Percolation Mathematical Model for Stepped Horizontal Well in Multilayer Fault Block Reservoir

Liu Hong1, *, Pang Jin1, Chang Xuejun2, Yu Xinan1, Zhang Xu1
1 Chongqing University of Science and Technology, Chongqing 401331, China
2 Jidong Oilfield Company of Petrochina, Tangshan 063299, China

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© 2015 Hong et al.;

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Correspondence: * Address correspondence to this author at the Chongqing University of Science and Technology, Chongqing 401331, China; Tel: +86 23 65022798; Fax: +86 23 65022798; E-mail:


The percolation mechanism and regularity for stepped horizontal well in multi-layer complex fault block reservoir are complex. A percolation mathematical model based on unsteady flow mathematical model is built up in this paper. In the model, the reservoir couples with one horizontal well in sealed reservoir which perforates through mutually unconnected formation. Laplace transform, Stehfest inversion and Conjugate gradient are used to solve the model. The pressure distribution results of different time and production distribution results of different well section can be obtained. The results of pressure drop and pressure drop derivative calculated by this model are close to the results calculated by the Saphir software, and the agreement rate is 99%, which proves the model is of great reliability. Compared with Saphir software, the capacity of horizontal section through multiple sand at the same time can be calculated, which is the advantage of this model. It is not suitable for heterogeneous reservoir and the reservoir with supply boundary, which is the limitation. A two-layer block fault reservoir has been used to carry out the field study through the model, simplifying the irregular shape of reservoir for rectangular reservoir at first. Then a double-stage horizontal well is used to pass through the upper layer and the lower layer orderly in this reservoir, the simulation calculation of the well can use the double-stage horizontal well model, and the model can calculate the average pressure drop and pressure drop derivative of various production phases in the bottom hole accurately .The reservoir flow stage and the flow time in different periods can be judged through pressure drop and pressure drop derivative in the bottom hole, which can also calculate the distribution of production along the horizontal section in different periods at the same time. It can provide theoretical foundation of reservoir research engineering and production engineering design for reservoir development with stepped horizontal well in multilayer complex fault block reservoir.

Keywords: Complex fault block, Horizontal well, Multilayer reservoir, Percolation Model, Stepped well.