Analytical Model for Vertical Interference Tests Across Low-Permeability Zones

1985 ◽  
Vol 25 (03) ◽  
pp. 407-418 ◽  
Author(s):  
R.E. Bremer ◽  
Winston Hubert ◽  
Vela Saul
Keyword(s):  
Point Source ◽  
Test Data ◽  
Low Permeability ◽  
Test Analysis ◽  
Type Curve ◽  
Type Curves ◽  
Pulse Test ◽  
Vertical Permeability ◽  
Interference Test ◽  
Interference Tests

Abstract A mathematical model is developed that describes fluid flow and pressure behavior in a reservoir consisting of two permeable zones separated by a zone of low permeability, Or a "tight zone." This model can be used to design and to interpret buildup, vertical, interference, and pulse tests conducted in a single well or multiple wells across lithological strata. Dimensionless pressure functions and corresponding parametric type curves are derived to interpret vertical interference test data for tight-zone vertical penneability. Application of these type curves is illustrated using field data from two vertical interference tests. Test results obtained with the tight-zone model are shown to compare favorably with results obtained by usingcomputer simulations andBurns' method based on the uniform anisotropy assumption. Computer simulation using a numerical model also shows that high near-wellbore conductivity from a packer leak or poor cement job could not have adversely affected test results. The model presented and the type-curve interpretation method outlined are accurate for designing and interpreting single-well vertical interference tests across low-permeability zones. Introduction The knowledge of vertical flow properties across a low-permeability stratum is becoming increasingly important in reservoir development, especially when enhanced recovery projects are proposed for stratified reservoirs. Vertical well testing is a technique commonly used to determine values for the in-situ vertical permeability of a formation. Either the vertical interference or vertical pulse test may be used, depending on the amount of time required to obtain the necessary pressure response. The method of vertical interterence testing first was introduced by Burns,1 and later developed by Prats.2 Burns' model is based on the assumption of a homogeneous, infinite-acting reservoir with an average vertical permeability smaller than horizontal permeability. Four geometric parameters are used to computer-generate a type curve for analyzing the test data. One difficulty is that each type curve generated is specific to the four geometric parameters and, hence, to the well completion used. The analysis method proposed by Prats uses a plotting technique that does not require computer solutions. However, his technique is restricted by a point-source assumption; that is, the perforated production and observation intervals must be short compared with the distance between them. The most widely used vertical pulse test analysis technique was developed by Falade and Brigham.3–5 Briefly, the method uses sets of correlation curves relating a dimensionless pulse length and dimensionless pulse amplitude. Corrections can be made to account for the upper and lower formation boundaries. It should be noted that the times as given in the Falade and Brigham technique4,5 are too low by a factor of four.6 A second vertical pulse test analysis method, published by Hirasaki,7 is less general in that it considers only the situation with perforations at the upper and lower boundaries. Both methods use a point-source assumption. All previous vertical interference1,2 and vertical pulse3,4,7 test interpretation techniques were developed to determine vertical permeability in a homogeneous single-layer reservoir. These methods may be applied to stratified reservoirs where permeability contrasts are known to occur; however, they may yield misleading results in these cases where the homogeneous reservoir assumption is not justified. This paper presents an analytical model and interpretation technique to analyze vertical interference test data for tight-zone vertical permeability in a reservoir consisting of two permeable zones separated by a tight zone or a zone of low permeability. Pressure response data in the observation zone are plotted in a ?p vs. ?t format on log-log coordinates and matched against one of two type curves. The result of this match is a value for horizontal permeability in the upper and lower layers and a value for the effective vertical permeability across the tight zone. The type curves included are applicable for a wide range of thickness ratios between the permeable and low-permeability layers. Additionally, use of the model is not restricted by a point-source assumption.

scholarly journals Investigation on Interference Test for Wells Connected by a Large Fracture

2019 ◽  
Vol 9 (1) ◽  
pp. 206
Author(s):  
Guofeng Han ◽  
Yuewu Liu ◽  
Wenchao Liu ◽  
Dapeng Gao
Keyword(s):  
Double Porosity ◽  
Flow In Porous Media ◽  
Connection Form ◽  
Analysis Model ◽  
Pressure Derivative ◽  
Type Curve ◽  
Type Curves ◽  
Multi Stage ◽  
Interference Test ◽  
Straight Lines

Pressure communication between adjacent wells is frequently encountered in multi-stage hydraulic fractured shale gas reservoirs. An interference test is one of the most popular methods for testing the connectivity of a reservoir. Currently, there is no practical analysis model of an interference test for wells connected by large fractures. A one-dimensional equation of flow in porous media is established, and an analytical solution under the constant production rate is obtained using a similarity transformation. Based on this solution, the extremum equation of the interference test for wells connected by a large fracture is derived. The type-curve of pressure and the pressure derivative of an interference test of wells connected by a large fracture are plotted, and verified against interference test data. The extremum equation of wells connected by a large fracture differs from that for homogeneous reservoirs by a factor 2. Considering the difference of the flowing distance, it can be concluded that the pressure conductivity coefficient computed by the extremum equation of homogeneous reservoirs is accurate in the order of magnitude. On the double logarithmic type-curve, as time increases, the curves of pressure and the pressure derivative tend to be parallel straight lines with a slope of 0.5. When the crossflow of the reservoir matrix to the large fracture cannot be ignored, the slope of the parallel straight lines is 0.25. They are different from the type-curves of homogeneous and double porosity reservoirs. Therefore, the pressure derivative curve is proposed to diagnose the connection form of wells.

Transient Rate Decline Analysis for Wells Produced at Constant Pressure

1981 ◽  
Vol 21 (01) ◽  
pp. 98-104 ◽  
Author(s):  
C.A. Ehlig-Economides ◽  
H.J. Ramey
Keyword(s):  
Pressure Drop ◽  
Flow Rate ◽  
Constant Pressure ◽  
Well Test ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Type Curve ◽  
Type Curves ◽  
Constant Rate ◽  
Cumulative Production

Abstract Although constant-rate production is assumed in the development of conventional well test analysis methods, constant-pressure production conditions are not uncommon. Conditions under which constant-pressure flow is maintained at a well include production into a constant-pressure separator or pipeline, steam production into a backpressured turbine, or open flow to the atmosphere.To perform conventional well test analysis on such wells, one common procedure is to flow the well at a constant rate for several days before performing the test. This procedure is not always effective, and often the delay could be avoided by performing transient rate tests instead. Practical methods for transient rate analysis of wells produced at constant pressure are presented in this paper. The most important test is the analysis of the rate response to a step change in producing pressure. This test allows type-curve analysis of the transient rate response without the complication of wellbore storage effects. Reservoir permeability, porosity, and the wellbore skin factor can be determined from the type-curve match. The reservoir limit test is also important. Exponential rate decline can be analyzed to determine the drainage area of a well and the shape factor.The effect of the pressure drop in the wellbore due to flowing friction is investigated. Constant wellhead-pressure flow causes a variable pressure at the sandface because the pressure drop from flowing friction is dependent on the transient rate. Finally, for testing of new wells, the effect of a limited initial flow rate due to critical flow phenomena is examined. Introduction Fundamental considerations suggest that conventional pressure drawdown and buildup analysis methods developed for constant-rate production should not be appropriate for a well produced at a constant pressure. However, a well produced at a constant pressure exhibits a transient rate decline which can be analyzed using techniques analogous to the methods for constant-rate flow. In this paper, analytical solutions for the transient rate decline for wells produced at constant pressure are used to determine practical well test analysis methods.Many of the basic analytical solutions for transient rate decline have been available for some time. The first solutions were published by Moore et al. and Hurst. Results were presented in graphical form for bounded and unbounded reservoirs in which the flow was radial and the single-phase fluid was slightly compressible. Tables of dimensionless flow rate vs. dimensionless time were provided later by Ferris et al. for the unbounded system and by Tsarevich and Kuranov for the closed-boundary circular reservoir. Tsarevich and Kuranov also provided tabulated solutions for the cumulative production from a closed-boundary reservoir. Van Everdingen and Hurst presented solutions and tables of the cumulative production for constant-pressure production. Fetkovich developed log-log type curves for transient rate vs. sine in the closed-boundary circular reservoir. Type curves for rate decline in closed-boundary reservoirs with pressure-sensitive rock and fluid properties were developed by Samaniego and Cinco. A method for determining the skin effect was given by Earlougher. Type curves for analysis of the transient rate response when the well penetrates a fracture were developed by Prats et al. and Locke and Sawyer. SPEJ P. 98^

Pulse Tests and Other Early Transient Pressure Analyses for In-Situ Estimation of Vertical Permeability

1974 ◽  
Vol 14 (01) ◽  
pp. 75-90 ◽  
Author(s):  
George J. Hirasaki
Keyword(s):  
Pressure Response ◽  
Gravity Drainage ◽  
Transient Pressure ◽  
Type Curve ◽  
Pulse Test ◽  
Recovery Processes ◽  
Vertical Permeability ◽  
Constant Rate ◽  
Rate Test

Abstract Formation vertical permeability is often the dominant influence in water or gas coning into a well, in gravity drainage of high-relief reservoirs, and in interlayer crossflow in secondary recovery projects. The advantages of either conducting a projects. The advantages of either conducting a pulse test or analyzing the early transient pressure pulse test or analyzing the early transient pressure response of a constant-rate test compared with previous techniques are simplicity of interpretation, previous techniques are simplicity of interpretation, short duration of test, and minimum interference from conditions some distance from the test well. The pulse test has a further advantage over the constant-rate test in that the rate does not have to be kept constant during the short flow period.Presented are the development of the theory and the curves of the dimensionless response time used in interpreting field data obtained by these techniques. The vertical permeability is determined with the pulse test from the time to the maximum pressure response and with the constant-rate test pressure response and with the constant-rate test from the extrapolated time to zero pressure response from the inflection point.Applications of the techniques to layered systems and to an oil zone with underlying water are demonstrated with results of numerical simulations. The vertical-permeability pulse test has been used to estimate the vertical permeability of a low-permeability zone in the Fahud field, Oman. Introduction The formation vertical permeability is often a dominant influence in reservoir recovery processes with vertical fluid flow such as water or gas coning, gravity drainage of high-relief reservoirs, the rising steam process, and displacement by water or gas in a heterogeneous formation. How reliably numerical reservoir simulators can predict the recovery performance of these processes depends upon how performance of these processes depends upon how accurately the significant reservoir parameters are estimated. Furthermore, in simulating a reservoir in two dimensions, the validity of the assumption of vertical equilibrium is based on the value of the vertical permeability.With the previously mentioned recovery processes, the reservoir cannot be modeled as a homogeneous reservoir with a single fluid. A well that has fluid coning or that is producing by gravity drainage will often have a fluid contact intersecting the well and thus dividing the reservoir into zones of differing mobility and compressibility. Reservoir stratification on a microscopic scale will result in a vertical permeability that is less than the horizontal permeability that is less than the horizontal permeability; but stratification on a macroscopic permeability; but stratification on a macroscopic scale will divide the reservoir into zones of differing permeabilities. Thus the design and interpretation permeabilities. Thus the design and interpretation of a vertical-permeability test for most practical reservoir situations will require that the reservoir zonation be represented.Transient pressure techniques for estimating in-situ vertical permeability have been introduced by Burns and by Prats. Both techniques require injection or production at a constant rate from a short perforated interval and measurement of the pressure response at another perforated interval pressure response at another perforated interval that is isolated from the first by a packer. The interpretation technique of Burns required a computer-generated type curve or a single-phase numerical reservoir simulator. This type-curve approach is applicable for an anisotropic, homogeneous, infinite reservoir model, and the numerical simulator with a regression analysis program is needed for finite or layered reservoir models. The technique presented by Prats did not require a computer program because the result of the analysis was presented on a single graph. The horizontal and vertical permeabilities could be estimated from the slope and the intercept of the pressure response and, the appropriate value from the graph. The method of Prats was based on an infinite, anisotropic, Prats was based on an infinite, anisotropic, homogeneous reservoir model.The pulse test and early transient analysis techniques presented here were developed to provide a simple means of interpretation for layered provide a simple means of interpretation for layered systems. Some advantages are thatno computer program is requiredlayered reservoirs can be program is requiredlayered reservoirs can be represented;test duration is shorter than for previous methods; andthere is less interference previous methods; andthere is less interference from reservoir conditions some distance from the test well. SPEJ P. 75

COMPREHENSIVE ANALYSIS OF DRILLSTEM TEST DATA WITH THE AID OF TYPE CURVES

1980 ◽  
Vol 20 (1) ◽  
pp. 229
Author(s):  
B.K. Sinha ◽  
J.M. Montgomery
Keyword(s):  
Test Data ◽  
Comprehensive Analysis ◽  
Insufficient Data ◽  
Type Curve ◽  
Type Curves ◽  
Correct Analysis

A substantial percentage of drillstem tests cannot be analysed by convential methods due to insufficient data. Numerous tests have been analysed by several published type curves.In this paper, many examples are included where the application of the appropriate type curve aided in providing correct analysis of data which otherwise may have been misinterpreted.

Hydrogeophysical Concepts in Aquifer Test Analysis

1994 ◽  
Vol 25 (3) ◽  
pp. 183-192 ◽  
Author(s):  
Zekâi Şen
Keyword(s):  
Test Data ◽  
Hydraulic Parameter ◽  
Test Analysis ◽  
Type Curve ◽  
Qualitative And Quantitative ◽  
Additional Information ◽  
Aquifer Test ◽  
Groundwater Flow Regime ◽  
Set Up ◽  
Parameter Identifications

Aquifer test data analysis is an art leading to reliable hydraulic parameter identifications rather than a mechanical curve fitting. Most often aquifer test data processing is achieved by matching the data with suitable type curve without detailed interpretations of deviations from this curve. In fact, relevant interpretations might yield valuable qualitative and quantitative features about the subsurface geological composition of the aquifer domain at least in the well vicinity. The view taken in this paper is to obtain additional information from various data segments by considering two or more successive measurements. Such a detailed investigation of aquifer test data is referred to herein as the “hydrogeophysical” approach since it yields important clues about the geological set up as well as the groundwater flow regime in the well vicinity. Main features of hydrogeophysical investigation are given based on author's experience. It is hoped that additional points will be supplemented in future applications by other groundwater hydrologists. The application of hydrogeophysical concepts are exemplified for some field data available in the groundwater literature.

scholarly journals Interactive computer processing and interpretation of pumping test data. A Micro-computer program using dynamic graphics

1985 ◽  
Vol 4 ◽  
pp. 1-98
Author(s):  
Bjarne Madsen
Keyword(s):  
Computer Program ◽  
Groundwater Flow ◽  
Test Data ◽  
Pumping Test ◽  
Flow Equation ◽  
Hard Copy ◽  
Type Curve ◽  
Type Curves ◽  
Wide Range ◽  
Graphic Screen

This paper presents a computer program for analysing pumping test data. The program is interactive and may be used with a minimum knowledge of computers. It can be applied to a wide range of transient problem types, from one dimensional groundwater flow to flow in anisotropic aquifers, horizontally as well as vertically. Various forms of type curves based on analytical solutions to the groundwater flow equation are available for the interpretation. The paper includes a listing of the entire computer program containing a total of about 1. 800 lines. The programming language is a BASIC-version suited for the Tektronix 4054, a graphic screen with a refresh option. This option allows the user to perform type curve matching directly on the screen by moving the chosen type curve to the position where it gives the best fit, in a manner similar to traditional manual chart interpretation. Plots of the measured data may be conveniently reproduced in semilog and log-log diagrams, either on the screen or as a hard copy printed by a plotter. The present version of the program makes use of tape cartridges, both for storing program and data files.

Analysis of Interference Tests with Horizontal Wells

2005 ◽  
Vol 8 (04) ◽  
pp. 337-347 ◽  
Author(s):  
Mohammed N. Al-Khamis ◽  
Erdal Ozkan ◽  
Rajagopal S. Raghavan
Keyword(s):  
Horizontal Well ◽  
Horizontal Wells ◽  
Observation Point ◽  
Integral Solution ◽  
Observation Well ◽  
Vertical Wells ◽  
Exponential Integral ◽  
Test Analysis ◽  
Interference Test ◽  
Interference Tests

Summary One of the common assumptions in horizontal-well interference-test analysis is to ignore fluid flow in and out of the horizontal observation well and represent it by a point. In some cases, the active well is also approximated by a vertical line source. Using a semianalytical model, this paper answers three fundamental questions:• What is the critical distance between the wells to represent the horizontal observation well by an observation point?• Where should the observation point be placed along the horizontal well?• Under what conditions may the active well be approximated by a vertical line source and the exponential integral solution be used to analyze observation-well responses? Two correlations are presented to simplify the analysis of horizontal-well interference tests. Example applications are presented, and error bounds are documented. Introduction Analysis of horizontal-well interference tests is an extremely difficult problem because the lengths, orientations, locations, and distances between wells need to be considered. One of the assumptions used to make the horizontal-well interference-test analysis a tractable problem is to ignore the flow pattern that results because of the existence of the horizontal well and to treat the horizontal observation well as an observation point. It also has been suggested that if the distance between the two wells were sufficiently large, then the active horizontal well could be replaced by a vertical well. In this case, the observation-well responses may be approximated by the exponential integral solution, and the analysis is reduced to the conventional interference-test analysis between vertical wells. For the application of the approximate analytical techniques, two questions need to be answered. The first question is whether the distance between the two horizontal wells is large enough for the geometry of the wells to be ignored. Malekzadeh investigated this question by considering the interference between a horizontal active well and a vertical observation well in an isotropic reservoir. Because anisotropy has a major effect on the pressure-transient responses of horizontal wells, the results of Malekzadeh have limited applicability. In addition, the influence of the geometry of the observation well cannot be deduced from the model used by Malekzadeh. The second question is, where should the equivalent observation point (EOP)be placed in the reservoir if the horizontal well were to be replaced by a vertical well? This question has yet to be addressed in the literature. The EOP is defined as the location at which the pressure recorded at the heel of the horizontal observation well would exist in the absence of the observation well. Because of the lack of theoretical guidance, the physical location of the heel or the center of the observation well is usually chosen as the observation point.1 But such an assumption ignores the fact that fluids enter and leave the horizontal observation well although there is no surface production. Therefore, some disturbance of equipotential lines around the observation well should be expected. Thus, if the horizontal well were to be removed from the system, we may expect the pressure recorded at the heel of the horizontal well to exist at a different location. The location of the EOP would be a function of the variables that determine pressure at the observation well. This work uses a semianalytical model to answer the above questions. The model has been discussed in detail in Refs. 4 and 5 and is capable of considering interference between two horizontal wells in a homogeneous but anisotropic reservoir. Based on the results of the semianalytical model, two correlations have been developed to significantly simplify the analysis of horizontal-well interference tests without sacrificing accuracy. The first correlation provides the location of the EOP, which has not been available in the literature. The second correlation provides information on the distance under which both horizontal wells may be treated as vertical wells and the exponential integral solution may be used to analyze the interference test. Compared with the correlation presented by Malekzadeh, the correlation presented here is more comprehensive because it accounts for the effects of anisotropy, location of the EOP, and relative position of the wells. To assess the adequacy of the correlations, error bounds have been calculated and are documented in this paper. The correlations enable us to analyze horizontal-well interference tests by the single-horizontal-well solutions or by the exponential integral solution. The convenience of the single-horizontal-well models for the regression techniques used in well-test-analysis software becomes clear if the computational complexity of the rigorous horizontal-well interference-test models4,5 is noted (the increase in the speed of computations is usually more than six-fold).

Mahakam Field Characterization Using Production Type-Curve With Business Intelligence Application

2020 ◽  
Author(s):  
P. Noverri
Keyword(s):  
Business Intelligence ◽  
Data Gathering ◽  
Production Data ◽  
Type Curve ◽  
Type Curves ◽  
Production Type ◽  
Efficient Data ◽  
Production Behavior ◽  
Factor Type ◽  
Mahakam Delta

Delta Mahakam is a giant hydrocarbon block which is comprised two oil fields and five gas fields. The giant block has been considered mature after production for more than 40 years. More than 2,000 wells have been drilled to optimize hydrocarbon recovery. From those wells, a huge amount of production data is available and documented in a well-structured manner. Gaining insight from this data is highly beneficial to understand fields behavior and their characteristics. The fields production characterization is analyzed with Production Type-Curve method. In this case, type curves were generated from production data ratio such as CGR, WGR and GOR to field recovery factor. Type curve is considered as a simple approach to find patterns and capture a helicopter view from a huge volume of production data. Utilization of business intelligence enables efficient data gathering from different data sources, data preparation and data visualization through dashboards. Each dashboard provides a different perspective which consists of field view, zone view, sector view and POD view. Dashboards allow users to perform comprehensive analysis in describing production behavior. Production type-curve analysis through dashboards show that fields in the Mahakam Delta can be grouped based on their production behavior and effectively provide global field understanding Discovery of production key information from proposed methods can be used as reference for prospective and existing fields development in the Mahakam Delta. This paper demonstrates an example of production type-curve as a simple yet efficient method in characterizing field production behaviors which is realized by a Business Intelligent application

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