Well Testing for Radially Heterogeneous Reservoirs Under Single and Multiphase Flow Conditions

Abstract

Summary In this work, we examine the behavior of pressure transient data for single and multiphase flow in heterogeneous reservoirs. In order to illustrate multiphase flow behavior in these systems, we focus on heterogeneous gas condensate reservoirs, however, we also consider other multiphase flow problems. It is well known that in some instances, e. g., water injection/falloff in homogeneous reservoirs, pressure transient data from buildup (or falloff) tests cannot be obtained by superposition of drawdown (injection) pressure responses. In fact, drawdown and buildup reflect properties in different regions of the reservoir. This behavior is common to most occurrences of multiphase reservoir flow, and is exaggerated in the presence of radial heterogeneity. This theoretical work describes the information contained in transient pressure derivative data, and explains the fundamental difference in behavior between multiphase drawdown and buildup pressure transient data in radially heterogeneous reservoirs. We show that whereas multiphase buildup data may be treated like single-phase buildup data, drawdown data is most indicative of properties in that region of the reservoir where mobility is changing most rapidly with time. Theory Isothermal multiphase flow in radially heterogeneous reservoirs is described by a system of partial differential equations that describe conservation of mass of oil, gas and water components in black oil systems and conservation of individual chemical species in compositional systems. When the mass conservation equations are satisfied, Darcy's law, which describes pressure losses in each flowing phase is also satisfied. Thus, for Black Oil systems, we can write at any radial location, (1) where, t is the total mobility, i.e., (2) and, C1 is a constant given by, (3) In writing Eq. (1), we have assumed negligible capillary pressure effects, and that all phase rates are in reservoir bbl/day. Equation (1) obviously applies equally to bounded or to infinite-acting reservoirs. If we consider infinite-acting reservoirs, we can separate variables in Eq. (1) and integrate over radius to obtain (4) Carrying out the indicated integration, noting that (5) we obtain the following equation for the wellbore pressure drop:

Effects of non-uniform fluid saturation distribution on pressure transient analysis

“…Among the three mentioned methods, only the Perrine's method has been widely used in industry due to its simplicity. Thompson and Reynolds (1997) defined a theoretical expression for pressure derivative in a radially heterogeneous reservoir under multiphase flow condition. They showed that the pressure derivative which is observed at the well bore reflects a weighted harmonic average permeability over the radial extent of the reservoir.…”

“…For this purpose, we developed a theoretical model based on Thompson and Reynolds (1997) equation which represents the pressure derivative that is observed at the wellbore as well as the effects on semi log analysis. The theoretical model applications are demonstrated using a simulation in the reservoir which is filled by oil and water with the variety of saturations at the initial condition.…”

Mapping of Reservoir Properties and Facies Through Integration of Static and Dynamic Data

“…As pressure data at producing wells are quite sensitive to changes in total mobility (Thompson and Reynolds, 1997), it is not completely surprising that one can obtain reasonable estimates of water relative permeability model parameters even if we history match only pressure data corresponding to times prior to water breakthrough. It is not clear why the information content of the GOR data is sufficient to resolve the parameters defining the oil and water relative permeability curves for the twophase water-oil system.…”

Geothermal reservoir simulation to enhance confidence in predictions for nuclear waste disposal

“…Many theoretical analytical techniques are available to gain significant information on the subsurface structure (de Marsily, 1986;Ehlig-Economides et al, 1994;Kuchuk, 1995;Shanyan and Wong, 1998;Thompson and Reynolds, 1997). Similarly, large-scale regional groundwater models have generally performed well (National Resource Council, 1990).…”