Q913 re1 w4 lec 14

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Reservoir Engineering 1 Course ( 1 st Ed.)

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Transcript of Q913 re1 w4 lec 14

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1. Productivity Index (PI)

2. Inflow Performance Relationship (IPR)

3. Generating IPRA. Vogel’s Method

B. Vogel’s Method (Undersaturated Reservoirs)

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1. Future IPR Approximation

2. Generating IPR for Oil WellsA. Wiggins’ Method

B. Standing’s Method

C. Fetkovich’s Method

3. Horizontal Oil Well Performance

4. Horizontal Well Productivity

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IPR Prediction

Quite often it is necessary to predict the well’s 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 Vogel’s method to predict future IPRs.

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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

Vogel’s equation to predict the future inflow performance relationships at (p–r)f.

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IPR Prediction: 1st Approximation Method (Cont.)Step 1. Calculate (Qomax)f at (p–r)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 (p–r)f, generate the IPR by:

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

(Qomax)f at (p–r)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 Vogel’s and are expressed as:

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Vogel’s vs. Wiggins’ IPR Curves

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Standing’s Method

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

He noted that Vogel’s equation can be rearranged as:

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

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Standing’s Zero-Drawdown Productivity IndexStanding then defined the present (current) zero

drawdown productivity index as:

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

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

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Standing’s 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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Standing’s 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 Standing’s Method

Standing’s 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.

Step 2. Calculate J* at the present condition, i.e., J*p.

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Summary of Standing’s Method (Cont.)Step 3. Using fluid property, saturation, and relative

permeability data, calculate both (kro/μoBo)p and (kro/μoBo)f.

Step 4. Calculate J*f by using below Equation. Use the other equation if the oil relative permeability data are not available.

Step 5. Generate the future IPR by applying below equation.

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Disadvantages of Standing’s MethodologyIt should be noted that one of the main

disadvantages of Standing’s methodology is that:It requires reliable permeability information;

In addition, it also requires material balance calculations to predict oil saturations at future average reservoir pressures.

It should be pointed out Fetkovich’s method has the advantage over Standing’s methodology In that, it does not require the tedious material balance

calculations to predict oil saturations at future average reservoir pressures.

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Fetkovich’s Method

Muskat and Evinger (1942) attempted to account for the observed nonlinear flow behavior (i.e., IPR) of wells by calculating a theoretical productivity index from the

pseudosteady-state flow equation.

They expressed Darcy’s equation as:

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Pressure Function Concept

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Fetkovich’s Method: 1st Case

In the application of the straight-line pressure function, three cases must be considered:Case 1: p–r and pwf > pb

Where Bo and μo are evaluated at (p–r+ pwf)/2.

Case 2: p–r and pwf < pb

Case 3: p–r > pb and pwf < pb

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Fetkovich’s Method: 2nd Case, Present IPR

The term (J/2pb) is commonly referred to as the performance coefficient C, or:

To account for the possibility of non-Darcy flow (turbulent flow) in oil wells, Fetkovich introduced the exponent n to yield:

The value of n ranges from 1.000 for a complete laminar flow to 0.5 for highly turbulent flow.

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Fetkovich’s Method: 2nd Case, Calculation of C and NThere are two unknowns in the Equation:

The performance coefficient C and the exponent n. At least two tests are required to evaluate these two

parameters:

A plot of p–2r− p2wf versus Qo on log-log scales will result in a straight line having a slope of 1/n and an intercept of C at p–2r− p2wf = 1.

The value of C can also be calculated using any point on the linear plot once n has been determined to give:

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Fetkovich’s Method: 2nd Case, Future IPRTo construct the future IPR when the average

reservoir pressure declines to (p–r)f, Fetkovich assumes that the performance coefficient C is

a linear function of the average reservoir pressure and, Therefore, the value of C can be adjusted as:

Fetkovich assumes that the value of the exponent n would not change as the reservoir pressure declines.

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Fetkovich’s Method: Comparison between Current and Future IPRs

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Fetkovich’s Method: 3rd Case

Case 3: p–r > pb and pwf < pb

μo and Bo are evaluated at the bubble-point pressure pb.

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Advantages of Horizontal Oil Well

Since 1980, horizontal wells began capturing an ever-increasing share of hydrocarbon production.

Horizontal wells offer the following advantages over those of vertical wells:Large volume of the reservoir can be drained by each

horizontal well.

Higher productions from thin pay zones.

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Advantages of Horizontal Oil Well (Cont.)

Horizontal wells minimize water and gas zoning problems.

In high permeability reservoirs, where near-wellbore gas velocities are high in vertical wells, horizontal wells can be used to reduce near-wellbore velocities and turbulence.

In secondary and enhanced oil recovery applications, long horizontal injection wells provide higher injectivity rates.

The length of the horizontal well can provide contact with multiple fractures and greatly improve productivity.

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Horizontal Oil Well vs. Vertical Oil Well

The actual production mechanism and reservoir flow regimes around the horizontal well are considered more complicated than those for the vertical well, especially if the horizontal section of the well is of a considerable length. Some combination of both linear and radial flow actually

exists, and the well may behave in a manner similar to that of a well that has been extensively fractured.

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IPRs for Horizontal Wells

Several authors reported that the shape of measured IPRs for horizontal wells is similar to those predicted by the Vogel or Fetkovich methods. The authors pointed out that the productivity gain from

drilling 1,500-foot (460m) long horizontal wells is two to four times that of vertical wells.

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Horizontal Well Illustration

Figure shows the drainage area of a horizontal well of length L in a reservoir with a pay zone thickness of h.

Each end of the horizontal well would drain a half-circular area of radius b, with a rectangular drainage shape of the horizontal well.

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Horizontal Well Drainage Area

A horizontal well can be looked upon as a number of vertical wells drilling next to each other and completed in a limited pay zone thickness.

Assuming that each end of the horizontal well is represented by a vertical well that drains an area of a half circle with a radius of b, Joshi (1991) proposed the following two methods for calculating the drainage area of a horizontal well.

Joshi noted that the two methods give different values for the drainage area A and suggested assigning the average value for the drainage of the horizontal well.

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Joshi Method I

Joshi proposed that the drainage area is represented by two half circles of radius b (equivalent to a radius of a vertical well rev) at each end and a rectangle, of dimensions L(2b), in the center. The drainage area of the horizontal well is given then by:

WhereA = drainage area, acres

L = length of the horizontal well, ft

b = half minor axis of an ellipse, ft

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Joshi Method II

Joshi assumed that the horizontal well drainage area is an ellipse and given by:

Where a is the half major axis of an ellipse.

Most of the production rate equations require the value of the drainage radius of the horizontal well, which is given by:

Where reh = drainage radius of the horizontal well, ftA = drainage area of the horizontal well, acres

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IPR Calculations for Horizontal Wells

From a practical standpoint, inflow performance calculations for horizontal wells are presented here under the following two flowing conditions:Steady-state single-phase flow

Pseudosteady-state two-phase flow

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Horizontal Well Productivity under SS FlowThe steady-state analytical solution is the simplest

solution to various horizontal well problems.

The steady-state solution requires that the pressure at any point in the reservoir does not change with time.

The flow rate equation in a steady-state condition is represented by:

Where Qoh = horizontal well flow rate, STB/dayΔp = pressure drop from the drainage boundary to wellbore, psiJh = productivity index of the horizontal well, STB/day/psi

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Productivity Index of the Horizontal WellThe productivity index of the horizontal well Jh can

be always obtained by dividing the flow rate Qoh by the pressure drop Δp, or:

Several methods are designed to predict the productivity index from the fluid and reservoir properties. Some of these methods include:Borisov’s MethodThe Giger-Reiss-Jourdan MethodJoshi’s MethodThe Renard-Dupuy Method

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Horizontal Well Productivity under PSS Regime The complex flow regime existing around a

horizontal wellbore probably precludes using a method as simple as that of Vogel to construct the IPR of a horizontal well in solution gas drive reservoirs.

If at least two stabilized flow tests are available, however, the parameters J and n in the Fetkovich equation could be determined and used to construct the IPR of the horizontal well. In this case, the values of J and n would not only account

for effects of turbulence and gas saturation around the wellbore, but also for the effects of nonradial flow regime existing in the reservoir.

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1. Ahmed, T. (2006). Reservoir engineering handbook (Gulf Professional Publishing). Ch7

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1. Vertical Gas Well Performance

2. Pressure Application Regions

3. Turbulent Flow in Gas WellsA. Simplified Treatment Approach

B. Laminar-Inertial-Turbulent (LIT) Approach (Cases A. & B.)

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