A Leak Location And Leak Strength Loss Model Posed

Nowadays, the detection of the position and the intensity of the leaks in the pipeline net of gas(oil) is the most popular problem in the research of engineering project and theory of preservation and transportation, and at the same time the problem in practice of the manufacture of the oil field. Many engineer and natural science workers in internal and overseas pay close attention to this difficult problem, and do their best to resolve it. During recent twenty to thirty years, there has been a great many of achievement, as well models and methods, which focus to find a fairly easy way of detecting the position and intensity of the leaks in the pipeline net of gas (oil) and other relative quantity. One kind of the models which are being researched are the simple models set up on the base of stable condition, they have a larger error in detection, so they can not suffice to engineering. The other kind of the models are the unlinear partial differential equation groups which set up from move equation, sequential equation, and condition equation. We used all kinds of numerical calculation means to seek the position and intensity of the leaks in pipeline net, but the effects are not satisfactory. Many large-size petroleum company have developed some examination software, they keep their technology secret and it's very expensive. Therefore, it stimulate strongly the confidence of countrymen to research the detection of the leaks in the pipeline net.This paper has described a unlinear partial differential equation group of the move in the pipeline net of gas(oil) on this base, use a method to make it linear, and set up a linear partial differential equation model to describe the single-leak in the pipeline net of gas(oil) in the examine stage for the first time. And then use the theory of inverse problem of partial deferential equation, select some feasible means of measurement and data, added some additional conditions reasonably, at last compose a complete model of detection of leaks. This model's engineering concept is clear, the direct problem's analysis solution is easy to express, so it's very easy to construct the math-express formula which contain the parameter of the position and intensity of leaks. These express formulas are easy and convenient, especially easy to discuss the quality of the equation. For this reason, we discuss following questions on this base:From the sequential equation, move equation, and condition equation we give a unlinear partial differential equation group which describe the move of the gas in pipeline net of gas(oil). Use KA linear method, make it into a linear heat conduct equation. Then according to the characteristic of the gas(oil) in examine stage, we set up a linear partial differential equation model which describes the single-leak in the pipeline net of gas(oil) for the first time. At last we use Laplace integral transform to gain the analysis solution of the direct problem of linear partialdifferential equation model which describes the single-leak in the pipeline net of gas(oil) in examine stage.According to the characteristic of the move of gas(oil) in examine stage, we make two additional conditions to detect the position and intensity of the leaks. After then we obtain the math-express formula of the position and intensity of the leaks. According to the express formula of the position of the leaks, we give and prove the theorem of the existence and uniqueness of the position of the leaks. This is the foundation of the discrimination of the most important parameter in leak model, it also offers the technical pledge to numerical calculation.According to the express formula of the intensity of the leaks, we use the condense map principle to prove the theory of the existence and uniqueness of the intensity of the leaks, moreover, we get the estimative formula of the intensity of the leaks, it offers the theoretic basis to the numerical calculation of the quantity of the leaks in the leak model.On the basis of the formula of we structure a numerical calculation form and compile the calculate procedure. We give some calculation example, the result indicate that the theoretic number is good fit the real number, it conform to the demand of the engineering project of preservation and transportation basically. We also discuss the simple inverse formula of the position and intensity of the leaks, and the method of using the simple formula to calculate the position and the intensity. In the formula that we have concerned above, on condition of the time of the measurement is longer enough, if we neglect the infinite series in the formula, we can gain the simple formula of the position and intensity of the leaks. Use these simple formula, we can calculate the position and the intensity easily. These formula is useful for us to preliminary calculate or give the initial approximation.Even though, the model that we have set up is also has some inadequacy, there are several difference between some supposing condition in the theory of the existence and uniqueness of the position and intensity of the leaks and the practical engineering problem. The analyses of the error which restrict and influence the position and intensity of the leaks are not enough, etc. we will make great effort continually to overcome the hard work of detecting the position and intensity of the leaks in the pipeline net of gas(oil).