T.A. Blasingame

Optimal Transformations for Multiple Regression: Application to Permeability Estimation From Well Logs

Conventional multiple regression for permeability estimation from well logs requires a functional relationship to be presumed. Due to the inexact nature of the relationship between petrophysical variables, it is not always possible to identify the underlying functional form between dependent and independent variables in advance. When large variations in petrological properties are exhibited, parametric regression often fails or leads to unstable and erroneous results, especially for multivariate cases. In this paper we describe a nonparametric approach for estimating optimal transformations of petrophysical data to obtain the maximum correlation between observed variables. The approach does not require a priori assumptions of a functional form and the optimal transformations are derived solely based on the data set. An iterative procedure involving the alternating conditional expectation (ACE) forms the basis of our approach. The power of ACE is illustrated using synthetic as well as field examples. The results clearly demonstrate improved permeability estimation by ACE compared to conventional parametric regression methods.

Decline Curve Analysis Using Type Curves - Fractured Wells

This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Abstract This work provides the development, validation, and application of new decline type curves for a well with a finite conductivity vertical fracture centered in a bounded, circular reservoir. This work fills a significant void in the modern inventory of decline type curves. In particular, this work is directly applicable to production data analysis for cases taken from low permeability gas reservoirs. Using an appropriate analytical solution for this case, we prepared decline type curves for F cD values from 0.1 to 1000 — individual type curves are generated for each F cD value using a range of r eD values from 2 to 1000. The following type curves are provided: l Fetkovich format rate-time decline type curves (constant pressure case): q Dd versus t Dd l Fetkovich-McCray format rate-time decline type curves (equivalent constant rate case): q Dd versus Dd t l Fetkovich-McCray format rate-cumulative decline type curves: q Dd versus N pDd We provide an example demonstration of the methodology for decline type curve analysis using a field case of continuously measured production rate and surface pressure data obtained from a low permeability gas reservoir. These solutions/type curves provide an analysis/interpretation mechanism that has not previously been available in the petroleum literature. Compared to field data, we find that the traditional type curve solutions for an infinite conductivity vertical fracture are typically inadequate — and, the new solutions for a well with a finite conductivity vertical fracture clearly show much more representative behavior. This validation suggests that the proposed type …

Type-Curve Analysis Using the Pressure Integral Method

This paper was aalscted for preaentafionby an SPE ProgramCommitteefollowingraview of informationcontained in an abstract submittedrrythe author(e).Gantentaof the pap as presented, have not been reviewed by the Sodefy of PetroleumEnginaeraand are subjacfto correctionby the author(a).The material, aa presented doaa not necessarilyrefk any poaltlonof the Societyof PetroleumEnginwrs, Ita offlcera,or membere. Papara presentedat SPE meetingsare aubjactto publicationreview by EditorialCommitteesof the SocI ofPetroleumEngineers.ParmieelontocopyIsrasfriofadtoen abatractofnotmorethanS00worde,Illuafrationamaynotbe Cupisd.The abstractshouldcontainconspicuousacknow[adgm of where and by whom the paper ia presented. Write PublicationsManager, SPE, P.O. Sox SS38S6, Richardson,7X 750S?-SS36.Telex, 730989 SPEDAL.

Variable-Rate Reservoir Limits Testing

This paper was selected for presentation by an SPE Program Committee following raview of information contained in an abstract submittad by the author(s).

The Variable-Rate Reservoir Limits Testing of Gas Wells

Thla papar was aalacfad for preaantatlon by an SPE Program Committee following review of information contained in an ebatract submitted by the author(e). Ca’Nenta of the papar, aa preaantad, have not bean reviewed by the Society of Petroleum Englnaara and are subject to corractlon by the author(a). The material, as preaamad, doaa not nacwaarily raflact any pwltlon of the Society of Petroleum Englnaars, ita officers, or members. Papara preaamad at SPE mwtings are subjeci to publication review by Editorial Orrmmittws of the Society of Petroleum Englnwra. Parmlsalon to copy Is raatrictad to an ebatracf of not more than S00 words. Illuatrationa may not be coplad, The abatraot should contain consplcuoua acknowledgment of where and by whom the papar Is presented. Write Put Watlona Manager, SPE, P.O. Sox 83W36, Rlchardwm, TX 7608S-SSSS. Telex, 730S89 SPEDAL.

Semianalytic Solutions for a Well With a Single Finite-Conductivity Vertical Fracture

In this paper,we developa simple,closedformapproximationfor the Laplaeetransformsolutionfor thecaseof a wellwitha finite conductivityverticalfracturein an infiite-acting reservoir. Our hybrid solution is based on a ooupling of the solution for a Minear Me conductivityvetticalfhwxuremodel(whichdoesnot model radial flow) and the solution for a uniform flwdiinfiinite conductivity vertical fracture (whichdoes model scudoradial f flow). ‘Ilxw solutionsarensadilyobtainedfromthe iterature. Overa.lLweconsideroursolutionto be validfor Cp~.S andwe show that our solutiongives leasthan 1percenterror in bothpD andpD’ for C~>2. We suggest that our hybrid solution is not valid for C@iM and do not recommendits use for CpCO.5 underanycltmtnstanoes. We have verifkd this solution against four different solutions given in the literature. Each comparisonwas excellent which suggestathat our simplifkd solution is more than adequatefor practiwdapplications, In particular,we provideveritlcationfor constantrate and constantpressureproductionfor vah-s of Cp between0.2S and 10,000. We also show that our solution is capableof producingveq accuratederivativefunctions. In addition,by reproducingthe literaturesolutions so well, we also verified that individual flow regimes (formation/fracture b-flow, formationlinearflow,andpaeudoradiaI flow)areall modeledaccumtelyby ournewsolution. INTRODUCTION Ourmotivationfor this paperis to providethe technicalaudience with an aoourate,but computationallysimple,approximationfor the Laphwetransformsolutionfor thecaseof a wellwith a f~tc conductivityvertiealfrsotwein an infiiite-actingte-servoir. Wehavethe followingobjectivesforthiswork

An Integrated Geologic and Engineering Reservoir Characterization of the North Robertson (Clearfork) Unit: A Case Study, Part 1

Infill drilling of wells on a uniform spacing, without regard to reservoir performance and characterization, must become a process of the past. Such efforts do not optimize reservoir development as they fail to account for the complex nature of reservoir heterogeneities present in many low permeability carbonate reservoirs. New and emerging technologies such as cross-borehole tomography, geostatistical modeling, and rigorous decline type curve analysis can be used to quantify reservoir quality and the degree of interwell communication. These results can be used to develop a 3-D simulation model for prediction of infill locations. In this work, the authors will demonstrate the application of reservoir surveillance techniques to identify additional reservoir ``pay`` zones, and to monitor pressure and preferential fluid movement in the reservoir. These techniques are: long-term production and injection data analysis, pressure transient analysis, and advanced open and cased hole well log analysis. The major contribution of this paper is the summary of cost effective reservoir characterization and management tools that will be helpful to both independent and major operators for the optimal development of heterogeneous, low permeability carbonate reservoirs such as the North Robertson (Clearfork) Unit.

Analysis of Slug Test Data From Hydraulically Fractured Coalbed Methane Wells

This paper presents new type curves for analyzingslug tests in hydraulically fractured coal seams. The type curves were viable producers, Therefore, these conventional slug test analysis developed using a finite-conductivity,vertical fracture model and techniques cannot be used to either assess the success of the fracturetreatmentor to evaluatethe px.t-fracture potentialof these are presented in terms of three parameters -dimensionless stimulated coal seams. Karsaki, et al,g studied the pressure welltme storage coefficient, dimensionlessfracture conductivity, response of slug tests in infinite-conductivity vertical fractures, and fracture-face skin. Whh these new curves, we may estimate but they did not investigate the behavior of finite-conductivity the hydraulic fkacturehslf-length, the fomlation permeability,and fractures. The purposes of this paper are to develop a male] for the fracture conductivity. We also present a procedure for using slug testingin coal seamswith finite-conductivityverticalfractures the new curves and illustrate the procedurewith an example, and tc illustrate application of this model to the analysis of slug ;ests, INTRODUCTION Slug testing has been proven to & an effective method for MATHEMATICAL MODEL characterizing the production potential of coal seams. A slug test We developed our slug test model using Cinco-ky, et al.’sg involvesthe impositionof an instantaneouschange in pressure(m fluid head) in a well and the measurementof the resulting change model which considers a well intersected by a fully-penetrating, finite-conductivity,vertical fracture. The reservoir is assumed to in pressure as a function of time. This change in pressure is be an isotropic,,homogeneous, infinite medium having a uniform created by either injecting into or withdrawing from the well a specific volume of fluid (i.e., a slug), From this measured thickness, h, permeability, k, and porosity, @. In addition, the pressure response, we may estimate the permeability and nearrescrvoir contains a slightly compressible fluid of viscosity, p, welltmreconditions. and compressibility,c, that are independentof pressure. Initially, slug testing methods and analysis techniques were developed for estimating the transmissivity of shallow, Cinco-Lcy, et al’sg modci assumes the fracture to be a homogeneous, uniform slab with height, h, width, bj and half underpressured aquifersl-s, but also have found applications in length, L { Because the fracture width is much smaller than the petroleum industry, especial)j for analyzing the flow period fracture ength and height, the model assumes the flow in the during drill stem tests4-6. Recently, slug testing has been fracture is linear and that fluid influx at the fracture tips is extended to the evaluation ot’ the production potential of coal negligible, In addition, the model assumes that fluid production seams7. Since most coal seams are saturated initially with water, from the reservoir to the wellbore occurs only through the slug testing provides a simple but effectivemethod for estimating fracture. Further, since the fracture volume is small, the model flow properties early in the productive life before the initiation of neglects the fracture compressibilityand assumes flow within the gas production. Reference 7 provides an overview of fractureis relativelyincompressible. Additionaldetailsconcerning conventionalslug testingin coal seams. the model formulation and problem solution may be obtained in Ref. 9 and Appendix A. Conventional slug test analysis techniquesare based on radial flow models, However, many wells completed in coal seams Under these conditions, Cinco-Ley, el al.g derived art require hydraulic fracturing in order to become economically expression for the dimensionless pressure drop at the wellbore (i.e., XD = O) during constant rate production from a WCII Referencesand illustrationsat end of paper intersectedby a finite-conductivityfractureas --2 Analysisof SlugTest Data From HydraulicallyI%ctured CoalbedMethaneWells SPE 21492

Application of Integrated Reservoir Management and Reservoir Characterization to Optimize Infill Drilling

Initial drilling of wells on a uniform spacing, without regard to reservoir performance and characterization, must become a process of the past. Such efforts do not optimize reservoir development as they fail to account for the complex nature of reservoir heterogeneities present in many low permeability reservoirs, and carbonate reservoirs in particular. These reservoirs are typically characterized by: o Large, discontinuous pay intervals o Vertical and lateral changes in reservoir properties o Low reservoir energy o High residual oil saturation o Low recovery efficiency

Pressure Transient Data Acquisition and Analysis Using Real Time Electromagnetic Telemetry

This paper presents the operational procedures and the results for two pressure buildup tests performed using a wireless telemetry acquisition system (TAS) tool at the North Robertson (Clearfork) Unit (NRU) in Gaines, Co. Tx. Using a single pressure gauge system downhole, we obtained real-time telemetry of pressure and temperature data at the surface, as well as a larger sampling of data that were stored in the downhole memory system. This new wireless telemetry acquisition system was developed to provide real-time pressure and temperature data at the surface by using an electromagnetic signal to transmit these data through the formation strata. The tool is fully programmable so that a wide range of sampling frequencies can be used. The system allows pressure and temperature data to be stored downhole (as in the case of a typical memory gauge), or these data can be transmitted to surface data acquisition systems. This provides real-time pressure and temperature data for pressure transient tests, stimulation monitoring, and long-term reservoir surveillance. Our objective is to demonstrate the use of this technology for pressure buildup tests in low permeability reservoirs. Our goal in utilizing this technology is to reduce the shut-in time requirements for pressure transient tests--which will ultimately result in a more cost-effective reservoir surveillance program as wells can be returned to production (or injection) as quickly as possible. Once the pressure data were acquired, we performed conventional semilog and log-log analysis, and we simulated test profiles to verify the analyses of the test data. Both surface and downhole pressure data were compared for consistency, and both types of data were analyzed in exactly the same fashion. The results of these analyses were essentially identical. This approach gave consistent estimates of reservoir pressure, permeability, skin factor, and fracture half-length for both of our case histories.