Effect of loading rate and time delay on the tangent modulus method(TMM)in coal and coal measured rocks

Non-destructive techniques of in-situ stress measurement from oriented cored rocks have great potential to be developed as a cost cost-effective and reliable alternative to the conventional overcoring and hydraulic fracturing methods.The tangent modulus method(TMM)is one such technique that can be applied to oriented cored rocks to measure in-situ stresses.Like the deformation rate analysis(DRA),the rock specimen is subjected to two cycles of uniaxial compression and the stress-tangent modulus curve for the two cycles is obtained from the stress-strain curve.A bending point in the tangent modulus curve of the first cycle is observed,separating it from the tangent modulus curve of the second cycle.The point of separation between the two curves is assumed to be the previously applied maximum stress.A number of experiments were conducted on coal and coal measured rocks(sandstone and limestone)to understand the effect of loading conditions and the time delay.The specimens were preloaded,and cyclic compressions were applied under three different modes of loading,four different strain rates,and time delays of up to one week.The bending point in the stress-tangent modulus curves occurred approximately at the applied pre-stress levels under all three loading modes,and no effect of loading rate was observed on the bending points in TMM.However,a clear effect of time delay was observed on the TMM,contradicting the DRA results.This could be due to the sensitivity of TMM and the range of its applicability,all of which need further investigation for the in-situ stress measurement.

Poroelastoplastic reservoir modeling by tangent stiffness matrix method

As oil and gas extraction activities move into deeper rock formations,many experimental studies and field investigations indicate rock exhibits a plastic behavior rather than a pure linear elastic behavior,so poroelastoplasticity must be taken into account in the reservoir simulation.Because reservoir rock is a porous material consisting of a compressible solid matrix and number of compressible fluids occupying the pore space,fully coupled modeling is required for reservoir simulation considering solid-fluid interaction,complex stress conditions and nonlinear behaviors.But the computational process could be cumbersome when constant tangent stiffness method is used to address the poroelastoplastic behavior.In this paper,a fully coupled poroelastoplasticity reservoir model based on Drucker-Prager yield criterion is implemented the tangent stiffness method,and the computational efficiency is compared with the constant stiffness method.The accuracy of these two methods is demonstrated in one-dimensional consolidation.In a case study,these two methods are used to analyze the stresses and pore pressure of a reservoir and computing results and running efficiency are compared.Also,the linear elastic and nonlinear solutions are compared in one-dimensional consolidation and reservoir modeling.It shows that the difference between results by constant stiffness method and tangent stiffness method is very small,while the tangent stiffness method shows significantly fewer iteration numbers and shorter running time than the constant stiffness method.

Control of orientation for spacecraft formations in the vicinity of the Sun-Earth L2 libration point

Formation flying in the vicinity of the libration point is an important concept for space exploration and demands reliable and accurate techniques for the control of a spacecraft.On the basis of previous works,this paper addresses the problem of relative orientation control of spacecraft formation flying utilizing the framework of the circular restricted three-body problem(CR3BP)with the Sun and Earth as the primary gravitational bodies.Two specific tasks are accomplished in this study.First,the tangent targeting method(TTM),an efficient two-level differential correction algorithm,is exploited to control the Chief/Deputy architecture to maintain a prespecified orientation.The time spent within the orientation error corridor between successive maneuvers is maximized while the relative separation between the vehicles is held constant at each target point.The second task is to further optimize the maneuver intervals by dropping the constraint imposed on the relative vehicle separation.Numerical investigation indicates that the number of maneuvers can be significantly reduced and the length of time between successive maneuvers can be greatly increased by utilizing the TTM.