Possible pitfalls in pressure transient analysis: Effect of adjacent wells
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Abstract
Well testing is one of the important methods to provide information about the reservoir heterogeneity and boundary limits by analyzing reservoir dynamic responses. Despite the significance of well testing data, misinterpreted data can lead us to a wrong reservoir performance prediction. In this study, we focus on cases ignoring the adjacent well’s production history, which may lead to misinterpretation. The analysis was conducted on both homogeneous and naturally fractured reservoirs in infinite-acting and finite-acting conditions. The model includes two wells: one is “tested well” and the other is “adjacent one.” By studying different scenarios and focusing on derivative plots, it was perceived that both reservoir and boundary models might be misinterpreted. Additionally, in all cases, a sensitivity analysis was performed on parameters affecting interpretation process. Studying the literatures, few articles have focused on drawbacks during diagnostic plot interpretation and also the effect of adjacent wells. Hence, these issues were addressed. Overall, considering several cases it was proved that neglecting the production effect of adjacent wells causes wrong interpretation, and this should be avoided in all interpretation cases. Regarding the importance of reservoir characteristics and its flow regime, any wrong interpretation may create huge uncertainties in the reservoir development. As a result, this paper aimed to address the well testing, especially in brown fields where the production of other wells may affect the pressure response of the tested well; therefore, it will be pivotal to consider the effect of adjacent wells’ production history.
Graphic abstract
Keywords
Well testing Production history Adjacent wells Pressure derivative MisinterpretationList of symbols
- B_{o}
Formation volume factor, bbl/STB
- C_{t}
Total compressibility, 1/ψ
- h
Thickness, ft
- k
Permeability, md
- p_{i}
Initial reservoir pressure, ψ
- \(p_{\text{wf}}\)
Wellbore flow pressure, ψ
- Q_{o}
Oil rate, STB/day
- r
Distance, ft
- t
Time, h
- \(t_{\text{s}}\)
Shut down time, h
Greek symbols
- λ
Dimensionless interporosity parameter
- μ_{o}
Oil viscosity, cp
- ω
Dimensionless storativity ratio
- φ
Porosity
Introduction
Well testing is divided into two types, constant rate (Dejam et al. 2018; Mashayekhizadeh et al. 2011) and constant pressure test (Dejam et al. 2017a, b). It is more common to design tests as constant rate, which in that case, the pressure transient is recorded. The numerical model is one of the technical advances for simulating pressure transient analysis (PTA). In recent years, numerical models have been utilized in order to analyze the well testing procedure not only for models with analytical and semi-analytical simulation, but also it can be applied for more elaborated cases. Numerical models can address the limitations of analytical approaches in modeling of complicated geometries and nonlinear diffusion terms in which the superposition of time and space does not work (Houze et al. 2008).
Conventional analysis just is usable with pressure versus time data, but sometimes it does not identify the correct flow regime. In well testing, the pressure variation is more significant than the pressure value itself (Bourdet 2002). So, Tiab and Kumar (1980a, b), and Bourdet (2002) addressed the issue of identifying the correct flow regime and choosing the proper interpretation model. Bourdet and his co-authors proposed that it is much easier to recognize the flow regimes with analyzing pressure derivative versus time in log–log plots in comparison with conventional semilog pressure curves (Ahmed and McKinney 2011). The modern analysis defines the derivative term and interprets pressure and derivative data together.
Derivative plots are usually known as diagnostic plots. It is due to the fact that they identify different flow regimes and distinguish the reservoir model much easier. For example, interpretation of well testing results of a naturally fractured reservoir is carried out remarkably easier with the aid of pressure derivative (Cinco-Ley 1996). Interpreting of the transition period of naturally fractured reservoirs is an obstacle which many analyzers tackle with (Aguilera 1987; Feng et al. 2016; Seyedi et al. 2014). Many authors applied this period for different models of naturally fractured reservoirs and their corresponding pressure transient analyses published in the literature (Dejam et al. 2018; Aguilera 1987; Najurieta 1980; Warren and Root 1963; Odeh 1965; Kazemi 1969; Kazemi et al. 1969; de Swaan 1976; Aguilera and Song 1988; Kuchuk and Biryukov 2014; Al-Rbeawi 2017).Wang et al. examined the characteristics of the flow period in a multiple-fracture model by considering the features wellbore pressure and also analyzing the pressure-derivative data (Xiaodong et al. 2014). Cinco and Ley reported that considering a naturally fractured reservoir and utilizing the interference test results, it is impossible to carry out the characterization by regarding the transient pressure data solely (Cinco et al. 1976). Examining the pressure-derivative approach for highly permeable reservoirs demonstrated that this approach is suitable-adapted to this type of reservoirs (Clark and Golf-Racht 1985). Also, many papers investigate the behavior of pressure transient in fractured wells (Kou and Dejam 2018; Zhang et al. 2018). Iraj and Woodbury (1985) studied examples of possible pitfalls in the well testing analysis using pressure versus time data. In 2001, Al-Ghamdi et al. pointed out uncertainties in model selection by modern well testing interpretation. They expressed that in pressure transient analysis, uncertainty associated with the non-uniqueness of model response can generally be summarized by the inability to identify the appropriate model and/or distinguish between similar patterns of pressure behavior (Al-Ghamdi and Issaka 2001). Also, some authors examine both the interpretation of diagnostic plots and their limitation for various reservoir models (Beauheim et al. 2004; Veneruso and Spath 2006; Renard et al. 2009; Engler and Tiab 1996).
Nearly all the published papers emphasize on the interpretation of models which only include one well, and this interpretation is done by using either wellbore pressure or pressure-derivative data. In this paper, we have scrutinized the models which include two wells. In other words, the effect of the other well’s production history on the interpretation of pressure responses was investigated.
To have a systematic investigation, we will initially present the symptoms of various reservoir characteristics. Then, we examine six infinite homogenous and fractured synthetic models that can be interpreted mistakenly. Finally, we will compare two homogenous reservoirs that are infinite and finite acting. More details will be given in the next section.
Various reservoirs characteristic symptoms
The curve that is obtained from the pressure-derivative versus time data was originally utilized for diagnostic purpose and recognition of reservoir models. Each type of flow exhibits a specific trend on the derivative which represents an excellent diagnostic tool (Bourdet 2002).
- 1.
Homogenous reservoirs: The signature of these types of reservoirs in derivative curve is depicted as a horizontal straight line in transient flow regimes (Bourdet 2002; Cinco-Ley and Samaniego 1982). After the transient time, during the pseudo-steady-state flow since pressure varies linearly versus time, it is characterized on the pressure derivative by a straight line with the unit slope on log–log plot (Bourdet 2002). If buildup test is run, the derivative will go down. In the case that reservoir boundary is a constant pressure, the pressure derivative indicates a sharp plunge in the log–log representation corresponding to the pressure stabilization (Bourdet 2002). These mentioned signatures are only valid for a test which is run in a reservoir where there is no effect of nearby wells. If some other wells exist close to the test well, the production history of them can effect on the well test results. This occurrence may show itself as a similar signature to cases, which is explained above. In this paper, some of these tests are discussed.
- 2.Naturally fractured reservoirs: The signature of naturally fractured reservoirs in derivative curve depends on the model, which is defined for fractures and also their role in fluid flow. Considering different literatures, many authors proposed a model for fluid flow simulation in a naturally fractured reservoir with respect to the assumptions measured for fluid flow in the fracture, matrix and interaction between them (Warren and Root 1963; Kazemi 1969; Barenblatt et al. 1960; Abdassah and Ershaghi 1986). The most famous model is the dual-porosity model. After radial flow, which is dominated by fractures, a valley in the derivative curve is observed, which is the indicator of transition between fracture and matrix. Subsequently, a horizontal line will appear. For a triple-porosity model, two continuous valleys are recorded (Al-Ghamdi and Ershaghi 1996). The typical shape of the pressure-derivative behavior in the logarithmic coordinates for different models is illustrated in Fig. 2 (Renard et al. 2009).
Analytical solution
Warren and Root developed an analytical solution for unsteady-state flow in a fractured reservoir model. In this model, matrix is considered as a storage source, while fractures are the main conductive paths (Warren and Root 1963). Their solution for drawdown and buildup is as follows:
Although the analytical models are used widely in the literature to obtain the pressure response of the reservoir quickly, they have many simplifying assumptions that may cause wrong response. Therefore, due to this fact, these analytical models cannot be used for complex reservoirs without enough modification.
Results and discussion
Effect of adjacent wells
Most of the well test interpretation is done only by focusing on the tested well. However, in most cases, there are several adjacent wells in the vicinity of the tested well that can have a different production history. The existence of adjacent wells in operational field can pose challenges in interpreting and analyzing the data. It is well accepted that production from the neighbor’s wells can be considered as an artificial no-flow boundary (Stewart 2011). However, in this study, it was shown that depending on the production history of the neighbor’s wells, both boundary and reservoir models can be misinterpreted and the situation would be more complicated.
Different scenarios for homogenous and naturally fractured reservoirs
Scenario number | 1 and 4 (infinite reservoir) | 2 and 5 (infinite reservoir) | 3 and 6 (infinite reservoir) | 7 (finite reservoir) |
---|---|---|---|---|
Property | ||||
Porosity | 0.1 | 0.1 | 0.1 | 0.1 |
Permeability (md) | 33 | 33 | 33 | 33 |
Thickness (ft) | 30 | 30 | 30 | 30 |
Well distance (ft) | 400 | 400 | 400 | 400 |
Rate of tested well (bbl/day) | 300 | 300 | 300 | 300 |
Rate of adjacent well (bbl/day) | 300 | 1000 | 2000 | 1000 |
Production time of tested well (h) | 70 | 70 | 70 | 50 |
Production time of adjacent well (h) | 70 | 70 | 140 | 50 |
Properties of fractured reservoir model
Property | |
Matrix porosity | 0.1 |
Fracture permeability (md) | 33 |
Thickness (ft) | 30 |
Omega | 0.2 |
Lambda | 2E−6 |
Well distance (ft) | 400 |
Homogenous reservoir’s base case
Scenario No. 1
Parameters obtained from the truth model and possible misinterpretation
Case | K (md) | S | ω | λ | |
---|---|---|---|---|---|
Truth case | Homogenous reservoir in the presence of adjacent well | 33 | 0 | – | – |
Possible misinterpretation | Dual-porosity model (if we ignore the adjacent well) | 31 | 0 | 0.0556 | 4.26E−8 |
Scenario No. 2
Scenario No. 3
Till this point, we focused on homogenous cases. Now, we will address these scenarios for naturally fractured reservoirs to find out what changes in the derivative curve will happen considering a situation that an adjacent well exists in this system. All of these scenarios which will have been examined below are similar to scenarios which were examined previously in the homogenous reservoir. Equations 4 and 5 are used to calculate the pressure at the tested well. Equation 6 is also applied for calculating derivative values.
Fractured reservoir’s base case
Scenario No. 4
Scenario No. 5
Scenario No. 6
Scenario No. 7 (special case)
Looking at the seven scenarios, we observed the importance of including the effect of the production history of adjacent wells in well test interpretation (if they can affect the pressure data in the tested wells). Here, seven cases were examined, but investigation can be extended to the more complex case (i.e., composite systems or multilayered systems).
Summary of results
Scenario number | Correct model | Wrong model |
---|---|---|
Scenario 1 | Homogenous reservoir, infinite acting | Dual porosity |
Scenario 2 | Homogenous reservoir, infinite acting | Constant pressure boundary |
Scenario 3 | Homogenous reservoir, infinite acting | No-flow boundary condition |
Scenario 4 | Naturally fractured reservoir (dual porosity), infinite acting | Triple porosity |
Scenario 5 | Naturally fractured reservoir (dual porosity), infinite acting | Homogenous reservoir, constant pressure |
Scenario 6 | Naturally fractured reservoir (dual porosity), infinite acting | Dual porosity, no-flow boundary condition |
Scenario 7 | Homogenous reservoir, finite acting | Radial flow |
As it is shown in Table 4, if reservoir engineers do not consider the effect of adjacent wells, the interpretation firmly can be wrong. Moreover, the scenarios that are discussed in this paper have only one adjacent well, and it has assumed that adjacent well produces at a constant rate. However, it will be interesting to examine other scenarios that have not only the more wells, but also produce at variable rates. Therefore, it is highly recommended that the other situations that may effect on the interpretation are to be considered in the future works. By doing this, the cases will be close to the real reservoir condition and wrong interpretations can be avoided.
Conclusions
Based on the results of this research, it was illustrated that neglecting the effect of the adjacent well production history on the tested well data can have a huge impact on well test interpretation.
It was demonstrated that an infinite-acting homogenous reservoirs or finite-acting cases can be misinterpreted as a naturally fractured reservoir or as a reservoir with artificial boundaries. Similar misinterpretation can happen for a naturally fractured reservoir. Such an issue can diminish the accuracy of future prediction of reservoir performance.
For having a valid interpretation, all neighbor wells and corresponding production histories should be included in a standard interpretation procedure.
We applied analytical models for both homogenous and fractured reservoirs considering the superposition principle. The results of the analytical model had completely matched with the response that had been obtained by commercial software. Consequently, it shows that these analytical models are applicable, if the assumptions behind it are considered.
The more the model is complex, the more the results should interpret precisely. Therefore, for interpretation of complex reservoir tests, the engineers should get help through other means such as petrophysics and geophysics to reduce the uncertainty in their interpretations.
Notes
Acknowledgements
The authors would like to thank the Kappa Engineering Company for providing licensed Kappa workstation v5.10.0.
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