The subject matter of the present invention relates to a system adapted to be disposed at the surface of a wellbore for determining mud filtrate volume data as a function of depth in a wellbore from a set of parameterized, processed, and wellbore corrected induction logging array signal data, which data is produced by an array induction tool disposed in the wellbore, and for generating an output record medium which reflects and illustrates the mud filtrate volume data in the form of a log, the log being analyzed in order to determine information regarding wellbore formation properties, such as layering, vertical permeability, and formation damage.
During the drilling of a wellbore, mud pumps introduce mud into the well in order to flush rock chips and other unwanted debris out of the wellbore. The mud is introduced into the wellbore under pressure, the mud pressure being slightly greater than the pressure of a formation traversed by the wellbore thereby preventing a phenomenon known as well blowout. The resultant pressure differential between the mud column pressure and the formation pressure forces mud filtrate into the permeable formation, and solid particles of the mud are deposited on the wellbore wall forming a mudcake. The mudcake usually has a very low permeability and, once developed, considerably reduces the rate of further mud filtrate invasion into the wellbore wall. In a region very close to the wellbore wall, most of the original formation water and some of the hydrocarbons may be flushed away by the mud filtrate. This region is known as the "flushed zone", or the "invaded zone". If the flushing is complete, the flushed zone pore space contains only mud filtrate; in addition, if the flushed zone was originally hydrocarbon bearing, it would contain only residual hydrocarbons. Further out from the wellbore wall, the displacement of the formation fluids by the mud filtrate is less and less complete thereby resulting in a second region, this second region undergoing a transition from mud filtrate saturation to original formation water saturation. The second region is known as the "transition zone". The extent or depth of the flushed and transition zones depends on many parameters, among them being the type and characteristics of the drilling mud, the formation porosity, the formation permeability, the pressure differential, and the time since the formation was first drilled. The undisturbed formation beyond the transition zone is known as the "uninvaded, virgin, or uncontaminated zone". In FIGS. 1a-1b, a schematic representation of an invasion and resistivity profile in a water-bearing zone is illustrated. FIG. 1a illustrates a cross section of a wellbore showing the locations of the flushed zone, the transition zone, and the uninvaded zone extending radially from the wellbore wall. FIG. 1b illustrates a radial distribution of formation resistivity extending radially from the wellbore wall, into the flushed zone, into the transition zone, and into the uninvaded zone. In FIGS. 2a-2b, a schematic representation of an invasion and resistivity profile in an oil-bearing zone is illustrated. FIG. 2a illustrates the radial distribution of fluids in the vicinity of the wellbore, oil bearing bed. FIG. 2b illustrates the radial distribution of resistivities for an oil bearing zone, similar to the radial distribution of resistivities for a water bearing zone shown in FIG. 1b. Sometimes, in oil and gas bearing formations, where the mobility of the hydrocarbons is greater than that of the water, because of relative permeability differences, the oil or gas moves away faster than the interstitial water. In this case, there may be formed, between the flushed zone and the uninvaded zone, an "annular zone or annulus", shown in FIG. 2b, with a high formation water saturation. Annuli probably occur, to some degree, in most hydrocarbon bearing formations; and their influence on measurements depends on the radial location of the annulus and its severity. However, the existence of these zones (the flushed, transition, annular, and uninvaded zones) influence resistivity log measurements and therefore the accuracy of the resistivity log itself that is presented to a client. The resistivity log is utilized by the client to determine if oil exists in the formation traversed by the wellbore. The client is mainly interested in the true and correct value of Rt, the resistivity (reciprocal of conductivity) of the uninvaded zone, since Rt is the best measure of the possibility of oil existing in the formation. However, the existence of the flushed and transition zones in the formation adjacent the wellbore wall adversely affect a measurement of Rt. Therefore, since large amounts of money may be spent based on the resistivity log presented to the client, it is important to understand the true resistivity of the formation in the flushed and transition zones in order to improve the accuracy of the resistivity log in general. Prior art well logging tools function to log the formation and generate signals, which signals are processed by a well logging truck computer situated at the well surface. The well truck computer produces a resistivity log. For a particular depth in the wellbore, the shape of a resistivity radial profile (hereinafter, resistivity profile), produced by the prior art well tool at the particular depth and extending radially outward from a point at the wellbore wall, is shown in FIG. 3. In FIG. 3, the resistivity profile indicates a flushed zone resistivity "Rxo" an uninvaded zone (true) resistivity "Rt", and a transition zone resistivity represented by an abrupt step function indicated generally by the diameter of invasion symbol "di". This step function transition zone resistivity does not accurately reflect the true resistivity distribution of the transition zone in the wellbore; therefore, the value of the resistivity Rt of the uninvaded zone is also adversely affected. The resistivity of the transition zone does not change abruptly as shown in FIG. 3; rather, it changes gradually as shown in FIG. 1b. Therefore, the resistivity profile generated by the prior art well logging tool was at least partially inaccurate. To correct this deficiency, a new transition zone has been defined. In FIG. 4, a resistivity curve is plotted using a set of invasion parameters, that is, the flushed zone 14 resistivity is Rxo, the uninvaded zone 16 resistivity is Rt, and the transition zone 10 resistivity is a gradual decrease (or increase) from Rxo to Rt. The flushed zone 14 extends a radius r1 from the borehole wall radially into the formation; the uninvaded zone 16 begins at a radius r2 from the borehole wall and extends into the formation. Therefore, the transition zone 10 lies within a region defined between radii r2 and r1. In FIG. 4, the transition zone resistivity changes gradually from Rxo to Rt, and not abruptly as shown in FIG. 3. A true and accurate reading of Rt must be obtained to determine if oil exists in the formation traversed by the borehole. In FIG. 5a, a diagram of depth in a borehole versus radius is illustrated, the diagram depicting the radial extension of the flushed zone, the transition zone, and the uninvaded zone over a plurality of depths in a borehole. For example, in FIG. 5a, the flushed zone extends from the borehole wall to radius r1; the transition zone extends from radius r1 to radius r2, and the uninvaded zone extends from radius r2 radially outward into the formation. Notice that there is a distinct difference between radius r2 and radius r1, indicating that the radial width of the transition zone is more than an abrupt step function, as in FIG. 3. In FIG. 5b, a resistivity log or diagram of depth in a borehole versus resistivity is illustrated. In this example, the lowest reading of resistivity is the uninvaded zone resistivity Rt (the conductivity is the highest). The highest reading of resistivity, relative to the other zones, is the flushed zone resistivity Rxo (the conductivity is the lowest). A complete description of the method and apparatus for deriving the invasion parameters useful for defining the transition zone of FIG. 4 is filed Apr. 16, 1991, entitled "Method and Apparatus for Determining Parameters of a Transition Zone of a Formation traversed by a Wellbore and Generating a More Accurate Output Record Medium", the disclosure of which is incorporated by reference into this specification.
Mud filtrate invasion analysis from resistivity logs is commonly attempted by qualitative inspection of the separation between measurement displays representing different depths of investigation. However, general comparisons cannot be based exclusively on radial resistivity differences. As described above, an improvement can be obtained by performing an inversion of resistivity differences through an assumed model to yield a parameter dimensioned in length, and FIG. 4 illustrates a model for a radial resistivity profile originating at the wellbore, incorporating a transition zone between undisturbed rock and rock flushed by drilling fluid invasion. The resulting invasion description in length units may adequately describe invasion in water zones, but may not adequately describe invasion in hydrocarbon zones which are the principle zones of interest. A number of variables should be taken into account. For example, hydrocarbon zones are more complicated because depth based variation in the saturation gradient through the flushed zone/undisturbed zone interface may be confused with changes in invasion character. In addition, variations in drilling mud properties between wells will change the radial resistivity profile, as will differences in formation water properties. Furthermore, depth variation in porosity and hydrocarbon saturation must also be taken into account. Therefore, unless these variables are taken into consideration, an interpretation of the resistivity profile could be wrong.
To solve this problem, invasion analysis should be performed in the volume domain in accordance with the present invention. This volume domain mud filtrate invasion analysis normalizes the effect of all these variables and is useful for comparing well to well and between zones within a well for both water and hydrocarbon zones of interest.