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The Capacitance-Resistance Model (CRM) is a set of mathematical models relating the production rate history to the bottomhole pressure and offset injection rate history with ability to account for the producers bottom-hole pressure variation.

In case the bottom-hole pressure data is not available it is considered constant over time.

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

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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CRM – Single-Tank Capacitance Resistance Model

The CRM model is trying

The simulation is based on the following equation:

q^{\uparrow}(t) =  f \, q^{\downarrow}(t)  - \tau \cdot \frac{ d q^{\uparrow}}{ dt }  - \beta \cdot \frac{d p_{wf}}{dt}

where

The target function is:

E[\tau, \beta, f] = \sum_k \big[ q^{\uparrow}(t_k) - \tilde q^{\uparrow}(t_k) \big]^2   \rightarrow \min 

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