TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractArchie's laboratory experiments established a relationship between the formation resistivity factor and porosity, which set forth the use of two constants: m and a. From Archie's work these constants were regression constants representing the slope and intercept, respectively. Subsequent researchers used the general form of Archie's relation, but they found differing values for m and a. The terms cementation factor and tortuosity factor have been used to describe each of these terms. Conventional wisdom believes that a higher m relates to vuggy porosity and a lower m suggests fracture porosity. This is generally true if the tortuosity factor is assumed (typically 0.81 or 1.0) and the cementation factor is calculated.However, if m and a are found simultaneously, theory and many laboratory observations suggest the opposite may be more likely. This study shows that the tortuosity factor, a, is a function of the average angle of electrical movement with respect to the bulk fluid flow, and cementation factor m is related to the flow area contrast between pore throat and pore body.
In support of the research project at the Center for Applied Petrophysical and Reservoir Studies in geologic storage of carbon dioxide in depleted gas reservoirs, the PVT laboratory at Texas Tech University performed compressibility factor (z-factor) measurements at various composition of CO2 with hydrocarbon (HC) gas mixture. For the sole purpose of the measured Z-factor data, three temperatures of 100°F, 160°F and 220°F and pressures ranges from 50 psia to 5000 psia are selected as representative of the depleted gas reservoirs (DGRs). In order to analyze the various phase behavior to be encountered in gas reservoirs (dry gas, wet gas and retrograde gas), the median gas compositions for dry, wet and retrograde gases are specified by gas type. The gas types are categorized by representative compositional analysis for the three types of gas reservoirs (dry gas, wet gas and retrograde gas). The measurements of z-factors for CO2-hydrocarbon mixtures in varying proportions and at the three specified temperatures for various pressures are performed on the median gas compositions of the type gases. The results of the z-factor measurements of CO2-hydrocarbon mixtures are used to interpret the expected phase behavior to be encountered in the geologic storage of CO2 in gas reservoirs. Also, the z-factor measurements of CO2-retrograde gas mixtures are used to quality the benefits of enhanced gas and condensate recovery in gas reservoirs. Introduction Since the earlier 1970, carbon dioxide has been used for enhanced oil recovery through miscible and immiscible displacement of oil at high pressures and moderate temperatures. Recently, research is being directed for the use of carbon dioxide in the oil refining through supercritical extraction of hydrocarbons.1 Current activities are to find ways for geologic storage of CO2 in oil or gas reservoirs.2 Although one laboratory measurement of CO2-hydrocarbon mixture in the limited ranges of temperatures and pressures used in this project has been reported in Venezuela (Rojas-Requena, 1992),3 this paper presents experimental measurements of z-factors for CO2-hydrocarbon mixtures at three specified temperatures and pressures ranging from 50 psia to 5000 psia. The results of the experimental z-factors are used to quantify economic benefits (such as enhanced oil recovery (EOR) and enhanced condensate vaporization) of geologic storage of CO2 in gas reservoir. Procedure for Z-factor Determination The compressibility factor, or Z-factor, is determined by manipulating the Real Gas Law and assuming that reservoir gas will behaves as an ideal gas at ambient pressure and temperature (McCain, 1990, page 106). The Real Gas Law is defined as follows:Equation 1 For a constant composition system, the product of pressure and volume is constant, thusEquation 2 Where the subscripts are:Condition in the cellAmbient condition
An experimental research program has been initiated to investigate the electrical properties of swelling shales across a wide frequency ranee, 10 Hz to 1.3 GHz. This range spans the spectrum of the commonly used downhole logging, measurements, from the deep laterologs to the microwave dielectric tools. Three distinct measurement techniques have been utilized to span the range: multiple electrodes at low frequencies, two-electrode with balanced bridge for the middle frequencies, and open-ended coaxial probe with network analyzer at the high end. The probe technique is simple to use, potentially enabling, field measurements of complex permittivity to be taken, although some accuracy is sacrificed. The effects of swelling, are most pronounced at the lowest frequencies. The weight of a shale which has been exposed to a change in relative humidity reaches equilibrium long before the electrical properties do. Introduction Anomalously low resistivity-log response in certain formations has been known to yield incorrect water saturation and to sometimes mask detection of hydrocarbon-bearing intervals. Shale, which is often the cause of the problem because of its clay content, may be in the form of laminations or grains, both detrital in origin. The interpretation problem is one of choosing the appropriate mixing rule based on both the C, distribution of the shale and the volume investigated by the C, logging measurement. An understanding, of the electrical properties of the shale itself is an important element of the problem. For example, complex permittivity can be used in model based on a volumetrically weighted mixing rule to interpret microwave-frequency measurements. In a shaly formation, these complex time average models require values for the complex permittivity of the shale. High resolution dielectric logging measurements may be able to detect individual shale laminae if they are thick enough, in which case the shale's properties must be accounted for in the interpretation. The electrical properties of massive shales are also of interest to the industry. The alteration of shales, caused by adsorption of water while drilling, is a problem which has acquired a logging perspective due to the increasing use of measurement while drilling. The capability of making real time and time-lapse measurements while still drilling introduces the possibility of detecting a swelling problem while something can still be done about it. Improved interpretation in both of these cases requires an understanding of the effect of the shale's composition, texture, chemistry, and water content on tool response. In particular, the effect on electrical measurements can be quite large. The availability of tools operating over a wide range of frequencies is of possible benefit since the mechanisms affecting the propagation of an electromagnetic wave differ with frequencies. Logging measurements at frequencies from 35 Hz to 1.1 GHz are commercially available. P. 131^
Although there have been many analytical studies on pressure-transient behavior of hydraulic fracture systems, no single analytical solution capable of describing both vertical and horizontal fracture transient state behaviors has been developed. The purpose of this work is to develop a single analytical solution that is robust enough to fit this need. This paper presents a type curve solution for a well producing from a solid bar source in an infinite-acting reservoir with impermeable upper and lower boundaries. Computation of dimensionless pressure reveals that the pressure-transient behavior of any hydraulic fracture system is governed by two critical parameters (i) aspect ratio, m, and (ii) dimensionless length, LD. Analysis of a typical log-log plot of pwD vs. tDxf indicated the existence of four distinct flow periods (i) fracture fill-up period causing a typical storage dominated flow, (ii) vertical linear flow period, (iii) transition period, and (iv) radial flow period. As aspect ratio tends to zero, the fracture fill-up periods disappear resulting in typical fully/partially penetrating vertical fracture pressure response. This analytical solution reduces to the existing fully/partially penetrating vertical fracture solution developed by Raghavan et al1 as aspect ratio tends to zero, and a horizontal fracture solution is obtained as aspect ratio tends to unity. This new horizontal fracture solution yields superior early time (tDxf < 10–3) solution compared with the existing horizontal fracture solution developed by Gringarten and Ramey2, and shows excellent agreement for tDxf > 10–3. Introduction Hydraulically fractured wells and horizontal well completions are intended to provide a larger surface area for fluid withdrawal and thus, improve well productivity. This increase in well productivity is usually measured in terms of negative skin generated as a result of a particular completion type. Hydraulic fractures leading to horizontal or vertical fractures could produce the same negative skin effect as a horizontal well, but possibly different transient pressure response; hence, having a good understanding of the transient behavior of hydraulic fractures systems and horizontal well completion is very vital for accurate interpretation of well test data. The orientation of hydraulic fractures is dependent on stress distribution. The orientation of fracture plane should be normal to the direction of minimum stress. Since most producing formations are deep, the maximum principle stress is proportional to the overburden load. Thus, vertical fractures are more common than horizontal fractures. The only difference between a vertical and a horizontal fracture system is the orientation of the fracture plane; a vertical fracture can be viewed as parallelepiped with zero width, while a horizontal fracture, as a parallelepiped with zero fracture height. This same argument can be extended to horizontal well completions; a horizontal wellbore can be viewed as a parallelepiped with the height and width equal to the wellbore diameter. This configuration makes a horizontal well completion behavior like a coupled fracture system made up of both vertical and horizontal fracture systems. Considering the similarity in the physical models, one will expect a single analytical solution can be developed for hydraulically fractured (vertical and/or horizontal) well and horizontal well completions. The primary purpose of this work is to present a general analytical solution for describing the transient pressure behaviors of (i) vertical fracture system, (ii) horizontal fracture system, and (iii) horizontal well or drainhole. New physical insights into the critical variables that govern the performance of these completions are also provided.
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