As a kind of mathematical model, grey systems predi ct ion model has been widely applied to economy, management and engineering technol ogy. In 1982, Professor Deng Ju-long presented GM prediction model. Then some o t...As a kind of mathematical model, grey systems predi ct ion model has been widely applied to economy, management and engineering technol ogy. In 1982, Professor Deng Ju-long presented GM prediction model. Then some o ther scholars made improvements on GM model. Of course, much still should be don e to develop it. What the scholars have done is to take the first component of X (1) as the starting conditions of the grey differential model. It occ urs that the new information can not be used enough. This paper is addressed to choose the nth component of X (1) as the starting conditions to improv e the models. The main results of the paper is given in Theorem 2: The time response function of the grey differential equation x (0)(k)+az (1)(k)=b is given by x (1)(k)=x (1)(n)-ba e -a(k-n )+ba. and Theorem4: The time response of the grey Verhulst model is given by (1)(k) =ax (1)(n)bx (1)(n)+(a-bx (1)(n))ae a(k-n). As the new information is fully used, the accuracy of prediction is improved gre atly. Therefore, the new model with a certain theoretical and practical value.展开更多
Ultra-deepmajor gas fields are typically characterized by high and ultra-high pressure,tightmatrix and developed fractures,so the reserve estimation is of higher uncertainty.In order to accurately estimate the reserve...Ultra-deepmajor gas fields are typically characterized by high and ultra-high pressure,tightmatrix and developed fractures,so the reserve estimation is of higher uncertainty.In order to accurately estimate the reserves of this type of gas reservoir,this paper analyzed the correlation between the effective rock compressibility and the cumulative effective rock compressibility based on the material balance equation of high and ultra-high pressure gas reservoirs,and accordingly selected the material balance based analysis method suitable for the reserves estimation of high and ultra-high pressure gas reservoirs.Then,the starting calculation conditions of reserve estimation were determined using the non-linear regressionmethod.In addition,a semilogarithmic type curvematchingmethodwas established for the caseswhere the starting conditions could not bemet.Finally,thismethodwas applied to calculate the reserves of three ultra-high pressure gas fields(reservoirs)to verify its reliability.And the following research results were obtained.First,the cumulative effective compressibility of gas reservoir in thematerial balance equation of high and ultra-high pressure gas reservoir is a key parameter influencing its reserves,and it is the function of original formation pressure and current average formation pressure,but its numerical value can be hardly obtained by core experiments.Second,it is recommended to adopt the nonlinear regressionmethod without compressibility to estimate the reserves of high and ultra-high pressure gas reservoirs.Third,the calculation starting point of reserves by the nonlinear regression method(the starting point of dimensionless apparent formation pressure-cumulative gas production curve deviating from the straight line relationship)cannot be theoretically calculated.The calculation starting point for different dimensionless linear coefficients(uD)obtained fromthe statistical results by the graphic method corresponds to the dimensionless apparent pressure depletion degree of 0.06-0.38,and that obtained based on the data statistics of the example gas reservoir falls within this interval.Fourth,when the starting conditions are not satisfied,the semi-logarithmic type curve matching method can be used for reserve estimation.The ratio of the reserves to the apparent geological reservesG/G_(app) is a function of uD.The higher the uD,the lower the G/G_(app).Fifth,for the high and ultra-high pressure gas reservoirs in the production test stage,the test production time shall be extended as long as possible to improve the reliability of reserve estimation.And for those in the middle and late stages of development,it is necessary to prepare the comprehensive treatment measures on the basis of reserves so as to improve the development effects of gas reservoirs continuously.展开更多
文摘As a kind of mathematical model, grey systems predi ct ion model has been widely applied to economy, management and engineering technol ogy. In 1982, Professor Deng Ju-long presented GM prediction model. Then some o ther scholars made improvements on GM model. Of course, much still should be don e to develop it. What the scholars have done is to take the first component of X (1) as the starting conditions of the grey differential model. It occ urs that the new information can not be used enough. This paper is addressed to choose the nth component of X (1) as the starting conditions to improv e the models. The main results of the paper is given in Theorem 2: The time response function of the grey differential equation x (0)(k)+az (1)(k)=b is given by x (1)(k)=x (1)(n)-ba e -a(k-n )+ba. and Theorem4: The time response of the grey Verhulst model is given by (1)(k) =ax (1)(n)bx (1)(n)+(a-bx (1)(n))ae a(k-n). As the new information is fully used, the accuracy of prediction is improved gre atly. Therefore, the new model with a certain theoretical and practical value.
基金supported by the Major Science and Technology Project of PetroChina Company Limited“Research and Application of Key Technologies for Development of Deep and Ultra-deep Gas Fields in Kuqa Depression”(No.2018E-1803).
文摘Ultra-deepmajor gas fields are typically characterized by high and ultra-high pressure,tightmatrix and developed fractures,so the reserve estimation is of higher uncertainty.In order to accurately estimate the reserves of this type of gas reservoir,this paper analyzed the correlation between the effective rock compressibility and the cumulative effective rock compressibility based on the material balance equation of high and ultra-high pressure gas reservoirs,and accordingly selected the material balance based analysis method suitable for the reserves estimation of high and ultra-high pressure gas reservoirs.Then,the starting calculation conditions of reserve estimation were determined using the non-linear regressionmethod.In addition,a semilogarithmic type curvematchingmethodwas established for the caseswhere the starting conditions could not bemet.Finally,thismethodwas applied to calculate the reserves of three ultra-high pressure gas fields(reservoirs)to verify its reliability.And the following research results were obtained.First,the cumulative effective compressibility of gas reservoir in thematerial balance equation of high and ultra-high pressure gas reservoir is a key parameter influencing its reserves,and it is the function of original formation pressure and current average formation pressure,but its numerical value can be hardly obtained by core experiments.Second,it is recommended to adopt the nonlinear regressionmethod without compressibility to estimate the reserves of high and ultra-high pressure gas reservoirs.Third,the calculation starting point of reserves by the nonlinear regression method(the starting point of dimensionless apparent formation pressure-cumulative gas production curve deviating from the straight line relationship)cannot be theoretically calculated.The calculation starting point for different dimensionless linear coefficients(uD)obtained fromthe statistical results by the graphic method corresponds to the dimensionless apparent pressure depletion degree of 0.06-0.38,and that obtained based on the data statistics of the example gas reservoir falls within this interval.Fourth,when the starting conditions are not satisfied,the semi-logarithmic type curve matching method can be used for reserve estimation.The ratio of the reserves to the apparent geological reservesG/G_(app) is a function of uD.The higher the uD,the lower the G/G_(app).Fifth,for the high and ultra-high pressure gas reservoirs in the production test stage,the test production time shall be extended as long as possible to improve the reliability of reserve estimation.And for those in the middle and late stages of development,it is necessary to prepare the comprehensive treatment measures on the basis of reserves so as to improve the development effects of gas reservoirs continuously.
