The distribution of fractures is highly uncertain in naturally fractured reservoirs (NFRs) and may be predicted by using the assisted-history-matching (AHM) that calibrates the reservoir model according to some high-quality static data combined with dynamic production data. A general AHM approach for NFRs is to construct a discrete fracture network (DFN) model and estimate model parameters given the observations. However, the large number of fractures prediction required in the AHM process could pose a high-dimensional optimization problem. This difficulty is particularly challenging when the fractures form a complex multi-scale fracture network. We present in this paper an integrated AHM approach of NFRs to tackle these challenges. Two essential ingredients of the method are (1) a 2D fractal-DFN model constructed as the geological simulation model to describe the complex fracture network, and (2) a mixture of multi-scale parameters, built according to the fractal-DNF model, as an inversion parameter model to alleviate the high-dimensional optimization burden caused by complex fracture networks. A reservoir with a multi-scale fracture network is set up to test the performance of the proposed method. Numerical results demonstrate that by use of the proposed method, the fractures well recognized by assimilating production data.
Summary
This paper considers the adaptive sliding‐mode control (ASMC) problem of spacecraft relative position tracking with maneuvering target in the presence of external disturbance and unknown mass property. Integrated with the spacecraft absolute orbit dynamics, the line‐of‐sight–based relative position motion model is established; further, the problem is formulated in the general mechanical second‐order form with unknown mass parameter and matching disturbance, which makes it convenient to use some useful physical properties in the control law design. As a stepping‐stone, the traditional ASMC law is proposed without prior knowledge of uncertainty/disturbance bound. Then, incorporated with the smooth‐projection algorithm and equivalent‐control‐dependent gain method, the modified control law is proposed, which can force the mass estimate to remain in a desired domain and efficiently overcome the drawback of the overestimation of the disturbance in the traditional ASMC law. Within the Lyapunov frame, the bounded stability is presented in the real case that the sign function is replaced by the hyperbolic tangent function. Finally, three different simulation cases are presented to show fine performance of the modified ASMC law.
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