基于储层砂岩微观孔隙结构特征的弹性波频散响应分析

The influence of pore structure in reservoir sandstone on dispersion properties of elastic waves

储层砂岩微观孔隙结构特征不仅影响干燥岩石的弹性波传播速度,也决定了岩石介质中与流体流动相关的速度频散与衰减作用.依据储层砂岩微观结构特征及速度随有效压力变化的非线性特征,将其孔隙体系理想化为不同形状的硬孔隙(纵横比α>0.01)与软孔隙(纵横比α<0.01)的组合(双孔隙结构).基于孔弹性理论,给出软孔隙最小初始纵横比值(一定压力下所有未闭合软孔隙在零压力时的纵横比最小值)的解析表达式,并在此基础上利用岩石速度-压力实验观测结果给出求取介质中两类孔隙纵横比及其含量分布特征的方法.通过逐步迭代加入软孔隙的方法对基于特征纵横比的"喷射流"(squirt fluid)模型进行了扩展,以考虑复杂孔隙分布特征对岩石喷射流作用的影响及其可能引起的速度频散特征.相较于典型的喷射流作用速度频散模式,对于岩石中软孔隙纵横比及其对应含量在较宽的范围呈谱分布的一般情况,其速度频散曲线不存在明显的低频段和中间频段,速度随频率的增大呈递增趋势直至高频极限.这说明即使在地震频段,微观尺度下的喷射流作用仍起一定作用,同样会造成流体饱和岩石介质的地震速度与Gassmann方程预测结果有不可忽略的差异.本文是对现有喷射流模型的重要补充,也为利用实验数据建立不同频段间岩石弹性波传播速度的可能联系提供了理论依据.

The pore structure of reservoir sandstone can significantly influence its elastic properties（e.g.elastic wave velocities）,and also determine fluid-flow related wave dispersion and attenuation.In the common velocity dispersion models,only the compliant pore or crack with a fixed aspect ratio and concentration has been taken into account,while the fixed aspect ratio is considered as the＂average＂value of the rock,which is not completely realistic in reservoir rock.Because rockusually contains compliant pore（crack）showing a distribution of aspect ratios.This study presents a procedure to determine the pore aspect distribution of compliant pore（crack）from the pressure dependence of velocities.Based on the pore aspect distribution of compliant pore,a new method is suggested to extend the existing squirt flow model to consider the complex pore structure,especially when the aspect ratio has a relatively wide distribution.Based on micro-structure of a reservoir sandstone and the non-linear feature of velocities as a function of effective pressure,the pore system of the sandstone can be ideally classified into two groups,i.e.stiff pores with an aspect ratio larger than 0.01 and soft pores with an aspect ratio smaller than 0.01.In light of the poroelasticity theory,an analytic expression for the minimal initial aspect ratio is deduced under the assumption that the shape of soft pores is spheroidal.With this equation,a method to invert the distribution of the aspect ratio and corresponding pore volumes is presented by using the measured ultrasonic velocities as a function of pressure.Using an iterative procedure to add soft pore with different aspect ratios into the rock frame,the existing squirt fluid model of Gurevich is extended to consider complex pore structure of reservoir sandstones,especially when the aspect ratio has a relatively wide distribution.With the pore aspect ratio distribution,the extended Gurevich′s squirt-flow model is used to compute the wave velocities and attenuation as functions of frequency as well as pressure.When considering aspect ratio distribution of crack pore in the reservoir rock,the overall dispersion curve shows rapid velocity increase around a relatively wide squirt-flow relaxation frequency range of 1～104 Hz,which covers the typical seismic and sonic logging frequencies,indicating the mechanism of a continuous relaxation spectrum of the complex pore system.Compared with typical velocity dispersion curves based on a single aspect ratio squirt fluid model,the dispersion curves of the sandstone with a relatively wide distribution of aspect ratios do not show the lowfrequency and middle-frequency range.This implies that for the rock samples at low pressure,it is not always profitable to employ Gassmann′s equation alone to predict the water-saturated velocities at typical seismic exploration frequencies. With the increasing pressure,velocity dispersion of the Gurevich′s squirt-flow model and the extended Gurevich′s squirt-flow model based on the aspect ratio distribution will decrease.To illustrate the validation of the extended Gurevich′s squirt-flow model,we compare predictions of our squirt model with laboratory measurement of two water-saturated sandstones at ultrasonic frequency of 700 kHz.We observe that the new model based on the pore structure is more accurate in predicting the pressure dependence of compression and shear velocities for the water-saturated sample than the Gassmann′s equation and Gurevich′s squirt-flow model.Our extended Gurevich′s squirt-flow model is consistent with Gassmann′s equation at low-frequency limit,and also with the MavkJizba model at high-frequency.Through this study,we suggest that the squirt flow may be still important even in the seismic frequency band,and can cause apparent velocity deviation from the predictions based on Gassmann′s equation.Thus,our work can be considered as an important extension of the existing squirt fluid models.