INTRODUCTION

Static and producing bottom hole pressures are important parameters for investigating the inflow and vertical lift performances of an oil well. There are different methods which can be used for determining bottom hole pressures of electric submersible pumped (ESP) wells:

1) Conventional pressure bomb: used if the ESP completion is equipped with Y-tool (by-pass system), usually the Y-tool is not used due to it's required large casing (not less than 9 5/8"), and the Y-tool plug can cause leakage and/or stuck. Generally, this method requires the following steps:

a. Switch-off the ESP,

b. Retrieve the plug of the Y-tool,

c. Install the pressure bomb at the bottom hole of the well,

d. Install the plug of the Y-tool above the pressure bomb,

e. Re-run the ESP and operate it for enough time,

f. Switch-off the ESP,

g. Retrieve the plug of the Y-tool,

h. Retrieve the pressure bomb,

i. Install the plug of the Y-tool, and

j. Re-run the ESP for operating the well.

It is clear enough, at this point, that the previously described method of BHFP measurement takes more time and it is economically infeasible (loss in oil production due to shut-in times). In addition, many expected problems may occur due to many wire-line jobs (six runs).

2) Pressure sensors: which may be installed with the down-hole pump assembly so that accurate pressure readings may be obtained whenever required, but the cost would be high if they were used in every pumped well in a field or area.

3) Acoustic well sounding technique: which records fluid level in the annulus, the bottom hole pressures are usually determined by this method. But this method can not be used if the annulus is to be packed off (a packer used).

It is clear enough that all the previously described methods of BHFP measurement require a device. Then, require added money.

Gibbs and Nolen3 and Podio et al4 introduced a well Analyzer's computer and A/D converter, that can be used in conjunction with an acoustic gas gun and microphone. The gas gun generates an acoustic pulse in the well-bore and the microphone converts the reflected acoustic pressure pulses to electrical signals, which are digitized by the analog to digital A/D converter and stored in the computer. The computer displays these signals and processes the data as introduced by software to automatically determine fluid level depth. To calculate the producing bottom-hole pressure, the casing pressure is measured at the time of fluid level determination. When liquid is present above the formation and gas is flowing upward in the casing annulus, the casing vent valve is closed and sequential measurements of casing-head pressure are made for approximately 10-15 minutes so that an accurate casing pressure build-up rate can be obtained. The program uses this rate and the annulus void volume to calculate the casing annulus gas flow rate. This allows determination of the gaseous liquid column gradient from empirical correlations. It is noted that the tubing joints should have the same length because the depth to the fluid level is computed by estimating the total number of collars from the surface to the fluid level.

Spath et al5 described a technique to exploit the measurements made below ESP installations to determine well and reservoir properties. Well testing using pressure gauges below ESP’s is not new; the key advantage of the technique described here is that the well and reservoir properties may be obtained more accurately with higher resolution and without shutting the well in. In addition, the properties may be continuously determined for purposes of real-time production management. The technique is based on changing the flow rate by using a variable speed device (VSD), which changes the frequency (Hz) of the power supplied to the ESP motor, the production rate of the well is perturbed about a nominal flow rate. The resulting variation in bottom-hole flowing pressure is measured and modeled using the appropriate theoretical reservoir response (type curves) and nonlinear regression. Once the reservoir model is obtained, the well and reservoir parameters are computed from the regression analysis; variation in the properties (e.g., skin, reservoir pressure or distance to fluid interface) can be continuously monitored. Knowledge of the well and reservoir properties, and their variation over time, from the described technique, allows operators to optimize production rates and recovery while minimizing capital investments and operating expenses.

El-noby16 discussed and evaluated the different practices and applications in concern of testing the naturally non-flowing wells. He recommend some appropriate methods to be used for monitoring and optimizing the well production performance. Also, new correlations have been proposed to identify the completion factors for each reservoir based on the actual productivity index measurements for better planning and forecast estimations.

The basic objective of this study is to develop a method capable of calculating the pump intake pressure (PIP), the bottom hole flowing pressure (BHFP), the dynamic fluid level (DFL) & net liquid above pump (NLAP) for ESP wells using production and completion data only.

PUMP PERFORMANCE CURVES

The performance curves of a submersible electrical pump (Figure 1) represent the variation of head, horsepower, and efficiency with capacity. Capacity refers to the volume of the produced fluid rate, which may include free and/or dissolved gas. These curves are for a fixed power cycle (normally 50 or 60 cycle) and can be changed with variable frequency controllers.

The head (in feet per stage) developed by a centrifugal pump is the same regardless of the type or specific gravity of the fluid pumped. But when converting this head to pressure, it must be multiplied by the gradient of the fluid in question. Therefore, the following can be stated7:

(pressure developed by pump) = (head per stage) × (gradient of fluid) ×

(number of stages) (1)

The total fluid rate (liquid plus gas) at any conditions of pressure and temperature is, then:

(2)

Where VF is formation volume’s factors.

When pumping gas with the liquid, the capacity and, consequently, the head per stage as well as the gradient vary as the pressure of the fluid is elevated from the intake value PIP to the discharge value Pdis. Thus, the above equation can be written as follows:

(3)

Note that parentheses are included to indicate that h and Gf are functions of the capacity V, which is given by Equation 2.

The gradient of the fluid at any pressure and temperature is given by:

(4)

but,

(5)

where W is the weight of the capacity V at any pressure and temperature, which is equal to the weight at standard conditions. Hence:

(6)

Substituting Equation 6 into Equation 4 gives:

(7)

ρfsc is the weight of 1 bbl of liquid plus pumped gas (per 1 bbl of liquid) at standard conditions, or:

(8)

Substituting Equation 7 into Equation 3 gives:

(9)

The total number of stages is obtained by integrating the above equation between the intake and the discharge pressures:

(10)

or:

(11)

For each pump, there is a capacity range within which the pump performs at or near its peak efficiency (see Figure 1). The volume range of the selected rate between the intake and the discharge pressures should remain within the efficiency range of the pump. This range, of course, can be changed by using a variable frequency controller.

HEAD PER STAGE

Calculating head per stage for submersible pumps is based on the head coefficients (as shown in Table 1) and the volume of the production rate as follows:

(12)

The production rate for submersible pumps is considered for two cases: pumping liquid only and pumping liquid & gas.

For liquid only:

(13)

For liquid and gas:

(14)

The head per stage which calculated from Equation 12 is based on fresh water. Then, the head per stage for viscous liquid need to the following:

Find equivalent water capacity (Qw) as follows:

(15)

Find the viscous head (h) as follows:

(16)

Where Cq & Ch are viscosity correction factors for capacity & head respectively, as shown in Table 2.

The head per stage (calculated from Equation 12) is based on 60 hertz motor frequency. Then, if the motor frequency is more or less than 60 hertz, the head per stage for this frequency need to the following:

Find equivalent capacity at 60 hertz (Q60) as follows:

(17)

Find the head @ motor frequency (hHZ) as follows:

(18)

TOTAL DYNAMIC HEAD

The total dynamic head developed by the pump is considered for two cases: pumping liquid only and pumping liquid & gas.

For liquid only, the head per stage is constant for all stages. Therefore, the total head given by:

(19)

For liquid and gas, the head per stage is changing from stage to stage. Therefore, the total head given by:

(20)

In case of pumping liquid and gas, the head per stage changes from stage to stage because the pressure changes from stage to stage, which may affect the production rate (volume capacity ) from stage to stage. The pressure at the last stage is equal to the discharge pressure of the pump:

(21)

Where the discharge pressure of the pump can be calculated from the two-phase flow correlations.

The pressure at the stage before the last stage is equal to the pressure at the last stage minus the pressure developed by the last stage, and so on:

(22)

(23)

Finally, the pressure at the first stage is equal to the pressure at the second stage minus the pressure developed by the second stage:

(24)

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