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The CRM is trained over historical records of production rates, injection rates and bottom-hole pressure variation.

The major assumptions in CRM model are:

• productivity index of producers stays constant in time
  
  
• drainage volume of producers-injectors system is finite and constant in time
  
  
• total formation-fluid compressibility stays constant in time
  

Application

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• Assess current production performance
  
  
  • current distribution of recovery against expectations
    
    
  • current status and trends of recovery against expectations
    
    
  • current status and trends of reservoir depletion against expectations
     
  • current status and trends of water flood efficiency against expectations
    
    
  • compare performance of different wells or different groups of wells 
    
    
• Identify and prioritize surveillance opportunities
  
  
• Identify and prioritize redevelopment opportunities

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\tau = \frac{\beta}{J} = \frac{c_t  V_\phi}{J}

where

Total formation compressibility is a linear sum of reservoir/fluid components:

c_t = c_r +  s_w c_w + s_o  c_w + s_g c_g

where

J = \frac{q_{\uparrow}(t)}{p_r(t) - p_{wf}(t)} = \rm const

p_r(t) = p_{wf}(t) + J^{-1} q_{\uparrow}(t)

V_\phi = V_{rocks} \phi = \rm const

c_t \equiv \frac{1}{V_{\phi}} \cdot \frac{dV_{\phi}}{dp} = \frac{1}{V_{\phi}} \cdot \frac{1}{p_i - p_r(t) } \cdot \Bigg[ \int_0^t q_{\uparrow}(\tau) d\tau - f \int_0^t q_{\downarrow}(\tau) d\tau  \Bigg] = \rm const

\int_0^t q_{\uparrow}(\tau) d\tau - f \int_0^t q_{\downarrow}(\tau) d\tau = c_t \, V_\phi \, [p_i - p_r(t)]

q_{\uparrow}(\tau) d\tau - f q_{\downarrow}(\tau) d\tau = - c_t \, V_\phi \, \frac{d p_r(t)}{d t}

q_{\uparrow}(\tau) d\tau - f q_{\downarrow}(\tau) d\tau = - c_t \, V_\phi \, \bigg[ \frac{d p_{wf}(t)}{d t} + J^{-1} \frac{d q_{\uparrow}}{d t} \bigg]

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