Mustafa Onur

The effect of calcite deposition on geothermal well inflow performance

Deposition of calcite in a formation may significantly reduce the inflow performance of geothermal wells producing brine with CO 2 content. The key operational and reservoir parameters influencing the magnitude of impairment by calcite deposition were identified through the derivation of analytical expressions for the rate of calcite deposition and its effect on flow rate assuming idealized flow conditions. A methodology for the use of derived expressions permits the investigation of calcite deposition processes for specific reservoir descriptions and well operations. The rate of calcite scaling in the formation was shown to be inversely proportional to the square of the radial distance from the well. For a given flow rate, the degree of calcite deposition around the well may be significantly reduced by decreasing the pressure gradient near the well and/or increasing the effective wellbore radius through well-stimulation techniques (e.g., acid treatments). Reducing the flow rate will generally increase the production time of a well before significant flow impairment by deposited calcite.

Estimating permeability distribution from 3D interval pressure transient tests

Abstract In this paper, the basic features of 3D (spatially r and z and time) interval pressure transient testing (IPTT) are described for the estimation of horizontal and vertical permeabilities and delineation of fracture and fault conductivities using the packer module and observation probe tool combination of the multiprobe wireline formation tester. Mathematical models for the pressure behavior of IPTT tests for using the packer module and the observation probes in multilayer (stratified) formations are presented. The maximum likelihood (ML) method is presented for nonlinear parameter estimation to handle uncertainty in error variances (weights) in observed data. The main advantage of the ML method over the traditional weighted least squares (WLS) is that it eliminates the trial-and-error procedure required to determine appropriate weights to be used in the WLS estimation. As shown by the examples presented in the paper, the ML method provides significant improvement in parameter estimation when working with pressure data sets of disparate orders of magnitude and noise, e.g., pressure measurements for the packer–probe and multiprobe interval tests. A field example where eight IPTT tests were conducted in a major carbonate formation is presented for characterization of vertical and horizontal layer permeabilities and vertical communication through the main producing reservoir section. These IPTT tests were conducted with a Formation Tester Dual Straddle Packer and two Probe Modules in a newly drilled well. An IPTT test at each location was interpreted using an appropriate geological model with the packer and probe pressure and flow rate measurements. The interpretation procedure consisted of identification of the different flow regimes followed by history (type curve) matching for the estimation of vertical and horizontal permeabilities for each layer. A detailed interpretation of two of the interval pressure transient tests is presented.

Nonlinear Regression Analysis of Well-Test Pressure Data with Uncertain Variance

The main objective of this study is to explore the use of parameter estimation techniques that handle cases where error variances (weights) in observed well-test data are uncertain. There are two main sources of uncertainty: 1) The gauge resolution and 2) measurement environment. Many gauges are used in well testing are not well characterized in terms of accuracy and resolution. The measurement environment in the wellbore is very noisy because of high frequency events in the wellbore (any producing interval), eg phase segregation. Because of these uncertainties, in this study, we investigated the use of parameter estimation methods based on the maximum likelihood and presented a new efficient method based on this method. The maximum likelihood method enables one to estimate error variances in pressure data along with the unklnown formation parameters. It is shown that the new method is efficient and powerful in estimating formation parameters from well-test data with uncertain variance. A simulated interval test from the multiprobe wireline formation tester in a single layer system as well as a field interval test in a three layer cross-flow system are used to demonstrate the applicability of the proposed methods.

A new general pressure-analysis procedure for slug tests

A new analysis procedure for determining formation flow capacity and skin factor from slug-test data is presented. The procedure arises from exact deconvolution equations that convert measured slug-test pressure data into equivalent pressure and pressure-derivative responses that would be obtained if the well were produced at a constant surface flow rate. The converted data then can be analyzed by use of existing wellbore-storage and skin type curves for the particular reservoir or well model represented by the field data. For cases where the slug test is short, we show that flow rate convolution can be incorporated to improve analysis reliability. The analysis procedures do not require direct knowledge of the sandface flow rate

A new approach for constructing derivative type curves for well test analysis

Recently, type curves based on pressure derivatives have become a highly popular method for analyzing well test data. Typically, these type curves represent a log-log plot of dimensionless pressure and the derivative of dimensionless pressure vs. dimensionless time. This work presents a new general procedure for constructing type curves based on a new combination of dimensionless pressure and the derivative of dimensionless pressure. The procedure can be used to construct type curves for all standard problems encountered in well testing. The new type curves always have good character so that nonuniqueness problems sometimes encountered in type-curve matching are eliminated;p thus, the type curves constructed by our method should improve our ability to obtain accurate estimates of reservoir parameters by type-curve matching. The basic procedure is used to construct new type curves for wellbore storage and skin problems and for fractured wells (uniform-flux and infinite-conductivity). These type curves are constructed so that the vertical scale of the dimensionless derivative groups is automatically aligned with the vertical scale of the field-data derivative groups; thus, type-curve matching of field derivative data is accomplished by moving the field data plot only in the horizontal direction. This automatic alignment of the vertical scales simplifies type-curvemorexa0» matching and also is advantageous for determining whether field data actually represent the solution assumed by a given type curve.«xa0less

Analysis of Well Tests From Naturally Fractured Reservoirs by Automated Type-Curve Matching

Due to the diversity of existing idealized naturally fractured reservoir models e.g. double porosity models with transient or pseudo-steady interporosity flow, etc., and the large numer of parameters needed to be estimated in these models, the analysis of well test data from naturally fractured reservoirs by the well-known conventional graphical techniques is often difficult if not impossible. In recent years, the computer-aided automated type curve matching techniques based on nonlinear regression methods (e.g. least-squares, least absolute value, etc.) have been increasingly popular in estimating well/reservoir parameters from transient well test data. In this work, we explore in detail the applicability of nonlinear regression techniques to obtain the parameter estimates from welltest pressure data from naturally fractured reservoirs. We implement both the nonlinear regression technique based on L 2 norm (least-squares) minimization and the nonlinear regression technique known as robust regression based on L 1 norm (least absolute value) minimization. Important characteristics of these nonlinear regression are discussed. In modeling the pressure data we consider the most commonly used double porosity models sugh as Warren and Roots pseudo steady state interporosity flow model as well as transient interporosity flow models with slab and spherical matrix blocks (with or without interporosity skin effects) including wellbore and storage effects. The analysis of multi-rate tests by nonlinear regression techniques is also given. As model functions, pressure (or pressure change), conventional pressure derivative, pressure plus pressure derivative, pressure/pressure derivative ratio and integral pressure functions are considered in regression. The advantages and disadvantages associated with use of each function in the analysis are discussed. it is shown that the pressure/pressure derivative ratio increases the changes of obtaining a unique fit, that is, that it is not very sensitive to different initial guesses for parameter values unlike the other model functions. In addition, we show that the regression method using the integral functions yields more accurate estimates (with narrower confidence intervals) than the methods based on pressure derivative in cases where the pressure data is very noisy. Guidelines for the effective use of nonlinear regression techniques when analyzing well tests from dual porosity reservoirs are also provided. The applicability of the proposed methods is demonstrated by analyzing several sets of synthetic and field data.

New Applications of the Pressure Derivative in Well-Test Analysis

This work represents and illustrates a new general procedure for constructing type curves on the basis of a new pressure-derivative group that involves the dimensionless pressure change divided by its logarithmic derivative. When type curves based on this group are constructed, the vertical scale of the dimensionless derivative group is automatically aligned with the vertical scale of the field-data derivative group. This automatic alignment of the vertical scales simplifies type-curve matching and is advantageous for determining whether field data actually represent the solution assumed by a given type curve. It is also shown that the basic idea used in constructing the type curves can be used to ensure that proper semilog straight lines are chosen when well-test pressure data are analyzed by semilog methods.

Interference Testing of a Two-Layer Commingled Reservoir

A two-well system in an infinite-acting, commingled, two-layer reservoir is considered. One well, the active well, is produced at a constant total rate, and the second well, the observation well, is shut in at all times. An analytical solution in Laplace space is presented, and the parametric groups that uniquely determine the pressure and rate solutions are identified. Results regarding crossflow through the observation well are presented. Conditions under which the line-source solution can be used to analyze observations-well pressure data are delineated.

New Type Curves for Analyzing the Transition Time Data From Naturally Fractured Reservoirs

This work prenents new type curves for the characterisation of a naturally-fractured (dual-porcssity) reservoir. These type curves were motivated by new apprcocimate solutions for the pressure derivative which apply during the transitional flow period which exists between the two classical aemilog straight lines. These apprcmcimaksolutions suggest the appropriate pressure, pressure-derivative, integral-pressure-derivative and time groups necessary to prepare type curves. New type curves are presented for both the paeudoeteedy-state interporoai~yIknvmodel of Warren and Root and the transient interpomeity flow model of Kazemi and de Swaan.

New Well-Testing Pressure Functions With Applications

New pressure and pressure-derivative functions for analyzing well-test data are presented. The new pressure function represents the integral of pressure with respect to time divided by time. Thus, this new pressure function represents a moving or cumulative average of the pressure over time. It is shown that the logarithmic derivative of this pressure function is equal to a moving or cumulative average of the standard logarithmic pressure derivative. It also is shown that this new derivative function is useful for analyzing well-tested pressure data in cases where the pointwise pressure-derivative data are difficult to interpret because of noise.