Type-curve Matching Technique Research Articles

Theories of complicated identifications exchange

The main objective of this study is to determine the pressure derivatives diagnoses for the infinite-conductivity horizontal well flow regimes identification which are not well studied so far in literature. The pressure derivatives diagnoses for the uniform-flux horizontal well flow regimes identification are fully studied in literature and presented here for comparison purposes only. The horizontal well flow regimes: early-radial, early-linear, late-radial, late-linear, and pseudo-steady state (PSS) are being identified. The identifications of flow regimes which have characteristic trends on log-log graph of pressure derivatives versus time represent unique technique in reservoir characterization. Five pressure derivatives are studied in detail: primary pressure derivative (PPD) (i.e., PPD=∂PD/∂tDA), Slope of PPD, PPD ×tDA, Bourdet derivative (i.e., tDA × PPD), and Slope of Bourdet derivative. For the first time, the pressure derivatives have been computed at high-resolution to diagnose the five infinite-conductivity horizontal well flow regimes identifications (i.e., the wellbore is discretized into twenty thousand of segments). In field application, synthetic pressure drawdown test data for infinite-conductivity horizontal well are analyzed by using type-curve matching technique.The novelties in this study are the following:1.The identifications of infinite-conductivity early-radial and early-linear flow regimes by Slope of Bourdet derivative are equal to −0.5 and 0 respectively which are different to their uniform-flux counterparts 0 and 0.5 respectively. Therefore, the pressure derivatives diagnoses are unique for a certain wellbore condition and there is a complicated identifications exchange between uniform-flux and infinite-conductivity flow regimes. The identification of infinite-conductivity early-radial flow regime is used for uniform-flux spherical flow regime and vice versa, and the identification of infinite-conductivity early-linear flow regime is used for uniform-flux early-radial and late-radial-flow regimes and vice versa.2.Theories of developing infinite-conductivity early-radial flow regime by multi aligned and merged uniform-flux spherical flow regimes and developing infinite-conductivity early-linear flow regime by multi aligned uniform-flux early-radial flow regimes are presented. The new theories prove the existence of the complex identifications exchange between uniform-flux and infinite-conductivity flow regimes.3.Without type-curve matching technique, downhole flow or pressure profile measurement, or presence of uniform-flux early-linear flow regime, or determination of mt at late-radial, late-linear, or PSS flow regime are crucial to distinguish if the wellbore is under uniform-flux or infinite-conductivity condition for correct horizontal well test analysis, mt = segments number of the half-length wellbore.4.At infinite-conductivity late-linear flow regime, qD distribution over the wellbore is uniform for any well and reservoir configuration as at infinite-conductivity PSS flow regime, qD = dimensionless inflow rate.

A transient flow solution to describe fluid flow to horizontal fractures applied to frac‐packed wells

AbstractThis paper presents an analytical model to describe the transient fluid flow to a horizontal fracture in frac‐packed vertical wells. A physical model is first established where a horizontal frac‐packed fracture is located in the middle of a cylindrical reservoir. The pressure distribution in the fracture is then derived concerning time and the distance to the wellbore. The analytical model assumes a homogeneous and isotropic reservoir where Darcy's law applies to a single‐phase fluid flow, a radial fracture with a radius much greater than pay zone thickness, and a constant fracture width. For ease of application, a Type Curve Matching approach is introduced which features the matching of a defined dimensionless pressure between field pressure data and model data, and some exemplar curves are illustrated in this paper. The principle of applying curve matching here is to tune model parameters to match the measured pressure/rate data. Once the curves are matched, the model parameters, that is, fracture permeability, etc, are naturally obtained. The validity of the derived model is informed in two ways. The results show that the model will degenerate to the classic radial flow equation for practical values of certain model parameters and upon reasonable simplification. Model validity is further verified by applying the type curve matching technique using field data. This model can be used as a quick and reasonable method to analyze the transient pressure/rate test data to reveal fundamental fracture and reservoir properties for a frac‐packed horizontal fracture at shallow depths where the vertical formation stress is the least in situ stress.

A practical calculation of the distance to a discontinuity in anisotropic systems from well test interpretation

Well testing is the cheapest and most accurate tool available to find the distance from a well to a linear constant-pressure boundary or fault. Several methods exist in the literature with which to determine this parameter. Most of them use conventional analysis and are only useful for isotropic reservoir systems. The few methods for anisotropic systems obtain the well-to-discontinuity distance through conventional analysis, type-curve matching and TDS technique, and then a correction by anisotropic effects is applied. In this work, a unified behavior of the pressure derivative was found, so the new shorter and most practical expressions used to find the distance from the well to the discontinuity, including the simultaneous effects of anisotropy angle and anisotropy index, are included. These new formulae were successfully tested with two synthetic examples and one field case example, and deviation errors higher than 30% are observed if an anisotropic system is treated as an isotropic one.

Modeling the Neuman’s well function by an artificial neural network for the determination of unconfined aquifer parameters

An artificial neural network is designed as an improved alternative approach to the conventional type-curve matching technique for the determination of unconfined aquifer parameters. The network is implemented in a six-step protocol consisted of input selection, data splitting, design of network architecture, determination of network structure, network training, and network validation. The network is trained for the well function of unconfined aquifers by the back-propagation technique, adopting the Levenberg-Marquardt optimization algorithm. By applying a principal component analysis (PCA) on the training input data and through a trial-and-error procedure, the structure of the network is optimized with the topology of (3 × 6 × 3). The replicative, predictive, and structural validity of the developed network are evaluated with synthetic and real field data. The network eliminates graphical error inherent in the type-curve matching technique and provides an automatic and fast procedure for aquifer parameter estimation, particularly when analyzing many alternative pumping tests routinely obtained from continuous data loggers/data collection systems.

Restoring disrupted data by wellbore storage effect using analytical models and type-curve matching techniques

Restoring disrupted data by wellbore storage effect using analytical models and type-curve matching techniques

Analysis of pressure and pressure derivative interference tests under linear and spherical flow conditions

Normalmente, la interpretación de las pruebas de interferencia se realiza en sistemas que actúan bajo condiciones de régimen flujo radial utilizando análisis convencional de la línea recta, curvas tipo y técnica TDS. Para los casos de flujos lineal y esférico, la interpretación de pruebas de interferencia se realiza mediante el método convencional y el ajuste con curvas tipo. Estos procedimientos no permiten verificación de los parámetros estimados, y por ello en este trabajo se presenta una formulación de una metodología más práctica, útil y práctica mediante el uso de rasgos características en el gráfico logarítmico de la presión y derivada de presión contra tiempo, que permitan desarrollar expresiones analíticas directas usadas para la caracterización del yacimiento en pruebas interferencia en condiciones de flujos esférico y lineal. Estas ecuaciones se verificaron satisfactoriamente mediante a su aplicación a pruebas sintéticas.

Analytical models & type-curve matching techniques for reservoir characterization using wellbore storage dominated flow regime

The applicability of early time data in reservoir characterization is not always considered worthy. Early time data is usually controlled by wellbore storage effect. This effect may last for pseudo-radial flow or even boundary dominated flow. Eliminating this effect is an option for restoring real data. Using the data with this effect is another option that could be used successfully for reservoir characterization. This paper introduces new techniques for restoring disrupted data by wellbore storage at early time production. The proposed techniques are applicable for reservoirs depleted by horizontal wells and hydraulic fractures. Several analytical models describe early time data, controlled by wellbore storage effect, have been generated for both horizontal wells and horizontal wells intersecting multiple hydraulic fractures. The relationships of the peak points (humps) with the pressure, pressure derivative and production time have been mathematically formulated in this study for different wellbore storage coefficients. For horizontal wells, a complete set of type curves has been included for different wellbore lengths, skin factors and wellbore storage coefficients. Another complete set of type curves has been established for fractured formations based on the number of hydraulic fractures, spacing between fractures, and wellbore storage coefficient. The study has shown that early radial flow for short to moderate horizontal wells is the most affected by wellbore storage while for long horizontal wells; early linear flow is the most affected flow regime by wellbore storage effect. The study has also emphasized the applicability of early time data for characterizing the formations even though they could be controlled by wellbore storage effect. As a matter of fact, this paper has found out that wellbore storage dominated flow could have remarkable relationships with the other flow regimes might be developed during the entire production times. These relationships can be used to properly describe the formations and quantify some of their characteristics.

Semi-analytical solutions for flow to a well in an unconfined-fractured aquifer system

Semi-analytical solutions of flow to a well in an unconfined single porosity aquifer underlain by a fractured double porosity aquifer, both of infinite radial extent, are obtained. The upper aquifer is pumped at a constant rate from a pumping well of infinitesimal radius. The solutions are obtained via Laplace and Hankel transforms and are then numerically inverted to time domain solutions using the de Hoog et al. algorithm and Gaussian quadrature. The results are presented in the form of dimensionless type curves. The solution takes into account the effects of pumping well partial penetration, water table with instantaneous drainage, leakage with storage in the lower aquifer into the upper aquifer, and storativity and hydraulic conductivity of both fractures and matrix blocks. Both spheres and slab-shaped matrix blocks are considered. The effects of the underlying fractured aquifer hydraulic parameters on the dimensionless drawdown produced by the pumping well in the overlying unconfined aquifer are examined. The presented solution can be used to estimate hydraulic parameters of the unconfined and the underlying fractured aquifer by type curve matching techniques or with automated optimization algorithms. Errors arising from ignoring the underlying fractured aquifer in the drawdown distribution in the unconfined aquifer are also investigated.

Transmitter Design for Uplink MIMO Systems With Antenna Correlation

We study the uplink transmission in multiple-input multiple-output (MIMO) systems with antenna correlation. We focus on schemes that require only channel covariance information at the transmitter (CCIT), which involves lower cost than full channel state information at the transmitter (CSIT). We start from mutual information analysis and show that a simple CCIT-based scheme, referred to as statistical water-filling (SWF), can perform close to the optimal full CSIT-based one in MIMO systems with more receive antennas than transmit ones. We then focus on the implementation of SWF in practically coded systems. An iterative linear minimum mean squared error (LMMSE) receiver is assumed and an extrinsic information transfer (EXIT) chart type curve matching technique is developed based on Hadamard precoding techniques. Simulation results show that the proposed scheme can obtain significant performance improvement compared to the conventional equal power transmission. Finally, we show that the proposed scheme is also very efficient in multi-user uplink MIMO systems with distributed channel information.

New application for well test analysis: Locating closed perforation zones and damaged sections

Abstract Closed perforations and damaged sections are two great challenges in the petroleum industry. Several reasons may cause these problems. Few of them depend on the type of formation and wellbore while others come from drilling, completion and stimulation activates before production process. Production rate and pressure drop may lead significantly to these two problems; therefore, production management sometimes plays a great role in controlling them. Millions of dollars are spent annually for the remedial process of these two problems. Therefore locating these closed or damaged sections is considered of great importance as an attempt to control them or reduce their negative impact on wellbore deliverability. This paper introduces a technique to locate the closed perforations and damaged sections using pressure transient analysis. Pressure behaviors and flow regimes in the vicinity of horizontal wellbores are affected by the existence of the closed perforated zones and the formation sections where the resistance to reservoir fluid flow toward the wellbore is maximized. This resistance occurs because of the damaged permeability and high skin factor. Analytical models for locating these sections and determining how many zones of the horizontal well that are considerably closed have been introduced in this study. These models have been derived based on the assumption that wellbore can be divided into multi-subsequent segments of producing and non-producing intervals. Producing intervals represent free flowing zones where there is no problem and both formation and wellbore are assumed to be clean. Non-producing intervals represent zones where both formation and wellbore's perforations are closed or damaged. The effective length of horizontal well where the perforated zones and the formation sections can not be considered problematic and the damaged length where both of them are significantly closed and damaged can be calculated. The numbers of the damaged zones can be calculated also. In addition, the locations of the damaged sections or closed perforated zones can be determined. Type-curve matching technique and the analytical models can be used for this purpose.

Pressure Behavior of Partially Penetrating Multiple Hydraulic Fractures

Horizontal wells with multiple hydraulic fractures have become a common occurrence in the oil and gas industry, especially in tight formations. Published models assume that hydraulic fractures are fully penetrating the formations. However, studies have shown that fractures are not always fully penetrating the formations. This paper introduces a new technique for analyzing the pressure behavior of a horizontal well with multiple vertical and inclined partially penetrating hydraulic fractures. The hydraulic fractures in this model could be longitudinal or transverse, vertical or inclined, symmetrical or asymmetrical. The fractures are propagated in isotropic or anisotropic formations and considered having different dimensions and different spacing. This technique, based on pressure and pressure derivative concept, can be used to calculate various reservoir parameters, including directional permeability, fracture length and percentage of penetration. The study has shown that the pressure behavior of small penetration rate is similar to the horizontal wells without hydraulic fractures. A type curve matching technique has been applied using the plots of the pressure and pressure derivative curves. A set of type curves, which will be included in the paper, have been generated for the partially penetrating hydraulic fractures associated to the horizontal wells with different penetration rates. A step-by-step procedure for analyzing pressure tests using these type curves is also included in the paper for several numerical examples.

Applying Parameter-Estimation Methods to Recovery-Test and Slug-Test Analyses

Parameter-estimation methods, including an exhaustive-search method and PEST (Parameter ESTimation) software, were applied to recovery-test data and slug-test data to obtain best estimates of transmissivity (T) by minimizing the sums of residuals. Each residual represents the difference between the field-measured water-level value and the value calculated by the appropriate non-linear equation. The exhaustive-search method in both cases involves computing the sums of residuals for an array of transmissivity and storativity values selected by the user for testing. Two new Fortran programs are presented that employ the exhaustive-search method. They utilize Picking's method for analyzing recovery-test data and the analytical equation for analyzing slug-test data derived by Cooper, Bredehoeft, and Papadopulos. Picking's method involves application of the Papadopulos and Cooper's equation for drawdown in finite-diameter wells. Utilizing field data reported in the literature, the estimated transmissivity values from the exhaustive-search methods were compared to the literature values obtained by type-curve matching techniques. The exhaustive-search values corresponded closely to the curve-matching values. Estimates for T were also obtained from recovery-test and slug-test data from two sites in southeastern Pennsylvania. For these sites, the PEST program was also applied to the data to evaluate the accuracy of the exhaustive-search methods. The results from the two methods were generally in good agreement. The two new Fortran programs are practical tools for the hydrogeologist, as they require less time compared to type-curve matching and the PEST method, and they yield accurate estimates of transmissivity.

Interference well testing—variable fluid flow rate

At present when conducting an interference well test a constant flow rate (at the 'active' well) is utilized and the type-curve matching technique (where only 2–3 values of pressure drops are matched) is used to estimate the porosity–total compressibility product and formation permeability. For oil and geothermal reservoirs with low formation permeability the duration of the test may require a long period of time and it can be difficult to maintain a constant flow rate. The qualitative term 'long' period of time means that (at a given distance between the 'active' and 'observational' well) more test time (for low permeability formations) is needed to obtain tangible pressure drops in the 'observational' well. In this study we present working equations which will allow us to process field data when the flow rate at the 'active' well is a function of time. The shut-in period is also considered. A new method of field data processing, where all measured pressure drops are utilized, is proposed. The suggested method allows us to make use of the statistical theory to obtain error estimates on the regression parameters. It is also shown that when high precision (resolution) pressure gauges are employed the pressure time derivative equations can be used for the determination of formation hydraulic diffusivity. An example is presented to demonstrate the data processing procedure.

A numerical model for estimating groundwater flux from subsurface temperature profiles

AbstractA simple numerical model is presented for estimating vertical groundwater flux from transient subsurface temperature profiles obtained from field measurements. The model developed utilizes the MacCormack scheme, which is based on the Finite Difference Method (FDM), for solving the governing partial differential equation of convection–diffusion heat transport with appropriate initial and boundary conditions within the subsurface. In order to validate the model, numerical solutions obtained for the study area located in the Nagoka plain, Japan are compared with the published measured data and results obtained by others. Results obtained show good agreement and fit the observed data with a correlation coefficient, R2, of 0·88. The estimated groundwater flux is 1·85 × 10−7 m s−1. Sensitivity analyses were also carried out to investigate the effect of variations in groundwater fluxes, thermal properties and the annual thermal variability due to climatic changes on the transient subsurface temperature profiles and to have a better understanding of the subsurface thermal dynamics. A substantial effect of annual climatic variability is observed on the temporal distributions of temperature depth profiles, and a better estimate of thermal parameters is required to estimate vertical groundwater flux. The largest change in subsurface temperature depth profiles due to groundwater flux over a year is within ± 4 °C. The influence of groundwater flux on subsurface temperature distributions in space and time may be more pronounced in areas where the top of the saturated layer fluctuates considerably. Variation in thermal diffusivity results in temperature change up to ± 1·5% and may cause change in groundwater flux estimate by ± 18%. The model presented has merits over analytical solutions (type curve matching techniques) in terms of suitability and applicability to real field problems, and can be a good asset to hydrological models as quantifying groundwater recharge or deducing it from other quantities, such as rainfall, evapotranspiration and runoff, is often complicated. Copyright © 2007 John Wiley & Sons, Ltd.

Determination of Aquifer Parameters by Least-Square Method Under Linear Flow Conditions in Fractures-Rocks

Sen' (1986) equation was modified for analysis of constant discharge pumping test-data in selected hydrogeological formation (Phyllite). The results obtained were compared with Sen (1986) graphical method. The least root mean square error was obtained by least-squares method. The advatage of the least squares method is the automatic objecting, which is lacking in the type-curve matching technique

Fracture Width Logging While Drilling and Drilling Mud/Loss-Circulation-Material Selection Guidelines in Naturally Fractured Reservoirs

Summary In this article we discuss drilling mud losses in naturally fractured reservoirs with fracture permeability larger than 50 odd md and much larger than the matrix permeability. Type curves are provided that describe mud loss volume vs. time and allow the determination of the hydraulic width of natural fractures through the usual type curve matching technique of log/log plots. Real time logging while drilling of natural fracture width permits the proper selection of loss-circulation material (LCM) with respect to particle size distribution. Efficient (rapid) mud loss control is made possible, increasing the chances of minimizing fracture damage by the drilling mud, the cuttings and the LCMs themselves. The total mud losses experienced when drilling a long horizontal section are shown to agree with reservoir properties (derived by well testing) in particularly well-documented examples of the central North Sea. The equations provided can therefore be utilized as well by reservoir engineers to properly evaluate the contribution of natural fractures to the permeability and skin of any well, whether these fractures are clear or are invaded by drilling mud.

Determination of hydraulic diffusivity of aquifers by spectral analysis

This study uses the cyclical frequency to develop the mathematical relationship between hydraulic diffusivity and spectral density functions calculated from groundwater level variation. Such relationship can be applied to (1) unsteady state, one-dimensional confined aquifer with time-dependent water level on both end boundaries, and (2) linearized unconfined aquifer with or without vertical recharge. The spectral density functions of groundwater fluctuations are largely affected by the spectral density functions obtained from time-dependent end boundaries and their cross-spectral density functions. Hydraulic diffusivity of an aquifer can be solved by type-curve matching technique at a specified frequency band under the conditions of (1) confined aquifer having equal time-dependent boundaries on both ends, (2) unconfined aquifer having equal time-dependent boundaries on both ends with surface recharge, and (3) unconfined aquifer subjected to surface recharge but neglecting the water table fluctuations on both end boundaries.

Pressure buildup analysis of gas wells with damage and non-Darcy flow effect

This paper presents a technique to analyze pressure buildup test data of gas wells with damage and non-Darcy skin effect. This technique allows the analyst to estimate reservoir permeability and mechanical and rate-dependent skin factors directly by using 2 analysis plots. Formation permeability and rate-dependent skin are obtained from the slope and the intercept of the first plot, respectively, whereas the mechanical skin factor is determined from the intercept of the second plot. In addition, a graphical method to determine the reservoir pressure at infinite shut-in time is proposed. Field and simulated tests are presented to demonstrate the applicability of the technique. The results obtained are compared with new, conventional, and pressure derivative type curve matching techniques.

Decline Curve Analysis For Canadian Oil Reservoirs Under Waterflood Conditions

Abstract Decline curve analysis using type-curve matching has become an established engineering tool to evaluate long-term production characteristics of oil and gas reservoirs producing under various drive mechanisms. Decline curve analysis is often used to satisfy various regulatory requirements, to establish reserves, and to evaluate the success or failure of operational changes made during a reservoir's producing life. In this study, a detailed investigation of production decline data from 78 Western Canadian Sedimentary Basin oil pools under waterflood conditions is presented. This study demonstrates that the majority of the waterflooded oil pools follow a hyperbolic decline with decline curve exponents ("b") less than 0.5. The decline exponent "b" does not exhibit any obvious functional relationship to the type of rock, oil density, geographical area, and/or geological formation. Nonetheless, such a study provides a basis for "b" values to be expected for Canadian oil reservoirs under waterflood conditions. Introduction Decline curve analysis is one of the oldest and most extensively used methods of predicting the future performance of a producing well, a lease, or a depleting reservoir. The purpose of this study is to present an analysis of the production declines of a group of waterflooded oil pools in Western Canada to establish any obvious decline trend. All of the pools selected are located in the Western Canadian Sedimentary Basin, which covers northeastern British Columbia, the southern half of Saskatchewan, and most of Alberta. This study uses a type-curve matching technique(1) based on the general hyperbolic decline equation: Equation 1 (available in full paper) Previous Studies Fetkovich(2) reported that in a predominantly solution-gas-drive reservoir in Texas, both the primary decline and the waterflood decline appeared to have the same decline exponent "b" of 0.3. Reasons for this phenomenon were uncertain to him. Schuldt et a l .(3), indicated that waterflooded oil reservoirs are generally expected to follow hyperbolic decline behaviour, but they neither explained why this should be so nor indicated their source of information. Mead(4) wrote that pools under different producing mechanisms, waterflood or water influx, should follow exponential or hyperbolic decline with decline exponents in the range of 0 to 0.2. Lijek(5) showed that if a plot of log (WOR) versus cumulative oil produced is linear, the decline curve of the pool is either hyperbolic or harmonic, depending on whether the gross rate is constant or variable. From his experience, he concluded that the decline exponent is very close to one (that is, harmonic decline) at a constant gross rate. Currier and Sindelar's work(6) was similar to that of Lijek(5). They used log (WOR) versus cumulative oil recovery and a frontal advance cross-plot to aid them in establishing waterflood production decline trends from early data of a waterflood field in Alaska. Their study also showed that waterflood declines are harmonic or hyperbolic with a decline exponent much higher than those presented by Mead(4). In their study, cases with a straight line log (WOR) versus cumulative oil produced yielded decline exponents between 0.6 and 0.7.

Analysis of pressure and pressure derivative without type-curve matching — Skin and wellbore storage

The current type-curve matching technique is essentially a trial-and-error procedure. A new technique for interpreting pressure tests using log-log plots of the pressure and pressure derivative versus time to calculate reservoir and well parameters without type-curve matching is presented. This paper concentrates on the interpretation of pressure tests in which wellbore storage and skin are present. Characteristic points are obtained of intersection of various straight line portions of the pressure and pressure derivative curve, slopes and starting times of these straight lines. These points, slopes and times are then used with appropriate equations to solve directly for permeability, wellbore storage and skin. A step-by-step procedure for calculating these parameters without type-curve matching for five different cases is included in the paper. The most important aspect of this new technique is its accuracy because it uses exact analytical solutions to calculate permeability, skin, and wellbore storage. The proposed technique is applicable to the interpretation of pressure buildup and drawdown tests and is illustrated by several numerical examples.