Отправлено: 08.07.13 02:48. Заголовок: Analysis and improvement of the equation of Hill and Milburn for electrical resistivity of shaly san

Analysis and improvement of the equation of Hill and Milburn for electrical resistivity of shaly sands
by Gotze Tenchov
"Abstract

Hill and Milburn equation (H&M) for the electrical conductivity of shaly sands is one of the first equations that involve electrochemical parameter. This is Cation Exchange Capacity (CEC) of shaly sands Qv. Advantages of this equation are: 1) It was tested on more than 300 cores covering different sedimentary rocks, and a wide range of concentration in equilibrating NaCl solution; 2) It is of non linear type and describes the resistivity of shaly sands in low NaCl concentration as well; 3) The term b correlates to the cation exchange capacity of shaly sands; 4) The term F0,01 correlates to porosity Φ by an Archie-Dakhnov- type equation. Disadavantages are: 1) Equation is of empirical type; 2) The term F0,01 is a formation resistivity factor referred to a hypothetical equilibrating solution with resistivity of 0,01ohm.m at 25oC. It cannot be measured directly in laboratory on a core sample or in a well; 3) CEC is obtained by destructive analyses of core samples. It can not be measured directly in a well.
In this paper H&M equation was tested on core data citied in References. There are composed 5 groups of samples. It was used regression analyses. F0,01 has a good correlation with porosity. The term b differs not very substantially from the linear equation proposed by Hill and Milburn. A polynomial regression has a better statistical coefficient than linear type. An explanation for this phenomenon is offer.
On the basis of the Dual Water Model (DWM) is involved the formation factor F0,1, that is close to the “true” formation factor and that can be measured on core sample in laboratory in equilibration solution of Rw=0,1ohm.m. The improved H&M equation was tested on the same core samples. It has the same or slightly better coefficient of correlation than original H&M equation. Using DWM is proposed the term Electrochemical Activity of shaly sands (A) that correlates with CEC and labeled as QvA. It correlates to Qv, and can be obtained by nondestructive measurement of electrical resistivity/conductivity on core samples. It is proposed the term “ideal shale” that has QvA=5,43gmol/l. The term b correlates to QvA linearly and with better coefficient of correlation than to Qv. It opens the possibility to obtain QvA by log data using the electrical conductivity/resistivity data in flushed and non invaded zones.
Key words: Shaly sands; Electrical conductivity; Electrochemical equation; Cation Exchange Capacity; Hill and Milburn equation; Dual Water Model.

http://academia.edu/3857656/Analysis_and_improvement_of_the_equation_of_Hill_and_Milburn_for_electrical_resistivity_of_shaly_sands