Page History

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	Metric name	Diagnostic plots	Objectives
1	Production History Map	Background = Structure Bubbles = q_o, q_g , q_w, q_inj Number = CurVRR, P_e	Production Distribution Overview
2	Recovery Map	Background = STOIIP Bubbles = Q_o, Q_g , Q_w, Q_inj Number = CumVRR, P_e	Recovery Distribution Overview
3	Cross-section	Background = STOIIP & Structure Bubbles = VRR Number = P_e , P_em	Vertical Flow Proifle Overview
3	Production History Graphs	Left Axis = q_o, q_g , q_w, q_inj, Rigth Axis = Y_w, GOR, P_e , N_p, N_inj Hor Axis = Elapsed Time	Production History Overview
4	Decline Curve Analysis	Left Axis = q_o1, q_liq₁, q_inj1, Rigth Axis = Y_w, GOR, VRR, P_e Hor Axis = Elapsed Time	Production Forecast
5	Recovery Diagnostic	Left Axis = q_o1, q_liq₁, q_inj1 Rigth Axis =Y_w, GOR, VRR, P_e, P_em Hor Axis = RF	Estimate recovery efficiency and pressure decline
6	Watercut Diagnostic	Left Axis = Y_w, Y_wm Hor Axis = q_liq	Check for water balance and thief water production
7	GOR Diagnostic	Left Axis = GOR, GOR_gm Hor Axis =q_o	Check for gas balance and thief gas production
8	Injection Efficiency Diagnostics	Left Axis = PIR , PIR_m Hor Axis = Y_w	Evaluate WI efficiency
9	Well Performance Analysis	Left Axis = P_{wf_IPR} , P_{wf_VLP} Hor Axis = q_o	Check for the optimal production/injection target
10	Productivity Index Diagnostic	Left Axis = J_PI, J_PIm Hor Axis = dP = P_wf - P_e	Check for PI dynamics

Expand

title	Expand on PRIME mathematics

Below is the list of the production properties involved in the above metrics.

Property Abbrevy

Property Name

Formula

VRR_cum

Cumulative Voidage Replacement Ratio

LaTeX Math Block

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{\rm VRR_{cum}} = \frac{B_w \, Q_{WI}}{B_w \, Q_W + B_o \, Q_O + B_g Q_G - B_g R_s Q_O}

VRRcur

Current Voidage Replacement Ratio

(month over month)

LaTeX Math Block

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{\rm VRR_{cur}} = \frac{B_w \, q_{WI}}{B_w \, q_W + B_o \, q_O + B_g (q_G - R_s Q_O)}

RF

Recovery Factor

LaTeX Math Block

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{\rm RF} = \frac{Q_O}{V_{STOIIP}}

Y_w

Watercut (production)

LaTeX Math Block

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{\rm Y_w} = \frac{q_W}{q_{LIQ}}

Y_wm

Watercut (proxy-model)

LaTeX Math Block

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{\rm Y_{wm}} = \frac{1}{1 + \frac{K_{ro}}{K_{rw}} \cdot \frac{ \mu_w}{\mu_o}  \cdot \frac{B_w}{B_o} }

LaTeX Math Block

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s_w = \frac{Q_o \, B_o}{V_\phi}

GOR

Gas-Oil Ratio (production)

LaTeX Math Block

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{\rm GOR} = \frac{q_g}{q_o}

GOR_m

Gas-Oil Ratio (proxy-model)

LaTeX Math Block

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{\rm GOR_m} = R_s +  \frac{k_{rg}}{k_{ro}} 
\cdot \frac{\mu_o}{\mu_g} 
\cdot \frac{B_o }{B_g}

q_LIQ

Liquid rate

LaTeX Math Block

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q_{LIQ} = q_O + q_W

PIR

Production Injection Ratio (production)

LaTeX Math Block

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{\rm PIR} = \frac{Q_O}{Q_{WI}}

PIR_m

Production Injection Ratio (model)

LaTeX Math Block

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{\rm PIR_m} = { \frac{1}{VRR} } \cdot { \frac{1-Y_w}{ Y_w + (1-Y_w) \bigg[ \frac{B_o}{B_w} - \frac{B_g}{B_w}(GOR - R_s) \bigg] } }

J_O

Oil Productivity Index

LaTeX Math Block

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{\rm J_{O}} = \frac{q_O}{P_e - P_{wf}} {\quad \Rightarrow \quad} P_{wf} = P_e - \frac{1}{J_O} q_O

J_PI

Total Productivity Index (production)

LaTeX Math Block

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{\rm J_t} = \frac{q_t}{P_e - P_{wf}}

J_PIm

Total Productivity Index (model)

LaTeX Math Block

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{\rm J_{tm} } = \frac{2 \pi \sigma}{\ln \frac{r_e}{r_w} +0.5 + S}

_jPI

Total Specific Productivity Index

LaTeX Math Block

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{\rm j_t} = \frac{q_t}{h \cdot (P_e - P_{wf})}

_jPIm

Total Specific Productivity Index (model)

LaTeX Math Block

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{\rm j_{tm} } = \frac{2 \pi <k/\mu>}{\ln \frac{r_e}{r_w} +0.5 + S}

Expand

title	PIR equation deduction

LaTeX Math Block

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VRR = \frac{B_w \, q_{WI}}{B_w \, q_W + B_o \, q_O + B_g \, [ q_G - R_s \, q_O] } =  \frac{B_w \, q_{WI}}{B_w \, q_W + B_o \, q_O + B_g \, [ GOR - R_s] q_O } = \frac{B_w \, q_{WI}}{B_w \, q_W + [ B_o  + B_g \, ( GOR - R_s) ] \, q_O }

LaTeX Math Block

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VRR = \frac{q_{WI}}{q_W + \bigg[ \frac{B_o}{B_w}  + \frac{B_g}{B_w} \, ( GOR - R_s) \bigg] \, q_O }

LaTeX Math Block

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Y_w=\frac{q_W}{q_W + q_O} \rightarrow \frac{q_O}{q_W} = \frac{1-Y_w}{Y_w} \rightarrow q_W =  \frac{Y_w}{1-Y_w} \, q_O

LaTeX Math Block

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VRR =  \frac{q_{WI}}{q_O} \cdot \frac{1}{\frac{Y_w}{1-Y_w}  + \bigg[ \frac{B_o}{B_w}  + \frac{B_g}{B_w} \, ( GOR - R_s) \bigg] } =
\frac{q_{WI}}{q_O} \cdot \frac{1-Y_w}{Y_w  + (1-Y_w) \, \bigg[ \frac{B_o}{B_w}  + \frac{B_g}{B_w} \, ( GOR - R_s) \bigg] }

LaTeX Math Block

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PIR=\frac{q_W}{q_{WI}} = \frac{1}{VRR} \cdot \frac{1-Y_w}{Y_w  + (1-Y_w) \, \bigg[ \frac{B_o}{B_w}  + \frac{B_g}{B_w} \, ( GOR - R_s) \bigg] }

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