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This work presents the basic pressure behavior differences between a finite condutivity fracture and different types of damaged fractures.
Two kinds of fracture damage conditions are studied: a) a damaged zone around the fracture, and b) a damaged zone within the fracture in the vicinity of the wellbore. The first case is caused by the fracturing fluid loss in the formation and the last case is originated by crushing, embedding or loss of propant within the fracture in the vicinity of the wellbore.
This paper emphasizes that although finite fracture conductivity and fracture damage condition are both flow restrictions, their effects on transient pressure behavior are quite different at early time.
Type curves and both linear flow and bilinear flow graphs can be used to identify different cases when applied properly.
Evaluation of hydraulic fracturing through transient pressure analysis has become a common practice today. Initially, the main objective of the application of pressure analysis in fractured wells was to pressure analysis in fractured wells was to estimate the formation flow parameters and fracture extension. These techniques considered an infinity conductivity vertical fracture and involved a trial and error procedure unless prefac information was procedure unless prefac information was available. To avoid these limitations Gringarten et al presented the type curve analysis method which allows the identification of different flow regimes and the estimation of both formation permeability and fracture half length.
Recently, the analysis of pressure data for fractured wells has been directed towards the determination of both flow and geometric characteristics of a fracture This has been possible because of the development of new solutions which consider a well intercepted by a finite conductivity vertical fracture.
Frequently, it is observed that the pressure behavior of a fractured well does pressure behavior of a fractured well does not match the infinite conductivity vertical fracture solution; instead these cases exhibit an extra pressure drop caused by a flow restriction somewhere in the system. Several models have been proposed: a) A damaged zone around the fracture (fluid loss damage) and b) a damaged region within the fracture in the vicinity of the wellbore (choked fracture); both cases consider an infinite conductivity vertical fracture and are referred as damaged fractures.
The purpose of this work is to show and emphasize that although finite fracture conductivity and fracture damage conditions are both flow restrictions their pressure transient behavior are quite different at early time.
While the finite conductivity case exhibit the bilinear flow behavior, the frac ture damage case is characaterized by an extra pressure drop caused by the damaged zone. pressure drop caused by the damaged zone. These differences become evident when pressure data are plotted on a log-log graph. pressure data are plotted on a log-log graph. PRESSURE BEHAVIOR OF FRACTURED WELLS PRESSURE BEHAVIOR OF FRACTURED WELLS For the better application of the transient data analysis techniques, it is necessary to understand the basic flow equations that describe the flow towards hydraulically fractured wells.
Production of either wells completed in low permeability reservoirs or damaged wells has been possible because of hydraulic fracturing. The estimation of both the geometric and flow characteristics of a fracture represent a useful information for the calibration of fracture design methods and permits forecasting well flow behavior.
Transient pressure well test analysis has been used with success to estimate well conditions and reservoirs parameters. Conventional methods of interpretation are based on radial flow theory. This is a limitation when applied to fractured wells because they exhibit other type of flow at different times in a test.
Several authors have presented different techniques to calculate both reservoir and fracture parameters. These methods include the linear flow graph (delta p vs root of t), the bilinear flow graph (delta p vs root of t), the semilog graph (delta p vs log t) and type curve matching. Among these techniques, the type curve method deserves special attention because it allows both the analysis of pressure data and the detection of different flow regimes.
Transient pressure analysis techniques have been proved to be an excellent formation evaluation tool. Interpretation of wellbore pressure data yields average values of pressure data yields average values of formation characteristics and allows to detect some heterogeneities in the reservoir. These techniques were developed initially, for radial flow conditions and later modified to take into consideration different types of flow geometry.
At the same time, stimulation techniques were developed to increase the productivity of both damaged wells or wells producing from low permeability reservoirs. Hydraulic fracturing stands as on of the most effective stimulation methods because its application generally allows production of wells to be economical.
It was recognized early that wells intercepted by a fracture have different flow behavior than unfractured wells, consequently, application of pressure analysis methods based on radial flow theory to these cases can yield erroneous results.
Many studies have been published to examine different flow situations for fractured wells. Table 1 presents a summary of these publications. Initially, most works dealt with steady state flow toward fractured wells; both horizontal and vertical fractures were considered and the main objective was to determine the effect of a fracture on well productivity.
The first study on the unsteady-state flow behavior for fractured wells was present ed by Dyes et al. They investigated the effect of a vertical fracture on the semilog straight line and concluded that the slope of the straight line is affected when a fracture extends over fifteen percent of the drainage radius.
Later, Prats showed that a well intersected by an infinite conductivity vertical fracture exhibits an effective wellbore radius equal to one half of the fracture length; this conclusion was reached before by Muskat.
Russell and Truitt studied the transient pressure behavior of an infinite conductivity vertical fracture in a closed square reservoir. They calculated the well bore pressure as a function of time for several fracture penetration ratios. It was demonstrated that the semilog analysis applies to these cases if the reservoir radius is much greater than the fracture length.
A mathematical model was developed to study the transient behavior of a well with a finite-conductivity vertical fracture in an infinite slab reservoir. For values of dimensionless time of interest, to >10 , the dimensionless wellbore pressure, p , can be correlated by the dimensionless group; wk / x k, where w, k , and x are the width, permeability, and half length of the fracture, respectively, and k represents the formation permeability.
Results when plotted as a function of P vs log to give, for large t , a 1.151-slope straight line; hence, semilogarithmic pressure analysis methods can be applied. When plotted in terms o/ log P vs log t , a family of curves of characteristic shape result. A type-curve matching procedure can be used to analyze early time transient procedure can be used to analyze early time transient pressure data to obtain the formation and fracture pressure data to obtain the formation and fracture characteristics.
Hydraulic fracturing is an effective technique for increasing the productivity of damaged wells or wells producing from low permeability formations. Much research has been conducted to determine the effect of hydraulic fractures on well performance and transient pressure behavior. The results have been used to improve the design of hydraulic fractures. Many methods have been proposed to determine formation properties and fracture characteristics from transient pressure and flow rate data. These methods have been based on either analytical or numerical solutions of the transient flow of fluids toward fractured wells. Recently, Gringarten et al. made an important contribution to the analysis of transient pressure data of fractured wells. They presented a type-curve analysis and three basic presented a type-curve analysis and three basic solutions: the infinite-fracture conductivity solution (zero pressure drop along a vertical fracture the uniform flux solution for vertical fractures, and the uniform flux solution for horizontal fractures.
Although the assumption of an infinite fracture conductivity is adequate for some cases, we must consider a finite conductivity for large or very low flow capacity fractures. Sawyer and Locke studied the transient pressure behavior of finite-conductivity vertical fractures in gas wells. Their solutions cannot be used to analyze transient pressure data because only specific cases were presented.
In this study, we wanted to prepare general solutions for the transient pressure behavior of a well intersected by a finite-conductivity vertical fracture. The solutions sought should be useful for short-time or type-curve analysis. We also wanted to show whether conventional methods could be applied to analyze transient pressure data for these conditions. A combination of both methods, as pointed out by Gringarten to al., should permit an pointed out by Gringarten to al., should permit an extraordinary confidence level concerning the analysis of field data.
STATEMENT OF THE PROBLEM AND DEVELOPMENT OF FLOW MODELS
The transient pressure behavior for a fractured well can be studied by analyzing the solution of the differential equations that describe this phenomenon with proper initial and boundary conditions. To simplify the derivation of flow models, the following assumptions are made.
1. An isotropic, homogeneous, horizontal, infinite, slab reservoir is bounded by an upper and a lower impermeable strata. The reservoir has uniform thickness, h, permeability, k, and porosity, which are independent of pressure.
2. The reservoir contains a slightly compressible fluid of compressibility, c, and viscosity, mu, and both properties are constant.
3. Fluid is produced through a vertically fractured well intersected by a fully penetrating, finite-conductivity fracture of half length, x , width, w, permeability, k , and porosity, phi . These fracture permeability, k , and porosity, phi . These fracture characteristics are constant. Fluid entering the wellbore comes only through the fracture.
A system with these assumptions is shown in Fig. 1. In addition, we assume that gravity effects are negligible and also that laminar flow occurs in the system.
The pressure transient behavior of hydraulically fractured wells has been the subject of considerable study over the past few years. Several investigators have presented solutions of the fundamental equations, identified qualitative diagnostic trends and suggested interpretation techniques. This paper presents a systematic approach to the problem along with substantial observations on the potential of unique interpretations.
Pretreatment tests are considered here as necessary. Well tests in tight formations are often of very short duration, to allow the use of established methodologies. Hence, a technique to calculate the maximum reservoir permeability from a short well test is offered.
In the case of post-treatment tests the data are treated using the convolution/deconvolution techniques and influence functions. The term "influence function" defines a relationship between pressure response and time at a constant unit surface flow rate. Although drawdown well tests have advantages over buildup tests because they are used while the well is producing, their interpretation has been hampered by varying flow rates. Conventional interpretation techniques assume either constant well flow rate or controlled variation of it. Pressure buildup tests are conducted with the well flow rate equal to zero and are, as a result, predominant.
In the case of post-treatment well tests of hydraulic fractures a lengthy buildup test and the ensuing shut-in may result in severe damage to the generated fracture. Thus buildup tests are not always desirable for post-treatment evaluation. The con-volution/deconvolution techniques and influence "functions,by normalizing the pressure response to a unit flow rate, permit the use of standard techniques for the analysis of drawdown tests. The interpretations presented here utilize new versions of pressure and pressure derivative type curves including the dimensionless fracture storage coefficient, and the dimensionless fracture conductivity. Based on observations of the sensitivity of the response to these parameters, three type curves have been developed, one for low, one for intermediate, and one for high conductivity fractures. The choice can be made on the basis of pretreatment analysis and the fracture design. The storage and the half-length of the generated fracture can then be calculated with reasonable confidence.
PRETREATMENT WELL ANALYSIS FOR TIGHT RESERVOIRS
Tight formations are characterized by permeabilities less than 10 md. The permeability is usually less than 1 md and is often less than 0.1 md.
Knowledge of the "undisturbed" reservoir permeability is considered essential for the preparation of an appropriate fracture stimulation design. As will be demonstrated later on in this paper it is also essential in the post-treatment evaluation of job effectiveness.
The standard and desirable methods of analysis for radial, infinite acting, reservoirs are usually not feasible in tight formations. Although the reservoir configurations would theoretically lend themselves to such analyses, the low permeability results in a slow response to pressure perturbations. The necessary pressure response patterns take a substantial amount of time to appear.
Techniques for analyzing tight formations, which attempt to extract reservoir data from very early data by deconvolving wellbore storage effects have appeared in the literature.
A method is presented for the determination of the orientation of fully penetrating vertical fractures by means of analysis of transient pressure data recorded at the active well and at two observation wells due to production or injection at the active fractured well. The fracture is considered to be of finite conductivity. The method discussed in thus work is an extension of the method of Uraiet et al. for the determination of compass orientation of vertical fractures. They considered uniform flux fractures. Results of this study show that when the pressure interference data, on the presence of finite pressure interference data, on the presence of finite conductivity fractures, are matched to the uniform flux-type curves, a match may not be obtained correctly.
It is important to know the flow patterns created after a number of wells in a reservoir have been hydraulically fractured. This is of prime interest for enhanced recovery projects. Also, the development of low-permeability reservoirs using fracturing techniques requires an accurate knowledge of the dimensions and orientation of the fractures. This is essential for well spacing purposes if interference effects are to be minimized.
Several methods have been suggested for determining the orientation of fractures. Elkins and Skov discussed a method for the determination of the orientation of natural fractures in a reservoir. They considered the fractured system (the reservoir) to be of anisotropic permeability and used the line-source solution to find the orientation of the major fracture trend. Reynolds et al. and Fraser and Pettit presented a method to obtain data about the fractures presented a method to obtain data about the fractures by means of an inflatable formation packer. They could get information about the type of fracture, vertical, horizontal or inclined, and the penetration and orientation. Pierce et al. described a way to us use pulse testing to determine the fracture length and orientation. Power et al. showed how acoustic, seismic, and surface electric-potential measurements can be applied to detect fracture orientation. Recently, Uraiet et al. discussed a method for determining the fracture orientation using transient pressure data recorded at the active fractured well, pressure data recorded at the active fractured well, production or injection, and at the observation wells. production or injection, and at the observation wells. They considered the fracture to be of uniform flux.
The purpose of this study is to extend the method recently presented by Uraiet et al. to the case of finite conductivity fractures, and provide type curves for the analysis of pressure interference data. It is also intended to show what kind of problems may arise when pressure interference data, created by an active finite conductivity fractured well, are matched to the uniform flux-type curves.
The mathematical model considered in thus study is the finite conductivity vertical fracture model of Cinco et al. It is assumed that the porous medium is isotropic, homogeneous, horizontal, of uniform thickness h, permeability k, and porosity phi. All formation properties are assumed to be independent of pressure. The reservoir contains a slightly pressure. The reservoir contains a slightly compressible fluid of compressibility c and viscosity mu, both properties being constant. Fluid is produced through properties being constant. Fluid is produced through a vertically fractured well intersected by a fully penetrating finite conductivity fracture of penetrating finite conductivity fracture of halflength xf, width w, and permeability kf. These fracture characteristics are constants and fluid entering the wellbore comes only via the fracture.
The system defined under the above assumptions is shown in Fig. 1.
It is also assumed that gravity effects are negligible and that Darcy flow occurs in the porous medium and in the fracture.
It can be shown that the dimensionless pressure drop at a point (xD, yD) in the reservoir, created by the fractured active well can be expressed approximately by the following equation.
PD(XD,YD,TDM) = PD(XD,YD,TDM) =