Static Formation Temperatures Research Articles

Thermal performance analysis of drilling horizontal wells in high temperature formations

An integrated circulation temperature model for horizontal well drilling was developed, field-tested, and compared with results from vertical wells in order to accurately predict bottomhole temperature while addressing the difference in bottomhole temperatures between horizontal and vertical wells. The model divides the well drilling operation into five distinct interconnected regions each characterized by their own distinct thermal and fluid flow processes, as well as the mechanical and hydraulic energy exchange and heat conversion. A finite volume method of numerical simulation is then used to solve the differential equations. The simulation results were then calibrated and validated using field measurements, and a subsequent analysis of the heat source distribution and sensitivity revealed that the variation in temperature of horizontal drilling is quite different than that experienced with vertical wells. The long horizontal section, heat transfer term and fluid specific heat capacity are found to be the main reasons why the bottomhole temperature for horizontal wells rises well above the static formation temperature. The parameters in vertical wells are more sensitive than that in horizontal wells. When the bottomhole temperature exceeds the static formation temperature in horizontal wells, parameters such as pumping rate have an opposite effect on bottomhole temperature, as compared to vertical wells.

Estimation of true formation temperature from well logs for basin modeling in Persian Gulf

Abstract Static formation temperature should be determined as accurately as possible for a number of reasons; especially it is an essential parameter in petroleum system modeling. In this study, the commonly used empirical methods for log derived temperature correction are reviewed. After that, new correlation was developed by adapting previously presented methods to calibrate log recorded temperature by using true formation temperature from reservoir tests like DST and MDT in Persian Gulf basin. A correction factor formula was proposed by considering both depth and TSC directly. The adapted method provides an accurate calibration of log recorded temperature. In addition, a sensitivity analysis was carried out to reveal the effect of log recorded temperature calibration on 1D petroleum system modeling.

Three dimensional temperature simulation from cooling of two magma chambers in the Las Tres Vírgenes geothermal field, Baja California Sur, Mexico

A three-dimensional (3D) numerical model is proposed for natural state simulation of the Las Tres Vírgenes (LTV) geothermal system from emplacement and cooling of the heat source. A conceptual model of the LTV volcanic system was developed considering tectonic regime, structural geology, outcropping geology, eruptive events and geochronology. The model includes the emplacement of two magma chambers, lateral variations of physical properties and the topography of the geographic area. Model calibration was carried out for several chamber volumes and depths, as well as thermal diffusivity of lithological units. Static formation temperatures (SFT) and homogenization temperatures were used as references. Chamber depths between 3000 and 3500 m below sea level with total chamber volumes of 429 and 563 km3, respectively, were inferred from the simulation results. The exergy of the reservoir was consistent with the current installed capacity of the power plant (10 MWe); however, an increase of at least 4 MWe would be attained with optimized power cycles.

Three-dimensional temperature field simulation of magma chamber in the Los Humeros geothermal field, Puebla, Mexico

Three-dimensional (3-D) thermal modeling of a magma chamber in the Los Humeros geothermal field of Mexico was carried out for the entire geological history of about 500,000 y. Earlier application of 3-D modeling for only about 30,000 y of total simulation time with discretization time of 1000 y and mesh size of 0.25 km, had indicated that the thermal regime is affected more by the depth of magma chamber than its volume. Now using a chamber depth of 5 km, chamber volume of 1400 km3, shorter discretization time of 10 years, mesh size of 0.25 km, convection in the geothermal reservoir, and magma recharge in the chamber, we present our best 3-D thermal model for the Los Humeros geothermal field. Although this model is consistent with the static formation temperature estimates from geothermal wells, ways to improve this model to make it suitable for the estimation of geothermal budget are also pointed out.

A new practical method for the determination of static formation temperatures in geothermal and petroleum wells using a numerical method based on rational polynomial functions

A new practical method based on rational polynomial (RP) functions to estimate the static formation temperatures (SFT) in geothermal and petroleum boreholes is described. Thermal recovery processes involved during borehole drilling and completion operations were represented by mathematical asymptotic trends. Measurements of bottom-hole temperature and shut-in times (at least three or more) have been used both to obtain a mathematical function that describes the thermal recovery process of drilled boreholes, and to estimate the SFT. Using build-up temperature logs, the SFT have been reliably estimated with precision and accuracy. With these results, it was successfully demonstrated that the new RP method provides a practical tool for the reliable prediction of SFT in geothermal and petroleum boreholes.

Numerical analysis of thermal effects during carbon dioxide injection with enhanced gas recovery: a theoretical case study for the Altmark gas field

Prediction about reservoir temperature change during carbon dioxide injection requires consideration of all, often subtle, thermal effects. In particular, Joule–Thomson cooling (JTC) and the viscous heat dissipation (VHD) effect are factors that cause flowing fluid temperature to differ from the static formation temperature. In this work, warm-back behavior (thermal recovery after injection completed), as well as JTC and VHD effects, at a multi-layered depleted gas reservoir are demonstrated numerically. OpenGeoSys (OGS) is able to solve coupled partial differential equations for pressure, temperature and mole-fraction of each component of the mixture with a combination of monolithic and staggered approaches. The Galerkin finite element approach is adapted for space discretization of governing equations, whereas for temporal discretization, a generalized implicit single-step scheme is used. For numerical modeling of warm-back behavior, we chose a simplified test case of carbon dioxide injection. This test case is numerically solved by using OGS and FeFlow simulators independently. OGS differs from FeFlow in the capability of representing multi-componential effects on warm-back behavior. We verify both code results by showing the close comparison of shut-in temperature profiles along the injection well. As the JTC cooling rate is inversely proportional to the volumetric heat capacity of the solid matrix, the injection layers are cooled faster as compared to the non-injection layers. The shut-in temperature profiles are showing a significant change in reservoir temperature; hence it is important to account for thermal effects in injection monitoring.

¿QUÉ MÉTODO UTILIZAR PARA ESTIMAR LA TEMPERATURA ESTÁTICA DE UNA FORMACIÓN DE PETRÓLEO?

The static formation temperature of a petroleum reservoir is relevant for evaluating its properties. There is a variety of methods for estimating it. However, each method assumes different hypotheses and simplifications which lead to diverging estimations, in some cases far from the real value. This makes difficult knowing in advance which method to use. In this paper, the most common methods (Horner, spheric and radial, two-measures and cylindric source) are applied to four different wells. The way of applying them to real cases is described, paying special attention to the necessary input data in each case: especially thermophysical properties and number of measurements. Criteria for estimating properties in case their real value cannot be known are also provided. The paper concludes suggesting a decision tree for selecting the most appropriate method depending on the available information.

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

An artificial neural network (ANN) approach was used to develop a new predictive model for the calculation of static formation temperature (SFT) in geothermal wells. A three-layer ANN architecture was successfully trained using a geothermal borehole database, which contains “statistically normalised” SFT estimates. These estimates were inferred from seven analytical methods commonly used in geothermal industry. Bottom-hole temperature (BHT) measurements and shut-in times were used as main input variables for the ANN training. Transient temperature gradients were used as secondary variables. The Levenberg–Marquardt (LM) learning algorithm, the hyperbolic tangent sigmoid transfer function and the linear transfer function were used for the ANN optimisation. The best training data set was obtained with an ANN architecture composed by five neurons in the hidden layer, which made possible to predict the SFT with a satisfactory efficiency ( R 2>0.95). A suitable accuracy of the ANN model was achieved with a percentage error less than ±5%. The SFTs predicted by the ANN model were statistically analyzed and compared with “true” SFTs measured in synthetic experiments and actual BHT logs collected in geothermal boreholes during long shut-in times. These data sets were processed both to validate the new ANN model and to avoid bias. The SFT estimates inferred from the ANN validation process were in good agreement ( R 2>0.95) with the “true” SFT data reported for synthetic and field experiments. The results suggest that the new ANN model could be used as a practical tool for the reliable prediction of SFT in geothermal wells using BHT and shut-in time as input data only.

Inverse Simulation Methods to Obtain Formation Temperatures in Wellbores

The performance of three inverse simulation methods to obtain formation temperatures (FTs) in wellbores is presented in this article. The inverse simulation methods are based on three solution schemes: nonlinear least-squares approach based on the Levenberg-Marquardt method, a feedback-based method, and a cognitive model. The first is an algorithm optimization and the other two are tracking algorithms. The simulations using data from an oil well show the performance to predict static formation temperatures (SFTs) with these inversion schemes.

Solute geothermometry of springs and wells of the Los Azufres and Las Tres Vírgenes geothermal fields, Mexico

Subsurface reservoir temperatures of two important Mexican geothermal systems (Los Azufres and Las Tres Vírgenes) were estimated by applying all available solute geothermometers for 88 and 56 chemical data measurements of the spring waters and fluids of the deep geothermal wells, respectively. Most of the chemical data for spring water of these two geothermal fields are for HCO3 water, followed by SO4 and Cl types. For the Los Azufres geothermal field (LAGF), the reservoir temperatures estimated by Na-K geothermometers for springs of HCO3 and SO4 waters, and by Na-Li and Li-Mg geothermometers for Cl water, are close to the average bottom-hole temperature (BHT) of the geothermal wells. However, all reservoir temperatures for spring waters from the Las Tres Vírgenes geothermal field (LTVGF) estimated by all solute geothermometers indicated significantly large differences (low temperatures) compared to the BHT. Evaluation of inferred reservoir temperatures for spring waters of the LAGF and LTVGF suggests that not all springs nor all solute geothermometers provide reliable estimation of the reservoir temperatures. Even though chemical equilibrium probably was not achieved in the water–rock system, Na-K geothermometers for HCO3 water (peripheral water mainly of meteoric origin with little geothermal component) and SO4 water (geothermal steam heated) and Na-Li and Li-Mg geothermometers for Cl-rich spring water (fully mature geothermal water) of the LAGF indicated reservoir temperatures close to the BHT. However, in comparison with the geothermometry of spring water of the LAGF and LTVGF, fluid measurements from geothermal wells of these two fields indicated reservoir temperatures in close agreement with their respective BHTs. For the best use of the solute geothermometry for spring water, it is advisable to: (1) chemically classify the springs based on water types; (2) identify and eliminate the discordant outlier observations by considering each water type as a separate sampled population; (3) apply all available solute geothermometers employing a suitable computer program such as SolGeo instead of using some specific, arbitrarily chosen geothermometers; and (4) evaluate the temperatures obtained for each solute geothermometer by considering the subsurface lithology, hydrological conditions, and BHTs or static formation temperatures whenever available.

Cognitive Model to Estimate Static Formation Temperatures in Oil Wells: Inverse Problem

A cognitive model was developed to solve an inverse heat transfer problem of estimating static formation temperatures (SFTs) from logged temperatures in oil wells. The cognitive model is based on formulation of a human expert knowledge with uncertainty, which is expressed in terms of fuzzy rules. Thus, mathematically speaking, an inverse heat transfer problem was solved in this way, based on reactive decision model. The performance of the present method of inverse problem is evaluated by means of oil well C-3007 from the maritime zone of the Gulf of Mexico. The results were compared with the Horner method. It was found that the cognitive method is very accurate, as well as efficient, due to the fact that the SFT can be obtained with only temperature log for each depth.

Application of a proportional-integral control for the estimation of static formation temperatures in oil wells

A strategy based on proportional-integral (PI) feedback control was applied to solve an inverse heat transfer problem for estimating static formation temperatures (SFTs) from logged temperatures in oil wells. The PI control feedbacks the error between logged and simulated temperatures during the shut-in time process, existing SFT proposal. Thus, mathematically speaking an inverse heat transfer problem was solved in this way, since SFT represents the initial conditions (which are unknown) to solve the partial differential equations governing the heat transfer process in the wellbore-formation system. The mathematical model considers transient convective heat transfer due to circulation losses to the rock surrounding a well. The methodology was tested analyzing two oil wells (MB-3007 and MB-3009) from the Gulf of Mexico and results were compared against two classic methods. The method presented in this work needs only one temperature measurement for each fixed depth to estimate the SFT.

Application of the error propagation theory in estimates of static formation temperatures in geothermal and petroleum boreholes

Abstract We used the error propagation theory to calculate uncertainties in static formation temperature estimates in geothermal and petroleum wells from three widely used methods (line-source or Horner method; spherical and radial heat flow method; and cylindrical heat source method). Although these methods commonly use an ordinary least-squares linear regression model considered in this study, we also evaluated two variants of a weighted least-squares linear regression model for the actual relationship between the bottom-hole temperature and the corresponding time functions. Equations based on the error propagation theory were derived for estimating uncertainties in the time function of each analytical method. These uncertainties in conjunction with those on bottom-hole temperatures were used to estimate individual weighting factors required for applying the two variants of the weighted least-squares regression model. Standard deviations and 95% confidence limits of intercept were calculated for both types of linear regressions. Applications showed that static formation temperatures computed with the spherical and radial heat flow method were generally greater (at the 95% confidence level) than those from the other two methods under study. When typical measurement errors of 0.25 h in time and 5 °C in bottom-hole temperature were assumed for the weighted least-squares model, the uncertainties in the estimated static formation temperatures were greater than those for the ordinary least-squares model. However, if these errors were smaller (about 1% in time and 0.5% in temperature measurements), the weighted least-squares linear regression model would generally provide smaller uncertainties for the estimated temperatures than the ordinary least-squares linear regression model. Therefore, the weighted model would be statistically correct and more appropriate for such applications. We also suggest that at least 30 precise and accurate BHT and time measurements along with the respective errors should be obtained for a reliable application of the proposed regression procedure.

Fluid chemistry and temperatures prior to exploitation at the Las Tres Vírgenes geothermal field, Mexico

Generation of electricity at the Las Tres Vírgenes (LTV) geothermal field, Mexico, began in 2001. There are currently nine geothermal wells in the field, which has an installed electricity generating capacity of 10 MW e. The chemical and temperature conditions prevailing in the field prior to its exploitation have been estimated, including their central tendency and dispersion parameters. These conditions were computed on the basis of: (i) geochemical data on waters from springs and domestic wells, and on geothermal well fluids (waters and gases); most of the sampling took place between 1995 and 1999; (ii) fluid inclusion studies; (iii) geothermometric data; and (iv) static formation temperatures computed using a modified quadratic regression Horner method. Fluid inclusion homogenization temperatures (in the 100–290 °C range) suggest that there is a high-temperature fluid upflow zone near wells LV3 and LV4 in the southern part of the field. Computed average chemical equilibrium temperatures for the geothermal fluids are ∼260 °C, based on the Na/K and SiO 2 geothermometers, and ∼265 °C, based on the H 2/Ar, and CO 2/Ar geothermometers. In general, the fluid inclusion homogenization temperatures are consistent with geothermometric data, as well as with static formation temperatures. Some of the observed differences could be related to well interference effects and different fluid production/sampling depths. The deeper geothermal waters show higher concentrations of Cl, Na, K, B, Ba, but lower concentrations of SO 4, Ca, and Mg than the shallower waters. Fluid inclusion salinities are also higher in the deeper rocks. The measured Na/Cl ratios of the geothermal well waters are more or less uniform throughout the field and are very similar to that of seawater, strongly suggesting a seawater component in the fluid of the LTV system. The heat stored in the LTV geothermal system was estimated to be at least 9 × 10 12 MJ, of which some 4 × 10 11 MJ (equivalent to about 148 MW e for 30 years of operation, assuming a conversion efficiency of ∼35%) might be extracted using wells. These results indicate that the installed capacity at LTV could be safely increased from the current 10 MW e.

Statistical evaluation of methods for the calculation of static formation temperatures in geothermal and oil wells using an extension of the error propagation theory

The feasibility of using the more sophisticated weighted least-squares (WLS) model, as opposed to the traditional ordinary least-squares (OLS), in linear regressions of BHT data to estimate the static formation temperatures (SFT) was investigated. The most commonly used analytical methods (line-source; spherical and radial heat flow; and cylindrical heat source) were applied. Error propagation equations were derived to calculate errors in the time function of each method. These errors were combined with the BHT measurement errors to compute weighting factors for applying the WLS. Intercept uncertainties were estimated for all regressions using sets of synthetic and actual borehole logs taken from geothermal and oil applications. SFT computed with the spherical and radial heat flow method were generally greater than those from the other two methods.

Uncertainty estimates of static formation temperatures in boreholes and evaluation of regression models

SUMMARY Three commonly used methods for estimating static formation temperatures were evaluated: (1) the line-source or Horner method; (2) the spherical and radial heat-flow method; and (3) and the cylindrical heat-source method. Ordinary least-squares linear regression model statistical tests (sequence of signs, regression using sequential subsets of an ordered array of data, and residual sum of squares) were used to evaluate the actual relationship between the bottomhole temperature and the time functions of the methods. The statistical tests for linearity and the resulting residual sum of squares show that bottom-hole temperature versus time-function relationships are of polynomial type. Standard deviation values of the slope and intercept were calculated for the linear as well as the quadratic regression model. The quadratic regression was found to be most appropriate for this purpose and was used for the first time for calculating static formation temperatures using four data sets of actual geothermal borehole logs and two synthetic sets. The F- and Student-t tests were applied to static formation temperatures obtained from linear and quadratic regression methods. Static formation temperatures computed with the spherical and radial heat-flow method are significantly greater (at the 95 per cent confidence level) than those from the other two methods under study. The spherical and radial heat-flow method seems to overestimate ‘true’ values of the static formation temperatures by about 10 per cent, whereas the other two methods (Horner and cylindrical heat source) provide unbiased estimates of these temperatures.

Behavioral design to model a reactive decision of an expert in geothermal wells

Software design based on agents represents a new perspective for computer science and more specifically, for Artificial Intelligence. It is a new theory that has innovated the analysis, design and implementation of system software. The design of agents poses problems related with: (1) autonomous decision-making process, (2) co-ordination, (3) negotiation, and (4) handling of mental states and communication. In a reactive multi-agent system, the group of agents is subject continually to local changes. These changes are designed by means of behavior rules whose results are influenced by the behavior of the rest of the agents. The design of these rules is inspired by the biological or cognitive sciences. Particularly, the design of cognitive rules corresponds with the principle of rationality; its perspective is focused on the interaction among the agents. One of the objectives of artificial intelligence refers to the development of systems that ease or increase the level of comfort in the daily life of humans. Such is the case for tasks with permanent focus on the input data in convergent methods or systems that help in the decision-making process involved in costly processes. In this paper we propose a design’s of the expert’s decision-making process trough the use of a cognitive model, and fuzzy sets to model the agents’ reactive deliberative process. Software system helps human expert in the estimation of the static formation temperatures. Furthermore, we will present an example based on a behavior developed from an expert in the field of geothermal sciences. The formulation of the human expert knowledge includes uncertainty, which is expressed in terms of fuzzy rules. An attempt to estimate formation temperatures from logged temperatures was solved whit this methodology based on reactive decision model. Thus, mathematically speaking an inverse problem is solved in this way. This paper describes and discusses the first experiences that form part of an incremental project whose final objective is to develop an expert system that allows the prediction of the degree of success of the drilling of geothermal wells.

Precision gravity monitoring of the Bulalo geothermal field, Philippines: independent checks and constraints on numerical simulation

Sixteen precision gravity surveys carried out since 1979 provide an additional constraint for numerical simulation of the Bulalo system. The gravity surveys were all run using the same LaCoste and Romberg gravity meter (D-33). Leveling surveys collected in conjunction with the gravity surveys used Wild N3 spirit levels. The leveling surveys were used to correct the gravity data for elevation changes. Since production began in 1979, the Bulalo field has experienced a gravity change of up to −600 microgal. The decline in gravity is interpreted to result from density changes in the reservoir, primarily due to the development of a two-phase zone where liquid saturation is lower in both the rock matrix and its fracture network. An accurate match of the trends and magnitudes of observed and simulated gravity changes provides a constraint for the mass balance of the numerical model beyond the matching of pressure and enthalpy evolution. Because of internal flow effects in most of the wells, pressure and temperature measurements do not necessarily represent static formation pressure and temperatures. Gravity data, therefore, became particularly important for calibrating the net depletion of the numerical model and for constraining reservoir mass replacement from re-injection and natural inflow from aquifers outside the production zone. Early comparisons of the observed and simulated gravity showed a too rapid gravity decrease prior to 1992, and a too slow gravity decrease after that time. Subsequent changes made to the numerical model, including modifying permeability structure and in-flow direction, resulted in an improved match to the gravity and available pressure data. The result has been a numerical model that accurately matches not only the quantity of net mass withdrawal, but also the location of the mass withdrawal including recharge from outside the producing reservoir.

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

The development and application of the computer code STATIC_TEMP, a useful tool for calculating static formation temperatures from actual bottomhole temperature data logged in geothermal wells is described. STATIC_TEMP is based on five analytical methods which are the most frequently used in the geothermal industry. Conductive and convective heat flow models (radial, spherical/radial and cylindrical/radial) were selected. The computer code is a useful tool that can be reliable used in situ to determine static formation temperatures before or during the completion stages of geothermal wells (drilling and cementing). Shut-in time and bottomhole temperature measurements logged during well completion activities are required as input data. Output results can include up to seven computations of the static formation temperature by each wellbore temperature data set analysed. STATIC_TEMP was written in Fortran-77 Microsoft language for MS-DOS environment using structured programming techniques. It runs on most IBM compatible personal computers. The source code and its computational architecture as well as the input and output files are described in detail. Validation and application examples on the use of this computer code with wellbore temperature data (obtained from specialised literature) and with actual bottomhole temperature data (taken from completion operations of some geothermal wells) are also presented.

Geothermics of Nile Delta and Southeast Mediterranean: Investigation and Geothermal Energy Potential: ABSTRACT

The authors collected 289 temperature readings from 66 exploratory wells randomly distributed in an area about 57,000 km{sup 2} from different rock units of Tertiary and Quaternary ages. The bottom-hole temperature (BHT) readings were corrected using an empirical equation based on actual static formation temperatures collected from the study area. The authors modified the Fertl and Wichmann method to apply to the study area. If the Fertl and Wichmann curve is applied, readings can be corrected using a deduced relation. The geothermal gradient for each well calculated used the best-fit method utilizing all recorded BHTs in that well. A new geothermal gradient map was constructed using the corrected BHT values. A genetic relationship between the geothermal gradient and lithology, tectonic setup, gas saturation, and water saturation of the subsurface formations in the Nile delta and southeast Mediterranean area was sought. Isothermal maps at different depths in the study area were constructed. Areas of relatively high subsurface temperature were delineated. The Abu Madi gas field as a case study for geothermal behavior was emphasized. The geothermal reservoirs in the study area as possible new and renewable energy resources were defined and classified as low-temperature reservoirs. Two geothermal reservoirs have been recorded:more » a shallow one associated with Mit Ghamr-El Wastani rock units and a deep one associated with abu Madi-Qawassim Formations.« less