak is one of the traditional medicines in Central Kalimantan, used to treat acne vulgaris. Previous research reported that a cream made with bawang dayak extract's active ingredient could inhibit Propionibacterium acnes' growth. However, bawang dayak has a pungent odor that causes discomfort, where the cream separates after 3 days of storage, which decreases its potency. This study aims to improve the quality of the anti-acne cream formulation of bawang dayak extract from previous studies with the addition of cinnamon, honey, and peppermint. The modified formula of bawang dayak extract cream was evaluated and tested for its antibacterial activity in vitro. The results showed an increase in the organoleptic test, especially the smell, which gave a more comfortable fragrance than the previous formula. The pH measurement of the cream shows the results suitable for topical applications. However, the homogeneity observations show that all the formulas are homogeneous, seen from uniform colors but contain coarse grains. The antibacterial activity test of all cream formulations against P. acnes showed inhibition zone diameter between 14.85 and 17.10 mm, all of which were moderate and larger than previous studies. It can be concluded that the modification of the cream formula with the active ingredient of bawang dayak extract showed an increase in the inhibition zone against P. acnes and improved organoleptic properties.

Modeling the Quantitative Effect of Alloying Elements on the Ms Temperature of High Carbon Steel by Artificial Neural Networks

Chemical composition affects the properties and the martensite start (Ms) temperature of steels. This study predicts the Ms temperature of high carbon steel via artificial neural networks. Meanwhile, it enables us to estimate the quantitative effect of alloying elements on the Ms temperature on a sizeable selectable scale, which is the first time to release such results exactly. Compared to the previous formulas, this one is simple, visual, with high accuracy.

Kugel Ball as an Interesting Application of Designing the Hydrosphere

Analytical solutions are not available for the partial hemispherical hydrosphere which called as the Kugel ball fountain or the Kugel ball. However, this study offers a comprehensive idea about this phenomenon presenting a design map that gives a panoramic sight enabling the designers to easily choose whatever specifications needed for their fountain. Through simplifying the author previous formulae for this type of bearings, this paper removes the mystery of the Kugel ball phenomenon and shows that no complicated mathematic or physics are needed, as believed, to be grasped for producing such fountains. A new simple design technique is used and the most two famous fountains (at the House of Science in Patras, Greece and the largest at the Science Museum of Virginia, Richmond, USA.) are checked as an application of this design. One of the most important side results of this study is finding the equilibrium point, discovered in the author previous papers, which was considered as the equilibrium point between the forces of centripetal inertia, viscosity and friction due to the surface roughness. It becomes clear that this point is a natural characteristic of this type of bearings.

The Bayesian Additive Regression Trees Formula for Safe Machine Learning-Based Intraocular Lens Predictions.

Purpose: Our work introduces a highly accurate, safe, and sufficiently explicable machine-learning (artificial intelligence) model of intraocular lens power (IOL) translating into better post-surgical outcomes for patients with cataracts. We also demonstrate its improved predictive accuracy over previous formulas. Methods: We collected retrospective eye measurement data on 5,331 eyes from 3,276 patients across multiple centers who received a lens implantation during cataract surgery. The dependent measure is the post-operative manifest spherical equivalent error from intended and the independent variables are the patient- and eye-specific characteristics. This dataset was split so that one subset was for formula construction and the other for validating our new formula. Data excluded fellow eyes, so as not to confound the prediction with bilateral eyes. Results: Our formula is three times more precise than reported studies with a median absolute IOL error of 0.204 diopters (D). When converted to absolute predictive refraction errors on the cornea, the median error is 0.137 D which is close to the IOL manufacturer tolerance. These estimates are validated out-of-sample and thus are expected to reflect the future performance of our prediction formula, especially since our data were collected from a wide variety of patients, clinics, and manufacturers. Conclusion: The increased precision of IOL power calculations has the potential to optimize patient positive refractive outcomes. Our model also provides uncertainty plots that can be used in tandem with the clinician’s expertise and previous formula output, further enhancing the safety. Translational relavance: Our new machine learning process has the potential to significantly improve patient IOL refractive outcomes safely.

A new formula of punching shear strength for fiber reinforced polymer (FRP) or steel reinforced two-way concrete slabs

This study is to propose a new punching shear strength formula for either FRP or steel reinforced two-way concrete slabs based on deterministic and probabilistic methods. Former is to employ the test to prediction ratio and latter is newly suggested approach that can guarantee more reliable prediction considering the significant uncertainties to minimize the possibility of over-estimating punching shear strength. For comparative study, the selected test results and the previous formulas are employed. The proposed new formula exhibits the most accurate test to prediction ratio among the existing formulas. Furthermore, it renders the lowest probability of exceedance that the predicted punching shear strength exceeds the nominal punching shear strength. The proposed new formula can minimize the probability of over-estimating the punching shear strength. Consequently, it can lead to enhance the accuracy, safety and reliability of punching shear strength design of either FRP or steel reinforced two-way concrete slabs.