Type-Curve Analysis: What It Can and Cannot Do

Abstract

Summary. Type-curve analysis has been used for more than 20 years in theoil industry and for more than 40 years in hydrogeology. Yet, what itinvolves and how useful it is in practice is still being debated within theoil industry. This paper attempts to answer some of the questions that aremost commonly raised about type curves and type-curve analysis. What Is a Type Curve? A type curve is a graphic representation of thetheoretical response during a test of an interpretationmodel that represents the well and the reservoir beingtested. For a constant-pressure test, the response isthe change in production rate: for a constant-rate test, the response is the change in pressure at the bottomof the well. Other types of response are also used, such as the time derivative of the bottomholepressure. Type curves are derived from solutions to the flowequations under specific initial and boundaryconditions. For the sake of generality, type curves areusually presented in dimensionless terms, such as adimensionless pressure vs. a dimensionless time. A given interpretation model may yield a single typecurve or one or more families of type curves, depending on the complexity of the model. What Is Type-Curve Analysis? Type-curve analysis consists of finding a type curvethat "matches" the actual response of the well andthe reservoir during the test. The reservoir and wellparameters, such as permeability and skin. can thenbe calculated from the dimensionless parametersdefining that type curve. The match can be found graphically, by physically, superposing a graph of the actual test data with asimilar graph of the type curve(s) and searching forthe type curve that provides the best fit. Alternatively, an automatic fitting technique involving a linear ornonlinear regression can be used. Fig. 1 gives an example of a graphic type-curvematch. The graph of the data is positioned over thegraph of the type curves, with the axes kept parallel, so that the test data match one of the type curves. Reservoir parameters are calculated from the value ofthe dimensionless parameter defining the type curvebeing matched and from the × and y axis shifts. How Can One Select a Type Curve ToMatch Test Data? First, one must find the interpretation model that bestrepresents the dynamic behavior of the well andreservoir during the test. This interpretation modelmust be identified from the test data because it isusually difficult to predict from static information. The most efficient way to identify the interpretationmodel is to use the derivative of the pressure withrespect to the natural log of some function of elapsedtime. A log-log plot of the pressure derivative vs. elapsed time yields a limited number of characteristicfeatures for the various components of theinterpretation model that are easy to recognize. Thesefeatures are illustrated in Fig. 2. The possibilities are(1) a maximum. (2) a minimum, (3) a stabilization, and (4) an upward or a downward trend. Themaximum is found at early times and indicateswellbore storage and skin: the higher the maximum, the more damaged the well. No maximum indicates anondamaged or a stimulated well. The stabilizationindicates semilog radial flow and corresponds to thesemilog straight line on a Horner plot. A minimumindicates heterogeneous behavior. An upward ordownward trend at the end of the data indicatesboundary effects. The complete interpretation modelis then obtained by combining these variouscomponents. Examples of interpretation models areshown in Fig. 3. Once the interpretation model has been identified, one must select the type curves corresponding to thatmodel that are the most appropriate for the range ofavailable test data. What Is the Difference Between theVarious Published Type Curves? For a given interpretation model, the mathematicalsolution to the flow equations is unique, and typecurves derived from that solution should all beidentical. In practice, however, type curves maydiffer by their presentation-e.g., if they use differentdimensionless or dimensional parameters-or by theirrange of application. As a result, some published typecurves may not be usable with the available test data, or may be more or less convenient to use. But evenif they look different, type curves corresponding tothe same interpretation model will give the sameanalysis results if they all cover the range of availabletest data. P. 11^