The development of unconventional resources in tight shales has stimulated considerable growth of oil and gas production in Northeastern Colorado, but has led to concerns about added demands on the region’s strained ...The development of unconventional resources in tight shales has stimulated considerable growth of oil and gas production in Northeastern Colorado, but has led to concerns about added demands on the region’s strained water resources. Northeastern Colorado’s semi-arid environment, population growth, competing water demands and uncertainty about drilling and hydraulic fracturing water requirements have resulted in scrutiny and conflict surrounding water use for tight shales. This study collects water use data from wells in Northeastern Colorado to improve water estimates and to better understand important contributing factors. Most water resource studies use estimates for the number of future wells to predict water demands. This study shows that the number of hydraulic fracturing stages is a better measure of the future water demands for horizontal wells. Vertical wells use significantly less water than horizontal wells and will be less prevalent in the future.展开更多
In 1980 F. Wattenberg constructed the Dedekind completion *Rd of the Robinson non-archimedean field *R and established basic algebraic properties of *Rd. In 1985 H. Gonshor established further fundamental properties o...In 1980 F. Wattenberg constructed the Dedekind completion *Rd of the Robinson non-archimedean field *R and established basic algebraic properties of *Rd. In 1985 H. Gonshor established further fundamental properties of *Rd. In [4] important construction of summation of countable sequence of Wattenberg numbers was proposed and corresponding basic properties of such summation were considered. In this paper the important applications of the Dedekind completion *Rd in transcendental number theory were considered. Given any analytic function of one complex variable , we investigate the arithmetic nature of the values of at transcendental points . Main results are: 1) the both numbers and are irrational;2) number ee is transcendental. Nontrivial generalization of the Lindemann-Weierstrass theorem is obtained.展开更多
文摘The development of unconventional resources in tight shales has stimulated considerable growth of oil and gas production in Northeastern Colorado, but has led to concerns about added demands on the region’s strained water resources. Northeastern Colorado’s semi-arid environment, population growth, competing water demands and uncertainty about drilling and hydraulic fracturing water requirements have resulted in scrutiny and conflict surrounding water use for tight shales. This study collects water use data from wells in Northeastern Colorado to improve water estimates and to better understand important contributing factors. Most water resource studies use estimates for the number of future wells to predict water demands. This study shows that the number of hydraulic fracturing stages is a better measure of the future water demands for horizontal wells. Vertical wells use significantly less water than horizontal wells and will be less prevalent in the future.
文摘In 1980 F. Wattenberg constructed the Dedekind completion *Rd of the Robinson non-archimedean field *R and established basic algebraic properties of *Rd. In 1985 H. Gonshor established further fundamental properties of *Rd. In [4] important construction of summation of countable sequence of Wattenberg numbers was proposed and corresponding basic properties of such summation were considered. In this paper the important applications of the Dedekind completion *Rd in transcendental number theory were considered. Given any analytic function of one complex variable , we investigate the arithmetic nature of the values of at transcendental points . Main results are: 1) the both numbers and are irrational;2) number ee is transcendental. Nontrivial generalization of the Lindemann-Weierstrass theorem is obtained.
