STATIC_TEMP: a useful computer code for calculating static formation temperatures in geothermal wells

Estimation of static formation temperatures in geothermal wells by using an artificial neural network approach

This study presents a new model to predict the static formation temperature at multiple oil fields using multiple machine learning algorithms. Results are compared with the real temperatures obtained from two wells. The model developed in this study predicts static formation temperature according to several machine learning algorithms including artificial neural networks, fuzzy logic, k-nearest neighbors, and random forest algorithms. The following are the key findings: various geothermal wells in distinct fields or formations may have different machine learning connections. However, if a connection is defined using adequate field data, it is clear that static formation temperature can be approximated with great accuracy. Based on machine learning models we developed a novel model for forecasting static formation temperature, examined the modeling data and outcomes, and found that Random Forest, Fuzzy logic, and K-nearest neighbors outperformed Artificial Neural Network. Therefore, the performance of the proposed model for estimating static well temperature achieved a mean absolute percentage (AAPE) of 0.003%, and the coefficient of determination (R 2 ) is 0.99%. When the classical (mathematical) methods were compared to the artificial intelligence methods, the artificial intelligence methods produced more accurate results with varying percentages. The findings generated by the unique new model computation and the measured test data are substantially matched when compared to computed data and observed temperature data. The novelty of this newly developed AI model is that it will serve as a practical and inexpensive tool for SFT determination in geothermal and petroleum wells.

A three-dimensional (3D) numerical model was proposed for natural state simulation of the Las Tres Virgenes (LTV) geothermal system from emplacement and cooling of the heat source. The conceptual model is based on the volcanic history of the field. Chamber volumes were estimated from outcropping geology and eruptive volumes. Simulation results were evaluated by comparison with static formation temperatures (SFT) estimated from field measurements. Due to the different temporal scales governing volcanological and hydrogeological processes, a convective model was not included in the reservoir. As a consequence, agreement between simulation results and SFT were only observed in geothermal wells which temperature profile is dominated by conduction. Present research is being developed to couple a 3D thermohydromechanical model in the reservoir. As a preparative work, numerical simulations of fluid flow in planar fractures are presented.

Just a few years ago, there existed a great uncertainty regarding the durability of oilwell cements in geothermal wells. Limited, and at times apparently unreliable, information suggested that conventional well cements may not be sufficiently resistant to geothermal well fluids and temperatures for the expected 20- or 30-year service life of the average geothermal well. Therefore, we began to investigate the performance of numerous oilwell cementing compositions in actual geothermal environments.Duplicate samples were exposed to actual geothermal well temperatures and fluids in the Baca, NM, and Imperial Valley, CA, geothermal fields for periods of up to 1 year.A novel testing procedure for geothermal cements was developed and successfully applied in these experiments. Laboratory evaluation of the exposed samples measured the durability of various compositions.The work indicated that some oilwell cements apparently can be rendered sufficiently resistant to geothermal well conditions for the service life of a geothermal well. Introduction The research completed and reported here was prompted primarily by uncertainty about the durability of any cement to be applied in geothermal wells with bottomhole temperatures ranging from 400 to 750 deg. F (204 to 399 deg. C) or produced flashing brine. The required well-service life ranged from 20 to 30 years. Several problems existed. First, the literature contained little applicable information about high-temperature hydrothermal cement chemistry. Prediction of the service life of cements in geothermal environments on the basis of known cement chemistry clearly was impossible. Prediction was of vital concern to operators responsible for safe, as well as competent, geothermal wells, particularly when serious cement-strength retrogression and deterioration generally was known to occur at elevated temperatures.Second, results of an early field test [which exposed samples of oilwell cements as 2-in. (5-cm) precured cement cubes to 600 deg. F (316 deg. C) brine in a geothermal well for periods up to 1 year] strongly suggested that even the three best cementing compositions tested might deteriorate to less than minimum acceptable compressive strengths within 3 to 9 years during geothermal well service. Other field experiments with oilwell cements in contact with produced geothermal fluids also yielded information showing extremely rapid (30- to 60-day) cement deterioration in strength and permeability. Thus, an API Class G cement (without silica) completely disintegrated (to granular size) in 30 days when exposed to 460 deg. F (238 deg. C) steam. Significantly we found that this sample contained (on X-ray diffraction analysis) both dicalcium silicate hydrate and large amounts of calcium hydroxide and carbonate. In another sample of this cement, compressive strength degraded by 77% from 5,050 to 1,150 psi (34.8 to 7.93 MPa) and permeability increased from 0.012 to 8.3 md in 60 days of aging in a produced geothermal brine of only 320 deg. F (160 deg. C) temperature. SPEJ P. 233＾

The accurate prediction of static formation temperature (SFT) is essential for ensuring safety and efficiency in ultra-deep well drilling operations. Excessive downhole temperatures (>150 °C) can degrade drilling fluids, damage temperature-sensitive tools, and pose serious operational risks. Conventional methods for SFT determination—including direct measurement, temperature recovery inversion, and artificial intelligence models—are often limited by post-drilling data dependency, insufficient spatial resolution, high computational costs, or a lack of adaptability to complex wellbore geometries. In this study, we propose a new pseudo-3D Kriging interpolation framework that explicitly incorporates real wellbore trajectories to improve the spatial accuracy and applicability of pre-drilling SFT predictions. By systematically optimizing key hyperparameters (θ = [10, 10], lob = [0.1, 0.1], upb = [20, 200]) and applying a grid resolution of 100 × 100, the model demonstrates high predictive fidelity. Validation using over 5.1 million temperature data points from 113 wells in the Shunbei Oilfield reveals a relative error consistently below 5% and spatial interpolation deviations within 5 °C. The proposed approach enables high-resolution, trajectory-integrated SFT forecasting before drilling with practical computational requirements, thereby supporting proactive thermal risk mitigation and significantly enhancing operational decision-making on ultra-deep wells.

Reliable subsurface temperature estimates are crucial for most geoenergy projects, as they directly influence the properties of both rocks and fluids. They are particularly important in geothermal energy exploration, where errors in estimating the static formation temperature (SFT) can lead to significant misinterpretations, potentially resulting in incorrect classification of the geothermal resource. Various corrections are applied to bottom-hole temperatures (BHTs), with the Horner correction being the most widely used. In addition, empirical methods have been developed to improve accuracy at the local scale. In this study, maximum temperature values (Tmax) reported for deep exploration wells in the Sava and Drava Basins were compared to both Horner-corrected temperatures (HPCTs) and those recorded during drill-stem tests (TDST). In both basins, Tmax values frequently significantly diverge from HPCT measurements, emphasizing the limited reliability of Tmax for estimating subsurface temperatures. In the Sava Basin, 61% of wells show Tmax-HPCT differences greater than 10 °C, and in seven wells the discrepancy exceeds 20 °C. Similarly, in the Drava Basin, nearly half of the wells exhibit differences greater than 10 °C, with five wells showing deviations above 20 °C. In most cases, the reported Tmax values do not represent true maxima, so the linear regression was performed between Tmax and temperatures obtained from DST measurements, providing a basis for refining subsurface temperature estimates.

Exploitation of super-critical water from deep geothermal resources can potentially give a 5–10 fold increase in the power output per well. Such an improvement represents a significant reduction in investment costs for deep geothermal energy projects, thus improving their competitiveness. The ongoing European Horizon2020 DESCRAMBLE (Drilling in dEep, Super-CRitical AMBients of continental Europe) project will demonstrate the drilling of a deep geothermal well with super-critical conditions (>374°C, >220 bar) by extending an existing well to a depth of around 3.5km. The drilling operation is depending on verification of the bottom hole pressure and temperature where state-of-the-art electronic logging tools cannot operate reliably. SINTEF has developed a novel pressure and temperature logging tool for this extreme environment. The target specification for the tool is 8 hours logging of temperature and pressure at 450°C and 450 bar. In this work, we describe the tool requirements and discuss the design choices made with emphasis on the electronics platform and limitations imposed by the available battery technology, as well as the casing and heat shielding. Test results of the tool are presented, including test data from a field-test in a 250°C geothermal well in Larderello, Italy.

The Chirag Field, located offshore in the Caspian Sea of Azerbaijan, uses permanent downhole gauges to record continuous pressure and temperature in the active producers. Bottom-hole pressure data is used extensively to understand interwell communication and reservoir properties, but bottom-hole temperature data had seen little use. However, we now find that flowing bottom-hole temperature detects interwell communication - with interference delay times consistent with pressure transient analysis - and can be used to estimate interwell permeability. To explain our observations we propose that FBHT responds to the impact of pressure changes. The principal result is a change in the producing GOR, which in turn depends on the speed and magnitude at which a pressure change is transmitted through the reservoir. The effect is pronounced when flowing pressures are below bubble-point and compounded by Chirag's steeply dipping reservoir having gradients versus depth in saturation, temperature, bubble-point, and solution-GOR. Field examples highlight the strong cause-effect relationship between producer-injector and producer-producer pairs, giving evidence of a new interference testing method with wide potential application. Chirag Field The Chirag Field in Azerbaijan (Fig-1 and 2) is located offshore in the Caspian Sea. It is part of the Azeri-Chirag-Guneshli (ACG) development and the principal production zone is the Middle Pliocene Pereriv sand. There are currently ten producers and six peripheral water injectors active in Chirag. Production, exported through the Baku-Tblisi-Ceyhan (BTC) pipeline, is 140 Mstb/D with 900 GOR (scf/stb) and less than 1% watercut; water injection is 140 Mbw/D. The structure is an elongated anticline with dips of up to 45 degrees, an overall hydrocarbon column height of up to 1000 meters, and an average stratigraphic thickness of 130 meters in the Pereriv. The two most permeable intervals, the Pereriv-B and Pereriv-D, have a total thickness of 80 meters with 20% porosity and 200 md permeability. Introduction The need to monitor, understand, and model temperature and its impact is important across all engineering and geologic disciplines in a producing field. The particular area wellbore temperature sensing is very importance as both early1–6 and recent work7,8 have showed its value. However, such wellbore temperature monitoring and interpretation has focused on the immediate region of the well. At Chirag we find that temperature data also contains interwell information. Chirag uses permanent downhole gauges (PDHG) to record pressure and temperature in the active producers. The bottom-hole pressure (BHP) data is used extensively to understand interwell communication and reservoir properties, but bottom-hole temperature (BHT) data had seen little use. However, we now find that flowing BHT (FBHT) detects interwell communication, with interference delay times consistent with pressure transient analysis (PTA), i.e., it can be used to estimate interwell permeability. The FBHT data also signals if a voidage change occurs from a location updip or downdip of the producer, as increased support downdip of a producer causes FBHT to increase while increased support updip of a producer (or from the opposite flank) causes FBHT to decrease. To explain our observations we propose that FBHT responds to the impact of pressure changes. The principal result is a change in the producing GOR, which in turn depends on the speed and magnitude at which a pressure change is transmitted through the reservoir, in addition to the reservoir pressure, FBHP, fluid saturations and properties, and drainage region. The effect is pronounced when FBHP is below bubble-point (the majority of Chirag's producers) and compounded by Chirag's steeply dipping reservoir having gradients versus depth in saturation, temperature, bubble-point, and solution-GOR. In such cases, a well's FBHT will increase (and GOR decrease) when downdip pressure support increases, i.e., the well's drainage area and streamlines skew downdip toward lower gas-saturations, lower solution-GOR's, and higher temperatures. Conversely, a well's FBHT will decrease (and GOR increase) when updip pressure support increases, i.e., the well's drainage area and streamlines skew updip toward higher gas-saturations, higher solution-GOR's, and lower temperatures. Several examples highlight our observations and estimates are provided for contributing factors.

The combined plot of log pressure change and log derivative of pressure with respect to superposition time as a function of log elapsed time was first introduced by Bourdet et al. as an aid to type-curving matching. Features that are hardly visible on the Horner plot or are hard to distinguish because of similarities between one reservoir system and another was easier to recognize on the pressure-derivative plot. Once the patterns have been diagnosed on the log-log plot, specialized plots can be used to compute reservoir parameters or the data can be matched to a type curve.

Numerical analysis of characteristics of multi-orifice nozzle hydrothermal jet impact flow field and heat transfer

We develop an analytical and numerical methodology for the analysis of large bottom-hole temperature (BHT) data sets from sedimentary basins, and test the methodology using temperature, stratigraphic, and lithologic data from 411 boreholes in the Michigan Basin. Least-squares estimates of temperature gradients in the formations and lithologies present are calculated as solutions to a large system of linear equations. At each borehole the temperature difference between the bottom and top of the hole is represented as a sum of temperature increments through the various formations or lithologies penetrated by the borehole. Quadratic programming techniques enable bounds to be placed on the gradient solutions in order to suppress or exclude improbable gradient estimates. Numerical experiments with synthetic data reveal that the estimates of temperature gradients for a given formation or lithology are sensitive to the degree of representation of that unit; well represented units have more stable gradient estimates in the presence of noise than do poorly represented units. The estimates of temperature gradients obtained for lithologies are more stable than those for formations and are believed to be good estimates of actual lithologic temperature gradients in the Michigan Basin. Formation temperature gradients obtained as a weighted sum of the estimates of the component lithologic temperature gradients appear to be good estimates of the average temperature gradients for the formations of the basin.At each borehole a temperature residual exists corresponding to the difference between the observed BHT and the BHT predicted by the estimated interval temperature gradients. Residuals are far more stable than estimated temperature gradients. The values of residuals change little regardless of whether lithology, formation, bounded, or unbounded gradient estimates are used to calculate them. Maps of residuals indicate well-defined and spatially coherent patterns of positive and negative temperature residuals. Filtered subsets of large-magnitude residuals alone show a pattern of negative residuals coinciding with the mid-Michigan gravity high, a geophysical feature thought to delineate a Precambrian (Keweenawan) rift zone in the crust beneath the basin. Thermal models of the Michigan Basin and the crust and upper mantle beneath the basin indicate that the suspected rift beneath the basin can cause a variation in basement heat flow sufficient to produce temperature residuals of the magnitude observed in the sediments, with negative temperature residuals over the area of the rift.

A computer code is developed for vertical two-phase flow in geothermal wellbores. The two-phase correlations used were developed by Orkiszewski (1967) and others and are widely applicable in the oil and gas industry. The computer code is compared to the flowing survey measurements from wells in the East Mesa, Cerro Prieto, and Roosevelt Hot Springs geothermal fields with success. Well data from the Svartsengi field in Iceland are also used. Several applications of the computer code are considered. They range from reservoir analysis to wellbore deposition studies. It is considered that accurate and workable wellbore simulators have an important role to play in geothermal reservoir engineering.

Structural well-bore integrity is an important issue for sustainable provision of geothermal energy. Raman scattering based fibre optic distributed temperature sensing (DTS) can help to monitor the status of a well and therefore help to optimize expensive work-over activities. This study reports on the installation of a fibre-optic cable in the cemented annulus behind the anchor casing in the high temperature geothermal well HE-53, Hellisheiði geothermal field, SW Iceland. Although the cable has been damaged during the installation, temperature data could be acquired during the entire length of installation down to 261.3 m. Temperature measurements were performed during the installation in spring 2009, during the onset of a flow test in summer 2009 and after a 8.5 month shut-in period in summer 2010. During the flow test, maximum temperatures of 230 °C were measured after 2 weeks fluid production. Using optical time domain reflectometry (OTDR), attenuation measurements at 850 and 1,300 nm enabled to identify mechanical, thermal, and chemical degradation along the optical fibre. The observed degradation led to erroneous temperature readings and limits, due to the optical budget of the DTS system, the accessible length of the fibre. The characteristics and the influence of the different degradation mechanisms on the accuracy of the DTS measurements are discussed and recommendations for an optimized installation are given.

The potential of geothermal energy for future electric power generation in New York State is evaluated using estimates of temperatures of geothermal reservoir rocks. Bottom hole temperatures from over 2000 oil and gas wells in the region were integrated into subsurface maps of the temperatures for specific geothermal reservoirs. The Theresa/Potsdam formation provides the best potential for extraction of high volumes of geothermal fluids. The evaluation of the Theresa/Potsdam geothermal reservoir in upstate New York suggests that an area 30 miles east of Elmira, New York has the highest temperatures in the reservoir rock. The Theresa/Potsdam reservoir rock should have temperatures about 136 {degrees}C and may have as much as 450 feet of porosity in excess of 8%. Estimates of the volumes of geothermal fluids that can be extracted are provided and environmental considerations for production from a geothermal well is discussed.

In the hot dry rock (HDR) concept of extracting geothermal energy, as developed by the Los Alamos Scientific Laboratory (LASL), a manmade geothermal reservoir is created by drilling a deep hole into relatively impermeable hot rocks, creating a large surface area for heat transfer by hydraulic fracturing, then drilling a second hole to intersect the fracture to complete the closed circulation loop. The completion of HDR geothermal wells presents cementing problems that are unique. Current presents cementing problems that are unique. Current well depths are from 10,000 to 14,500 ft (3 to 4.4 km) with bottom hole temperatures up to 525 degrees F (275 degrees C). During investigation and development of the reservoir, water injection flows may lower the temperature of the entire wellbore to 104 degrees F (40 degrees C). As a result, the casing string may be subjected to temperature stress cycles representing differential temperatures of up to 455 degrees F (235 degrees C). Experience has shown that the conventional high-temperature completion cement formulation of Class A or B portland cement, stabilized with 40% silica sand, does not withstand these cyclic stresses, and that rapid deterioration of casing-to-cement and cement-to-formation bonds occurs, which allows significant flow in the resulting microannulus. Investigations and tests (both laboratory and downhole) are being conducted by LASL, and other national and private laboratories, to determine other portland cement formulations, thermal setting cements, and special packer completion techniques which will better withstand the temperature, pressure, and flow requirements of HDR geothermal systems. This paper will describe (a) the performance history of casing cement for the existing EE-1 injection well, (b) the proposed cementing plan for the EE-2 injection well presently being drilled, and (c) the completion system being tested in EE-1 for expanded use in EE-2. Introduction The Los Alamos Scientific Laboratory (LASL) for the past six years has been actively investigating the potential for and problems associated with extracting geothermal energy from hot, but essentially dry, rock at moderate depths. In the Los Alamos concept, a manmade geothermal reservoir is formed by drilling into a region of suitably hot rock and then creating a large fracture, using conventional hydraulic fracturing techniques developed by the oil industry. After forming a circulation loop by drilling a second hole into the top of the fractured region, the heat contained in this reservoir is transported to the surface by circulation of water. The water in the earth loop is maintained as a liquid by pressurization at the surface, increasing both the rate of heat removal from the fractured reservoir and the amount of heat transported up the withdrawal hole. To test this concept, a deep exploratory hole (GT-2) was completed in 1974 to a depth of 9610 ft (2929 m) in the granitic basement rocks of the Jemez Mountains of northern New Mexico at Fenton Hill (Fig. 1). The bottomhole temperature was 388 degrees F (197 degrees C). A near-vertical hydraulic fracture with a radius of about 400 ft (120 m) was created near the bottom of GT-2. Drilling of the second deep hole, Energy Extraction Well No. 1 (or EE-1), to intersect the fracture began in May 1975, about 250 ft (75 m) north of GT-2. It was completed in October at a depth of 10,053 ft (3064 m) and a bottomhole temperature of 400 degrees F (205 degrees C). Below 6240 ft (1957 m), EE-1 was directionally drilled to turn the hole through a 205 degrees spiral to create the underground connection. EE-1 was cased to a depth of 9600 ft (2926 m) with 7-5/8-in. casing and forms the injection well of the underground loop.