scholarly journals Fluid and Heat Flow In Gas-Rich Geothermal Reservoirs

1985 ◽  
Vol 25 (02) ◽  
pp. 215-226 ◽  
Author(s):  
M.J. O'Sullivan ◽  
G.S. Bodvarsson ◽  
K. Pruess ◽  
M.R. Blakeley

Abstract Numerical simulation techniques are used to study the effects of noncondensable gases (CO2) on geothermal reservoir behavior in the natural state and during exploitation. It is shown that the presence Of CO2 has a large effect on the thermodynamic conditions of a reservoir in the natural state, especially on temperature distributions and phase compositions. The gas will expand two-phase zones phase compositions. The gas will expand two-phase zones and increase gas saturations to enable flow of CO2 through the system. During exploitation, the early pressure drop primarily results from "degassing" of the system. This primarily results from "degassing" of the system. This process can cause a very rapid initial pressure drop, on process can cause a very rapid initial pressure drop, on the order of megapascals, depending on the initial partial pressure of CO2. The flowing gas content from wells can pressure of CO2. The flowing gas content from wells can provide information on in-place gas saturations and provide information on in-place gas saturations and relative permeability curves that apply at a given geothermal resource. Site-specific studies are made for the gas-rich, two-phase reservoir at the Ohaaki geothermal field in New Zealand. A simple lumped-parameter model and a vertical column model are applied to the field data. The results obtained agree well with the natural thermodynamic state of the Ohaaki field (pressure and temperature profiles) and a partial pressure of 1.5 to 2.5 MPa [217 to 363 psi] is calculated in the primary reservoirs. The models also agree reasonably well with field data obtained during exploitation of the field. The treatment of thermophysical properties of H2O/CO2 mixtures for different phase compositions is summarized. Introduction Many geothermal reservoirs contain large amounts of non-condensable gases, particularly CO2. The proportion of noncondensable gas in the produced fluid is an extremely important factor in the design of separators, turbines, heat exchangers, and other surface equipment. In the reservoir itself, the presence of CO2 significantly alters the distribution of temperature and gas saturation (volumetric fraction of gas phase) associated with given heat and mass flows. Therefore, when modeling gas-rich reservoirs it is essential to keep track of the amount of CO2 in each gridblock in addition to the customary fluid and heat content. Several investigators have considered the effects of CO2 on the reservoir dynamics of geothermal systems. A lumped-parameter model using one block for the gas zone and one for the liquid zone was developed by Atkinson et al. for the Bagnore (Italy) reservoir. Preliminary work on the Ohaaki reservoir was carried out by Zyvoloski and O'Sullivan, but these studies were limited because-the thermodynamic package used could only handle two-phase conditions. Generic studies of reservoir depletion and well-test analysis also were made in the previous works. The present study describes the effects of CO2 in geothermal reservoirs in a more complete and detailed way. We emphasize the potential for using the CO2 content in the fluid produced during a well test as a reservoir diagnostic aid, and as a means of gaining information about relative permeability curves. The aim of the present study is to investigate the effects of CO2 on both the natural state of a reservoir and its behavior under exploitation. Several generic simulation studies are described. First, the effect of CO2 on the depletion of a single-block, lumped-parameter reservoir model is briefly examined. Secondly, the relationship between the mass fraction Of CO2 in the produced fluid and the mass fraction in place in the reservoir is studied. It is demonstrated that in some cases the in-place gas saturation can be determined for a given set of relative permeability curves. Finally, the effects of CO2 on the permeability curves. Finally, the effects of CO2 on the vertical distribution of gas saturation, temperature, and pressure of geothermal reservoirs in the natural state are pressure of geothermal reservoirs in the natural state are investigated. The numerical simulator with the H2O/CO2 thermodynamic package is applied to field data from the Ohaaki (formerly Broadlands) geothermal field in New Zealand. Two simple models of the 1966–74 large-scale field exploitation test of the Ohaaki reservoir are presented. The first is a single-block, lumped-parameter model similar to those reported earlier by Zyvoloski and O'Sullivan and Grant. In the former work, a less accurate thermodynamic package for H2O/CO2 mixtures is used; the latter uses approximate methods to integrate the mass-, energy-, and CO2-balance equations. The second model described in the present work is a distributed-parameter model, in the form of a vertical column representing the main upflow zone at Ohaaki. This model produces a good fit to the observed distribution of pressure and temperature with depth in the natural state at Ohaaki and a good match to the observed response of the reservoir during 5 years of experimental production and 3 years of recovery. SPEJ p. 215

1971 ◽  
Vol 11 (04) ◽  
pp. 419-425 ◽  
Author(s):  
Carlon S. Land

Abstract Two-phase imbibition relative permeability was measured in an attempt to validate a method of calculating imbibition relative permeability. The stationary-liquid-phase method was used to measure several hysteresis loops for alundum and Berea sandstone samples. The method of calculating imbibition relative permeability is described, and calculated relative permeability curves are compared with measured curves. The calculated relative Permeability is shown to be a reasonably good Permeability is shown to be a reasonably good approximation of measured values if an adjustment is made to some necessary data. Due to the compressibility of gas, which is used as the nonwetting phase, a correction to the measured trapped gas saturation is necessary to make it agree with the critical gas saturation of the imbibition relative permeability curve. Introduction The existence of hysteresis in the relationship of relative permeability to saturation has been recognized for many yews. Geden et al. and Osoba et al. called attention to the occurrence of hysteresis and the importance of the direction of saturation change on the relative permeability-saturation relations. It is generally believed that relative permeability is a function of saturation alone for a permeability is a function of saturation alone for a given direction of saturation change, but that there is a distinct difference in relative permeability curves for saturation changes in different directions. The reservoir engineer should be aware of this hysteresis, and he should select the relative permeability curve which is appropriate for the permeability curve which is appropriate for the recovery process of interest. The directions of saturation change have been designated "drainage" and "imbibition" in reference to changes in the wetting-phase saturation. In a two-phase system, an increase in the wetting-phase saturation is referred to as imbibition, while a decrease in wetting-phase saturation is called drainage. The solution-gas-drive recovery mechanism is controlled by relative permeability to oil and gas in which the saturation of oil, the wetting phase, is decreasing. In waterflooding a water-wet reservoir rock, the saturation of water, the wetting phase, is increasing. These two sets of relative permeability curves, gas-oil and oil-water, do not have the same relationship to the wetting-phase saturation. This difference is not due to the difference in fluid properties, but is a result of the difference in properties, but is a result of the difference in direction of saturation change. The flow properties of the drainage and imbibition systems differ because of the entrapment of the nonwetting phase during imbibition. As drainage occurs, the nonwetting phase occupies the most favorable flow channels. During imbibition, part of the nonwetting phase is bypassed by the increasing wetting phase, leaving a portion of the nonwetting phase in an immobile condition. This trapped part phase in an immobile condition. This trapped part of the nonwetting phase saturation does not contribute to the flow of that phase, and at a given saturation the relative permeability to the nonwetting phase is always less in the imbibition direction phase is always less in the imbibition direction than in the drainage direction. The concept that some of the nonwetting phase is mobile and some is immobile during a saturation change in the imbibition direction previously was used to develop equations for imbibition relative permeability. In this development, it was assumed permeability. In this development, it was assumed that the amount of entrapment at any saturation can be obtained from the relationship between initial nonwetting-phase saturations established in the drainage direction and residual saturations after complete imbibition. The equations for imbibition relative permeability were not verified by laboratory measurements. The purpose of this report is m give the results of a laboratory study of imbibition relative permeability and to present a comparison of calculated relative permeability with relative permeability from laboratory measurements. permeability from laboratory measurements. In two-phase systems, hysteresis is more prominent in the relative permeability to the nonwetting phase than in that to the wetting phase. The hysteresis in the wetting-phase relative permeability is believed to be very small, and thus difficult to distinguish tom normal experimental error. SPEJ P. 419


1970 ◽  
Vol 10 (04) ◽  
pp. 381-392 ◽  
Author(s):  
John D. Huppler

Abstract Numerical simulation techniques were used to investigate the effects of common core heterogeneities upon apparent waterflood relative-permeability results. Effects of parallel and series stratification, distributed high and low permeability lenses, and vugs were considered. permeability lenses, and vugs were considered. Well distributed heterogeneities have little effect on waterflood results, but as the heterogeneities become channel-like, their influence on flooding behavior becomes pronounced. Waterflooding tests at different injection rates are suggested as the best means of assessing whether heterogeneities are important. Techniques for testing stratified or lensed cores are recommended. Introduction Since best results from waterflood tests performed on core plugs are obtained with homogeneous cores, plugs selected for testing are chosen for their plugs selected for testing are chosen for their apparent uniformity. We know, however, that uniform appearance can be misleading. For example, flushing concentrated hydrochloric acid through an apparently homogeneous core plug often produces "wormholes" in higher permeability regions. Also, we sometimes find that all core plugs from a region of interest have obvious heterogeneities, so any flooding tests must be run on nonhomogeneous core plugs. plugs. Nevertheless, relative permeabilities, as obtained routinely from core waterflood data, are calculated using the assumption that the core is a homogeneous porous medium. While it is obvious that porous medium. While it is obvious that heterogeneties mill affect these apparent relative permeabilities, there appear to be no experimental permeabilities, there appear to be no experimental results reported in the literature to indicate just how serious the problem is. Accordingly, a computer simulation study of core waterfloods was conducted to systematically examine the effects of different sizes and types of core heterogeneities on flood results. The study was performed by numerical simulation using two-dimensional, two-phase difference equation approximations to describe the immiscible water-oil displacement. For each simulation the permeability and porosity distribution of the heterogeneous core to be studied was specified; fluid flow characteristics of the system, including a single set of input relative-permeabilities curves, were stipulated The system was set in capillary pressure equilibrium at the reducible water saturation. Then a waterflood simulation was performed. From the resulting fluid production and pressure-drop data a set of production and pressure-drop data a set of relative-permeability curves was calculated using the standard computational procedure applicable to homogeneous cores. In this paper these calculated relative-permeability curves are denoted as "waterflood" curves to distinguish them from the specified input curves. The waterflood relative-permeability curves should closely match the input curves for homogeneous systems. Since the same set of input relative-permeability curves was used for all rock sections, deviations of the waterflood from the input relative-permeability curves gave an indication of the effects of heterogeneities. When the system was heterogeneous and there was good agreement between waterflood and input relative-permeability curves, then the heterogeneities did not strongly influence the flow behavior and the system responded homogeneously. MATHEMATICAL MODEL AND METHOD The waterflood simulations were carried out using two-dimensional, two-phase difference equation approximations to the incompressible-flow differential equations:* .....................(1) ....................(2) SPEJ P. 381


Geothermics ◽  
2017 ◽  
Vol 65 ◽  
pp. 269-279 ◽  
Author(s):  
Noriaki Watanabe ◽  
Takuma Kikuchi ◽  
Takuya Ishibashi ◽  
Noriyoshi Tsuchiya

1997 ◽  
Vol 119 (2) ◽  
pp. 183-191 ◽  
Author(s):  
Xiang-Dong He ◽  
Sheng Liu ◽  
Haruhiko H. Asada

This paper presents a new lumped-parameter model for describing the dynamics of vapor compression cycles. In particular, the dynamics associated with the two heat exchangers, i.e., the evaporator and the condenser, are modeled based on a moving-interface approach by which the position of the two-phase/single-phase interface inside the one-dimensional heat exchanger can be properly predicted. This interface information has never been included in previous lumped-parameter models developed for control design purpose, although it is essential in predicting the refrigerant superheat or subcool value. This model relates critical performance outputs, such as evaporating pressure, condensing pressure, and the refrigerant superheat, to actuating inputs including compressor speed, fan speed, and expansion valve opening. The dominating dynamic characteristics of the cycle around an operating point is studied based on the linearized model. From the resultant transfer function matrix, an interaction measure based on the Relative Gain Array reveals strong cross-couplings between various input-output pairs, and therefore indicates the inadequacy of independent SISO control techniques. In view of regulating multiple performance outputs in modern heat pumps and air-conditioning systems, this model is highly useful for design of multivariable feedback control.


2010 ◽  
Author(s):  
Andres Chima ◽  
Efren Antonio Chavez Iriarte ◽  
Zuly Himelda Calderon Carrillo

Materials ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 990
Author(s):  
Mingxing Bai ◽  
Lu Liu ◽  
Chengli Li ◽  
Kaoping Song

The injection of carbon dioxide (CO2) in low-permeable reservoirs can not only mitigate the greenhouse effect on the environment, but also enhance oil and gas recovery (EOR). For numerical simulation work of this process, relative permeability can help predict the capacity for the flow of CO2 throughout the life of the reservoir, and reflect the changes induced by the injected CO2. In this paper, the experimental methods and empirical correlations to determine relative permeability are reviewed and discussed. Specifically, for a low-permeable reservoir in China, a core displacement experiment is performed for both natural and artificial low-permeable cores to study the relative permeability characteristics. The results show that for immiscible CO2 flooding, when considering the threshold pressure and gas slippage, the relative permeability decreases to some extent, and the relative permeability of oil/water does not reduce as much as that of CO2. In miscible flooding, the curves have different shapes for cores with a different permeability. By comparing the relative permeability curves under immiscible and miscible CO2 flooding, it is found that the two-phase span of miscible flooding is wider, and the relative permeability at the gas endpoint becomes larger.


1997 ◽  
Author(s):  
Y.V. Fairuzov ◽  
J. Gonzalez ◽  
G. Lobato ◽  
F. Fuentes ◽  
R. Camacho

2014 ◽  
Vol 1010-1012 ◽  
pp. 1676-1683 ◽  
Author(s):  
Bin Li ◽  
Wan Fen Pu ◽  
Ke Xing Li ◽  
Hu Jia ◽  
Ke Yu Wang ◽  
...  

To improve the understanding of the influence of effective permeability, reservoir temperature and oil-water viscosity on relative permeability and oil recovery factor, core displacement experiments had been performed under several experimental conditions. Core samples used in every test were natural cores that came from Halfaya oilfield while formation fluids were simulated oil and water prepared based on analyze data of actual oil and productive water. Results from the experiments indicated that the shape of relative permeability curves, irreducible water saturation, residual oil saturation, width of two-phase region and position of isotonic point were all affected by these factors. Besides, oil recovery and water cut were also related closely to permeability, temperature and viscosity ratio.


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