title: "ECS-研究成果-阅读笔记4"
Matrix density and Porosity
- Paper:Application Of Nuclear Spectroscopy Logs To The Derivation Of Formation Matrix Density
- PaperAuthors:Susan L. Herron ,Michael M. Herron (Schlumberger Doll Research)
- Document ID:SPWLA-2000-JJ *Source:SPWLA 41st Annual Logging Symposium, 4-7 June, Dallas, Texas
- Publication Date:2000
- Publisher:Society of Petrophysicists and Well-Log Analysts
- Language:English
- Copyright:2000. Society of Petrophysicists & Well Log Analysts
- ABSTRACT:
Formation matrix properties, such as matrix density, can be estimated from the elemental concentrations available from modern, openhole, nuclear spectroscopy logging techniques. Although this estimation is similar to that of mineral-based interpretation frequently practiced today, it can preempt the a priori selection of minerals by solving for matrix properties directly from the elements. This simple approachgreatly enhances the ability to perform wellsite interpretations in both simple and complex formations.The interpretation for the matrix density is derived from a comprehensive database containing hundreds of core samples analyzed for both mineralogy and chemistry. The chemical analysis includes not only the major elements, but also the minor and trace elements that significantly influence wireline log responses. These data are used to forward model the matrix which is then solved as a linear combination of four elements (silicon, calcium, iron, sulfur) that are measured by prompt neutron capture spectroscopy. Comparisons are shown between measured and derived matrix density along with statistical measures of goodness of fit. Although in many cases the errors could be reduced by local optimization, the overall agreement is quite good.Although matrix density is empirically derived, the rationale is straightforward. For example, in sandstone, matrix density is approximately equal to that of quartz and feldspar, and it increases as the concentration of calcium- and iron-bearing minerals increases. Therefore calcium and iron heavily influence matrix density. The feldspar minerals are less dense than quartz and are not well sensed by the elements Si, Ca, Fe, and S. Therefore, separate algorithms are presented for non-arkosic, sub-arkosic, and arkosic environments.
假设岩石模型为岩石骨架+孔隙两部分，那么利用元素、矿物就能干很多事，比如计算骨架密度，计算孔隙度。当然，实际上现在的岩石精细模型已经不在这样粗糙，至少可以进一步刻画为岩石骨架+有机质（干酪根）+孔隙（水+气）。这个骨架密度概念第一次接触，有必要记录一下，很重要，平常用到的密度应该是体积密度。
- 骨架密度：Matrix density
- 体积密度：Bulk density
有的地方好像把Bulk density也叫做块密度，把Matrix density叫住真密度？？
在这个粗糙的岩石模型的基础上，可以建立一个关于孔隙度的公式：
Denbulk × Vbulk = Denmatrix × Vmatrix +Denfluid × Vfluid
这个公式中：
Vbulk = VMatrix + V_fluid
而Vfluid也就是Vbulk × Porosity
即：Vbulk = （1 - Porosity） × Vbulk +Porosity × V_bulk
代入第一个公式变换后就得到了孔隙度的计算公式：
Porosity=（Denmatrix - Denbulk)/(Denmatrix -Denfluid)
其中流体密度，假设全是水，密度为1。
Element：Den=a+bSi+cFe+dCa+eS
即：密度与Si、Ca、Fe、S四种元素含量呈线性关系，尤其是Fe，呈现为一种极好的线性相关，通过Jinye1的ECS数据线性拟合，也证实Den与这四种元素相关，与其他几种元素相关性较弱，其中Fe是主控元素。Jinye用ECS回归出来的参数为：
- 2620+227Ca+1990Fe+4.9Si+1190S
Mineral：1/Denmatrix = Σ(Mi/Den_i)
其中：
M_i——第i种矿物的含量
Den_i——第i种矿物的密度
这里比较麻烦的是，很多矿物的密度是一个变化的范围，如何取值是个问题，同时，获取具体的粘土矿物种类很麻烦，很多时候获取的是粘土矿物总量，不同的粘土矿物的密度差异很多，需要借鉴岩心分析的数据来作为参考。
常见的矿物密度：
- 黄铁矿 5.01
- 磁铁矿 5.26
- 石英 2.65
- 斜长石 2.61-2.75
- 方解石 2.71
- 铁白云石 2.97
- 硬石膏 2.9-3.0
- 石 膏 2.3-2.37
- 重晶石 4.3
- 钙芒硝 2.75-2.85
- 浊沸石 2.25-2.36
- 粘土矿物
- 天青石 3.97-4
- 辉 石 3.2-3.4
- 菱镁矿 2.9-3.1
- 白云石 2.85
- 钾长石 2.54-2.57
比较而言，按理说矿物得到的密度应该更准确，而在Jinye1HF中应用发现，元素的结果貌似更让人信服？