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In case the bottomhole pressure data is not available it is considered constant over time.

Motivation

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Production rate in producing well depends on its productivity index 

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bodyJ
, current formation pressure 
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bodyp_e
 and current BHP 
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body--uriencoded--p_%7Bwf%7D
:

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q=J \cdot (p_e - p_{wf})

and as such depends on how formation pressure is maintained 

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bodyp_e = p_e(t)
 over time.

The reservoir pressure maintenance is performed by either aquifer or Fluid Injection.

One of the main purpose of injection wells is to maintain pressure in producers and correspondingly maintain production rates.

The ability of injection well to maintain the pressure in producer depend son cross-well connectivity which is a function of reservoir properties extending between the wells.


The ultimate purpose of CRM
 is to correlate  between the long-term (few months or longer) flowrate history and BHP history (recorded by PDG).



The CRM is trained over historical records of production rate, injection rates and bottomhole pressure variation.


The major assumptions in in CRM model are:

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Assumption 2 means that interference between producers is fairly constant in time despite the rate variations and their impact on the dynamic drainage volumes.


Goals

Objectives

Identify and prioritise production optimisation opportunitiesGenerate production and formation pressure forecasts based on the bottom-hole pressure and injection rates
Identify and prioritise redevelopment opportunitiesAssess productivity index of producing wells
Identify and prioritise surveillance candidatesAssess dynamic drainage volume around producing wells

Quantify connectivity between injectors and producers

Assess water flood efficiency against expectations and / or between wells or well groups



Advantages

Limitations

Fast-trackIt only models injector-producer system
Requires minimum input data (BHP and rates only)Requires eventful history of injection rates variations

Robust procedure (no manual setups)

Requires productivity index of producers to stay constant
Does not involve full-field 3D dynamic modelling and associated assumptionsRequires the drainage volumes of all producers stay the same throughout the modelling period

Only applicable for specific subset of PSS fluid flow regimes


Technology

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The CRM trains linear correlation between variation of production rates against variation of injection rates with account of bottom-hole pressure history records in producers.

See Capacitance-Resistivity Model @model


InputsOutputs
Production rate historyProductivity Index for the focus producer
Bottom-hole pressure historyDrainage volume by the focus produce producer
Injection rate historyShare of injection going towards the focus producer
PVT model



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CRM is a specific case of MDCV with the following unit-rate transient responses:


DTRCTR from offset producersCTR from offset injectors


UTR


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p_{1nn}(t) =J_n^{-1} \left( 1 - \frac{t}{\tau_n} \right)



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p_{1nm}(t) = 0



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p_{1nm}(t) =  \frac{f_{nm}}{J_n \tau_n} \cdot t



Pressure drop 


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\delta p_{1nn}(t) =  \frac{1}{J_n \tau_n} \cdot t



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\delta p_{1nm}(t) = 0



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\delta p_{1nm}(t) =  \frac{f_{nm}}{J_n \tau_n} \cdot t



Log Der


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p'_{1nn}(t) = \delta p_{1nn}(t) 



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p'_{1nm}(t) = 0



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p'_{1nm}(t) = \delta p_{1nm}(t)



See also CRM as MDCV @model for derivation.


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