Rate Decline Behavior of Selectively Completed Horizontal Wells in Naturally Fractured Oil Reservoirs

• Published in: Mathematical problems in engineering Vol. 2019; no. 2019; pp. 1 - 13
• Main Authors: Ji, An-zhao, Li, Long-xin, Xu, You-jie, Liu, Qiguo
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2019; Hindawi; Hindawi Limited
• Subjects: Boundary conditions; Collapse; Conservation equations; Cross flow; Derivatives; Differential equations; Equations of motion; Equations of state; Exact solutions; Fairs & exhibitions; Flow coefficients; Fluids; Fourier transforms; Fractured reservoirs; Horizontal wells; Industrial development; Integrals; Laplace transforms; Mathematical models; Mathematical problems; Natural gas; Permeability; Productivity; Reservoirs; Seepage
• ISSN: 1024-123X; 1563-5147
• DOI: 10.1155/2019/7281090

Selectively completed horizontal wells (SCHWs) can significantly reduce cost of completing wells and delay water breakthrough and prevent wellbore collapse in weak formations. Thus, SCHWs have been widely used in petroleum development industry. SCHWs can shorten the effective length of horizontal wells and thus have a vital effect on production. It is significant for SCHWs to study their rate decline and flux distribution in naturally fractured reservoirs. In this paper, by employing motion equation, state equation, and mass conservation equation, three-dimension seepage differential equation is established and corresponding analytical solution is obtained by Laplace transform and finite cosine Fourier transform. According to the relationship of constant production and wellbore pressure in Laplace domain, dimensionless rate solution is gotten under constant wellbore pressure in Laplace domain. Dimensionless pressure and pressure derivate curves and rate decline curves are drawn in log-log plot and seven flow regimes are identified by Stehfest numerical inversion. We compared the simplified results of this paper with the results calculated by Saphir for horizontal wells in naturally fractured reservoirs. The results showed excellent agreement. Some parameters, such as outer boundary radius, storativity ratio, cross-flow coefficient, number and length of open segments, can obviously affect the rate integral and rate integral derivative log-log curves of the SCHWs. The proposed model in this paper can help better understand the flow regime characteristics of the SCHWs and provide more accurate rate decline analysis of the SCHWs data to evaluate formation.