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.

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