随钻地层测试压力响应数学模型及物理实验考察

基于随钻地层测试基本原理和渗流理论，建立了圆柱坐标系下压力下降和压力恢复阶段的压力扩散微分方程，确定出随钻地层压力测试定解问题，通过对定解问题的边界进行齐次化处理，并采用有限差分方法建立了四维空间下的显格式差分方程，以解析方法和有限差分方法分析了点源单相单测试室均质球形渗流问题，两种方法计算误差小于2.00%，检验了有限差分方法的正确性.采用有限差分方法定量分析了不同渗透率（0.1×10-3μm2、1.0×10-3μm2和10.0×10-3μm2）地层下，表皮效应、储集效应、地层非均质性、抽吸速率、抽吸探头半径等因素对压力响应的影响，分析表明，这些因素对压力响应曲线的影响十分显著，主要表现在抽吸压降、压降速率、压力恢复速率、恢复时间等几个方面，而且不同渗透率地层的敏感程度差异比较大.建立了地层压力测试模拟实验平台，模拟了3种不同渗透率（108.81×10-3μm2、16.10×10-3μm2和4.79×10-3μm2）地层的压力抽吸测试，并采用有限差分方法对实验进行了数值模拟.结果表明，数值模拟与实测压力响应一致性非常好，二者绝对误差小于1.60 MPa，相对误差低于5.00%（最大误差4.92%），验证了有限差分数值方法的正确性和准确性.

Mathematical model and physical experimental research for pressure response of formation testing while drilling

Based on the fundamental principle of formation testing while drilling (FTWD) and filtration theory, we built the pressure diffusion differential equation between pressure decline and pressure buildup in the cylindrical coordinate, and determined the definite solutions problem of FTWD. After homogenizing the boundary of definite solutions problem, the finite difference approach was adopted to establish the explicit difference equation under four-dimensional space and the analytic and finite difference methods were used to analyze homogeneous and spherical filtration problem in the condition of point source, single phase, single testing room. The calculation error of the two methods is less than 2.00%, indicating the validity of the finite difference method. With finite difference approach the influences of following factors on the response of different permeability (0.1×10^-3μm², 1.0×10^-3μm² and 10.0×10^-3μm²) formation were quantitatively analyzed, including, skin effect, storage effect, formation heterogeneity, suction rate and suction probe radius. The analysis indicated that the impact of these factors on the pressure response curve is significant, which mainly manifested in the following respects, such as suction pressure drop, pressure drop rate, rate of pressure recovery, build-up time. And the sensitive degree of different permeability formation differs significantly. We established a formation pressure test simulation experiment platform to stimulate pressure suction testing in three different permeability (108.81×10^-3μm², 16.10×10^-3μm² and 4.79×10^-3μm²) formations and adopted finite difference approach to carry out numerical simulation for the experiment. The result shows that numerical simulation and the measured pressure response are consistent. The absolute error is less than 1.60MPa and the relative error less than 5.00% (maximum error is 4.92%). The correctness and accuracy of the finite difference numerical method were confirmed.