Well-Test Characterization of Wedge-Shaped, Faulted Reservoirs

2001 ◽  
Vol 4 (03) ◽  
pp. 221-230 ◽  
Author(s):  
D.D. Charles ◽  
H.H. Rieke ◽  
R. Purushothaman
Keyword(s):  
Gulf Of Mexico ◽  
Test Data ◽  
Radial Flow ◽  
Constant Pressure ◽  
Depositional Environments ◽  
Well Test ◽  
Linear Flow ◽  
Drainage Systems ◽  
Reservoir Models ◽  
Flow Boundaries

Summary Two offshore, wedge-shaped reservoirs in south Louisiana were interpreted with pressure-buildup responses by comparing the results from simulated finite-element model studies. The importance of knowing the correct reservoir shape, and how it is used to interpret the generated boundary-pressure responses, is briefly discussed. Two different 3D computer models incorporating different wedge-shaped geometries simulated the test pressure-buildup response patterns. Variations in the two configurations are topologically expressed as a constant thickness and a nonconstant thickness, with smooth-surface, wedged-shaped reservoir models. The variable-thickness models are pinched-out updip at one end and faulted at the other end. Numerical well-test results demonstrated changes in the relationships between the pressure-derivative profile, the wellbore location, and the extent of partial penetration in the reservoir models. The wells were placed along the perpendicular bisector (top view) at distances starting from the apex at 5, 10, 20, 40, 50, 60, 80, and 90% of the reservoir length. Results demonstrate that boundary distance identification (such as distance, number, and type) based solely on the log-log derivative profile in rectangular and triangular wedge-shaped reservoirs should be strongly discouraged. Partial-penetration effects (PPE's) in wedge-shaped reservoirs are highly dependent on the wellbore location relative to the wedge, and the well-test-data analysis becomes more complex. Introduction The interpretation of the effect of reservoir shape on pressure-transient well-test data needs improvement. It is economically imperative to be able to generate an accurate estimate of reserves and producing potential. This is especially critical for independent operators who wish to participate in deepwater opportunities in the Gulf of Mexico. Proper interpretation of data extracted from cost-effective well tests is an integral part of describing, evaluating, and managing such reservoirs. Well-test information such as average reservoir pressure, transmissivity, pore volume, storativity, formation damage, deliverability, distance to the boundary, and completion efficiency are some of the technical inputs into economic and operational decisions. Several key economic decisions that operators have to make are:Should the reservoir be exploited?How many wells are needed to develop the reservoir?Is artificial lift necessary (and if so, when)? The identification of morphological demarcation components such as impermeable barriers (faults, intersecting faults, facies changes, erosional unconformities, and structural generated depositional pinchouts) and constant-pressure boundaries (aquifer or gas-cap) from well testing help to establish the reservoir boundaries, shape, and volume. One must remember that the geological entrapment structure or sedimentological body does not always define the reservoir's limits. Our present study provides insight into wedge-shaped reservoirs in the Gulf of Mexico. Seismic exploration can define geological shapes in either two or three dimensions in the subsurface. These shapes are expressions of the preserved structural history and depositional environments and are verified by observations of such structures in outcrops and present-day depositional environments. From a sedimentological viewpoint, the following sedimentary deposits can exhibit wedge-shaped geometries. Preserved barchan sand dunes, reworked transgressive sands, barrier-island sands, offshore bars, alluvial fan deposits, delta-front sheet sands, and lenticular channel sands form the more plausible pinchout, wedge-shaped geological models recognized in the Gulf of Mexico sedimentary sequence. Wedge-Shaped Reservoirs Reviewing the petroleum engineering literature, we found very few technical papers addressing wedge-shaped reservoir geometries and their effects on reservoir performance. Their detailed analytical results are discussed and applied to the interpretations of our model results. An overview of the conceptual models is presented as a quick orientation to emphasize some model issues. Horne and Temeng1 were the first to address the problem of recognizing, discriminating, and locating reservoir pinchouts with the Green's functions method proposed by Gringarten and Ramey2 in pressure-transient analysis. The analytical solution considered a dimensionless penetration depth of the well. Their results showed that pinchout boundaries appear similar to constant-pressure boundaries with respect to pressure-drawdown behavior and not as a perpendicular sealing boundary. Yaxley3 presented a set of simple equations for calculating the stabilized inflow performance of a well in infinite rectangular and wedge-shaped drainage systems. The basis for Yaxley's mathematical model is the application of transient linear flow (as opposed to radial flow conditions assumed for the reservoir) and the mathematical difference between a plane source and a line source in linear-flow drainage systems for various rectangular drainage shapes. The equations were derived from transient linear-flow relationships for a well located between parallel no-flow boundaries. This concept was applied to intersecting no-flow boundaries and an outer circular, no-flow, constant-pressure boundary. His approach involved a constant ßr that is interpreted as an extra pressure drop relative to a well of radius ro (radial distance to the well location), which is a result of the distortion of the radial streamline pattern. Chen and Raghavan4 developed a solution to compute pressure distributions in wedge-shaped drainage systems using Laplace transforms. Their mathematical approach overcame existing limitations in some of the previous solutions, which were mentioned earlier. By applying the inversion theorem to the Laplace transformation, they verified that the slope of the pressure profile is inversely proportional to the wedge angle of the drainage system. An examination of their results is important to the interpretation of our own simulated pressure-response issues. Generally, their model solutions showed three radial-flow periods in the absence of wellbore-storage effects. The radial-flow periods showed that:During an initial radial-flow period, neither of the impermeable boundaries registered either singly or jointly.In the second phase, one or two boundaries became evident on the pressure signature.A third radial-flow period exhibited a semi logarithmic slope proportional to p/?o, where ?o=the angle of the wedge.

Unsteady-State Spherical Flow With Storage and Skin

1985 ◽  
Vol 25 (06) ◽  
pp. 804-822 ◽  
Author(s):  
Jeffrey A. Joseph ◽  
Leonard F. Koederitz
Keyword(s):  
Boundary Condition ◽  
Radial Flow ◽  
Linear Partial Differential Equation ◽  
Flow Profile ◽  
Unsteady State ◽  
Well Test ◽  
Linear Flow ◽  
Dimensionless Groups ◽  
Short Time ◽  
Suitable Expression

Abstract This paper presents short-time interpretation methods for radial-spherical (or radial-hemispherical) flow in homogeneous and isotropic reservoirs inclusive of wellbore storage, wellbore phase redistribution, and damage skin effects. New dimensionless groups are introduced to facilitate the classic transformation from radial flow in the sphere to linear flow in the rod. Analytical expressions, type curves (in log-log and semilog format), and tabulated solutions are presented, both in terms of pressure and rate, for all flow problems considered. A new empirical equation to estimate the duration of wellbore and near-wellbore effects under spherical flow is also proposed. Introduction The majority of the reported research on unsteady-state flow theory applicable to well testing usually assumes a cylindrical (typically a radial-cylindrical) flow profile because this condition is valid for many test situations. Certain well tests, however, are better modeled by assuming a spherical flow symmetry (e.g., wireline formation testing, vertical interference testing, and perhaps even some tests conducted in wellbores that do not fully penetrate the productive horizon or are selectively penetrate the productive horizon or are selectively completed). Plugged perforations or blockage of a large part of an openhole interval may also promote spherical flow. Numerous solutions are available in the literature for almost every conceivable cylindrical flow problem; unfortunately, the companion spherical problem has not received as much attention, and comparatively few papers have been published on this topic. papers have been published on this topic. The most common inner boundary condition in well test analysis is that of a constant production rate. But with the advent of downhole tools capable of the simultaneous measurement of pressures and flow rates, this idealized inner boundary condition has been refined and more sophisticated models have been proposed. Therefore, similar methods must be developed for spherical flow analysis, especially for short-time interpretations. This general problem has recently been addressed elsewhere. Theory The fundamental linear partial differential equation (PDE) describing fluid flow in an infinite medium characterized by a radial-spherical symmetry is (1) The assumptions incorporated into this diffusion equation are similar to those imposed on the radial-cylindrical diffusivity equation and are discussed at length in Ref. 9. In solving Eq. 1, the classic approach is illustrated by Carslaw and Jaeger (later used by Chatas, and Brigham et al.). According to Carslaw and Jaeger, mapping b=pr will always reduce the problem of radial flow in the sphere (Eq. 1) to an equivalent problem of linear flow in the rod for which general solutions are usually known. (For example, see Ref. 17 for particular solutions in petroleum applications.) Note that in this study, we assumed that the medium is spherically isotropic; hence k in Eq. 1 is the constant spherical permeability. This assumption, however, does not preclude analysis in systems possessing simple anisotropy (i.e., uniform but unequal horizontal and vertical permeability components). In this case, k as used in this paper should be replaced by k, an equivalent or average (but constant) spherical permeability. Chatas presented a suitable expression (his Eq. 10) obtained presented a suitable expression (his Eq. 10) obtained from a volume integral. It is desirable to transform Eq. 1 to a nondimensional form, thereby rendering its applicability universal. The following new, dimensionless groups accomplish this and have the added feature that solutions are obtained directly in terms of the dimensionless pressure drop, PD, not the usual b (or bD) groups. ......................(2) .......................(3) .........................(4) The quantity rsw is an equivalent or pseudospherical wellbore radius used to represent the actual cylindrical sink (or source) of radius rw. SPEJ p. 804

Evaluation of Multi-Well Test Data in a Faulted Aquifer Using Linear and Radial Flow Models

Ground Water ◽  
1998 ◽  
Vol 36 (6) ◽  
pp. 938-948 ◽  
Author(s):  
Diana M. Allen ◽  
Frederick A. Michel
Keyword(s):  
Test Data ◽  
Radial Flow ◽  
Well Test ◽  
Flow Models

scholarly journals Estimation of Aquifer Parameters by Least-Squares Method under Linear Flow Conditions in Fractured Rocks

1995 ◽  
Vol 26 (2) ◽  
pp. 111-124 ◽  
Author(s):  
M.L. Jat ◽  
M.S. Acharya ◽  
J. Singh
Keyword(s):  
Least Squares ◽  
Test Data ◽  
Least Squares Method ◽  
Graphical Method ◽  
Large Diameter ◽  
Well Test ◽  
Flow Conditions ◽  
Linear Flow ◽  
Cent Level ◽  
Level Of Significance

Pumping and recovery test data in phyllite formations were analysed under linear flow conditions by incorporating modification in the method proposed by Şen (1986). Although the Şen (1986) method is developed for analysis of borewell test data, this method has been used for large-diameter well-test data by taking average inflow rate in the well. The results obtained were compared with Şen's graphical method. Lower values of root mean-square error were obtained by least-squares method. The estimated values of transmissivity and storage coefficient were acceptable at 1 per cent level of significance. An advantage of the least-squares method is the automization, which is lacking in the graphical method utilising curve-matching technique.

Conditioning Stochastic Reservoir Models to Well-Test Data

1997 ◽  
Author(s):  
Nanqun He ◽  
Dean S. Oliver ◽  
Albert C. Reynolds
Keyword(s):  
Test Data ◽  
Well Test ◽  
Reservoir Models

Linearly Supported Radial Flow-A Flow Regime in Layered Reservoirs

2002 ◽  
Vol 5 (02) ◽  
pp. 103-110 ◽  
Author(s):  
Boyun Guo ◽  
George Stewart ◽  
Mario Toro
Keyword(s):  
Radial Flow ◽  
Constant Pressure ◽  
Low Permeability ◽  
Well Test ◽  
High Permeability ◽  
Reservoir Model ◽  
Well Test Analysis ◽  
Pressure Derivative ◽  
Test Analysis ◽  
Diagnostic Plot

Summary This paper discusses pressure responses from a formation with two communicating layers in which a fully penetrated high permeability layer is adjacent to a low-permeability layer. An analytical reservoir model is presented for well-test analysis of the layered systems, with the bottom of the low-permeability layer being a constant-pressure boundary. The strength of the support from the low-permeability layer is characterized with two parameters: layer bond constant and storage capacity. Introduction The log-log plot of pressure derivative vs. time is called a diagnostic plot in well-test analysis. Special slope values of the derivative curve usually are used for identification of reservoir and boundary models. These slopes include 0-slope, 1/4-slope, 1/2-slope, and unity slope. In many cases, however, the derivative curves do not exhibit slopes of these special values, and it is believed that some nonspecial slopes also reflect certain flow patterns in the reservoirs. Layered, thick reservoirs are one such example.1 In a layered reservoir, it is common practice to perforate a high-permeability section intentionally (adjacent sections are known to be less permeable) or unintentionally (adjacent sections are believed to be impermeable). It is expected that the flow in the perforated high-permeability layer will be partially fed by fluids in the adjacent layers. Warren and Root2 classified this type of layered reservoir as one of the dual-porosity systems in which the storage effect of the low-permeability layer is considered while the crossflow between layers is neglected. They presented a model based on the mathematical concept of superposition of the two media, as introduced previously by Barenblatt et al.3 This paper discusses the pressure response from a formation with two communicating layers. The flow in the two-layer system is referred to as Linearly Supported Radial Flow (LSRF) in this study. The reservoir model is depicted in Fig. 1. The LSRF may exist in the drainage area of a vertical well where radial (normally horizontal) flow prevails in a high-permeability layer and linear (normally vertical) flow into the high-permeability layer dominates in a low-permeability layer. The LSRF also may exist in the drainage area of a horizontal well after pseudoradial flow in the high-permeability layer is reached. Two LSRF systems were investigated:an LSRF system with a no-flow boundary at the opposite side of (not adjacent to) the high-permeability layer, andan LSRF system with a constant boundary pressure at the opposite side of (not adjacent to) the high-permeability layer. Model Description LSRF With No-Flow Boundary at Bottom. An LSRF system with a no-flow boundary at the bottom of the low-permeability layer was investigated with a finite-element-based numerical simulator. The simulator was fully tested and commercially available in the market. Model configuration and input data are summarized in Table 1. The model well flowed 1,000 hours at a constant flow rate of 1,000 STB/D. A diagnostic plot of the generated response is shown in Fig. 2. It is seen from the figure that the radial-flow derivative is V-shaped in a certain time period. This is an expected signature of dual-porosity systems. It is concluded that the radial-flow derivative curve is similar to the derivative curve of single-layer double-porosity reservoirs. The signature of the pressure-derivative responses cannot be used for further diagnostic purposes. Other information from fracture/void detections is required. LSRF With Constant-Pressure Boundary at Bottom. Pressure response from an LSRF system with a constant-pressure boundary at the bottom of the low-permeability layer was also investigated with the numerical simulator. Model configuration and input data were kept the same as those in Table 1. The model well flowed 300 hours. A diagnostic plot of the generated response is shown in Fig. 3. It is seen from the figure that pressure derivative drops sharply in the later time. This is an expected signature of reservoirs with bottomwater or gas-cap gas drive. One may use a bottomwater- drive reservoir model to determine horizontal and vertical permeabilities in the perforated layer. However, one cannot be sure whether the derived vertical permeability is the permeability of the perforated layer or the low-permeability layer. Also, one cannot characterize the strength of the waterdrive based on the pressure-transient data. To retrieve true reservoir properties and characterize the strength of the waterdrive based on pressure-transient data, an analytical reservoir model was derived in this study. The mathematical formulation of the model is shown in the Appendix. When U.S. field units are used, the resultant constant-rate solution for oil takes the following form:Equation 1 where pd = p-pwf. The constants B and C are defined asEquations 2 and 3 Noticing that the derivative of Ei (t) is given byEquation 4 the diagnostic derivative of pressure for radial flow becomesEquation 5 Taking the 10-based logarithm of this equation givesEquation 6 This equation indicates that the diagnostic derivative currently used in well-test-analysis practice for radial-flow identification is not a constant during the LSRF (i.e., the radial-flow pressure derivative curve will not have a plateau but will decrease with time). This rate of increase depends on B and C if no other boundary effect exists. Therefore, constants B and C can be used to characterize the strength of the supporting layer.

scholarly journals A Single Equation to Depict Bottomhole Pressure Behavior for a Uniform Flux Hydraulic Fractured Well

2022 ◽  
Vol 12 (2) ◽  
pp. 817
Author(s):  
Jang Hyun Lee ◽  
Juhairi Aris Bin Muhamad Shuhili
Keyword(s):  
Radial Flow ◽  
Early Stage ◽  
Error Function ◽  
Well Test ◽  
Transition Flow ◽  
Linear Flow ◽  
Pressure Transient ◽  
Flow Equations ◽  
Transition Flow Regime ◽  
Fractured Well

Pressure transient analysis for a vertically hydraulically fractured well is evaluated using two different equations, which cater for linear flow at the early stage and radial flow in the later stage. However, there are three different stages that take place for an analysis of pressure transient, namely linear, transition and pseudo-radial flow. The transition flow regime is usually studied by numerical, inclusive methods or approximated analytically, for which no specific equation has been built, using the linear and radial equations. Neither of the approaches are fully analytical. The numerical, inclusive approach results in separate calculations for the different flow regimes because the equation cannot cater for all of the regimes, while the analytical approach results in a difficult inversion process to compute well test-derived properties such as permeability. There are two types of flow patterns in the fracture, which are uniform and non-uniform, called infinite conductivity in a high conductivity fracture. The study was conducted by utilizing an analogous study of linear flow equations. Instead of using the conventional error function, the exponential integral with an infinite number of wells was used. The results obtained from the developed analytical solution matched the numerical results, which proved that the equation was representative of the case. In conclusion, the generated analytical equation can be directly used as a substitute for current methods of analyzing uniform flow in a hydraulically fractured well.

Multiple Realizations of the Permeability Field From Well Test Data

SPE Journal ◽  
1996 ◽  
Vol 1 (02) ◽  
pp. 145-154 ◽  
Author(s):  
Dean S. Oliver
Keyword(s):  
Test Data ◽  
Well Test ◽  
Permeability Field

Connecting Data, Model and Process to Streamline and Enhance Single-Point Production Well Test Validation

2021 ◽  
Author(s):  
Mohamad Mustaqim Mokhlis ◽  
Nurdini Alya Hazali ◽  
Muhammad Firdaus Hassan ◽  
Mohd Hafiz Hashim ◽  
Afzan Nizam Jamaludin ◽  
...  
Keyword(s):  
Test Data ◽  
Single Point ◽  
Database Systems ◽  
Test Validation ◽  
Well Test ◽  
Production Well ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Digital Ecosystem ◽  
Well Model

Abstract In this paper we will present a process streamlined for well-test validation that involves data integration between different database systems, incorporated with well models, and how the process can leverage real-time data to present a full scope of well-test analysis to enhance the capability for assessing well-test performance. The workflow process demonstrates an intuitive and effective way for analyzing and validating a production well test via an interactive digital visualization. This approach has elevated the quality and integrity of the well-test data, as well as improved the process cycle efficiency that complements the field surveillance engineers to keep track of well-test compliance guidelines through efficient well-test tracking in the digital interface. The workflow process involves five primary steps, which all are conducted via a digital platform: Well Test Compliance: Planning and executing the well test Data management and integration Well Test Analysis and Validation: Verification of the well test through historical trending, stability period checks, and well model analysis Model validation: Correcting the well test and calibrating the well model before finalizing the validity of the well test Well Test Re-testing: Submitting the rejected well test for retesting and final step Integrating with corporate database system for production allocation This business process brings improvement to the quality of the well test, which subsequently lifts the petroleum engineers’ confidence level to analyze well performance and deliver accurate well-production forecasting. A well-test validation workflow in a digital ecosystem helps to streamline the flow of data and system integration, as well as the way engineers assess and validate well-test data, which results in minimizing errors and increases overall work efficiency.

A Novel Well Test Data Analyzer and Process Optimizer Using Artificial Intelligence and Machine Learning Techniques

2021 ◽  
Author(s):  
Nagaraju Reddicharla ◽  
Subba Ramarao Rachapudi ◽  
Indra Utama ◽  
Furqan Ahmed Khan ◽  
Prabhker Reddy Vanam ◽  
...  
Keyword(s):  
Artificial Intelligence ◽  
Machine Learning ◽  
Real Time ◽  
Test Data ◽  
Oil Field ◽  
Well Testing ◽  
Well Test ◽  
Time Data ◽  
Real Time Data ◽  
Well Tests

Abstract Well testing is one of the vital process as part of reservoir performance monitoring. As field matures with increase in number of well stock, testing becomes tedious job in terms of resources (MPFM and test separators) and this affect the production quota delivery. In addition, the test data validation and approval follow a business process that needs up to 10 days before to accept or reject the well tests. The volume of well tests conducted were almost 10,000 and out of them around 10 To 15 % of tests were rejected statistically per year. The objective of the paper is to develop a methodology to reduce well test rejections and timely raising the flag for operator intervention to recommence the well test. This case study was applied in a mature field, which is producing for 40 years that has good volume of historical well test data is available. This paper discusses the development of a data driven Well test data analyzer and Optimizer supported by artificial intelligence (AI) for wells being tested using MPFM in two staged approach. The motivating idea is to ingest historical, real-time data, well model performance curve and prescribe the quality of the well test data to provide flag to operator on real time. The ML prediction results helps testing operations and can reduce the test acceptance turnaround timing drastically from 10 days to hours. In Second layer, an unsupervised model with historical data is helping to identify the parameters that affecting for rejection of the well test example duration of testing, choke size, GOR etc. The outcome from the modeling will be incorporated in updating the well test procedure and testing Philosophy. This approach is being under evaluation stage in one of the asset in ADNOC Onshore. The results are expected to be reducing the well test rejection by at least 5 % that further optimize the resources required and improve the back allocation process. Furthermore, real time flagging of the test Quality will help in reduction of validation cycle from 10 days hours to improve the well testing cycle process. This methodology improves integrated reservoir management compliance of well testing requirements in asset where resources are limited. This methodology is envisioned to be integrated with full field digital oil field Implementation. This is a novel approach to apply machine learning and artificial intelligence application to well testing. It maximizes the utilization of real-time data for creating advisory system that improve test data quality monitoring and timely decision-making to reduce the well test rejection.

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