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Metric name

Diagnostic plots

Objectives

1

Production History Map

Background = STOIIP & Structure

Bubbles = q_o, q_g , q_w, q_inj

Number = VRR, P_e

Production Distribution Overview

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}

Instantaneous Voidage Replacement Ratio

LaTeX Math Block

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

2

Recovery Map

Background = STOIIP & Structure

Bubbles = Q_o, Q_g , Q_w, Q_inj

Number = VRR, P_e

Recovery Distribution Overview

Recovery Factor

LaTeX Math Block

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1

alignment

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

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

LaTeX Math Block

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{\rm Y_w} = \frac{q_w}{q_{lis}}

LaTeX Math Block

anchor

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alignment

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

LaTeX Math Block

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q_{liq} = q_o + q_w

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 Forecast5Recovery 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 decline6Watercut Diagnostic

Left Axis = Y_w, Y_wm

Hor Axis = q_liq

Check for water balance and thief water production LaTeX Math Block

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{\rm Y_w} = \frac{1}{1 + \frac{K_{ro}}{K_{rw}} \cdot \frac{\mu_w}{\mu_o} \cdot \frac{B_w}{B_o}}7GOR Diagnostic

Left Axis = GOR, GOR_gm

Hor Axis =q_o

Check for gas balance and thief gas production8

Injection Efficiency Diagnostics

Left Axis = PIR , PIR_m

Hor Axis = Y_w

Evaluate WI efficiency

LaTeX Math Block

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{\rm PIR} = \frac{Q_o}{Q_i}

LaTeX Math Blockanchor1alignmentleft

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

9Well Performance Analysis

Left Axis = P_{wf_IPR} , P_{wf_VLP}

Hor Axis = q_o

Check for the optimal production/injection target LaTeX Math Block

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P_{wf} = P_e - \frac{1}{J_{PI}} q_o10

Productivity Index Diagnostic

Left Axis = J_PI, J_PIm

Hor Axis = dP = P_wf - P_e

Check for PI dynamics LaTeX Math Blockanchor1alignmentleft

{\rm J_{PI}} = \frac{Q}{P_e - P_{wf}} {\quad \Rightarrow \quad} P_{wf}=P_e - \frac{1}{PI}Q

LaTeX Math Block

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{\rm J_{PIm} } = \frac{q_o}{P_e - P_{wf}}

Below is the list of the production properties involved on 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}

VRR_inst

Instantaneous Voidage Replacement Ratio

LaTeX Math Block

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{\rm VRR_{inst}} = \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

LaTeX Math Block

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{\rm Y_w} = \frac{q_w}{q_{lis}}

GOR

Gas-Oil Ratio

LaTeX Math Block

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

q_liq

Liquid rate

LaTeX Math Block

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q_{liq} = q_o + q_w

Y_wm

Watercut 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}}

PIR

Production Injection Ratio

LaTeX Math Block

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{\rm PIR} = \frac{Q_o}{Q_i}

PIR_m

Production Injection Ratio Model

LaTeX Math Block

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

JPIo

Bottom-hole pressure

J_PIo

Oil Productivity Index

LaTeX Math Block

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P_{wf} = P_e - \frac{1}{J_{PIo}} q_o

Productivity Index Diagnostic

Left Axis =

J_PI

, J_PImHor Axis = dP = P_wf - P_e

Total Productivity Index

LaTeX Math Block

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{\rm J_{PI}} = \frac{Q}{P_e - P_{wf}} {\quad \Rightarrow \quad} P_{wf}=P_e - \frac{1}{PI}Q

J_PIm

Total Productivity Index Model

LaTeX Math Block

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{\rm J_{PIm} } = \frac{q_o}{P_e - P_{wf}}

Expand

title	PIR equation deduction

LaTeX Math Block

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Y_w=\frac{q_q}{q_w + q_o} \rightarrow \frac{q_o}{q_w} = \frac{1-Y_w}{Y_w}

LaTeX Math Block

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PIR=\frac{q_o}{q_i}

LaTeX Math Block

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PIR = \frac{q_o}{q_i}={ \frac{1}{VRR} }*{ \frac{1-\gamma}{ \gamma +  [ \frac{B_o}{B_w} - \frac{B_g}{B_w}(GOR - R_s) ] } }

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