@misc{kazanskii1978methods1,
    author = "Kazanskii, V. V. et al",
    title = "Methods of influencing low permeability collector seams of East Siberia during teats",
    year = "1978",
    howpublished = "Geology of Oil and Gas, v. 4, p. 60-64",
    note = "talkorigins\_source = {true}; raw\_reference = {Kazanskii, V. V. et al., 1978, Methods of influencing low permeability collector seams of East Siberia during teats: Geology of Oil and Gas, v. 4, p. 60-64.}"
}

@inproceedings{vankruijsdijk1999testing,
    author = "van Kruijsdijk, Cor P. J. W. and Cox, Richard J. W.",
    title = "Testing While Underbalanced Drilling: Horizontal Well Permeability Profiles",
    year = "1999",
    booktitle = "SPE European Formation Damage Conference",
    abstract = "Underbalanced drilling has gained popularity during the last years as it is well-suited to the drilling of low-pressured reservoirs and provides a method to prevent formation damage, especially in horizontal wells. The production rate of formation fluids during drilling carries information on reservoir characteristics. In particular, the permeability profile along the well may be inferred from a combination of well pressure and total rate. The transient well inflow can be interpreted as a complex well test. The complexity arises from the fact that the boundary conditions (i.e. the well trajectory open to flow) change with time during the test. Moreover, the transient rate is influenced by variation in underbalance (i.e. well pressure) and well penetration rate. However, the signal (transient rate) carries detailed information on the permeability profile along the well. Analysis is preceded by the elimination of the effects of the variable underbalance and drill speed using deconvolution techniques. An accurate approximation of the permeability profile can be obtained by a direct analysis (i.e. without having to resort to history matching) of the corrected well influx. Note that only the total well rate trqnsient is required rather than the full inflow profile along the open well trajectory. In previous work we considered the analysis of the transient rate during underballanced drilling of a vertical well under a constant underbalance. Both the variable underbalance and the more complex outer boundary conditions of a horizontal well (the transient is very likely to see the cap-and base-rock boundaries during the test) distinguish the current study from the previous one.",
    url = "https://doi.org/10.2118/54717-ms",
    doi = "10.2118/54717-ms"
}

@inproceedings{cox2000well,
    author = "Cox, D. O. and Stinson, S. H. and Stellavato, J. N.",
    title = "Well Testing in Ultra-High Permeability Formations",
    year = "2000",
    booktitle = "SPE Annual Technical Conference and Exhibition",
    abstract = "Nye County, Nevada is the home of the Yucca Mountain Project, which is the proposed site for a high-level nuclear waste disposal facility. Over the last several years, Nye County has conducted an independent scientific program to evaluate the properties of the rock units around the proposed disposal site. This work has included drilling and testing several water monitor wells in clastic, valley-fill deposits. These tests indicated extraordinarily high permeability (up to 300 darcies) in some units. Well testing in reservoirs with such ultra-high permeabilities provides a unique opportunity to identify and evaluate reservoir heterogeneities. Analyses of three tests are presented. The Nye County tests demonstrate the applicability of petroleum-industry well-test analysis methods even for ultrahigh permeability reservoirs. The tests show a large number of unusual effects (ultra-high permeability, extreme wellbore storage, linear flow, radial flow, hemispherical flow, multiple layers, multiple boundaries, wide range of compressibility, atmospheric corrections for a pumping well, etc.) in just a few tests. The test data and interpretations are publicly available and constitute an important database for well test analysis education and training.",
    url = "https://doi.org/10.2118/63279-ms",
    doi = "10.2118/63279-ms"
}

@inproceedings{zeng2004well,
    author = "Zeng, F. and Zhao, G.",
    title = "Well Testing Analysis for Variable Permeability Reservoirs",
    year = "2004",
    booktitle = "Canadian International Petroleum Conference",
    abstract = "Stimulation of carbonate formations by acid dissolution of the rock has been an efficient and successful method of bimproving production in oil and gas wells. Hydrochloric acid is the normal fluid of choice. However, in high temperature applications corrosion issues limit usage, especially in chrome completions. Acetic acid has been used with some success and with adequate corrosion protection. But due to its low reactivity at higher temperatures, the efficiency with which a gallon of acid dissolves the formation is perceived as low. This perception comes from reaction efficiency of acetic acid reported in the literature ranging in values from 90\% at 25 °C to 40\% at 121 °C for 2 to 15 wt\%, respectively. Acetic acid reaction on calcium carbonate is controlled by its small dissociation constant, 1.754E-05 at 25 °C (77 °F) and therefore is labeled a weak acid. Abstract The effects of permeability variable in formation on pressure derivative curve are studied in this paper. We view the general heterogeneous reservoir as a base homogeneous reservoir modified with multiple variable permeabilities at some locations. The sections where permeabilities are different from the base permeability are called as the variable permeability sections. A heterogeneous reservoir with only one variable permeability section can be well defined as long as the permeability, the size and the location of the section are specified. Its pressure derivative deviation from that of the base homogeneous reservoir has been thoroughly studied. Results show that the start time and the value and the occurred time of maximum magnitude of the pressure derivative deviation suggest the start position, the permeability and the end position of the variable permeability section, respectively. In order to analyze a heterogeneous reservoir with multiple variable permeability sections, we proposed that its pressure derivative difference with respect to the base homogeneous reservoir is the summation of the pressure derivative differences, with respect to the base homogeneous reservoir, of the single-section multiple heterogeneous reservoirs, each of them possesses only one variable permeability section. This method has been proved and verified in the reservoirs with radial and areal permeability distribution using both analytical and numerical methods. Applications show that this method provides a useful clue for heterogeneity reservoir well testing analysis. If the test noise can be ignored in pressure derivative curve, this method is very practicable for well testing analysis of variable permeability reservoirs. In the cases where pressure noise makes the pressure derivative zigzag, some de-noising methods, for example Schroeter's deconvolution method, wavelets and optimal model, can be used to de-noise pressure data in order to get smooth pressure derivative curve. Then, this de-noised test data can be diagnosed using the method proposed. Introduction Traditional well testing analysis tends to determine an overall permeability, which cannot reflect the variation of permeability in formation. In our experiences on practical well testing interpretation, we often encounter the situations that we can match the shape and the trend of the pressure derivative curve perfectly, but we cannot match the slight waves in the pressure derivative curve. Generally there are two sources that produced these kinds of waves, pressure measurement noise and the response of heterogeneity of the reservoir. The waves generated from the pressure measurement noise are random and discontinuous, while those from the heterogeneity of the reservoir behave continuously and smoot",
    url = "https://doi.org/10.2118/2004-037",
    doi = "10.2118/2004-037"
}

@article{zeng2007well,
    author = "Zeng, F. and Zhao, G.",
    title = "Well Testing Analysis for Variable Permeability Reservoirs",
    year = "2007",
    journal = "Journal of Canadian Petroleum Technology",
    abstract = "The effects of spatial permeability variations of a reservoir on the pressure derivative curve are studied. The presence of a permeability anomaly causes the pressure derivative to locally deviate from that of the corresponding homogeneous reservoir. For a simple variable permeability reservoir that has only one permeability anomaly, the start time, the value and the time of maximum local derivative deviation suggest the originating location, the permeability and the end location of the permeability anomaly, respectively. To analyze the transient pressure behaviour of a well located in a reservoir with multiple permeability anomalies, an approximate equation is presented. The study shows that the pressure derivative difference, with respect to that of the base homogeneous reservoir, is the summation of the pressure derivative differences of all simple variable permeability reservoirs with respect to the same base. This method has been proved and validated in reservoirs with radial and areal permeability distribution using both analytical and numerical methods. Applications show that this method provides a useful clue for well testing analysis of heterogeneous reservoirs and the maximum error caused by the proposed approximate equation is less than 3\%. The practice guidelines for field test data interpretation are proposed. Introduction Traditional well testing analysis tends to determine an overall average permeability. Generally, it cannot reflect the spatial variation in the permeability of a reservoir. Typically, in practical well testing interpretation, the shape and the trend of the pressure derivative curve can be matched very well, but the local waves in the derivative curve cannot be matched at all. Generally, there are two sources producing local waves: the noise of tested data and the heterogeneity of the reservoir. The waves generated by the noise of tested data are random and discontinuous. This kind of wave may lead to interpretation errors. Consequently, many methods, such as wavelet analysis, Schroeter's deconvolution method and the optimal method, have been developed to de-noise the tested data. Different from the noise of tested data, the heterogeneity of the reservoir produces local continuous and smooth waves in the pressure derivative curve. Analyzing this kind of wave may provide more detailed reservoir information than traditional well testing. Many researchers have discussed some aspects of well testing analysis for heterogeneous reservoirs. Niko(1) presented analytical solutions for stratified and heterogeneous systems with interlayer crossflow. Yaxley(2) studied transient pressure behaviour when a partially communicating fault exists and observed that it can be diagnosed by drawing a semi-log derivative plot. Britto and Grader(3) studied the effects of size, shape and orientation of an impermeable region on transient pressure testing and found that the presence of an impermeable region caused the pressure response to deviate from the homogeneous line source response. They also pointed out that the four major parameters (the shortest distance between the well and the impermeable region, the size, the shape and the orientation of the region) affect the pressure response of the active source well located in such reservoirs. After investigating the transient pressure behaviours of wells located in composite reservoirs, Oliver(4, 5) derived a solution to the problem of a well located in an infinite reservoir with a small arbitrary spatial permeability variation, as demonstrated in the following equation:",
    url = "https://doi.org/10.2118/07-02-01",
    doi = "10.2118/07-02-01",
    number = "02",
    volume = "46"
}

@article{zhang2013numerical,
    author = "Zhang, Yu Chen and Zhou, Jiu Ning and Cui, Jing Wen",
    title = "Numerical Well-Testing Model of Fractured-Well in Low Permeability Reservoir Based on Mutative Permeability Effect",
    year = "2013",
    journal = "Applied Mechanics and Materials",
    abstract = "At present, threshold pressure gradient method is usually used for describing fluid flow in low-permeability media. However, it is only an approximate approach. In this paper, a 2-D fractured-well model for numerical well-testing considering non-darcy mutative-permeability effect was established, and PSOR iterative algorithm was used for solving the sets of algebraic equations. Based on this model, the typical curves of pressure and pressure derivative were drawn with different sets of parameters. When considering mutative-permeability effect, the pressure derivative curves move upward in each flowing period compared with darcy flowing model. In addition, the range of upward movement is larger as the non-darcy effect is more notable.",
    url = "https://doi.org/10.4028/www.scientific.net/amm.433-435.1984",
    doi = "10.4028/www.scientific.net/amm.433-435.1984",
    pages = "1984-1987",
    volume = "433-435"
}

@incollection{crossref2014collector,
    title = "collector well",
    year = "2014",
    booktitle = "Dictionary Geotechnical Engineering/Wörterbuch GeoTechnik",
    url = "https://doi.org/10.1007/978-3-642-41714-6\_33189",
    doi = "10.1007/978-3-642-41714-6\_33189",
    pages = "252-252"
}

@inproceedings{kulyatin2019dfit,
    author = "Kulyatin, Oleg and Lomukhin, Alexander and Prokhorov, Alexey and Romashkin, Sergey and Samoilov, Mikhail",
    title = "DFIT Survey for Reservoir Evaluation of a Low Permeability Formation during Well Testing",
    year = "2019",
    booktitle = "SPE Russian Petroleum Technology Conference",
    abstract = {Conventional well testing methods and techniques on low permeability formation are not practical and inefficient due to weak natural flow rates. For such formations performing hydraulic fracturing is planned to increase flow rates and engage formation into flowing, but at such status it is impractical to carry out hydrodynamic testing survey, as it required long duration of survey, up to several weeks and months. As a sound option for low permeability formation could serve Diagnostic Fracture Injection Test (DFIT) survey. The main interest of this paper was to execute DFIT survey, full cycle from planning to wellsite job execution, obtain the required data, results and confidence to decide if DFIT is effective method to practice at exploration and appraisal phase. For performing reliable evaluation of formation permeability it is important to design and execute fracturing job in optimal to obtaining descriptive and timely formation response. The target fluid filtration "pseudo-radial" regime takes place at latest stage of pressure fall-off, develops at investigation radius beyond fracture length and usually non-observed, as takes tremendous time for low permeability formation. In frame of present project, the intention was to initiate compact fracture with small length, therefore to be capable to register pseudoradial flow regime at reasonably short time, up-to three days. DFIT survey with small length fracture was executed with well shut-in bottomhole with tester valve. For first time on low permeability formations in Urengoy area DFIT survey was performed with well shut-in bottomhole with tester valve immediately after fracture placement. High resolution descriptive bottomhole data was gathered. Targeted "pseudo-radial" regime was achieved starting at 50 hours and lasted to the end of 72 hours fall-off period duration. DFIT data processing and After-closure-analysis (ACA) allowed deriving initial pressure and fluid mobility in remote formation zone. DFIT data processing and After-closure-analysis (ACA) was carried out in three alternative software packages, data discrepancies were analyzed for conclusions and decision for future usage. Within complex well testing program set of formation evaluation parameters – formation pressure, permeability and skin – was targeted to be extracted from various conventional methods, such as initial Drill Stem Test (DST) with short opened and closed periods, extended flowing on fixed chokes with stabilized rates, descriptive build-up at end of flow testing sequence. These evaluated formation parameters are to be compared with those, derived from DFIT survey to justify DFIT survey applicability and uncertainties. Based on data, results and experience gathered through project execution built our confidence in claiming DFIT as sound instrument for evaluating properties of low permeability formation wells. This applies for wells at exploration and appraisal phase, and potentially can bring corresponding benefits when expanded to exploitation drilling wells to be put into production.},
    url = "https://doi.org/10.2118/196738-ms",
    doi = "10.2118/196738-ms"
}

@article{zarereisabadi2022stress,
    author = "Zare Reisabadi, Mohammadreza and Sayyafzadeh, Mohammad and Haghighi, Manouchehr",
    title = "Stress and permeability modelling in depleted coal seams during CO2 storage",
    year = "2022",
    journal = "Fuel",
    url = "https://doi.org/10.1016/j.fuel.2022.124958",
    doi = "10.1016/j.fuel.2022.124958",
    pages = "124958",
    volume = "325"
}