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Model Input/Output

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• Input:   N^↑ , Pwf,  q_W^↓,  Q_W^↓, Q_O^↑ , Q_G^↑ , Q_W^↑
  
  
• Output:  q_O , q_G , q_W , P

Model Parameters

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Model Parameters:

• M = {  V_O , y_W , x_W , x_G , y_W ,   x_J , J_W0 }  – totally7 constants 

Restrictions:

• all constants are positive

Model fitting

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Source data corrections:

• one time-array P_wf(t)

Restrictions:

• 0 < P_{wf, min} < P_wf(t) < P_{wf, max}

Goal function:

• E[M] =  w_O ‧ Σ δ[q_O] +  w_W ‧  Σ δ[q_W] +  w_G ‧ Σ δ[q_G] + w_P ‧ Σ δ[P] +  w_f ‧ Σ δ[P_wf]    →  min
  
  

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A*(t) – historical value (if any)

Weights: 

• w_O + w_W + w_G + w_P + w_f = 1  (although it is not necessary)
  
  

Default settings:  w_O = 0.5 ,  w_W  = 0.1,  w_G = 0.1 , w_P = 0.2 ,  w_f = 0.1

Model function

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q_O^↑ = q_O1^↑ ‧ N^↑  |   q_O1^↑= J_O ‧ ( P - P_wf )

q_W^↑ = q_W1^↑ ‧ N^↑  |   q_W1^↑ = J_W(t) ‧ ( P - P_wf )

q_G^↑ = J_G ‧ N^↑  |   q_G1^↑= J_G ‧ ( P - P_wf ) 

P = P_i +   ( y_W ‧  Bw ‧ ΣQ_W^↓ + Bo ‧ ΣQ_O^↑ + x_W ‧  Bw ‧ ΣQ_W^↑ + x_G ‧  Bg ‧ ΣQ_G^↑  )‧ P_i ‧ x_P /V_O 

d = DFO = ΣQ_O^↑ / V_O

J_O = kro(d) ‧ x_J

J_W = J_W0 + krw(d) ‧ x_J

J_G = R_s ‧ J_O