## Gas Lift Operations Require Accurate Predictions of Downhole Annulus Pressure

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Downhole annulus pressure is required for any gas lift design. This paper presents several methods of determining annulus pressure at depth and helps determine which method is most appropriate for specific conditions. It also provides advice on the accuracy of a combination of different critical properties and compressibility correlations, offers an alternative design technique to account for changing annulus temperature during unloading, and provides guidelines for modeling changes in annulus pressure during unloading.

## Introduction

While many methods of computing gas pressure in a flowing environment are available, what is needed in the case of gas lift is the static annulus pressure at depth.

Historically, the method of using average temperature and pressure to compute compressibility factors and assuming linear well-temperature gradients made gas lift design relatively simple. The small errors were tolerable and within the normal design safety margins of operating systems with surface pressures of less than 1,500 psi.

When surface injection pressures exceed 1,500 psi, calculations become more important. Computers are now used to calculate downhole annulus pressure, and the designer must trust the number that appears on the computer screen. That trust may not be warranted, depending on the method of calculation. The small errors that creep into computer calculations increase linearly as surface injection pressure increases. Additionally, the choice of which correlation to use to model the critical properties of the gas and which compressibility factor correlation to use also affect the accuracy of the calculation.

As a gas lift well transitions from a geothermal to a flowing temperature profile during unloading and lifting, the annulus pressure at depth decreases despite surface injection pressure remaining unchanged. The change in annulus pressure is governed by the volume of gas present in the annulus. Reduction in gas volume decreases pressure.

Traditional design techniques ignore this reality and substitute a simplified analogy of valve performance that incurs errors and misconceptions about how the annulus pressure changes during unloading. A more-detailed discussion of these issues and proposed questions for program developers is presented in the complete paper.

## Annulus Pressure Calculation Methods

Methods of determining downhole annulus pressure include monographs, density equations used to full depth with average pressure and temperature, and density equations used in small depth increments with average temperature and pressure within the increment. An examination of one of these monographs is shown in **Fig. 1. **The choice of which method to use comes with limitations on the accuracy of the predicted pressure at depth.

**Monographs.** Monographs were the original method for calculating annulus pressure at depth. Various assumptions such as temperature, temperature gradient, depth, and gas gravity were incorporated into each monograph. When conditions did not match the assumptions inherent in the monograph, charts provided a means to correct the raw gradient. Today, computer programs offer more-accurate simulations of annulus pressure over a wide range of conditions but often at the expense of the designer’s opportunity to exercise judgment in assigning an annulus pressure gradient.

**Full-Depth Calculation With Density Equation. **When the integral form of the density equation is used to calculate pressure at full depth, the user is allowed to enter the well’s actual average temperature—an improvement over the monograph’s assumed average temperature. The average temperature and average compressibility (ATAC) method, as originally proposed, calculated the pressure drop over the entire depth of the well using this depth in a single calculation. Later work provided techniques for segmenting the wellbore to increase accuracy. With current computing power, ATAC achieves comparable results by using a smaller depth increment. When the full-depth calculation is compared with the incremented method for linear temperature profiles, the difference in annulus pressure prediction at 10,000 ft is less than ±5 psi for wellhead pressures of 1,200 psig and light gas gravities. However, the amount of error associated with the full-depth method, when the pressure is 2,000 psig and the gas gravity is 0.85, is 36 psi. This amount of error is considerable and will affect the design. Generally, the amount of error increases with pressure and gravity. In the complete paper, the authors emphasize the need for ample safety margins when using a full-depth method of annulus pressure calculation.

**Incremental Calculation With Density Equation. **The pressure at depth is sensitive to temperature directly as a result of the real gas law and the effect on gas density. Accounting for the actual temperature of the annulus during the different phases of gas lift will produce a more-accurate pressure at depth. Calculating the integral form of the density equation at 500-ft increments to full depth with average temperature and compressibility within the increment enables accurate determination of annulus pressure at geothermal, design, and flowing temperatures. This is the most-accurate downhole pressure prediction method because it allows a variety of temperature profiles to be mapped to the well. If a computer is being used to assist with the gas lift design, the incremental calculation method should be used and the program should allow nonlinear temperature profiles.

**Critical Constants and Z-Factor Correlations.** The calculation of annulus pressure is highly dependent on gas gravity and the resulting gas compressibility factor (Z-factor). The authors do not recommend the simple methods of calculating the Z-factor mentioned in gas lift literature because of a lack of reliability under varying conditions. Instead, they say, the most-accurate methods are derived from equations of state.

Because the calculation of gas Z-factor is based on the calculation of pseudoreduced pressure and temperature, pseudocritical pressure and temperature of the gas must be determined. The complete paper includes a detailed discussion and suggestions for ensuring accurate Z-factors.

## Specific Gravity of Injected Gas

The paper provides an example to show that the most-accurate computing method with the most-accurate Z-factor correlation and well-temperature profile can still lead to significant errors if the specific gravity of the gas used in the well is not what the designer thought. The issue of gas gravity, which can change through time as a result of operational changes in surface facilities, is important during both design and producing phases. These changes affect annulus pressure at depth. If a gas lift design is installed and operated with the expectation of a specific gravity and the specific gravity of the gas changes over time, the operating parameters also will change, and troubleshooting methods must account for it. Monthly analysis of sales-gas composition is a good way to obtain a periodic value of gas gravity. When production rate, well composition, or separator conditions change, specific gravity is affected. The importance of designing and troubleshooting with the most-accurate available specific gravity of the gas being injected cannot be understated. This is especially true at higher injection pressures.

## Design Considerations

With the majority of gas lift designs now performed using computers, incremental annulus pressure calculation at depth provides the most-robust and -accurate outcomes. The question of which pseudocritical properties correlation to use in combination with which Z‑factor correlation is left to the user’s discretion. This issue does not become significant until surface injection pressures exceed 1,500 psig. However, for higher-gravity gases, even low-pressure systems are affected by the choice of calculation method. When that occurs, the user must pay particular attention to the composition of the injected gas and ensure that the specific gravity of the gas regularly matches that used for the design.

Gas lift design safety margins for annulus pressure use a flowing temperature profile for the annulus pressure during the design phase. The valves’ bellows pressure continues to use the design temperature profile. This strategy predicts less annulus pressure at depth during design, which could cause valves to be spaced closer together. However, the benefit is that the actual annulus pressure during unloading and lifting will always be higher than the design annulus pressure, regardless of well temperature.

The current design technique for injection-pressure-operated gas lift valves advises that the annulus pressure used to calculate the bellows pressure be reduced by 20–40 psi for each lower unloading valve. This stair-stepping gas injection scenario allows the most efficient use of gas to lift fluids.

The current, experience-based design methodology is successful, but the authors claim that the theories and flow-performance models that justify the experience are incorrect. This paper presents an approach that may explain the annulus pressure changes using physical laws that can be applied when experience is lacking.

## Conclusions

- Accurate estimates of pressure/volume/temperature properties (gas Z-factor) are necessary to calculate accurate pressure at depth.
- Methods for calculating gas Z-factor fall into two groups: direct calculation and iterative equation of state derived. The latter is more accurate.
- Gas Z-factor calculations require pseudocritical properties, which can be correlated with hydrocarbon gas gravity.
- Accurate calculations of gas pressure at depth require knowledge of the injection gas gravity and should be performed using segmented length increments over the depth of the well. The increment size should capture the character of a nonlinear temperature profile if present.
- The change in wellhead injection pressure during unloading can be modeled using the real gas law.
- Surface gas-injection-rate and valve-performance models can be used to model the annulus pressure during unloading and provide a means for refining the gas lift design.

*For a limited time, the complete paper SPE 190929 is free to SPE members.*

*JPT*Technology Editor Judy Feder, contains highlights of paper SPE 190929, “Gas Lift Annulus Pressure,” by

**Kenneth Decker,**SPE, retired, and

**Robert P. Sutton,**SPE, consultant, prepared for the 2018 SPE Artificial Lift Conference and Exhibition—Americas, The Woodlands, Texas, USA, 28–30 August. The paper has not been peer reviewed.

Gas Lift Operations Require Accurate Predictions of Downhole Annulus Pressure

01 March 2019

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