Computation Theory and Mathematics
en
articles
https://scigraph.springernature.com/explorer/license/
2016-12-01
A new technique for solving pressure–rate deconvolution problem in pressure transient testing
false
http://link.springer.com/10.1007%2Fs10665-016-9854-x
2019-04-10T13:15
189-200
2016-12
research_article
The transient pressure–rate deconvolution problem is formulated in the form of a linear convolution Volterra equation of the first kind. In addition to its ill-posedness, the problem is characterized by multiscale behavior of the solution and discontinuous input data with possibly large measurement errors (noises). These do not allow us to apply standard algorithms for solving the Volterra equation. Therefore, in most cases, deconvolution algorithms may implicitly or explicitly include regularization and take into account a priori information. In general, the solution has to satisfy certain conditions, such as positivity, monotonicity, and/or convexity. However, as is well known, the solution of the deconvolution problem satisfies an infinite system of inequalities. In this paper, we construct two effective regularization algorithms (methods) to obtain smooth approximate solutions satisfying all a priori constraints for the deconvolution problem. The convergence properties of the methods are proven. Finally, the methods are applied to a few sets of pressure–rate data with large measurement errors, and the deconvolution results of the data are discussed.
dimensions_id
pub.1006136553
Vladimir V.
Vasin
Skorik
Georgy G.
0022-0833
1573-2703
Journal of Engineering Mathematics
doi
10.1007/s10665-016-9854-x
Springer Nature - SN SciGraph project
Kuchuk
Fikri
1
readcube_id
1d3b3d7fd9590e78410e9d961f33482219429c5b8f21cffd82569696c90846ae
Ural Federal University
Institute of Mathematics and Mechanics, UB RAS, 620990, Yekaterinburg, Russia
Ural Federal University, 620002, Yekaterinburg, Russia
Information and Computing Sciences
Schlumberger (France)
Schlumberger Ltd, 92142, Clamart Cedex, France
101