Using Monte Carlo simulation to estimate geothermal resource in Dholera geothermal field, Gujarat, India
 509 Downloads
 2 Citations
Abstract
After effective investigation on various exploration activities, from a geothermal prospect, stakeholders are constantly anxious to know of its potential. Geothermal resource assessment is estimation of the amount of thermal energy that is stored beneath the earth’s surface and can be extracted from a geothermal reservoir and used economically for a time frame, normally a very long while. A study was undertaken to calculate energy potential of the Dholera Geothermal Field. Using various parameters from the geoelectrical model, the resource potential beneath the subsurface was calculated by applying Monte Carlo simulation. Using various parameters from the geoelectrical model and applying Monte Carlo simulation, the resource potential beneath the subsurface was calculated. It was calculated considering all uncertain parameters (random values) within the span of the minimum, the most likely and the maximum triangular distribution. The result shows the frequency distribution of energy values. Energy estimated at 3 km depth in Dholera is \(3.73\times 10^{10}\ \hbox {J}\) (P50 Case). Energy estimated for P90 case is \(2.90\times 10^{10}\ \hbox {J}\) and for P10 case is \(3.73\times 10^{10}\ \hbox {J}\).
Keywords
Volumetric method Monte Carlo simulation Geothermal energy Resource estimationList of Symbols
 \(\mu \)
Mean
 \(\sigma ^{2}\)
Variance
 \(Q_{\mathrm{T}}\)
Total thermal energy (kJ/kg)
 \(Q_{\mathrm{r}}\)
Heat in rock (kJ/kg)
 \(Q_{\mathrm{s}}\)
Heat in steam (kJ/kg)
 \(Q_{\mathrm{w}}\)
Heat in water (kJ/kg)
 A
Area of the reservoir \((\hbox {m}^{2})\)
 h
Average thickness of the reservoir (m)
 \(C_{\mathrm{r}}\)
Specific heat of rock at reservoir condition (kJ/kgK)
 \(C_{\mathrm{l}}\)
Specific heat of liquid at reservoir condition (kJ/kgK)
 \(C_{\mathrm{s}}\)
Specific heat of steam at reservoir condition (kJ/kgK)
 \(\phi \)
Porosity
 \(T_{{i}}\)
Average temperature of the reservoir \(({^{\circ }}\hbox {C})\)
 \(T_{{c}}\)
Final or abandonment temperature \(({^{\circ }}\hbox {C})\)
 \(S_{\mathrm{w}}\)
Water saturation
 \({\rho }_{\mathrm{si}}\)
Steam density at reservoir temperature \((\hbox {kg}/\hbox {m}^{3})\)
 \({\rho }_{\mathrm{wi}}\)
Water density at reservoir temperature \((\hbox {kg}/\hbox {m}^{3})\)
 \(H_{\mathrm{si}}\)
Steam enthalpy at reservoir temperature (kJ/kg)
 \(H_{\mathrm{wi}}\)
Water enthalpy at reservoir temperature (kJ/kg)
 \(H_{\mathrm{wf}}\)
Final water enthalpy (kJ/kg)
1 Introduction

Power density method

Surface thermal flux method

Magmatic heat budget method

Numerical reservoir modeling

Stored heat or volumetric assessment

Lumped parameter models

Decline analysis

Natural state matching

History matching

Probabilistic and deterministic method

Genetic algorithm.
Lumped parameter modeling technique is most often used in fields where only water is present. For multiphase system, this method is not reliable. Therefore, only the volumetric methods and reservoir simulation are the preferred methods for defining proven and probable reserves. However, numerical simulation method is not applicable in early stages of exploration as it is applicable only when actual well data are available. Based on aforementioned points, stored heat and volumetric methods are used for the resource estimation of geothermal reservoir. In volumetric methods, Monte Carlo method is the most reliable method for resource estimation.
The volumetric method is chosen for estimating the thermal energy of the system. In volumetric calculation, the reservoir is normally considered as a single body or it is divided into layers which are then subdivided into blocks. Each block contains one unique value for each parameter assigned. Main parameters of a reservoir are temperature, porosity, area, thickness, density, and heat capacity of the fluid and rock matrix (Martinez 2009). Quantification of uncertainties in the parameters of the probability distribution can be dealt quite well using the Monte Carlo simulation method (Gauxuan 2008).
The arbitrary conduct in a session/game of chance is the manner by which Monte Carlo chooses the event of an unknown variable in one calculation. The calculation is repeated many times until the specified iteration cycle is completed. In nutshell, Monte Carlo is a practical method which solves problems by numerical operations on random number. For instance, while playing dice, 1, 2, 3, 4, 5 or 6 are probable outcomes, yet we do not know the possible result of each roll. The same is legitimate for the distinctive parameters (area, thickness, porosity, and reservoir temperature) utilized as a part of computing the geothermal reserves. They vary within a certain range of values, which is uncertain for a particular sequence in the calculation. To deliver qualitative and accurate results, obscure variables for each reservoir property are fitted into a picked demonstrate dispersion (e.g., normal, triangular, uniform and log normal) which is based on some predetermined conditions or criteria of the geothermal field being evaluated. The simulation then continues to extract numbers representing the unknown variable and utilizing these as input to the cells in the spreadsheet until the process is complete (Sarimiento and Steingrimsson 2008). So with a combination of sampling theory and numerical analysis, the Monte Carlo method is a special contribution to the science of computing different properties (Baalousha 2016).
The Monte Carlo method uses stochastic techniques to evaluate the effect of measurements and uncertainty on the petrophysical results. Monte Carlo technique is chosen because it involves processing the interpretation model several times with randomly varying parameters. The method is frequently utilized when a model is perplexing, nonlinear or includes uncertain parameters. The method utilizes distinctive approaches; however, every one of them has a tendency to follow a particular pattern. With the help of Monte Carlo technique, all the possible of results for shale volume, porosity, water saturation, etc. are obtained with a cumulative distribution function for total heat in place, for each iteration, in the form of P10, P50 and P90 cases. It also generates a range for hydrocarbon in place, nettogross ratios, average porosities and saturations for the percentile cases selected by the interpreter (Stoian 1965).

Selecting or designing a probability model by statistical data reduction, analogy and theoretical considerations.

Generating random numbers and corresponding random variables.

Designing and implementing variancereducing techniques.
2 Salient characteristics of Monte Carlo method
 1.
The Monte Carlo method is associated with the probability theory. So the relationships of probability theory have been derived from theoretical considerations. Monte Carlo method uses probability to find answers to physical problems that may or may not be related to probability.
 2.
The application of the Monte Carlo method offers a penetrating insight into the behavior of the systems being studied.
 3.
The results of Monte Carlo computations are treated as estimates within certain limits rather than true exact values. All meaningful physical measurements are expressed in this way. Monte Carlo techniques can be used to obtain approximations too.
 4.
The method is flexible to the extent that it elaborates the complexity of a problem. This is reflected by a fact that a greater number of parameters or complicated geometry does not alter its basic character and the penalty paid for complexity is increased computing time and costs (McGlade et al. 2013).
 5.
A practical consideration is that the iterative calculations necessary for attaining a certain level of confidence can be distributed among several computers, working simultaneously in one or more places.
 6.
The Monte Carlo solutions are approximate and they can be upgraded with time.
 7.
Solutions of the Monte Carlo method are numerical and apply only to the particular case studies (Dur 2005).
3 Methodology
Monte Carlo uses different stochastic techniques and probabilistic approach to properly estimate the range of reservoir’s generating capacity, to identify major uncertainties, and to quantify the risks associated with the proposed expansion.
 1.
We have to define the reservoir’s performancedependent variable and perform screening process to identify various parameters’ uncertainties.
 2.
Use the different experimental methodology to create a series of dynamic reservoir simulation models which capture the full range of reservoir performance.
 3.
Calibrate and validate these models by history matching and natural state matching.
 4.
Create the response for reservoir performance using multiple regression analysis.
 5.
Then apply this to the Monte Carlo simulation to generate full probabilistic performance and derive P10, P50 and P90 model, and also verify Monte Carlo simulation results.
 6.
Use the P10, P50 and P90 models for future development like in energy calculation and plan size (Hoang et al. 2005).
4 Workflow of Monte Carlo method
 (a)
Define a domain of possible inputs: each Monte Carlo simulation begins off with developing a deterministic model which intently looks like the genuine situation. In this deterministic model, we utilize the most likely value of the input parameters. The domain of these parameters is defined around an initial value, used in the standard deterministic module. This part is the core of Monte Carlo simulation. The distribution must also be specified (Square, Triangular or Gaussian) for generation of random values.
 (b)
Generate inputs randomly from a probability distribution over the domain: once the distributions have been identified, the random numbers are generated. At the start of each simulation, every parameter is changed using a random number. If the random number generator comes up with a value outside of the selected range, then another random number will be chosen. This is done to try and keep the distribution within reasonable limits, because very large shifts in parameters can give ambiguous results. This may cause difficulty for the model to run.
 (c)
When a satisfactory deterministic model is obtained, the risk components are added to it. Since, risk originates due to stochastic behavior of input parameters; the distribution that can represent the input parameter correctly is identified. If historical data are available for the input parameter, history matching is done by fitting the data to obtain a discrete or continuous distribution. Some of the standard procedures for fitting data to distributions are method of maximum likelihood, method of moments and nonlinear optimization.
 (d)
Perform a deterministic computation on the inputs: parameters for each simulation iteration, IP will run the interpretation modules, like clay volume, porosity and saturation, cutoff parameters and summations, in the order displayed (in the given order)
 (e)
Aggregate the results: parameters for each simulation are saved. Iterations are carried out to obtain the values for every desired parameter ranking from low to high probability. Result is described in terms of mean and a percentile for each parameter. Sample output is collected and statistical analysis is performed. The output is usually displayed in the form of frequency histogram which gives an idea about the probability density function of the output parameter (Raychaudhuri 2008).
5 Monte Carlo model distributions
This section describes how to generate a procedure for various single variate continuous distributions.
 1.
Normal distribution
 2.
Lognormal distribution
 3.
Uniform distribution
 4.
Triangular distribution
5.1 Normal distribution
It is the most commonly used distribution model. It is a bellshaped curve and has a continuous probability distribution curve. Figure 3 shows a typical Normal distribution curve.
5.2 Lognormal distribution
5.3 Uniform distribution
It is a continuous probability distribution function and describes a random variable in which any numerical value has an equal chance of occurrence. Mean and median values are concurrent and occur at midpoint of the random variable as can be seen in Fig. 5 (Rubinstein 1981).
5.4 Triangular distribution
It is a continuous distribution and is in a shape of triangle. The triangle can be symmetrical or skewed in both directions and is defined by specifying minimum, most likely and maximum values of variables (Fig. 6) (Rubinstein 1981).
6 Guidelines for the determination of reservoir parameters
Guidelines followed in determining the various parameters for reserve estimation (Sarimiento and Steingrimsson 2008)
Parameter  Proven  Probable  Possible/Inferred 

Area  Defined by drilled wells or measured high temperatures in wells at selected depth interval, allowing some zones around wells to be included and considering well spacing as a guide to define reservoir character  Defined by wells with high temperature at selected depth interval. This interval based on At least one well intercept at resource depth Geophysics surveys Shallow temperature gradients, surface heat flow Presence of adjacent proven area  Defined by wells with high temperature at selected depth interval. This interval based on Locations of surface activity, e.g., springs and fumaroles Surface heat flow Some geophysical mapping may be available. 
Depth  Maximum depth attained by drilling plus reasonable drainage distance below bottom of well  Part of thickness intercepted by well and which is extrapolated by geophysics or adjacent wells. Maximum depth attained by drilling plus reasonable drainage distance below the bottom of well  Estimated from hydrology, structure analogy and geophysical data 
Fluid temperature  Measured from well temperatures or discharge enthalpy  Reservoir temperature measured in at least one borehole, lateral extrapolation of known temperatures or using chemical geothermometry using conceptual hydrological model  Estimated temperatures from surface geochemistry, heat flow estimates and thermal conductivity measurements 
Cutoff temperature  Minimum temperature required for wells to selfdischarge in convective geothermal development  Minimum temperature required for wells to selfdischarge in convective geothermal development. Estimated from assumptions on reservoir character  Minimum temperature required for wells to selfdischarge in convective geothermal development. Estimated from assumptions on reservoir character 
Base temperature  The lowest temperature that will be reached in the reservoir as part of extraction process  The lowest temperature that will be reached in the reservoir as part of extraction process  The lowest temperature that will be reached in the reservoir as part of extraction process 
Permeability & Pressure  Proven sustained discharge from deep wells  Inferred extension of faults or aquifer permeability. Liquid pressures inferred from wells in adjacent proven area or shallow wells  Liquid pressures and permeability inferred from shallow wells or spring flows 
Chemistry  No major problems with fluid chemistry or uncontrollable solids deposition from fluid discharged by existing wells  No major problems with fluid chemistry or uncontrollable solids deposition from fluid discharged by existing wells  No major problems with fluid chemistry or uncontrollable solids deposition from fluid discharged by existing wells 
Porosity  Measured on cores or inferred from reservoir transient behavior, demonstrated ability to stimulate in enhanced geothermal system (EGS) system  Inferred from rock type, based on surface mapping, wireline logs, or lithostratigraphic interpretation  Inferred from rock type, based on surface mapping, wireline logs, or lithostratigraphic interpretation 
Fracturing  Imaged or deduced from wireline logs  Inferred spacing of major fractures and whether regular, localized or fractal in nature  Inferred spacing of major fractures and whether regular, localized or fractal in nature 
7 Application of Monte Carlo in geothermal
The estimation of the geothermal energy reserves in view of the different reservoir parameters could be carried out using Monte Carlo simulation. It uses a probabilistic approach for evaluating geothermal energy reserves or resources. Due to the complexity and heterogeneity of the geologic formations and geological arrangement of most geothermal reservoirs. Monte Carlo simulation method is the preferred deterministic approach. It assumes a single value for each parameter to represent the whole reservoir. Instead of assigning a fixed value to reservoir parameters, a range of values are randomly selected and drawn for each cycle of calculation over a thousand iteration (Ofwona 2011).
 1.
Make development plans that can cover the range of possible outcomes.
 2.
Provide a range of production forecasts to evaluate the expected outcome of their ventures.
 3.
Measure exploration, appraisal, and commercial risks.
 4.
Ensure that they can handle an unfavorable outcome.
 5.
Understand and communicate the confidence level of their reserves estimate.
 1.
Probabilistic method.
 2.
Deterministic method.
7.1 Probabilistic method
In the probabilistic method, we use the full range of values that could reasonably occur for each unknown parameter (from the geosciences and engineering data) to generate a full range of possible outcomes for the resource volume. To do this, we identify the parameters that make up the reserves estimate and then determine a socalled probability density function (PDF). The PDF describes the uncertainty around each individual parameter based on geosciences and engineering data. Using a stochastic sampling procedure, we then randomly draw a value for each parameter to calculate a recoverable or heat inplace resource estimate (Lawless 2010).
7.2 Deterministic method
The deterministic method uses a single value for each parameter, based on a welldefined description of the reservoir, resulting in a single value for the resource or reserves estimate. Typically, three deterministic cases are developed to represent either low estimate (1P or 1C), best estimate (2P or 2C), or high estimate (3P or 3C), or proved, probable, and possible estimates. Each of these categories can be related to specific areas or volumes in the reservoir and a specific development plan.

The method describes a specific physical case; physically inconsistent combinations of parameter values can be spotted and removed.

The method is direct, easy to explain, and manpower efficient.

The estimate is reproducible.

Because of the last two advantages, investors and shareholders like this method, and it is widely used to report proved reserves for regulatory purposes.
Deterministic models use a certain number of input parameters in few equations to give a set of outputs. They give the same results no matter how many times the calculation is repeated. Stochastic models, on the other hand, use variable (random) inputs and give different results depending on the distribution functions of the input parameters. They are often used when the model is complex, nonlinear or has uncertain parameters. The random numbers turn the deterministic model into a stochastic model (Sarimiento and Steingrimsson 2008; Pandey and Joshi 2015).
 1.
Create a parametric deterministic model, \(y = f(x1, x2, {\ldots }, xq)\).
 2.
Generate a set of variable inputs, \(xi1, xi2, {\ldots }, xiq\).
 3.
Evaluate the model and store the results as yi.
 4.
Repeat steps 2 and 3 for \(i = 1\) to n.
 5.
Analyze the results using different statistical methods.
8 Deterministic model for volumetric stored heat
The volumetric method is used for the calculation of total thermal energy in place of the rock and fluid which could be extracted for a specified reservoir volume and reservoir temperature (Muffler 1978).
9 Monte Carlo simulation software
 1.
Graphs of input parameters, output frequency, cumulative frequency, linear plot, etc.
 2.
Statistics: minimum, mean, median, mode, and maximum values; skewness, standard deviation, etc.
 3.
Sensitivity test.
10 Monte Carlo output
Input parameters for energy calculations at 3 km depth at Dholera
Parameters  Min value  Most likely value  Max value  Simulation results 

Area, A (\(\hbox {km}^2\))  2  19  36  19 
Pay, H (m)  18  20  30  22.67 
Porosity, \(\phi \)  0.03  0.05  0.1  0.06 
Density of rock, \({\rho }_{\mathrm{r}}\) (\(\hbox {kg}/\hbox {m}^{3}\))  2700  2800  2900  2800 
Density of water, \({\rho }_{\mathrm{w}}\) (\(\hbox {kg}/\hbox {m}^{3}\))  970  980  1000  983.33 
Heat capacity of rock, \(C_{\mathrm{Pr}}\) (\(\hbox {J}/\hbox {kg}\, {^{\circ }}\hbox {C}\))  600  800  1000  800 
Heat capacity of water, \(C_{\mathrm{Pw}}\) (\(\hbox {J}/\hbox {kg}\,{^{\circ }}\hbox {C}\))  3000  4000  4200  3733.33 
Temp reservoir, \(T_{\mathrm{R}}\ ({^{\circ }}\hbox {C})\)  170  180  190  180 
Surface temp, \(T_{\mathrm{S}}\ ({^{\circ }}\hbox {C})\)  40  44  49  44 
Volume matrix, \(V_{\mathrm{m}}\)  A priori values  A priori values  A priori values  99.43 
Volume fluid, \(V_{\mathrm{f}}\)  A priori values  A priori values  A priori values  6.35 
Energy, \(E_{\mathrm{t}}\) (J)  A priori values  A priori values  A priori values  \(3.73\times 10^{10}\) (P 50) 
11 Study area
The present study area is located in the Ahmedabad district of Gujarat state in India. The Dholera Geothermal Field, an ancient port city in the Gulf of Khambhat (Fig. 7), lies 30 km to the southwest of the Dhandhuka village in the Ahmedabad district and is around 60 km to the north of the city of Bhavnagar. Dholera is in close proximity to the coast. It is surrounded by water on three sides, namely on the east face by Gulf of Khambhat, on the north side by Bavaliari creek and on the southern side by Sonaria creek (Aghil et al. 2014). The Dholera Special Investment Region will be a major new industrial hub located on a greenfield site about 100 km to the south of Ahmedabad and about 130 km from Gandhinagar. The project is the first investment region to be designated under the proposed Delhi–Mumbai Industrial Corridor project (DMIC), a joint Indian and Japanese Government initiative to create a linear zone of industrial development nodes along a dedicated freight corridor (DFC).
Input parameters for energy calculations at 4 km depth at Dholera
Parameters  Min value  Most likely value  Max value  Simulation results 

Area, A (\(\hbox {km}^2\))  2.5  14.5  27.5  14.83 
Pay, H (m)  18  20  30  22.67 
Porosity, \(\phi \)  0.03  0.05  0.1  0.06 
Density of rock, \({\rho }_{\mathrm{r}}\) (\(\hbox {kg}/\hbox {m}^{3}\))  2700  2800  2900  2800 
Density of water, \({\rho }_{\mathrm{w}}\) (\(\hbox {kg}/\hbox {m}^{3}\))  970  980  1000  983.33 
Heat capacity of rock, \(C_{\mathrm{Pr}}\) (\(\hbox {J}/\hbox {kg}\,{^{\circ }}\hbox {C}\))  600  800  1000  800 
Heat capacity of water, \(C_{\mathrm{Pw}}\) (\(\hbox {J}/\hbox {kg}\,{^{\circ }}\hbox {C}\))  3000  4000  4200  3733.33 
Temp reservoir, \(T_{\mathrm{R}}\ ({^{\circ }}\hbox {C})\)  170  180  190  180 
Surface temp, \(T_{\mathrm{S}}\ ({^{\circ }}\hbox {C})\)  40  44  49  44 
Volume matrix, \(V_{\mathrm{m}}\)  A priori values  A priori values  A priori values  99.43 
Volume fluid, \(V_{\mathrm{f}}\)  A priori values  A priori Values  A priori values  6.35 
Energy, \(E_{{t}}\) (J)  A priori values  A priori values  A priori values  \(3.82\times 10^{10}\) (P 50) 
Cambay basin rests on the Deccan trap, which lies at a depth of 500–600 m. Quaternary alluvial deposits of a thickness up to 100 m occur by the side of the basin (Sircar et al. 2015). Villages here show an easterly trend in elevation changes, wherein the lowlying plain falls gradually from the 8m contour on the western boundary to 4 m in the East. The area is marked by the presence of old mud flats, flood plains and salt flat areas. The soil in this region mainly consists of alternate layers of gravels, fine to coarse grained sand and clay. Chemically the soil is loamy, mixed montmorillonitic, calcareous and mostly saline. The subsurface lithology of the area is mostly sand dominant consisting of alternating layers of coarse and fine sand.
To analyze various physicochemical properties of the reservoir fluid and subsequently establish the basic idea of the subsurface geology, prevalent temperature and other crucial reservoir parameter, geochemical analysis of the water from hot spring at Dholera was carried out. Gravity, magnetic and magnetotelluric (MT) studies were carried out to recognize the areal extension of the geothermal prospect. The Landsat imagery study was carried out to trace the candidate zones for drilling based on small Vegetation Index and positive anomalies in surficial temperature (Kumar and Shekhar 2016).
2D magnetotelluric (MT) and audiofrequency magnetotelluric (AMT) surveys were undertaken for geothermal exploration along six profiles in the study area. Field AMT and MT measurements were performed in Dholera at 66 MT/AMT sounding stations along six profiles (Fig. 8). Orientation of five profiles was WSW–ENE and one was normal to five profiles. Frequency of the MT/AMT data is in the range of 0.001–10,000 Hz. Simultaneously synchronized measurements on reference station located in Kamalpura (Fig 7c) were carried out. The shallow geoelectric maps along with the deep maps portray that the reservoir is shale or sandstone body packed between excessively resistive basalts. 2D data have been used to prepare crosssectional APS at deep and shallow levels (PBG 2014) .
In addition to the magnetotelluric studies, gravity data were obtained along the same profiles with offset at some stations. Residual Bouguer gravity was modeled subsequent to application of corrections. The gravityderived subsurface picture shows lowdensity zones sandwiched between highdensity zones providing further evidence of the picture derived from MT cross sections presented in this paper. Integration of the gravity and magnetotelluric interpretation supports that beneath the surface manifestations (hot springs), less resistive geophysical anomaly with low density is present which indicates that a geothermal reservoir might be existent.
Resistivity closures in shallow as well as deep cross sections observed around the hot springs are true affirmation of the model postulated. Sections showing areal resistivity distribution at the depth of 3 and 4 km verify the same. Hence, the results give an optimistic idea of the study area being a promising geothermal prospect. Exploitation of this energy can be put to wide range of smallscale domestic to largescale commercial uses. The resource potential of the prospect and the temperature gradient of the subsurface can be better described by drilling of wells and running temperature log.
12 Geothermal resource estimation: Dholera
12.1 Stored heat calculation at 3 km depth:
Figure 9 shows the resistivity distribution at the depth of 3 km below sea level at Dholera. Also lowresistivity anomalies were found between the 2nd and 3rd profiles, i.e., D2 and D5 (Fig. 8).
Various input parameters to this analysis are summarized in Table 2. Most likely estimates are given as well as estimated probability distributions and minimum and maximum values for different input parameters. Two most sensitive parameters for energy calculations are area and temperature. These input parameters are used in Monte Carlo simulation in Excel spreadsheet. The simulation runs can be as many as time and computer allows. More runs give accurate results. In this case the runs were 100. The thermal energy is usually plotted using the relative frequency histogram and the cumulative frequency distribution. The vertical axis represents the cumulative frequencies greater than or equal to given values of the random variable. The cumulative frequency greater than or equal to the maximum value is always 1 and the cumulative frequency greater than or equal to the minimum value is always 0 (Mwarania 2014; Ofwona 2011). The result shows the frequency distribution for energy values. Energy estimated at 3 km depth in Dholera is \(3.73 \times 10^{10}\ \hbox {J}\) (P50 Case) (\(\hbox {Proven} + \hbox {Probable}\)). Energy estimated for P90 case is \(2.90 \times 10^{10}\ \hbox {J}\) (proven) and for P10 case is \(3.73 \times 10^{10}\ \hbox {J}\) (\(\hbox {Proven} +\hbox {Probable} + \hbox {Possible}\)) (Fig. 10).
12.2 Stored heat calculation at 4 km depth
Figure 11 shows the resistivity distribution at the depth of 4 km below sea level. Also lowresistivity anomalies were found between the 2nd and 3rd profiles, i.e., D2 and D5 (Fig. 8).
13 Conclusion
The preferred method for reservoir assessment in the early phases of geothermal development is the volumetric method. The volumetric method refers to the calculation of thermal energy in the rock and the fluid which could be extracted based on specified reservoir volume, reservoir temperature, and reference or final temperature. Monte Carlo simulation is one of the best methods generally used for resource estimation. In this study, resource potential of the Dholera geothermal system has been estimated based on the geoscientific information available. The method was applied to estimate the resource of identified Dholera prospect and the energy was estimated to be \(3.7 \times 10^{10}\ \hbox {J}\) (P50 case). Estimation of power potential for Dholera Geothermal Field by Monte Carlo method produces reasonable and realistic estimates .This method has been applied in other geothermal fields around the world and will be appropriate for the estimation of power potential in geothermal fields in India.
Notes
Acknowledgements
Authors are thankful to PBG Geophysical Exploration Ltd., Poland, for conducting 2D and 3D magnetotelluric survey at Dholera geothermal site and providing technical support. Authors acknowledge the support provided by School of Petroleum Technology, Pandit Deendayal Petroleum University, Gandhinagar, Gujarat, India. Furthermore, authors are thankful to Ms. Hiteshri Yagnik for drafting the figures for the manuscript. Authors are also thankful to the school for giving permission to publish this research.
Compliance with ethical standards
Availability of data and material
All relevant data and material are presented in the main paper.
Funding
Not applicable.
Competing interests
The authors declare that they have no competing interests.
References
 Aghil TB, Mohna K, Srinivas Y, Rahul P, Paul J, Alby ER, Nair NC, Chandrasekar N (2014) Delineation of electrical resistivity structure using Magnetotellurics: a case study from Dholera coastal region. J Coast Sci 1(1):41–46 Gujarat, IndiaGoogle Scholar
 Baalousha HM (2016) Using Monte Carlo simulation to estimate natural groundwater recharge in Qatar. Model Earth Syst Environ 2:87. https://doi.org/10.1007/s4080801601408 CrossRefGoogle Scholar
 Biswas SK (1987) Regional tectonic framework, structure and evolution of the western marginal basins of India. Tectonophysics 135:307–327CrossRefGoogle Scholar
 Biswas SK (1988) Structure of the Western continental margin of India and related activity in Deccan flood Basalt. Memoir Geol Soc India 10:371–390Google Scholar
 Dur F (2005) The usage of stochastic and multi criteria decisionaid methods evaluating geothermal energy exploitation projects. İzmir Institute of Technology, pp 1–116Google Scholar
 Gauxuan G (2008) Assessment of the Hofsstadir geothermal field, WIceland, by lumped parameter modelling, Monte Carlo simulation and tracer test analysis. Geothermal training programme, Iceland, pp 247–279Google Scholar
 Hoang V, Alamsyah O, Roberts J (2005) Darajat geothermal field performance—a probabilistic forecast. In: Proceedings world geothermal congress, antalya, pp 24–29Google Scholar
 Kalos MH, Whitlock PA (2007) Monte Carlo methods. Wiley, New York, pp 1–203zbMATHGoogle Scholar
 Kumar D, Shekhar S (2016) Linear gradient analysis of kinetic temperature through geostatistical approach. Model Earth Syst Environ 2:145. https://doi.org/10.1007/s4080801601983 CrossRefGoogle Scholar
 Lawless J (2010) Geothermal lexicon for resources and reserves definition and reporting. Australian Geothermal Energy Group, Australia, pp 1–90Google Scholar
 Martinez AM (2009) Assessment of the Northern part of the Los Azufres geothermal field, Mexico, by Lumped Parameter modelling and Monte Carlo simulation. Geothermal training programme, iceland, pp 345–364Google Scholar
 McGlade C, Speirs J, Sorrell S (2013) Methods of estimating shale gas resources—comparison, evaluation and implications. Elseveir, Amsterdam, pp 116–125Google Scholar
 Muffler LJP (1978) USGS Geothermal resource assessment. In: Proceedings: Stanford geothermal workshop Stanford University, Stanford, California, pp 1–163Google Scholar
 Mwarania FM (2014) Reservoir evaluation and modelling of the Eburru geothermal system, Kenya. Submitted at University of Iceland, pp 1–88Google Scholar
 Ofwona C (2011) Geothermal resource assessment—case example, Olkaria I. Presented at short course VI on exploration for geothermal resources, Kenya, pp 1–8Google Scholar
 Pandey B, Joshi PK (2015) Numerical modelling spatial patterns of urban growth in Chandigarh and surrounding region (India) using multiagent systems. Model Earth Syst Environ 1:14. https://doi.org/10.1007/s4080801500056 CrossRefGoogle Scholar
 PBG Report (2014) 2D Magnetotelluric survey for four locations for geothermal exploration namely (No. of MT soundings) Unai (66), Gandhar (66) and Dholera (66) (Excluding Tulsishyam, Tuwa and Chabsar). Exploration Geophysics Service. Poland, pp 1–24. (CEGE Report)Google Scholar
 Raychaudhuri S (2008) Introduction to Monte Carlo simulation. In: Proceedings of the 2008 winter simulation conference, U.S.A., pp 91–100Google Scholar
 Rubinstein RY (1981) Simulation and the Monte Carlo method. Wiley, New York, pp 1–277zbMATHGoogle Scholar
 Sanyal SK (2003) One discipline, two arenas—reservoir engineering in geothermal and petroleum industries. In: Proceedings twentyeighth workshop geothermal reservoir engineering Stanford University, California, pp 1–11Google Scholar
 Sanyal SK, Sarmiento Z (2005) Booking geothermal energy reserves. GRC Trans 29:467–474Google Scholar
 Sarimiento ZF, Bjornsson G (2007) Geothermal resource assessmentvolumetric reserves estimation and numerical modelling. Presented at short course on geothermal development in central America—resource assessment and environmental management, El Salvador, pp 1–13Google Scholar
 Sarimiento ZF, Steingrimsson B (2008) Computer programme for resource assessment and risk evaluation using Monte Carlo simulation, Presented at short course on geothermal project management and developement in Uganda, pp 1–11Google Scholar
 Sircar A, Shah M, Sahajpal S, Vaidya D, Dhale S, Choudhary A (2015) Geothermal exploration in Gujarat: case study from Dholera, India. Geotherm Energy 3:22CrossRefGoogle Scholar
 Stoian E (1965) Fundamentals and application of the Monte Carlo method. 16th Annual technical meeting, The Petroleum Society of C.I.M, Calgary, pp 120–129Google Scholar
 Swinkles J (2011) Guidelines for the application of petroleum resource management system. Chapter 5:78–88Google Scholar
 Zarrouk SJ, Simiyu F (2013) A review of geothermal resource estimation methodology. \(35{{\rm th}}\) New Zealand geothermal workshop, New Zealand, pp 1–8Google Scholar