A subnano-g electrostatic force-rebalanced flexure accelerometer is designed for the rotating accelerometer gravity gradient instrument. This accelerometer has a large proof mass, which is supported inversely by two pairs of parallel leaf springs and is centered between two fixed capacitor plates. This novel design enables the proof mass to move exactly along the sensitive direction and exhibits a high rejection ratio at its cross-axis directions. Benefiting from large proof mass, high vacuum packaging, and air-tight sealing, the thermal Brownian noise of the accelerometer is lowered down to less than 0.2 ng/Hz with a quality factor of 15 and a natural resonant frequency of about 7.4 Hz. The accelerometer’s designed measurement range is about ±1 mg. Based on the correlation analysis between a commercial triaxial seismometer and our accelerometer, the demonstrated self-noise of our accelerometers is reduced to lower than 0.3 ng/Hz over the frequency ranging from 0.2 to 2 Hz, which meets the requirement of the rotating accelerometer gravity gradiometer.

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The methane desorption and diffusion characteristics in coal are key factors affecting coalbed methane productivity. In this paper, we developed a lattice Boltzmann model for methane migration in the multiscale porous media of coal. In the simulation, the diffusion of methane in macropores/fractures is assumed to follow Fick's law, and that in the coal matrix is treated as Knudsen diffusion. In addition, the Langmuir adsorption kinetics equation is employed to describe the dynamic process of methane adsorption and desorption. The results indicated the following: (1) The specific surface area and fracture proportion of the coal will increase with the employment of hydraulic fracturing, which may prompt the gas desorption-diffusion efficiency. (2) The flow and diffusion of methane are closely related to each other. When the gas diffusivity is poor, the desorption-diffusion can be effectively accelerated by increasing the drainage intensity, but when the gas diffusivity is fine, the flow velocity has little influence on the methane desorption. In practice, if the estimated methane diffusion coefficient is below the order of 10 −5 m 2 /s, more attention should be paid to its accuracy; otherwise, the obtained results may have a large deviation from the real value. (3) In the typical range of average pore sizes of coal, gas desorption rate growth with the increase of pore size makes the low-rank coal more advantageous in exploitation due to its larger average pore size. With the decline of reservoir pressure, the low-and high-rank coals more easily desorb methane than medium-rank coal. (4) In the kinetic study of the coalbed methane desorption-diffusion process, the accuracy of the obtained results may depend on the adsorption and desorption rate constants if the desorption rate constant is less than 10 6 1/s.

A new and simple method to adjust the scale factor of a magnetic force feedback accelerometer is presented, which could be used in developing a rotating accelerometer gravity gradient instrument (GGI). Adjusting and matching the acceleration-to-current transfer function of the four accelerometers automatically is one of the basic and necessary technologies for rejecting the common mode accelerations in the development of GGI. In order to adjust the scale factor of the magnetic force rebalance accelerometer, an external current is injected and combined with the normal feedback current; they are then applied together to the torque coil of the magnetic actuator. The injected current could be varied proportionally according to the external adjustment needs, and the change in the acceleration-to-current transfer function then realized dynamically. The new adjustment method has the advantages of no extra assembly and ease of operation. Changes in the scale factors range from 33% smaller to 100% larger are verified experimentally by adjusting the different external coefficients. The static noise of the used accelerometer is compared under conditions with and without the injecting current, and the experimental results find no change at the current noise level, which further confirms the validity of the presented method.

The diffusion–adsorption behavior of methane in coal is an important factor that both affecting the decay rate of gas production and the total gas production capacity. In this paper, we established a pore-scale Lattice Boltzmann (LB) model coupled with fluid flow, gas diffusion, and gas adsorption–desorption in the bi-dispersed porous media of coalbed methane. The Knudsen diffusion and dynamic adsorption–desorption of gas in clusters of coal particles were considered. Firstly, the model was verified by two classical cases. Then, three dimensionless numbers, Re, Pe, and Da, were adopted to discuss the impact of fluid velocity, gas diffusivity, and adsorption/desorption rate on the gas flow–diffusion–adsorption process. The effect of the gas adsorption layer in micropores on the diffusion–adsorption–desorption process was considered, and a Langmuir isotherm adsorption theory-based method was developed to obtain the dynamic diffusion coefficient, which can capture the intermediate process during adsorption/desorption reaches equilibrium. The pore-scale bi-disperse porous media of coal matrix was generated based on the RCP algorithm, and the characteristics of gas diffusion and adsorption in the coal matrix with different Pe, Da, and pore size distribution were discussed. The conclusions were as follows: (1) the influence of fluid velocity on the diffusion–adsorption process of coalbed methane at the pore-scale is very small and can be ignored; the magnitude of the gas diffusivity in macropores affects the spread range of the global gas diffusion and the process of adsorption and determines the position where adsorption takes place preferentially. (2) A larger Fickian diffusion coefficient or greater adsorption constant can effectively enhance the adsorption rate, and the trend of gas concentration- adsorption is closer to the Langmuir isotherm adsorption curve. (3) The gas diffusion–adsorption–desorption process is affected by the adsorption properties of coal: the greater the pL or Vm, the slower the global gas diffusivity decay. (4) The effect of the gas molecular adsorption layer has a great impact on the kinetic process of gas diffusion–adsorption–desorption. Coal is usually tight and has low permeability, so it is difficult to ensure that the gas diffusion and adsorption are sufficient, the direct use of a static isotherm adsorption equation may be incorrect.

Nano-g accelerometers are widely used in the space exploration and measurement of the earth's gravitational field. It is essential to precisely evaluate error effects at high orders such as cross-coupling for applications in a dynamic environment. Nevertheless, it remains challenging to meet the precision requirements using conventional calibration measures. In this paper, we propose a method to separate the cross-coupling coefficients of a linear single-axis accelerometer by mounting it on a steadily rotating rate table that is tilted at a fixed deviation angle with respect to the horizontal plane. The gravity component is periodically modulated along the input axis per revolution. Simultaneously, a series of centripetal acceleration is applied along the cross axis in sequence while adjusting the rotation frequency of the rate table by steps. Thus, the cross-coupling coefficient can be separated by its dependence both on the modulated gravity acceleration and the centripetal acceleration. In comparison with the static multipoint angular rotation test on a tilted dividing head, the proposed dynamic modulation method demonstrates improved robustness against corruption from bias drift, with an improved uncertainty. This method to separate the cross-coupling coefficient is suitable for testing high-resolution accelerometers, without requiring high bias stability or sensitive response sustaining at ultra-low frequency. INDEX TERMNano-g accelerometer, cross-coupling coefficient, rotation modulation, static multipoint, parameter identification, model equation. I. INTRODUCTIONAccelerometers with a resolution in the order of magnitude of ng/√Hz (where g ≈ 9.8 m/s 2 denotes the earth's gravity) are important for the exploration of the temporal and spatial variation of gravitational field, providing information on the substance density distribution of our planet 1,2 . The applications range from Earth's crust movement, through resource exploration to gravity-aided navigation 3,4 . In many application scenarios like moving-base gravity measurements, accelerometers are required to resolve acceleration of nano-g or sub nano-g in airborne or shipborne environments with relatively large dynamic noises 5,6 . This requirement is demanding since the severe mechanical vibration of the moving vehicle can easily lead to corrupting effects through non-ideal responses of accelerometers. For example, the principle of the commercial airborne gravity gradiometer is based on measuring the differences between matched pairs of rotating accelerometers. In such a gradiometer, second-order coefficients of a few μg/g 2