Analysis of Simultaneously Measured Pressure and Sandface Flow Rate in Transient Well Testing (includes associated papers 13937 and 14693 )
Authors: Kucuk F. , Ayestaran L. 
Published: December 2007

Analysis of Simultaneously MeasuredPressure and Sandface Flow Rate in Pressure and Sandface Flow Rate in Transient Well Testing

Summary
New well test interpretation methods are presented thateliminate wellbore storage (afterflow) effects. These new methods use simultaneously measured sandface flow rateand wellbore pressure data. It is shown that formationbehavior without storage effects (unit response orinfluence function) can be obtained from deconvolution of sandface flow rate and wellbore pressure data. The storage-free formation behavior can be analyzed to identify the system (reservoir flow pattern) that isunder testing and to estimate parameters. Convolution(radial multirate) methods for reservoir parameter estimation and a few synthetic examples for deconvolution and convolution also are presented.

Introduction
Well testing with measured sandface flow rate can betraced to the beginning of reservoir engineering. The rate must be measured over time to calculate and/or approximate constant rate to obtain even a single reservoir parameter from pressure measurements. This approximate parameter from pressure measurements. This approximate constant rate has been sufficient for estimating permeability, skin, and initial formation pressure during permeability, skin, and initial formation pressure during the radial infinite-acting period. During this period, the well should produce at a constant rate at the sandfaceor at a zero rate if a build up test is conducted. Becauseof compressible fluid in the production string (wellbore storage effects), it takes a long time to reach the radial infinite-acting period. The effect of outer boundaries alsomay start before the end of the wellbore storage effects. In general, the storage capacity of the wellbore, wellbore geometry, near-wellbore complexities, and external boundaries affect transient behavior of a well. During the analysis of pressure-time data, each of these phenomena and its duration must be recognized for the phenomena and its duration must be recognized for the application of semilog and type curve techniques to determine formation flow capacity (kh), damage skin, and average formation pressure. The influence of these phenomena on transient behavior of a well progresses over phenomena on transient behavior of a well progresses over time. For the sake of convenience, the test time can be divided into three periods according to which phenomenonis affecting the pressure. These periods are defined as follows.

Early-Time Period
The combined effects of wellborestorage, damage skin, and pseudoskin (which includepartial penetration, perforation, acidizing, fractures, partial penetration, perforation, acidizing, fractures, non-Darcy flow, and permeability reduction caused by gassaturation around the wellbore)dominate pressurebehavior. The stratification and dual porosity also mayaffect wellbore pressure during this period.

Middle-Time Period
During this period, radial flow isestablished. Conventionally, semilog techniques are usedto determine formation, kh and initial pressure and skin.

Late-Time Period
During this period, outer boundaryeffects start to distort the semilog straight line. For example, the gas cap shows a curve-flattening effect on log-log and Horner plots. Sometimes the separation of these periods from eachother is impossible; particularly, the effects of bottom-water influx and/or gas cap may start during themiddle-time period. Thus, the semilog approach sometimescannot be applied at all. Furthermore, the drawdown or buildup tests as conductedtoday tend to homogenize the reservoir behavior. In other words, most of the reservoirs behave homogeneously duringthe storage-free radial infinite-acting period because mostof the heterogeneous behavior takes place during theearly-time period. The type-curve approaches have been introduced toovercome some of these problems. The theories, applications, and elaborations of the type curve methods, as wellas many references, can be found in Ref. 1. In 1979, Gringarten et al. introduced new type curves that usedifferent parametrization than the earlier ones, namelyRamey, Agarwal et al., McKinley, and Earlougher and Kerschtypes. All the type curves presented by these authors, andmany others, were developed under the assumption that thefluid compressibility (density) in the tubing and annulusremains constant during the test period. During the earlytime, particularly for buildup tests, shut-in pressureincreases very rapidly; thus, the compressibility is usuallyhigher than the compressibility of the fluid in the reservoirfor producing wells. Since the pressure in the wellbore is afunction of the depth, the compressibility of the fluid atthe wellhead can be 10 or even 100 times greater than thecompressibility of the fluid at the bottom. Thus, theassumption that the wellbore storage coefficient is constantduring the drawdown, and particularly during buildup, maynot be correct.
JPT
p. 323