| 1. Preface Designing Casing string is a basic and important work in the petroleum engineering, the string bears the internal pressure, axianl tension, strata outside crush stress; at the same time it also bears the thermal stress, complex stress of the underground equipment like slips and packers and so on. With traditional method, we decide the stress which the casing string bears under conditions of the most bad work environment, and made reasonable design to ensure the safety of casing string and to meet the needs of the oil field production for a long time. We usually also consider the well depth, density of the drilling fluid and the data of the geological terrane, which could effect the results. The method mainly depends on the designer's level and experience, and lacks of science and reliability. So it is an important to seek out a new method to ensure the safety and decrease the cost of the enterprise. A new intellectual optimal method, improved Genetic Algorithms is introduced to study how to solve a series of problems. The emphases of this paper are that, GA combines with the casing string design method to optimize the selection of casing string. In the paper, the math model is built up according that the smallest cost of the string is object. The selection, crossover, mutation operators of Genetic Algorithm and parameter coded by binary genes are designed. On the basis of it, the string optimal program is wrote in C++ and appled the program to examples. The results shown that it is successful to apply the Genetic Algorithm to optimize the casing string. 2. Build up the Model of GAs Optimizing the casing string is to optimize the selection of casing string. Our target is to decrease the cost of casing as possible. 2.1 Optimizing Model 2.1.1 Variable designing In order to simplize the model, we use the wall (δ) and grade (Z) of the casing as the individual gene. 2.1.2 Object function W = wZπ[ D_c~2 -(D_c-2δ)~2]……………………………(1) 2.1.3 Restricted condition While selecting casing, we should make sure to fit casing into primary collapse pressure. Collapse pressure: p ca ≥Scpce pce is strata outside crush stress, it has relationship with depth and the type of casing; pca is triaxiality anti-collapse strength, it has relationship with the wall and the grade of casing. 2.2 Coding and decoding We use two 4-bit binary code to present wall (δ) and grade (Z). The first 4-bit binary code is the wall and the second is the grade, the following tables shown the details of code. Because the casing with different OD has different walls, so we only use OD of 219mm as an example.Cmax is the maximum value of object function when the population evolutes to the latest generation. 2.4 GAs operator and parameter There are selection operator, crossover operator and mutation operator in the GAs. In order to ensure the quick convergency, we use elitist model as selection operator, use one-point crossover operator, and simple mutation operator. The operators are decided as followed: Generations: T=50, Crossover rate: Pc=0.65, Mutation rate: Pm=0.001. 2.5 Realize the method and programming3. Results and analyzing After building up model, coding and programming, we made attempt designing of surface casing, intermediate casing, and production casing. We contrasted and analyzed the results of traditional and Gas', from the tables following we should ensure that the new method can be used into practice, and the results fitted our expectation. 3.1 Surface casing Contrast:Analyzing: Cost coefficient of traditional one's W=1.0*10-5*110*3.14*[339.712-(339.71-2*12.19)2]=55.16 Cost coefficient of Gas'W=1.0*10-5*95*3.14*[339.712-(339.71-2*12.19)2]=47.64 3.2 Intermediate casing Constrast: Cost coefficient of traditional one's W=1.0*10-5*3.14*[125*[244.52-(244.5-2*11.99)2]*1560/3500+ 90* [244.52-(244.5-2*11.05)2]*1940/3500]=35.67 Cost coefficient of GAs W=1.0*10-5*3.14*[110* [244.52-(244.5-2*11.99)2]*1930/3500+ 80* [244.52-(244.5-2*11.05)2]*1570/3500]=32.87 3.3 Production casing Constrast: Analyzing: Cost coefficient of traditional one's W=1.0*10-5*3.14* [75* [177.82-(177.8-2*11.51)2]*1800/4500+ 75* [177.82-(177.8-2*12.65)2]*2400/4500+ 95* [177.82-(177.8-2*13.72)2]*300/4500]=19.50 Cost coefficient of GAs W=1.0*10-5*3.14*[75*[177.82-(177.8-2*11.51)2]*1050/4500+ 75*[177.82-(177.8-2*12.65)2]*2700/4500+ 75*[177.82-(177.8-2*13.72)2]*750/4500]=19.55 Although the cost coefficient of GAs is little bigger than the traditional one's, we should get another information is that the grade of three parts of casing are the same. It is very significant in field using. 4. Conclusion From the analysis of above, we can conclude that: a. GAs is a intellectual optimum method, and it used as a lasest optimum technology in the optimization field. In this paper, it is a new attempt and a new method, and it is also successful when applying GAs in designing of casing string. b. According to the object and characteristic of the casing string optimization, and use the triaxial stress and GAs as a foundation, an improved GAs, elitist model, has been used in this paper. We also built up model and programmed. The results of practice is presented that, the method has good convergency and stability. c. The GAs decreased the restricted conditions in designing casing string optimization, because of it has good ability to search solution. It is not only to enhance the...
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