Patent ID: 11940590
Assignee: CHINA UNIVERSITY OF PETROLEUM (EAST CHINA)
Field: Measurement (Instruments)
Classification: CPC G  E  Y | IPC E  G

Claim 3:
4. The fast forward method for gamma-ray logging of highly-deviated and horizontal wells according to claim 2, wherein step S12 comprises the following processes:
under the condition of the straight well, in the case that the formation is considered to be in the shape of a parallel slab, a scintillator in the gamma-ray detector is considered to be in the shape of a point and coincides with the center of the detector, and the influence of a wellbore environment and the outer wall of the instrument is ignored, establishing a cylindrical coordinate system with the center of the gamma detector as the origin;
within the effective detection radius r0 of the gamma detector, considering a formation at a vertical distance of z from the center of the gamma detector along the well axis as an infinitely thin slab surface source perpendicular to the well axis;
dividing the surface source into several sector differentials ds with the well axis as the center, where the contribution of the sector differential ds to the gamma-ray flux at the center of the gamma detector is as follows:, d
   ⁢
   
    ϕ
    
     
      r
      0
     
     ⁢
     z
    
   
  
  =
  
   
    
     
      I
      0
     
     
      4
      ⁢
      
       π
       ⁡
       (
       
        
         r
         2
        
        +
        
         z
         2
        
       
       )
      
     
    
    ⁢
    
     e
     
      
       -
       μ
      
      ⁢
      
       
        (
        
         
          r
          2
         
         +
         
          z
          2
         
        
        )
       
      
     
    
    ⁢
    ds
   
   =
   
    
     
      I
      0
     
     
      4
      ⁢
      
       π
       ⁡
       (
       
        
         r
         2
        
        +
        
         z
         2
        
       
       )
      
     
    
    ⁢
    
     e
     
      
       -
       μ
      
      ⁢
      
       
        (
        
         
          r
          2
         
         +
         
          z
          2
         
        
        )
       
      
     
    
    ⁢
    rdrd
    ⁢
    φ
   
  
 

so in the effective detection space r0, the gamma-ray flux of the thin slab surface source of the formation at a distance of z from the center of the detector along the well axis to the detector is expressed as follows:, ϕ
   
    
     r
     0
    
    ⁢
    z
   
  
  =
  
   
    
     I
     0
    
    2
   
   ⁢
   
    
     ∫
     
      μ
      ⁢
      z
     
     
      μ
      ⁢
      
       r
       0
      
     
    
    
     
      
       e
       
        -
        t
       
      
      t
     
     ⁢
     d
     ⁢
     t
    
   
  
 

replacing a gamma-ray flux Φz of the thin slab surface source of the infinitely large formation (at a distance of z from the center of the gamma detector along the well axis) to the gamma detector in the infinitely large space with the above formula:, ϕ
   z
  
  =
  
   
    
     I
     0
    
    2
   
   ⁢
   
    
     ∫
     
       
      0
     
     
       
      
       π
       2
      
     
    
    
     
      e
      
       
        -
        μ
       
       ⁢
       z
       ⁢
       s
       ⁢
       e
       ⁢
       c
       ⁢
       θ
      
     
     ⁢
     tan
     ⁢
     θ
     ⁢
     d
     ⁢
     θ
    
   
  
 

under the condition of the straight well, enabling the contribution coefficients of the formations at different distances from the detector in the effective detection space to the gamma-ray flux of the detector to be equivalent to the contribution coefficients of the formations at different distances from the detector in an infinitely large integral space to the gamma-ray flux of the detector;
where,
I0 refers to the gamma source intensity density of the formation, unit: number of photons·cm−3;
ds refers to the sector differential in the thin slab surface source of the formation at a vertical distance of z from the center of the gamma detector along the well axis;
μ refers to the average linear attenuation coefficient of gamma-rays passing through the formation, unit: cm−1;
r refers to a distance between the sector differential in the formation and the well axis, and a value interval is, [
   
    0
    ,
    
     
      
       r
       0
       2
      
      -
      
       z
       2
      
     
    
   
   ]
  
  ;
 

 unit: cm;
θ is an included angle between a line of connecting a certain point on a circle with the well axis as the center and with a radius of r to the center O of the gamma detector and the well axis from the center of the gamma detector to the surface source of the infinitely thin slab formation at a distance of z from the center of the gamma detector along the well axis;
φ refers to an included angle between a certain point with a radius vector of r and an X axis in the cylindrical coordinate system, and dφ refer to a differential thereof.