A Review of Geothermal Type-Curves with Damage Effect: A Case of Practical Apply to a Mexican Geothermal Field ()

Siomara López-Blanco, Alfonso Aragón-Aguilar, Víctor Arellano-Gómez, Georgina Izquierdo-Montalvo, Sócrates Santoyo-Gutiérrez, Abel Hernández-Ochoa

Instituto de Investigaciones Eléctricas, Reforma 113, Col. Palmira, Cuernavaca, Morelos, México.

Universidad Popular de la Chontalpa, Carr. Cárdenas-Huimanguillo km. 2.0, Cárdenas Tabasco, México.

**DOI: **10.4236/ijg.2012.33059
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Instituto de Investigaciones Eléctricas, Reforma 113, Col. Palmira, Cuernavaca, Morelos, México.

Universidad Popular de la Chontalpa, Carr. Cárdenas-Huimanguillo km. 2.0, Cárdenas Tabasco, México.

A review of the art state was developed about the inflow relationships and their application for reservoir characterization. The theoretical development of the methodology for determining the damage effect using type-curves of the inflow relationships was shown. We show the process followed for achieve the geothermal type-curve affected with damage for reservoirs with mean salinities of 30000 ppm and temperatures up to 350℃. This type-curve was applied using measurement production data in a Mexican geothermal field. According with the obtained results is shown that the methodology for determining the damage effect using production measurements is a sure alternative for the damage effect calculation. It was used an alternative methodology in order to validate the damage presence and the obtained results were consistent. Last thing shows that both methodologies can be combined as a confident manner.

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S. López-Blanco, A. Aragón-Aguilar, V. Arellano-Gómez, G. Izquierdo-Montalvo, S. Santoyo-Gutiérrez and A. Hernández-Ochoa, "A Review of Geothermal Type-Curves with Damage Effect: A Case of Practical Apply to a Mexican Geothermal Field," *International Journal of Geosciences*, Vol. 3 No. 3, 2012, pp. 591-600. doi: 10.4236/ijg.2012.33059.

1. Introduction

Geothermal resources ordinarily remain in the reservoir as a mixture of H_{2}O-CO_{2}-NaCl [1,2] with conditions up to 360˚C and 500 bar, with solids concentrations of NaCl dissolved up to 30,000 ppm. In relation with the salinity, the geothermal reservoir of Salton Sea is considered as extremely saline [1], whose NaCl concentration is estimated in 10 times the concentration of the sea water. The wells are the means to extract the geothermal energy from the reservoir to surface through its commercial exploitation. So, the drilling of a well is focused to an efficiently exploitation of the geothermal resource and the criteria applied in the production designs are grounded to achieve high productivities [3].

However the different operations during drilling are the reason of the alterations in the walls of the hole. Examples of these alterations can be found in the changes of formation permeability, due to influence of drilling muds, whose sediments clog the pores spaces. The results of all the alterations provoked to formation during drilling jobs affect to abnormal behavior of the well in the production and in additional losses of the pressures. Last thing is known as skin factor and is called with “s”, because the drilling mud adheres to walls of the hole leaving a thin film similar to skin. During exploitation stage is an ordinary task to characterize the well performance, using production tests at different diameters of opening. Using the values pair, flow rate and pressure (W, p) of the measured data, can be obtained the production characteristic curves (or output curves). These characteristic curves taken at different stages of the productive life of the wells allow characterize their performance. The decrease in the productive characteristics of the well can be related with its decline productivity [3].

Originally the technique of well performance analysis using production characteristic curves was applied in the petroleum industry. With the development of the analysis methodology were incorporated the parameters at reservoir conditions (W, p_{wf}) resulting thus, the inflow performance relationships (IPR). The corresponding graphs are known as inflow curves.

Similarly to petroleum engineering in the geothermal engineering was developed [4] the geothermal inflow performance relationship (GIPR). These relationships relate the flow rate and bottom hole flowing pressure [5]. It were researched abnormal diminutions of the pressure, found [6,7] in the well, which are not related with those expected according to its variations in the flow rate changes. Founding that decrease in the well productivity is related with the presence of the damage that provokes alterations in the permeability formation. Ordinarily the damage effect, have been determined through the analysis of the transient pressure tests [8-15]. However recently was introduced [16] the methodology for determining the damage effect from equations for the analysis of production performance using production measured data.

2. Background

The methodology for determining the damage effect from production measurements uses the data of mass flow rate and pressure (W, p), that are the same used in the technique for production characteristic curves. Through the use of reservoir and wellhead conditions can be obtained the inflow curves [4] and characteristic curves respectively.

One of the possible reasons for the additional decrease in the pressure due to the changes in the flow rate was identified [7,17-19]. Gilbert [20] initially started with the analysis of the inflow behavior and after, Vogel [21] applied this in the characterization of the well in order to establish its exploitation designs. The numerical inflow performance relationships (IPR) were developed [22] for be applied in petroleum systems. Different authors [22- 27, among others] incorporated the analysis of inflow performance relationships in the reservoir engineering. Similarly [28-33] did applications with this type of technical tool for geothermal reservoir characterization.

Additionally were developed inflow relationships assuming the geothermal fluid is composed by: 1) Pure water [34]; 2) A binary mixture H_{2}O-CO_{2} [35,36]; 3) A ternary mixture H_{2}O-CO_{2}-NaCl with salinity less than 5000 ppm of NaCl [37]; 4) [38] Assumes a ternary mixture H_{2}O-CO_{2}-NaCl with salinities between 5000 and 30,000 ppm of NaCl; and 5) A ternary mixture H_{2}OCO_{2}-NaCl with salinities greater than 30,000 ppm of NaCl [39]. The incorporation of the damage effect in the inflow relationships was proposed for petroleum systems [25] and for geothermal systems [16,39-41].

3. Theoretical Review

The inflow relationships are applied for production characterization in a well. One of the main objectives is the determination of the maximum mass flow rate (W_{max}) that the well can produce. The knowledge of this value is used as technical criterium for establishing its exploitation designs and as a reference value of its conditions at the time stage of the production test. Through the comparison of the different production curves, obtained in the well at different stages of its operative life is feasible to determine its decline tendency during its exploitation. The inflow performance relationships are associated with the respective dimensionless parameters of flow rate (W_{D}) and pressure (p_{D}), whose expressions are:

(1)

(2)

where p_{wf} is the bottom hole flowing pressure, p_{e} is the static pressure of the reservoir, W is the mass flow rate of the well and W_{max} is the maximum mass flow rate that the well can produce at the time of the production test.

The inflow performance relationships use as input data, the flow rate and pressure at bottom-hole conditions. During a production test, these values (flow rate and pressure) are measured at wellhead conditions. So, the values at bottom-hole conditions are calculated using well flow simulators. Therefore, by this manner are determined the dimensionless parameters of Equations (1) and (2). Such dimensionless parameters are useful in the reservoir characterization [4].

The methodology of analysis using this technique initially was applied [22] for petroleum systems with different physical properties of the reservoir. Through the use of production measurements of different fields [22] modified the methodology of Weller [21] and proposed an equation useful for two phase fluid:

(3)

where q_{o} is the petroleum flow rate, (q_{o})_{max} is the maximum flow rate of oil, p_{wf} and p_{e} as defined previously. The main assumption used in this equation is a compressible fluid with gas content. Standing [23] uses more widely last expression [22] in order to predict the behavior of inflow performance relationships and introduced the productivity index (), resulting the next expression:

(4)

The research, focused to turbulent flow in wells [24] incorporates the turbulence factor (τ), whose expression is:

(5)

where F is an auxiliary variable in the analysis, resulting a proportionality constant of the flow as a function of the pressure decrease. The values of the turbulent factor vary between 1.0 (laminar flow) and 0.5 (high turbulent flow). Assuming known the static reservoir pressure (p_{e}) is recommended carry out at least two production tests for evaluate the parameters F and τ.

Using data of more than 30 fields were modified the coefficients [25] of the proposed polynomial in [22] resulting the next equation:

(6)

Besides was improved in [26] the predictive capacity of the Vogel equation [22] incorporating the decay factor (d), whose expression is:

(7)

where

(8)

There are different procedures for obtaining the inflow curves of a well through the use of the above equations, but the used in this paper is [4]:

• Determine the bubble point pressure (p_{b}) of the fluid and the reservoir pressure (p_{e}) using the analysis results of its chemical composition.

• Determine the exponent value (b) using Equation (8).

• Solve Equation (7) for obtaining (Q_{o})_{max} using a pair values (Q_{o}, p_{wf}).

• Plot the inflow curve for different Q_{o} values, starting from zero, up to the (Q_{o})_{max} obtained in Equation (7).

Similar inflow relationships were proposed [27] one for oil systems, whose form is:

(9)

And another one for water:

(10)

where Q_{w} is the water flow rate and (Q_{w})_{max} is the maximum water flow rate.

The first geothermal inflow relationships (GIPR) were developed [34] assuming pure water at 300˚C, whose expression for mass productivity is:

(11)

And for thermal productivity:

(12)

Assuming a binary system H_{2}O-CO_{2} [35] the corresponding dimensionless inflow relationships were obtained.

(13)

The binary model was applied [3,36,42] to cases of Mexican geothermal fields. The obtained results agree very good with measured data and from these, was feasible to obtain output curves. The inflow curves were validated [43] through comparison with measurements at bottom-hole conditions. Besides, the methodology also was applied for determining the permeability formation [5,44]. Later on, was obtained an expression assuming the fluid as a ternary mixture [37] H_{2}O-CO_{2}-NaCl with salinity less than 5000 ppm, which is the next:

(14)

[38] proposed an inflow relationship assuming fluid as a ternary mixture with salts content up to 30,000 ppm in the liquid phase.

(15)

The change of variables for obtaining the equation in p_{D} function in place of W_{D} as appears in Equation (15) was did [40] and the expression is:

(16)

Due that around the world different reservoirs produce fluid with high salinity content, in this research is proposed [39], the inflow relationship considering the fluid as a ternary mixture H_{2}O-CO_{2}-NaCl with high salinity (greater than 30,000 ppm of NaCl) and high temperature (350˚C).

(17)

It seems that above expression produces more accuracy when the reservoir fluid is with high salinity content. A comparative analysis of the five geothermal inflow performance relationships, Equations (11), (13), (14), (16) and (17), is shown in Figure 1. From the comparison, it can be observed the similarity of the results of these five inflow relationships. Also can be seen that the maximum differences between these inflow relationships, occur in the rank for p_{D} values between 0.3 and 0.8. Table 1 shows the W_{D} values obtained using the above mentioned relationships and the maximum percentage differences found. It can be observed that the maximum values of W_{D} consistently correspond to those obtained considering the fluid as pure water [34]. By other side the minimum values of W_{D} are obtained with inflow relationship of Montoya [37] for 0.1 ≤ p_{D} ≤ 0.7.

Incorporation of the Damage Effect

The first authors [25] that researched the damage effect in the inflow relationships included the M coefficient in Equations (3) and (6) proposed above [22,25]. The resulting expressions are:

Figure 1. Comparison of the five geothermal inflow performance relationships, proposed by different authors.

(18)

(19)

The parameter M involves the damage effect(s) and is function of the ratio between the radius of drainage area of the reservoir (r_{e}) and the well bore radius (r_{w}). According with Equations (18) and (19) the M value is slightly different for each considered case, so, the expressions for each M value [45] are:

(20)

(21)

The M parameter acts as inverse function in the Darcy’s law, so the coefficient values of 0.492 and 0.476 were obtained [25] from different simulations done. They [25] assume as a drainage radius, values between 67 and 91 m (220 and 300 ft. respectively) and 0.0635 m (2.5 in.) as average radius of a well. According with the last considerations, the Equations (20) and (21) take next expressions:

(22)

(23)

According with different authors [28] for geothermal reservoirs, it is possible to assume as drainage radius r_{e}, a value of 400 m (1312 ft.) and as a wellbore radius r_{w} of 0.0889 m (3.5 in.). Therefore the M value in a geothermal system is expressed with next form:

(24)

During exploitation stage, the damage effect in a well is identified by its productivity decrease. However the concept of the damage effect is related with the alteration of its initial conditions. Therefore the damage effect in a well could have positive, negative or zero values [45].

Table 1. Values of W_{D} obtained using the five geothermal inflow performance relationships and maximum percent differences found.

The positive values of the damage effect indicate diminution in the well productivity, while negative values indicate improvement in its productivity. Zero value of damage effect indicates a natural effect of the reservoir without any artificial manipulation. A negative value of the damage effect could be present after the well has been washed, stimulated and/or fractured. According with Equation (24) the damage effect(s) is an inverse function of M parameter. So, while the s value increases, M value decreases and contrarily, while s decreases, M increases. Combining M parameter into GIPR and considering that the fluid is a mixture of H_{2}O-CO_{2}-NaCl with salinity less than 5000 ppm is obtained [45] next expression:

(25)

Considering the fluid as a mixture of H_{2}O-CO_{2}-NaCl with salinity greater than 5000 ppm [38], the expression is:

(26)

While that, considering a mixture of fluid composed by H_{2}O-CO_{2}-NaCl with salinity of 30,000 ppm and 350˚C of temperature [39], the expression is:

(27)

Figure 2 represents Equation (27) using different damage

Conflicts of Interest

The authors declare no conflicts of interest.

[1] | A. Battistelli, C. Calore and K. Pruess, “The Simulator TOUGH2/EWASG for Modeling Geothermal Reservoirs with Brines and Non-Condensibles Gas,” Geothermics, Vol. 26, No. 4, 1997, pp. 437-464.doi:10.1016/S0375-6505(97)00007-2 |

[2] | L. N. Gutiérrez, “Recursos Geotérmicos de México,” Pro- ceedings Simposio Internacional de Geología Ambiental para Planificación del uso de Territorio, Puerto Varas, 4-6 November 2002, pp. 67-70. |

[3] | S. L. Moya, A. Aragón and L. González, “Estimación de Curvas Características de Producción de Pozos Geotér- micos Empleando dos Curvas de Referencia Adimen- sionales del Comportamiento de Influjo,” Ingeniería Hi- dráulica en México, Vol. 12, No. 3, 1997, pp. 35-40. |

[4] | A. Aragón, G. Izquierdo, M. Pal-Verma and S. Santoyo, “Análisis de Influjo en Pozos Geotérmicos para la De- terminación de sus Flujos Máximos,” Ingeniería Hidr- áulica en México, Vol. 24, No.1, 2009, pp. 73-83. |

[5] | S. L. Moya, D. Uribe, A. Aragón and A. García, “For- mation Permeability at the Feedzone of Geothermal Wells Employing Inflow Type-Curves,” Geofísica Internacional, Vol. 40, No. 3, 2001, pp. 163-180. |

[6] | H. H. Evinger and M. Muskat, “Calculations of The- oretical Productivity Factor,” Transaction of American Institute of Mining, Metallurgical, and Petroleum Engi- neers, Vol. 146, No. 1, 1942, pp. 126-139. |

[7] | D. R. Horner, “Pressure Build-Up in Wells,” Proceedings of 3rd World Petroleum Congress, E. J. Brill, Leiden, 1951, p. 503. |

[8] | J. E. Warren and P. J. Root, “The Behavior of Naturally Fractured Reservoirs,” SPE Journal, Vol. 3, No. 3, 1963, pp. 245-255. |

[9] | C. S. Matthews and D. G. Russell, “Pressure Buildup and Flow Test in Wells,” Monograph, Vol. 1, Society of Petroleum Engineers of AIME, Henry L. Doherty Series, Dallas, 1977. |

[10] | R. G. Agarwal, R. Al-Hussainy and H. J. Ramey Jr., “An Investigation of Wellbore Storage and Skin Effect in Unsteady Liquid Flow: I. Analytical Treatment,” SPE Journal, Vol. 10, No. 3, 1970, pp. 279-290. |

[11] | H. J. Ramey, “Short-Time Well Test Data Interpretation in the Presence of Skin Effect and Wellbore Storage,” Journal of Petroleum Technology, Vol. 22, No. 1, 1970, pp. 97-104. |

[12] | R. C. Earlougher Jr., “Advances in Well Test Analysis,” Monograph, Vol. 5, Society of Petroleum Engineers of AIME, Dallas, 1977. |

[13] | J. R. Rivera and H. J. Ramey Jr., “Application of Two- Rate Flow Tests to the Determination of Geothermal Reservoirs Parameters,” Proceedings of 52th Annual Fall Meeting of Society of Petroleum Engineers, Denver, 9-12 October 1977, pp. 346-353. |

[14] | J. Barua and R. Horne, “Computerized Analysis of Ther- mal Recovery Well Test Data,” SPE Journal, Formation Evaluation, Vol. 2, No. 4, 1997, pp. 560-566. |

[15] | C. S. Chen and C. C. Chang, “Theoretical Evaluation of Non-Uniform Skin Effect on Aquifer Response under Constant Rate Pumping,” Journal of Hydrology, Vol. 317, No. 3-4, 2006, pp. 190-201.doi:10.1016/j.jhydrol.2005.05.017 |

[16] | A. Aragón, G. Izquierdo and V. Arellano, “Practical Application of the Damage Determination in a Well,” Geothermal Resources Council Transactions, Vol. 34, 2010, pp. 1125-1130. |

[17] | M. Muskat, “The Production Histories of Oil Producing Gas-Drive Reservoirs,” Journal Applied Physics, Vol. 16, 1945, pp. 147-153. doi:10.1063/1.1707566 |

[18] | A. F. Van Everdingen and W. Hurst, “The Application of the LaPlace Transformation to Flow Problems in Re- servoirs,” Petroleum Transactions AIME, Vol. 196, 1949, pp. 156-164. |

[19] | A. F. Van Everdingen, “The Skin Effect and Its Influence on the Productive Capacity of a Wells,” Transaction of American Institute of Mining, Metallurgical, and Petro- leum Engineers, Vol. 203, 1952, pp. 171-176. |

[20] | W. E. Gilbert, “Flowing and Gas-Lift Well Performance,” Drilling and Production Practice, Vol. 13, 1954, pp. 126-157. |

[21] | W. T. Weller, “Reservoir Performance during Two-Phase Flow,” Journal of Petroleum Technology, Vol. 18, No. 2, 1966, pp. 240-246. doi:10.2118/1334-PA |

[22] | J. V. Vogel, “Inflow Performance Relationships for Solu- tion Gas Drive Wells,” Annual Fall Meeting of Society of Petroleum Engineers, Dallas, 29 September-2 October 1968, pp. 66-79. |

[23] | M. B. Standing, “Inflow Performance Relationships for Damaged Wells Producing by Solution-Gas Drive,” Journal of Petroleum Technology, Vol. 21, No. 11, 1970, pp. 1399-1400. |

[24] | J. J. Fetkovich, “The Isochronal Testing of Oil Wells,” SPE 48th Annual Fall Meeting, Las Vegas, 30 Sep- tember-3 October 1973, pp. 78-84. |

[25] | M. A. Klins and M. W. Majcher, “Inflow Performance Relationships for Damaged or Improved Wells Producing under Solution-Gas Drive,” Journal of Petroleum Tech- nology, Vol. 44, No. 12, 1992, pp. 1357-1363.doi:10.2118/19852-PA |

[26] | M. A. Klins and L. Clark, “An Improved Method to Predict Future IPR Curves,” SPE Reservoir Engineering, Society of Petroleum Engineers, San Antonio, 1993, pp. 243-248. |

[27] | M. L. Wiggins, “Generalized Inflow Performance Rela- tionships for Three-Phase Flow,” Production Operations Symposium, Oklahoma City, 25-28 March 1994, pp. 275-286. |

[28] | A. Grant, G. Donaldson and F. Bixley, “Geothermal Re- servoir Engineering,” Academic Press, New York, 1982. |

[29] | S. P. Kjaran and J. Elliasson, “Geothermal Reservoir Engineering,” Lecture Notes, University of Iceland, Reykjavik, 1982, pp. 222-236. |

[30] | S. K. Garg and T. D. Riney, “Analysis of Flow Data from the DOW/DOE, L.R. Sweezy No. 1 Well,” Topical Report, La Jolla, 1984, pp. 78-83. doi:10.2172/5096904 |

[31] | M. H. Chu, “Inflow Performance Relationships for Geo- pressured Geothermal Wells,” Geothermal Resources Council Transactions, Vol. 12, 1988, pp. 437-440. |

[32] | R. James, “One Curve Fits All,” Proceedings of 14th Workshop on Geothermal Reservoir Engineering, Stan- ford University, Stanford, 24-26 January 1989, pp. 329-334. |

[33] | C. Gunn and D. Freeston, “Applicability of Geothermal Inflow Performance and Quadratic Drawdown Relation- ships to Wellbore Output Curve Prediction,” Geothermal Resources Council Transactions, Vol. 15, 1991, pp. 471- 475. |

[34] | E. Iglesias and S. L. Moya, “Geothermal Inflow Perfor- mance Relationships,” Geothermal Resources Council Transactions, Vol. 14, 1990, pp. 1201-1205. |

[35] | S. L. Moya, “Efectos del Bióxido de Carbono Sobre el Transporte de Masa y Energía en Yacimientos Geotér- micos,” Tesis de Doctorado, Universidad Nacional Autó- noma de México, México City, 1994. |

[36] | S. L. Moya, A. Aragón, E. Iglesias and E. Santoyo, “Prediction of Mass Deliverability from a Single Well- head Measurement and Geothermal Inflow Performance Reference Curves,” Geothermics, Vol. 27, No. 3, 1998, pp. 317-329. doi:10.1016/S0375-6505(98)00005-4 |

[37] | D. Montoya, “Estimación de Permeabilidades de Yaci- mientos Geotérmicos Mediante la Aplicación de Curvas Tipo de Influjo Geotérmico,” Tesis de Maestría, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, 2003. |

[38] | O. Meza, “Efecto de la Precipitación de Sales en el Diagnóstico de Permeabilidades Rocosas,” Tesis de Maestría, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, 2005. |

[39] | S. López, “Análisis del Comportamiento de Influjo con Efecto de Da?o en Yacimientos Altamente Salinos y de Alta Temperatura,” Tesis de Licenciatura, Universidad Popular de la Chontalpa, H. Cárdenas, 2011. |

[40] | A. Aragón, “La Influencia del Factor de da?o en Curvas- Tipo de Influjo Geotérmico y su Impacto en el Diag- nóstico de Permeabilidades,” Tesis de Doctorado, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, 2006. |

[41] | A. Aragón, S. L. Moya and A. García, “Inflow Per- formance Relationships in Geothermal and Petroleum Reservoir Engineering: A Review of the State of the Art,” Geothermics, Vol. 37, No. 4, 2008, pp. 635-650. |

[42] | S. L. Moya, E. Iglesias and A. Aragón, “Curvas de Re- ferencia Adimensionales para Estimar Productividades de Masa y Energía en Yacimientos Geotérmicos con/sin Bióxido de Carbono,” Geotermia, Revista Mexicana de Geoenergía, Vol. 11, 1995, pp. 167-179. |

[43] | E. Iglesias and S. L. Moya, “Applicability of Geothermal Inflow Performance Reference Curves to CO2-Bearing Reservoirs,” Geothermics, Vol. 27, No. 3, 1998, pp. 305- 315. doi:10.1016/S0375-6505(98)00004-2 |

[44] | S. L. Moya, D. Uribe and D. Montoya, “Computational System to Estimate Formation Permeabilities and Output Curves of Geothermal Wells,” Computer & Geosciences, Vol. 29, No. 9, 2003, pp. 1071-1083.doi:10.1016/S0098-3004(03)00031-1 |

[45] | A. Aragón, S. L. Moya and M. Suárez, “Determination of the Damage Effect in Geothermal Wells Using Inflow Type Curves,” Geothermal Energy Research Trends, Nova Publishers Inc., New York, 2008, pp. 163-201. |

[46] | S. López and A. Aragón, “Caracterización de Yaci- mientos a Partir de Análisis de Mediciones de Pro- ducción,” Investigación y Posgrado Revista de la Uni- versidad Popular de la Chontalpa, Vol. 2, 2011, pp. 24- 29. |

[47] | S. de Estudios, “Características de Producción Actuales del Campo Geotérmico de Los Azufres, Mich., México,” Informe Interno ISE-045-2002, Gerencia de Proyectos Geotérmoeléctricos de la CFE, Morelia, 2002. |

[48] | M. C. Salto and A. F. Hernández, “Simulación Numérica de Yacimientos Geotérmicos Mediante el Simulador de Volúmenes Finitos, TOUGH2,” Reporte Interno AIT, Gerencia de Geotermia del IIE, Cuernavaca, 2011. |

[49] | G. Jones, M. Blount and H. Glaze, “Use of Short Term Multiple Rate Flow Tests to Predict Performance of Wells Having Turbulence,” SPE 51st Annual Fall Meeting, New Orleans, 3-6 October 1976, pp. 378-383. |

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