Previously, we showed using a computational agent-based model that a group of animals moving together can make a collective decision on direction of motion, even if there is a conflict between the directional preferences of two small subgroups of “informed” individuals and the remaining “uninformed” individuals have no directional preference. The model requires no explicit signaling or identification of informed individuals; individuals merely adjust their steering in response to socially acquired information on relative motion of neighbors. In this paper, we show how the dynamics of this system can be modeled analytically, and we derive a testable result that adding uninformed individuals improves stability of collective decision making. We first present a continuous-time dynamic model and prove a necessary and sufficient condition for stable convergence to a collective decision in this model. The stability of the decision, which corresponds to most of the group moving in one of two alternative preferred directions, depends explicitly on the magnitude of the difference in preferred directions; for a difference above a threshold the decision is stable and below that same threshold the decision is unstable. Given qualitative agreement with the results of the previous simulation study, we proceed to explore analytically the subtle but important role of the uninformed individuals in the continuous-time model. Significantly, we show that the likelihood of a collective decision increases with increasing numbers of uninformed individuals.

The aim of this study was to propose the workflow for integrated analysis of the 3D geostress and 1D geomechanics of an exploration in a new gas field. This integrated analysis will allow for problems associated with the inaccuracy of 1D geomechanical analysis to be overcome in a region with obvious anticline/syncline structures. The 1D geomechanical analysis of the well in the exploration of a new gas field mainly included the prediction of pore pressure and calculation of the mud weight window for safe drilling. In general, this integrated workflow included both a method for pore pressure prediction and a method for the calculation of the mud weight window, with the numerical solution of 3D geostress plus the interval velocity of formations. The procedure for the calculation of the 3D geostress of a target block was also introduced. Numerical solution of the 3D geostress of the target gas field, as well as solutions of 1D geomechanical analysis, have demonstrated the efficiency and practical use of the proposed theory in the successful drilling of the LT-1 well in the Junggar Basin, Xinjiang, China. For this LT-1 well in the target TS block, there was no logging data to refer to when predicting the pore pressure of undrilled formations. Only 3D geostress could be used to calculate the mud weight window. Influences of anticline structures were considered in the calculation of 3D geostress. Since the accuracy of the numerical solution of 3D geostress is higher than the accuracy of the 1D geostress solution for a single well analysis, the results of pore pressure and the mud weight window are more accurate than those obtained with conventional 1D geostress analysis. Details of the finite element modeling of the 3D geostress field of the TS block is presented along with the solution of the 3D geostress field. With the data of the interval velocity of formations and 3D geostress solution of the TS block, pore pressure prediction was carried out for the 7000 m-deep pilot LT-1 well. Finally, calculations were performed for the values of the mud weight window of the LT-1 well.

The presence of natural fractures can significantly affect the quality of hydraulic fracturing operations in tightsand and shale or oil/gas formations. This paper describes the procedure used to model natural fractures with continuum damage tensor and the resulting orthotropic permeability tensor. A damage model that uses damage variable in tensor form is presented. In the procedure presented, a nonnegligible angle is assumed to exist between directions of principal stresses in the formation and in the natural-fractures-related damage tensor, and this difference in orientation is modeled by introducing local directions in the model. A damage-dependent permeability tensor in tabular form is then proposed. A second case scenario when the directions of principal stresses and natural fractures align is also analyzed. Numerical results of fracture distribution are presented for both cases, and differences can be seen from the computed contour of the damage variable. The results indicate that the model can effectively simulate the fracture propagation phenomena during hydraulic fracturing.