Building a Mathematical Model to Predict Transient Drilling Temperature Responses

1969 ◽  
Vol 91 (3) ◽  
pp. 641-651 ◽  
Author(s):  
U. K. Saxena ◽  
S. M. Wu
Keyword(s):  
Mathematical Model ◽  
Statistical Model ◽  
Functional Form ◽  
Model Building ◽  
Design Procedure ◽  
Drilling Temperature ◽  
Confirmatory Tests ◽  
Temperature Responses ◽  
Theoretical Considerations ◽  
Building Technique

A transient drilling temperature predicting equation is developed using a statistical model-building technique. The functional form of the model is obtained by combining both theoretical considerations and an empirical approach. The parameters of this model are estimated and improved using a sequential procedure in designing the experiments. Confirmatory tests show that the model describes the transient drilling temperature responses remarkably well. The effectiveness of the design procedure for obtaining the “best” estimates of the parameters is also demonstrated.

Imprecision of Laboratory Determinations and Diagnostic Accuracy: Theoretical Considerations

1974 ◽  
Vol 13 (03) ◽  
pp. 151-158 ◽  
Author(s):  
D. A. B. Lindbebo ◽  
Fr. R. Watson
Keyword(s):  
Mathematical Model ◽  
Diagnostic Accuracy ◽  
Diagnostic Process ◽  
Clinical Laboratories ◽  
Non Linear ◽  
Theoretical Considerations ◽  
Made In

Recent studies suggest the determinations of clinical laboratories must be made more precise than at present. This paper presents a means of examining benefits of improvement in precision. To do this we use a mathematical model of the effect upon the diagnostic process of imprecision in measurements and the influence upon these two of Importance of Diagnosis and Prevalence of Disease. The interaction of these effects is grossly non-linear. There is therefore no proper intuitive answer to questions involving these matters. The effects can always, however, be calculated.Including a great many assumptions the modeling suggests that improvements in precision of any determination ought probably to be made in hospital rather than screening laboratories, unless Importance of Diagnosis is extremely high.

Matrix Acidization with Highly Reactive Acids

1971 ◽  
Vol 11 (04) ◽  
pp. 390-398 ◽  
Author(s):  
J.A. Guin ◽  
R.S. Schechter
Keyword(s):  
Mathematical Model ◽  
Pore Structure ◽  
Pore Size ◽  
Acid Treatment ◽  
Explicit Knowledge ◽  
Experimental Studies ◽  
Design Procedure ◽  
Permeability Change ◽  
Pore Size Distributions ◽  
Matrix Acidization

Abstract A mathematical model representing the changes in pore structure attending the invasion of a porous material by a reactive fluid tending to dissolve the solid bas previously been tested and found to be valid. This mathematical model is solved by a simulation procedure using Monte Carlo techniques. The results so obtained are indicative of the acidization of sandstone using a last-reacting acid (diffusion limited). A correlation relating the permeability improvement to the change in porosity is presented and found to be applicable to a wide class of initial pore-size distributions. This means that the designer need not have explicit knowledge of the initial pore structure to utilize the correlation. The generality of the correlation stems from the fact that after exposure to fast-acting acids (diffusion-controlled reactions) wormholing tends to occur in all porous matrices, and the acid allows preferentially through these channels. Thus, the process is independent of the fine pore structure since the fine pores receive no acid Wormholing bas been observed in almost all experimental studies of acidization, thus further confirming the validity of the model. Introduction Matrix acidization as practiced in the petroleum industry is a simple operation. Acids treated so as to prevent their corrosive attack on metal parts contacted are pumped down the wellbore and forced into the pore spaces of an oil-bearing rock. The rate of penetration is normally maintained small enough to prevent fracturing of the reservoir The aim of matrix acidization is to enhance the permeability of the region around the wellbore by permeability of the region around the wellbore by dissolving either a portion of the rock or of the foreign impurities that may have been introduced during the drilling operations. The success of this technique of oilwell stimulation is attested to by the fact that a significant fraction of the acids used for stimulation are injected at matrix rates. There were, moreover, in excess of 87 million gal of hydrochloric acid used last year in carbonate formations with many other special purpose acids such as acetic and formic having also been used for stimulation purposes. Despite the fact that acids have long been routinely used as a means of stimulating oil wells to greater production, there is, as yet, no reliable design procedure incorporating all of the essential features into a prediction of the new production that will result from a given acid treatment of a particular well. This lack of a design procedure particular well. This lack of a design procedure has been responsible for the rather minimal efforts expended in obtaining meaningful reaction rate data, for there is very little enthusiasm for obtaining data which cannot be put to practical application. This paper is an extension of some recently reported work on predicting the permeability change resulting from acid treatment of an oil-bearing rock. It has been proposed that the changes in the microstructure owing to acidization in a porous rock can be simulated by considering the effect of acidization of a collection of small, randomly distributed capillaries that are interconnected to the extent that a fluid will be conducted from point to point under the influence of an external pressure gradient. This model, the capillaric model, has been used with varying success in understanding the behavior of porous media. The use of the capillaric model in determining only the results of the evolution of a pore-size distribution, rather than as a vehicle for predicting a number of mare or less independent phenomena, such as capillary pressure curves and dispersion, is, as has been pressure curves and dispersion, is, as has been noted by Schechter and Gidley, a more limited and perhaps attainable goal. Taking the capillaric model to be correct, Guin et al. have shown that an equation relating the porosity change and the permeability change caused by an ideally retarded permeability change caused by an ideally retarded acid can be derived without any assumptions. SPEJ P. 390

Application of Aerodynamically Induced Prewhirl to a Small Turbocharger Compressor

1980 ◽  
Vol 102 (4) ◽  
pp. 943-950 ◽  
Author(s):  
N. Kyrtatos ◽  
N. Watson
Keyword(s):  
Mathematical Model ◽  
Design Procedure ◽  
Performance Data ◽  
Inlet Flow ◽  
Guide Vanes ◽  
Inlet Guide Vanes ◽  
Compressor Performance

A design procedure is described which allows the development of an arrangement to aerodynamically impart prewhirl to the inflow of a compressor. The procedure uses compressor performance data and inducer inlet flow distributions together with a mathematical model of the aerodynamic prewhirl inducing arrangement to arrive at the parameters which completely define an arrangement suitable for a particular compressor. The application of the procedure to design an arrangement for a small turbocharger compressor is presented. The effect of the aerodynamically imparted prerotation on the compressor performance was found to be similar to that produced by inlet guide vanes.

Research on Modeling of Screw Pump Characteristic Mathematical Model

2011 ◽  
Vol 361-363 ◽  
pp. 540-546
Author(s):  
Yun Ping Zheng ◽  
Yan Bin Yu ◽  
Yu Chun Wang ◽  
Xun Li ◽  
Jie Shu ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Pressure Difference ◽  
Model Building ◽  
Pso Algorithm ◽  
Optimization Method ◽  
Design Quality ◽  
Screw Pump ◽  
Management Efficiency ◽  
Operational Management ◽  
Shaft Power

For the design and management of the modern heavy oil piplines, the application of mathematical model to describe the characteristics of screw pump is crucial to the improvement of design quality and operational management efficiency. According to the features of HOW7T.3(50mm) screw pump’s actual measured data, this research established two groups of mathematical model.The first one described the change of screw pump’s displacement along with the variation of pressure difference and viscosity, while the second group described the change of shaft power along with the variation of pressure difference and viscosity, and then it solved all the four models by a particle swarm optimization (PSO) algorithm. The model-building and model-solving of these two examples showed that the PSO algorithm could rapidly search the best model regression parameter. Through the four target test, the research finally selected two models with relatively high accuracy. In the end, the paper put forward that it is necessary to take further research on the forms of screw pump characteristic mathematical model, and the corresponding optimization method of model-solving, in order to make the models more succinct and with higher fitting precision.

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