• 应用地球物理学Ⅰ •

### 有效介质对称导电理论在复杂泥质砂岩中应用基础研究

1. 1. 东北石油大学地球科学学院, 大庆 163318;
2. 非常规油气成藏与开发省部共建国家重点实验室培育基地, 大庆 163318
• 收稿日期:2016-01-09 修回日期:2016-05-30 出版日期:2016-08-20 发布日期:2016-08-20
• 通讯作者: 宋延杰，男，1963年生，黑龙江五常人，博士生导师，教授，主要从事测井方法与资料解释研究.(E-mail:syj1963@263.net) E-mail:syj1963@263.net
• 作者简介:唐晓敏，女，1981年生，黑龙江齐齐哈尔人，博士研究生，讲师，主要从事测井方法与资料解释研究.(E-mail:txmdqpi@163.com)
• 基金资助:

国家自然科学基金项目（41274110）资助.

### Basic research on application of symmetrical effective medium conduction theory in complex shaly sands

TANG Xiao-min1,2, SONG Yan-jie1,2, LIU Yue1, WANG Chao1, YU Bao1,2, LI Peng-ju1,2, ZHANG Qing-guo1,2

1. 1. College of Geo-science, Northeast Petroleum University, Heilongjiang Daqing 163318, China;
2. Accumulation and Development of Unconventional Oil and Gas, State Key Laboratory Cultivation Base Jointly-constructed by Heilongjiang Province and the Ministry of Science and Technology, Heilongjiang Daqing 163318, China
• Received:2016-01-09 Revised:2016-05-30 Online:2016-08-20 Published:2016-08-20

Abstract:

Evaluation of saturation in complex shaly sand reservoirs is a difficult problem in logging interpretation. Compared with the conduction models derived with parallel conductance theory and Archie formula, symmetrical effective medium conduction theory can be extended to describe the conductivity law of shale-rich and calcite-rich sand reservoirs with more complex pore structures well, and will have a good application prospect. Even so, basic research on application of symmetrical effective medium conduction theory in complex shaly sands is still need to be made. Firstly, symmetrical effective medium conduction model for clean sands is derived with symmetrical effective medium conduction theory, and analyzed as parameters vary theoretically, and validated with experimental data. It shows that symmetrical effective medium conduction model can describe the conductivity law of clean sands better than Archie equation, and not only explains both Archie and non-Archie behaviors, but also complies with meaningful physical bounds, that is, as porosity is 100%, formation factor is equal to 1 and as water saturation is 100%, resistivity index is equal to 1. Secondly, the symmetrical effective medium conduction model for dispersed shaly sands is given with symmetrical effective medium conduction theory. Theoretical analysis shows the model has the advantage over resistivity models and electric double-layer models, that is, it can describe the curved and linear relations between the conductivity of water saturated dispersed shaly sand and that of formation water without empirical fitting, and also the influence of clay content and clay conductivity on the conductivity law of sands calculated from the model is consistent with the common theoretical knowledge about clay, and so the model can describe the conductivity law of dispersed shaly sand better. Thirdly, three conduction equations for a two-component mixture are derived with symmetrical effective medium conduction theory, parallel conductance theory and series conduction theory respectively. Theoretical comparison shows that symmetrical effective medium conduction theory is neither equivalent to parallel conductance theory nor to series conduction theory, that is, as the conductivity law of a two-component mixture follows parallel conduction theory or series conduction theory, its conductivity law can't be described by symmetrical effective medium conduction theory. Symmetrical effective medium conduction theory can describe the conductivity law of sands with three continuous components: sand grain, water and clay. In it, geometric parameters such as percolation exponents and percolation rates are introduced to describe the effect of the connectivity, the surface roughness, shape and wettability of each component on the conductivity law of sands. Therefore, symmetrical effective medium conduction theory has a wide applicability and can be extended to describe the conductivity law of shale-rich and calcite-rich sand reservoirs with more complex pore structures.