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Reservoir Engineering 1 Course (2nd Ed.)

1. SuperpositionA. Multiple Well

B. Multi Rate

C. Reservoir Boundary

2. Productivity Index (PI)

3. Inflow Performance Relationship (IPR)

1. Generating IPR for Oil WellsA. Vogels Method

B. Vogels Method (Undersaturated Reservoirs)a. Future IPR Approximation

C. Wiggins Method

D. Standings Method

E. Fetkovichs Method

Vogels Method

Vogel (1968) used a computer model to generate IPRs for several hypothetical saturated-oil reservoirs that are producing under a wide range of conditions.Vogel normalized the calculated IPRs and expressed the

relationships in a dimensionless form. He normalized the IPRs by introducing the following dimensionless parameters:

Where (Qo) max is the flow rate at zero wellbore pressure, i.e., AOF.

Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 5

Vogels IPR

Vogel plotted the dimensionless IPR curves for all the reservoir cases and arrived at the following relationship between the above dimensionless parameters:

Where Qo = oil rate at pwf

(Qo) max = maximum oil flow rate at zero wellbore pressure, i.e., AOF

pr = current average reservoir pressure, psig

pwf = wellbore pressure, psig

Notice that pwf and pr must be expressed in psig.

Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 6

Vogels Method for Comingle Production of Water and OilVogels method can be extended to account for

water production by replacing the dimensionless rate with QL/(QL) max where QL = Qo + Qw.This has proved to be valid for wells producing at water

cuts as high as 97%.

The method requires the following data:Current average reservoir pressure pr

Bubble-point pressure pb

Stabilized flow test data that include Qo at pwf

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Vogels Methodology Applications

Vogels methodology can be used to predict the IPR curve for the following two types of reservoirs:Saturated oil reservoirs pr pb

Undersaturated oil reservoirs pr > pb

Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 8

Vogels Method: Saturated Oil ReservoirsWhen the reservoir pressure equals the bubble-

point pressure, the oil reservoir is referred to as a saturated-oil reservoir.

The computational procedure of applying Vogels method in a saturated oil reservoir to generate the IPR curve for a well with a stabilized flow data point, i.e., a recorded Qo value at pwf, is summarized below:

Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 9

Vogels Method: Saturated Oil Reservoirs (Cont.)Step 1. Using the stabilized flow data, i.e., Qo and

pwf, calculate (Qo)max from:

Step 2. Construct the IPR curve by assuming various values for pwf and calculating the corresponding Qo from:

Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 10

Vogels Method: Undersaturated Oil ReservoirsBeggs (1991) pointed out that in applying Vogels

method for undersaturated reservoirs, there are two possible outcomes to the recorded stabilized flow test data that must be considered, as shown schematically in next slide:The recorded stabilized Pwf is greater than or equal to

the bubble-point pressure, i.e. pwf pb

The recorded stabilized pwf is less than the bubble-point pressure pwf < pb

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Stabilized flow test data

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Vogels Method: Undersaturated Oil Reservoirs (PwfPb)Beggs outlined the following procedure for

determining the IPR when the stabilized bottom-hole pressure is greater than or equal to the bubble point pressure:

Step 1. Using the stabilized test data point (Qo and pwf) calculate the productivity index J:

Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 14

Vogels Method: Undersaturated Oil Reservoirs (PwfPb) (Cont.)Step 2. Calculate the oil flow rate at the bubble-

point pressure:

Where Qob is the oil flow rate at pb

Step 3. Generate the IPR values below the bubble-point pressure by assuming different values of pwf < pb and calculating the corresponding oil flow rates by applying the following relationship:

Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 15

Vogels Method: Undersaturated Oil Reservoirs (PwfPb) (Cont.)The maximum oil flow rate (Qo max or AOF) occurs

when the bottom hole flowing pressure is zero, i.e. pwf = 0, which can be determined from the above expression as:

It should be pointed out that when pwf pb, the IPR is linear and is described by:

Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 16

- Vogels Method: Undersaturated Oil Reservoirs (Pwf
- Vogels Method: Undersaturated Oil Reservoirs (Pwf
IPR Prediction

Quite often it is necessary to predict the wells inflow performance for future times as the reservoir pressure declines.

Future well performance calculations require the development of a relationship that can be used to predict future maximum oil flow rates.

Several methods are designed to address the problem of how the IPR might shift as the reservoir pressure declines.

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IPR Prediction (Cont.)

Some of these prediction methods require the application of the material balance equation to generate future oil saturation data as a function of reservoir pressure. In the absence of such data, there are two simple

approximation methods that can be used in conjunction with Vogels method to predict future IPRs.

Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 21

IPR Prediction: 1st Approximation Method This method provides a rough approximation of the

future maximum oil flow rate (Qomax)f at the specified future average reservoir pressure (pr)f. This future maximum flow rate (Qomax) f can be used in

Vogels equation to predict the future inflow performance relationships at (pr)f.

Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 22

IPR Prediction: 1st Approximation Method (Cont.)Step 1. Calculate (Qomax)f at (pr)f from:

Where the subscript f and p represent future and present conditions, respectively.

Step 2. Using the new calculated value of (Qomax)f and (pr)f, generate the IPR by:

Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 23

IPR Prediction: 2nd Approximation Method A simple approximation for estimating future

(Qomax)f at (pr)f is proposed by Fetkovich (1973). The relationship has the following mathematical form:

Where the subscripts f and p represent future and present conditions, respectively.

The above equation is intended only to provide a rough estimation of future (Qo)max.

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Wiggins Method

Wiggins (1993) used four sets of relative permeability and fluid property data as the basic input for a computer model to develop equations to predict inflow performance.

The generated relationships are limited by the assumption that the reservoir initially exists at its bubble-point pressure.

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Wiggins Method (Cont.)

Wiggins proposed generalized correlations that are suitable for predicting the IPR during three-phase flow.

His proposed expressions are similar to that of Vogels and are expressed as:

Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 28

Vogels vs. Wiggins IPR Curves

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Standings Method

Standing (1970) essentially extended the application of Vogels to predict future inflow performance relationship of a well as a function of reservoir pressure.

He noted that Vogels equation can be rearranged as:

Standing introduced the productivity index J as defined by J=Qo/ ((pr)-pwf) into above Equation to yield:

Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 31

Standings Zero-Drawdown Productivity IndexStanding then defined the present (current) zero

drawdown productivity index as:

Where J*p is Standings zero-drawdown productivity index. The J*p is related to the productivity index J by:

J=Qo/ ((pr)-pwf) Equation permits the calculation of J*p from a measured value of J.

Fall 13 H. AlamiNia Reservoir Engineering 1 Course (2nd Ed.) 32

Standings Final Expression for IPR PredictionTo arrive at the final expression for predicting the

desired IPR expression, Standing combines Equations to eliminate (Qo)max to give:

Where the subscript f refers to future condition.

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Standings Drawdown Productivity Index (J*P)Standing suggested that J*f can be estimated from

the present value of J*p by the following expression:

Where the subscript p refers to the present condition.

If the relative permeability data are not available, J*f can be roughly estimated from:

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Summary of Standings Method

Standings methodology for predicting a future IPR is summarized in the following steps:

Step 1. Using the current time condition and the available flow test data, calculate (Qo)max from Equations below.