Well Testing Theory & Practice

Based on a workshop sponsored by PTTC's Appalachian Region in Morgantown, West Virginia on August 16, 2005.

BOTTOM LINE

Determination of the relationship between wellbore pressure and the wellbore flow rate is a basic test of the reservoir. These tests allow the engineer to determine the average wellbore pressure for use in volumetric and material balance calculations as well as forming the foundation to estimate the physical characteristics of the reservoir. The type of information obtained by well testing includes estimates of permeability, formation damage or stimulation, pressure, length and conductivity of fractures, flow barriers, communication between wells and drainage volume.

PROBLEM ADDRESSED

The three areas addressed by well testing are (1) reservoir evaluation - to determine if the well has sufficient flow capacity to complete and to obtain reservoir information for predicting and analyzing reservoir behavior; (2) reservoir management - to diagnose the condition of production and injection wells to optimize performance, identify candidates for workover and track the movement of fluid fronts in the reservoir; and (3) reservoir description - to identify heterogeneities such as different rock types, stratigraphic interfaces, and faults and barriers.

KEY WORDS:

Dual porosity, Formation damage, Pressure build-up, Pressure drawdown, Productivity Index, Reservoir boundary, Well geometry

SPEAKERS:

Petroleum and Natural Gas Engineering Department
Dr. Kashy Aminian, West Virginia University
 

TECHNOLOGY OVERVIEW

Introduction
Well testing is the science of measuring pressure changes in wells and interpreting those pressure changes. The analysis of test data provides estimates of flowing properties and reservoir geometry. Well testing and analysis is a highly technical specialized field. There is a vast wealth of literature on the practical and theoretical aspects of the topic. A one day workshop will not prepare the engineer to perform well tests or analyze well test data, but will inform the engineer as to what information can be obtained or estimated, what tests are commonly performed, the costs of obtaining the information, the assumptions inherent in the estimates and the limitations of the tests.

The commonly performed tests include:

• Pressure drawdown
• Pressure build-up
• Step rate
• Drill stem
• Productivity
• Injectivity
• Multi-rate
• Interference
• Pulse

The applications of these tests include:

• Degree of reservoir damage
• Area of drainage
• Potential well productivity
• Injectivity
• Permeability of different intervals
• Transmissibility (kh/µ)
• Capacity (kh)
• Productivity Index
• Length of fracture system
• Radius of drainage
• Distance to fault or barrier
• Open flow potential
• Oil and/or gas in place

All of these tests, regardless of the end purpose, are based on the principle that the flow rate is proportional to the driving forces (static or capillary pressure) over resisting forces (matrix geometry and fluid properties). The input to the test is a measured period of shut-in and flowing rates. The output is the reservoir response (pressure). A computational model that describes the relationship between the pressure, flow rate and reservoir rock and fluids properties is required. In its simplest form, the relationship of input to output is a form of the diffusivity equation for a well in the center of a circular, homogeneous, horizontal reservoir of uniform thickness and a one phase fluid that obeys Darcy's law. While this equation cannot be solved directly, indirect techniques provide a satisfactory estimate.

The actual reservoir model is constructed from the basic equation described above. It must take into account the geometry of the reservoir, the number and types of fluids and the flow regime. The flow geometry for that area affected by the test can be radial linear, elliptical or spherical. The most common model used to represent the pressure behavior of the reservoir is radial flow, where all flow occurs radially toward the well between impermeable upper and lower boundaries at a constant surface flow rate. The interpretation of test data will yield average reservoir properties even when reservoir heterogeneities exist.

The presence of a single barrier or a finite reservoir is evident when comparing actual well build-up data to the theoretical build up curve with no after production and no completion damage in an infinite reservoir. This is evident in the Horner plot with pressure as the vertical axis, and the log of (t + Δt)/ Δt on the horizontal. The degree of skin damage is evident in the plot in the early time as a deviation from the theoretical plot. Skin factor is a function of skin due to damage, restricted entry, perforations, turbulence, and slanted wells.

The reservoir behavior can be categorized as homogeneous, dual porosity, or dual permeability. The dual porosity systems consist of two porous media regions, primary and secondary porosity. Most of the fluid is contained within the primary porosity, which has very low permeability. Fluid flow to wells only occurs through the secondary porosity system because it has much greater permeability than the primary porosity system. The flow periods are modeled in three phases: (1) the high permeability (fissure) phase in which only the secondary porosity is contributing, (2) the transition phase characterized by transient interporosity and pseudosteady state interporosity flow, and (3) total system flow, which is controlled by flow from the lower permeability primary porosity.

Well Test Data Interpretation
There are three major steps to a unified approach to well test data interpretation: Identification of the proper model for the classification of the reservoir (finite, infinite, homogeneous, dual porosity, dual permeability, skin, fractures), specific analysis and calculations to estimate well and reservoir characteristics, and verification of results to ensure that the process resulted in the best answer.

By plotting the Δp vs Δt the proper model can be selected based on the nature of the curve. In addition, plotting the pressure and pressure derivative versus time provides a powerful tool in distinguishing between different behaviors and finding a unique solution. For instance, the difference between plots of single and dual porosity reservoirs can be seen clearly and the proper model selected. However, accurate pressure measurements are required for the evaluation of the pressure derivative.

Well test interpretation is based on patterns of pressure change and the derivative of pressure change to identify the type of reservoir behavior. An effective way to interpret pressure data is by using a diagnostic graph. A diagnostic graph is a plot of the pressure change and the derivative of the pressure change versus time on log-log paper. It can be used to identify each flow period. Behavior specific plots can be useful to identify heterogeneous behavior, effects of wellbore storage and high and low conductivity fractures.

The second step in the unified approach to interpretation methodology is the calculations of the basic reservoir parameters, such as the kh, skin and wellbore storage capacity. This can be done conventionally, through the use of specific plots, or with type curves.

Using the conventional method, the engineer identifies the various flow periods from the diagnostic shape of each of the flow periods and determines the stabilized derivative value, if present. Kh and skin can then be calculated directly. The wellbore storage coefficient can be estimated if the unit slope line appears in both the derivative and pressure change data.

It may not be possible to recognize the diagnostic shape of the derivative, if the derivative values are erratic. If the infinite-acting period can be identified from the diagnostic pressure plot, semilog analysis can be used to analyze the pressure data during infinite-acting period.

The type cure matching technique is used when it is not possible to accurately identify the location of the flow periods from the diagnostic plot. The curves are dimensionless well model solutions that are plotted on log-log paper. The shapes apparent in the diagnostic log-log plat are matched to the type curves. The best way to analyze the post-stimulation well tests is by type curve matching. The procedure is similar to that used for the radial flow model.

The final step in the in the interpretation methodology is the verification of the validity of the model and calculations. The engineer can compare the result from well to well and from time to time with the same well for matching. Another method is to prepare and analyze a dimensionless semi-log plot. Finally, the calculated parameters can be used as input to a reservoir simulation model and run to see if it matches the input data.
 

CONNECTIONS:

Dr. Kashy Aminian
Petroleum and Natural Gas Engineering
West Virginia University
P.O. Box 6070
Morgantown, WV 26506-6070
Phone: 304-293-7682
Email: khaminian@mail.wvu.edu

For information on PTTC’s Appalachian Region and its activities contact:

Douglas G. Patchen, Program Director
West Virginia University, Appalachian Basin Regional Lead Organization
P.O. Box 6064, Evansdale Drive, Morgantown, WV 26506-6064
Voice: (304) 293-2867 ext. 5443; Fax: (304) 293-7822
Email: dpatch@wvunrcce.nrcce.wvu.edu

Disclaimer: No specific application of products or services is endorsed by PTTC. Reasonable steps are taken to ensure the reliability of sources for information that PTTC disseminates; individuals and institutions are solely responsible for the consequences of its use.

The not-for-profit Petroleum Technology Transfer Council is funded primarily by the US Department of Energy’s Office of Fossil Energy, with additional funding from universities, state geological surveys, several state governments, and industry donations.

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toll-free 1-888-THE-PTTC; fax 281-921-1723; Email hq@pttc.org; web www.pttc.org