复杂介质参数反演的小生境蚁群算法研究
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摘要
当今世界的资源紧缺,尤其是对油气资源的需求与日俱增,油气勘探的理论研究和实际应用受到全球各国研究者们的关注。特别的,我国的资源分布比较分散、隐蔽,增大了油气勘探的难度。因此,复杂介质参数反演问题在实际应用中显得越来越重要。对于实际地下介质来说,大多数的储层都是由流体和固体两部分组成,即双相介质,如砂岩储层和碳酸盐储层。单相介质理论过于理想化,与现实世界有一定的差距,双相介质理论对实际地层结构以及地层性质的描述更加准确。因而,双相介质理论被广泛的应用于地震工程、地球物理勘探和岩土动力学等地球物理科学研究中,人们的研究重心也越来越多的偏向于双相介质理论的研究。在进行油气储层勘探时,我们需要事先知道孔隙度、渗透率、饱和度等储层参数以预测地层结构,而这些参数的获得往往都要通过地球物理反演来得到。
本文在分析和总结了传统的几种反演方法的基础上,详细介绍了蚁群算法、双相介质中Biot模型和BISQ模型的基础理论和研究发展现状。考虑到储层参数的反演问题属于非线性多模态函数的极值问题,为了防止“早熟”,避免求取全局最优值时陷入局部最优,本文就小生境蚁群算法进行了改进,提出了基于适应值共享的小生境蚁群算法,我们首先将改进的小生境蚁群算法应用于多模态函数优化问题中,并将结果与小生境遗传算法进行了对比,模拟结果显示无论是局部寻优还是全局寻优,小生境蚁群算法都显示出较高的有效性和优越性。其次,我们利用该算法,基于Biot模型和非饱和孔隙介质BISQ模型,对孔隙度,渗透率等参数进行了反演计算,得到了较好的反演结果。
在基于Biot模型的参数反演中,根据双相介质一维波动方程瞬态位移响应的解析解和双相介质材料的真值求得精确的地表位移以及流体位移,作为反演的附加条件。然后,基于上述解析解,在预反演参数的反演区间上计算出相应的地表位移和流体位移,取目标函数为上述两类位移差的绝对值之和,这时使目标函数值达到最小的参数值即为我们要求的参数反演值。在基于BISQ模型的参数反演中,我们根据高维非饱和孔隙介质BISQ正演模型和各个参数的真值计算出横纵波的实际波速,再根据上述正演模型在预反演参数区间上求得横纵波波速的理论预测值,选取两种波速的差值的绝对值之和作为反演的目标函数,反演的结果即为目标函数达到最小时的参数值。
本文采用的小生境蚁群算法是第一次被应用于地球物理参数反演中,取得了较好的结果,反演的精度非常高。在Biot模型参数反演中,单参数反演的相对误差都在0.4%以内,双参数(孔隙度和渗透率)反演的误差可以达到7%左右,在BISQ模型反演中,单参数反演相对误差都可以保持在0.08%以下,双参数(孔隙度和饱和度)反演可以达到与单参数反演相同的精度,三参数(孔隙度、固体密度和流体密度)反演效果稍差一些,但相对误差也都保持在4%以内。在反演的过程中,我们发现反演的精度对算法中蚂蚁个体总数的要求并不高,只要很少个体就能达到很高的精度,说明了改进的小生境蚁群算法在复杂介质参数反演中的有效性和优越性。因此,本文的反演算法有望被广泛的应用于油气储集层的动态监测开发、静态描述以及地震理论研究和实际应用。
Because of the scarcity of resources in today’s world, especially the increasing demand for oil and gas resources, the theoretical study and practical application in oil and gas exploration have been the concern of researchers around the world. In particular, resource distribution in our country is more decentralized and more concealed, which increased the difficulty of oil and gas exploration. Therefore, parameters inversion problem in complex media plays more and more important role in the practical application. For the actual underground media, most of reservior are made of two parts including fluid and solid, namely two-phase media, such as standatone reserior and carbonate reservior. The single-phase medium theory which is too idealistic has a certain gap with the real world. The discription that two-phase medium theory made for actual stratum structure and stratum properties is more accurate. Thus, two-phase medium theory has been widely used in geophysical research such as earthquake engineering, geophysical exploration and soil dynamics. The research focus is also biased in favor of two-phase medium theory gradually. For carrying out exploration in oil and gas reserviors, we need to know the reservior parameters, such as porosity, permeability, saturation and so on, to predict the stratum structure. However, we have to adopt the geophysical inversion in order to obtain these parameters generally.
Based on the analysis and summary of several traditional inversion methods, this thesis introduces the basic theory and research status of ant colony algorithm, Biot model and BISQ model in two-phase medium in detail. Taking into account the reservior parameter inversion problem is extreme value problem of nonlinear milti-modal function. In order to prevent“preneture”and avoid a global optimal falling into a local optimal, we proposed the niche ant colony algorithm based on the fitness sharing by improving the niche ant algorithm. First, we use the improved niche ant colony algorithm in multi-modal function optimization problem, and we compare the results obtained by niche ant colony algorithm with the results found by niche genetic algorithm. It can be shown that the former has higher effectiveness and superiority in both local optimization and global optimization. Second, we perform the inversion of reservior parameters such as porosity and permeability by tne niche ant colony algorithm based on the Biot model and the unsaturated porous media BISQ model, and we get better inversion results.
In the parameter inversion based on the Biot model, according to the analytic solutions of transient displacement response of one dimensional wave equation in two-phase medium and the true value of the two-phase medium material, we can obtain accurate surface displacement and fluid displacement, which is the additional condition of inversion. Then, calculate the corresponding surface displacement and fluid displacement in the inversion intervals of pre-inversion parameters based on the analytic solution. The objective function is the sum of absolute value of the two types of displacement differences. The parameters value when the objective function attained the minimum are the inversion value of parameters we require. In the parameter inversion based on the BISQ model, we calculate the actual value of transverse and longitudinal waves according to the high-dimensional unsaturated porous media BISQ forward model and the true value of each parameter. Then, calculate the theoretical predicted velocity of transverse and longitudinal waves in the inversion intervals of pre-inversion parameters under the forward model. The objective function we selected is the sum of absolute value of the two kinds of velocity. The inversion results are just the parameters value when the objective function attained the minimum.
In this thesis, the niche ant colony algorithm adopted is applied to paraneters inversion for the fisrt time in geophysics, the results achieved is very well and the inversion accuracy is very high. In the parameter inversion based on the Biot model, the relative error of single parameter inversion are all less than 0.4 percent, and the relative error of two parameters (porosity and permeability) inversion can reach about 7 percent. In the parameter inversion based on the BISQ model, the relative error of single parameter inversion can be maintained at less than 0.08 percent, the relative error of two parameters (porosity and saturation) inversion can attain the same accuracy with single parameter inversion, and the inversion effect of three parameters (porosity, solid density and fluid density) inversion is a bit weaker, but the relative error can still maintain less than 4 percent. In the process of inversion, we found the demand for the number of the ants in the algorithm is not high, as long as very few individuals, the inversion results can achieve higher accuracy. It represented the effectiveness and the superiority of the improved niche ant colony algorithm applied to the parameter inversion in complex media. Therefore, the inversion algorithm we adopted in this thesis is expected to be widely used in oil and gas reservoir dynamic monitoring development, static description and the theoretical study and practical application of earthquake.
本文在分析和总结了传统的几种反演方法的基础上,详细介绍了蚁群算法、双相介质中Biot模型和BISQ模型的基础理论和研究发展现状。考虑到储层参数的反演问题属于非线性多模态函数的极值问题,为了防止“早熟”,避免求取全局最优值时陷入局部最优,本文就小生境蚁群算法进行了改进,提出了基于适应值共享的小生境蚁群算法,我们首先将改进的小生境蚁群算法应用于多模态函数优化问题中,并将结果与小生境遗传算法进行了对比,模拟结果显示无论是局部寻优还是全局寻优,小生境蚁群算法都显示出较高的有效性和优越性。其次,我们利用该算法,基于Biot模型和非饱和孔隙介质BISQ模型,对孔隙度,渗透率等参数进行了反演计算,得到了较好的反演结果。
在基于Biot模型的参数反演中,根据双相介质一维波动方程瞬态位移响应的解析解和双相介质材料的真值求得精确的地表位移以及流体位移,作为反演的附加条件。然后,基于上述解析解,在预反演参数的反演区间上计算出相应的地表位移和流体位移,取目标函数为上述两类位移差的绝对值之和,这时使目标函数值达到最小的参数值即为我们要求的参数反演值。在基于BISQ模型的参数反演中,我们根据高维非饱和孔隙介质BISQ正演模型和各个参数的真值计算出横纵波的实际波速,再根据上述正演模型在预反演参数区间上求得横纵波波速的理论预测值,选取两种波速的差值的绝对值之和作为反演的目标函数,反演的结果即为目标函数达到最小时的参数值。
本文采用的小生境蚁群算法是第一次被应用于地球物理参数反演中,取得了较好的结果,反演的精度非常高。在Biot模型参数反演中,单参数反演的相对误差都在0.4%以内,双参数(孔隙度和渗透率)反演的误差可以达到7%左右,在BISQ模型反演中,单参数反演相对误差都可以保持在0.08%以下,双参数(孔隙度和饱和度)反演可以达到与单参数反演相同的精度,三参数(孔隙度、固体密度和流体密度)反演效果稍差一些,但相对误差也都保持在4%以内。在反演的过程中,我们发现反演的精度对算法中蚂蚁个体总数的要求并不高,只要很少个体就能达到很高的精度,说明了改进的小生境蚁群算法在复杂介质参数反演中的有效性和优越性。因此,本文的反演算法有望被广泛的应用于油气储集层的动态监测开发、静态描述以及地震理论研究和实际应用。
Because of the scarcity of resources in today’s world, especially the increasing demand for oil and gas resources, the theoretical study and practical application in oil and gas exploration have been the concern of researchers around the world. In particular, resource distribution in our country is more decentralized and more concealed, which increased the difficulty of oil and gas exploration. Therefore, parameters inversion problem in complex media plays more and more important role in the practical application. For the actual underground media, most of reservior are made of two parts including fluid and solid, namely two-phase media, such as standatone reserior and carbonate reservior. The single-phase medium theory which is too idealistic has a certain gap with the real world. The discription that two-phase medium theory made for actual stratum structure and stratum properties is more accurate. Thus, two-phase medium theory has been widely used in geophysical research such as earthquake engineering, geophysical exploration and soil dynamics. The research focus is also biased in favor of two-phase medium theory gradually. For carrying out exploration in oil and gas reserviors, we need to know the reservior parameters, such as porosity, permeability, saturation and so on, to predict the stratum structure. However, we have to adopt the geophysical inversion in order to obtain these parameters generally.
Based on the analysis and summary of several traditional inversion methods, this thesis introduces the basic theory and research status of ant colony algorithm, Biot model and BISQ model in two-phase medium in detail. Taking into account the reservior parameter inversion problem is extreme value problem of nonlinear milti-modal function. In order to prevent“preneture”and avoid a global optimal falling into a local optimal, we proposed the niche ant colony algorithm based on the fitness sharing by improving the niche ant algorithm. First, we use the improved niche ant colony algorithm in multi-modal function optimization problem, and we compare the results obtained by niche ant colony algorithm with the results found by niche genetic algorithm. It can be shown that the former has higher effectiveness and superiority in both local optimization and global optimization. Second, we perform the inversion of reservior parameters such as porosity and permeability by tne niche ant colony algorithm based on the Biot model and the unsaturated porous media BISQ model, and we get better inversion results.
In the parameter inversion based on the Biot model, according to the analytic solutions of transient displacement response of one dimensional wave equation in two-phase medium and the true value of the two-phase medium material, we can obtain accurate surface displacement and fluid displacement, which is the additional condition of inversion. Then, calculate the corresponding surface displacement and fluid displacement in the inversion intervals of pre-inversion parameters based on the analytic solution. The objective function is the sum of absolute value of the two types of displacement differences. The parameters value when the objective function attained the minimum are the inversion value of parameters we require. In the parameter inversion based on the BISQ model, we calculate the actual value of transverse and longitudinal waves according to the high-dimensional unsaturated porous media BISQ forward model and the true value of each parameter. Then, calculate the theoretical predicted velocity of transverse and longitudinal waves in the inversion intervals of pre-inversion parameters under the forward model. The objective function we selected is the sum of absolute value of the two kinds of velocity. The inversion results are just the parameters value when the objective function attained the minimum.
In this thesis, the niche ant colony algorithm adopted is applied to paraneters inversion for the fisrt time in geophysics, the results achieved is very well and the inversion accuracy is very high. In the parameter inversion based on the Biot model, the relative error of single parameter inversion are all less than 0.4 percent, and the relative error of two parameters (porosity and permeability) inversion can reach about 7 percent. In the parameter inversion based on the BISQ model, the relative error of single parameter inversion can be maintained at less than 0.08 percent, the relative error of two parameters (porosity and saturation) inversion can attain the same accuracy with single parameter inversion, and the inversion effect of three parameters (porosity, solid density and fluid density) inversion is a bit weaker, but the relative error can still maintain less than 4 percent. In the process of inversion, we found the demand for the number of the ants in the algorithm is not high, as long as very few individuals, the inversion results can achieve higher accuracy. It represented the effectiveness and the superiority of the improved niche ant colony algorithm applied to the parameter inversion in complex media. Therefore, the inversion algorithm we adopted in this thesis is expected to be widely used in oil and gas reservoir dynamic monitoring development, static description and the theoretical study and practical application of earthquake.
引文
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