气举作业的成功执行需要准确预测井下环空压力！

编译 | 惊蛰

任何气举设计都需要用到井下环空压力，而传统设计技术往往忽略了这一事实，取而代之的是对气举阀性能进行简化类比。然而，在排液过程中，这种类比会造成环空压力变化的误差与误解。

业内已总结出多种井下环空压力的计算方法，包括经验公式、基于平均压力与温度的全井段密度方程、基于某段平均压力与温度的密度方程。对这些经验公式进行测试，不同方法的选用，会限制预测某个深度压力的准确性。

经验公式：经验公式是计算某个深度环空压力的原始方法。每个经验公式都设定了各种假设，如温度、温度梯度、深度以及气体比重。当计算条件与经验公式中的内在假设不匹配时，表格中给出了校正原始梯度的方法。如今，计算机程序可在各种条件下，提供更准确的环空压力模拟。但在计算环空压力梯度时，设计者失去了执行自己判断的机会。

采用密度方程进行全井段计算。当使用密度积分方程来计算全井段的压力时，用户可以输入该井的实际平均温度，这是对经验公式中假设平均温度的改进。最初提出的平均温度与平均可压缩性（ATAC）法，只是利用单个计算来求出全井段的压降。后续的研究，提出了将井眼分段，来提高计算精度。凭借当前的计算能力，ATAC通过使用更小的深度增量，得出了更精确的结果。

将全井段计算法与线性温度分布的增量计算法进行比较，针对井口压力1200psi的轻质气井，两种方法算出10000英尺处的环空压力差值小于5psi。然而，当井口压力为2000psi且气体比重为0.85时，两者的差值达到了36psi。这个误差量很大，会影响气举设计。通常，误差量会随着井口压力与比重的增加而增加。完整的论文中，作者强调，在使用全深度环空压力计算方法时，需要考虑充足的安全裕度。

密度方程的增量计算。基于真实气体定律，温度会对气体密度造成影响，从而井下环空压力会对温度有直接的敏感性。考虑气举不同阶段环空的实际温度，可计算出更精确的井下环空压力。采用密度积分方程，以500英尺为增量，考虑每个增量井段的平均温度与可压缩性，可以精确地确定地热、设计以及流动温度下的环空压力。这是最精确的井下压力预测方法，因为它可以将各种温度剖面映射到井中。如果使用计算机辅助气举设计，则应使用增量计算方法，而且软件程序也必须允许使用非线性温度剖面。

环空压力的计算高度依赖于气体比重，以及由此产生的气体压缩系数（Z因子）。专家不推荐使用气举研究中所述的简单计算z因子的方法，因为在不同工况下的可靠性较差。相反，他们都表示，最精确的方法是从状态方程推导出来的。

由于气体Z因子的计算，是基于拟对比压与拟对比温度的计算，因此必须确定气体的拟临界压力与温度。完整的论文包括详细的讨论与建议，以确保Z因子的准确性。

本文通过一个实例说明，如果井内气体比重与设计思想不符，即使采用具有最精确的Z因子相关性与井温曲线的最精确的计算方法，仍然可能会造成严重误差。在设计与生产阶段，由于地面设施的操作变化，气体比重可能会随着时间而变化，这一点非常重要。这些变化会影响井下环空压力。

如果在预期比重的情况下执行气举设计，气体比重会随着时间的推移而变化，则气举的作业参数也会发生变化，故障排除方法必须考虑到这一点。每月分析天然气的组分是获得气体比重周期值的好方法。当产量、井构造或分离器状况发生变化时，气体比重都会受到影响。使用最准确的注入气体比重进行设计与故障排除，其重要性不言而喻。在较高的注入压力下尤其如此。

目前，大多数气举设计都是使用计算机进行的，因此，环空压力的深度增量计算法提供了最可靠、最精确的结果。关联哪些伪临界性质？与哪个Z因子关联结合使用？把这些问题的决定权都交给用户。在井口注入压力超过1500 psi之前，这些问题并不重要。然而，对于更高比重的气体，即使是低压系统也会受到计算方法选择的影响。当发生这种情况时，用户必须特别注意注入气体的成分，并确保气体的比重定期与设计比重相匹配。

在气举设计中，使用流动温度曲线来确定环空压力的安全裕度。气举阀的波纹管压力继续使用设计温度曲线。在设计阶段，该策略预测的环空压力较小，这可能会导致气举阀的间隔更近。然而，有益的是，无论井中温度如何，排液与举升期间的实际环空压力，将始终高于设计环空压力。

目前，注压式气举阀的设计技术建议，对于每个后续卸油阀，用于计算波纹管压力的环空压力都应降低20至40psi。这种阶梯式气体注入方案可最有效的利用气体来举升流体。

可以说，基于经验的设计方法是成功的，但是，证明经验合理性的理论以及流动特征模型是错误的。本文介绍了一种可以解释环空压力变化的方法，该方法能够在缺乏经验时，应用物理定律来计算。

Downhole annulus pressure is required for any gas lift design. 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.

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. 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. How-ever, 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.