Fluid Placement Model for Horizontal-Well Stimulation

Abstract

Summary Acidizing is a common method used to stimulate horizontal wells. The acidizing process is fundamentally different when applied in a horizontal well compared with application in a vertical well. The fluid distribution in a horizontal well is affected by a longer wellbore length, a broader variation in the reservoir properties along the wellbore, and possibly different mechanical means by which to place the fluids in the wellbore. A comprehensive fluid placement model linked with a reservoir acidizing simulator is essential to precisely design acidizing treatments for horizontal wells. In this paper we present a model of fluid placement in a horizontal well. The model predicts the placement of injected fluids by tracking the interfaces of different fluids in the wellbore. It is capable of tracking multiple interfaces for multiple injection stages in horizontal wells. For injection with coiled tubing, the model allows tubing tail movement during injection. It also handles simultaneous injection from the annulus and from a tubing string. The fluid distribution generated from the model can be used as input information in a reservoir acidizing model for sandstone acidizing design. Both analytical and discretized solutions of the model are presented in the paper. Examples in the paper illustrate the effects of such factors as velocity of tubing movement, annular injection, and a nonuniform distribution of flow into the reservoir on fluid placement in an acidizing treatment. The fluid placement model can help to determine optimum tubing tail locations and optimal injection volumes of acids, to select the most appropriate diverting methods, and, hence, to maximize the benefits of an acidizing treatment. Introduction An effective acidizing treatment requires that at any particular location along the wellbore, live acid penetrates deeply enough into the reservoir to restore the permeability in the damaged region and that sufficient acid is distributed to all the damaged zones along the well (good acid placement). Because of the long extent of reservoir contacted by a horizontal well, it is critical to minimize the acid volume for each unit length of wellbore. Reduced acid volume for each length of wellbore makes the problem of acid placement a more important aspect of acidizing design for horizontal wells than it is for vertical wells. Previous work on acid placement demonstrated the difficulties with acid placement and diversion in vertical wells.1–3 Jones and Davies4 showed how these concerns are even more overriding when designing acid treatments for horizontal wells. Acid treatments typically consist of the injection of several stages of different fluids including acids of various types, organic solvents, inert spacer fluids, and diverter stages. In horizontal wells, the acid is usually injected through coiled tubing, which may be moved during the course of a treatment. It is also common practice to inject an inert fluid through the coiled tubing/casing annulus while other stimulation fluids are being pumped through the coiled tubing. All of these factors must be considered to predict where the various stages of injected fluids will be placed in the formation. In this paper we present a model of fluid placement in a horizontal well. The model predicts the placement of injected fluids by tracking the interfaces of different fluids in the wellbore. The primary result is the determination of the volume of fluid injected into the formation along the length of the wellbore, i.e., the fluid placement, as a function of time, injection schedule, number of sequences of injection, and tubing tail location. The fluid placement model is linked with a reservoir acidization model to provide the boundary condition (type of fluid and concentration) for acidizing simulation. We first present the theory behind the fluid placement model. Two solutions to the problem of tracking the inner-wellbore interface are addressed—analytical and discretized methods. The analytical method affords a general explanation of how interface movement varies with wellbore length. However, the analytical model is limited to certain idealizations, such as a uniform flux distribution from the wellbore. The discretized solution provides the basis of the fluid placement model, allowing for nonuniform flux distribution, injection of multiple sequences, movement of the tubing, and simultaneous injection through the tubing and the tubing-casing annulus. The discretized model can also easily be integrated with the reservoir acidization model. Examples from the discretized model illustrate the effects of nonuniform distribution of flow into the formation, tubing movement, and annular injection on fluid placement. Fluid Placement Model A schematic of the horizontal wellbore with important associated parameters is displayed in Fig. 1 which illustrates the wellbore at some point in time after injection of fluid through the tubing. The locations of two fluid interfaces are shown: one moving to the left and the other to the right. The length of the wellbore and the flow rate into the formation are also labeled. The fluid placement and reservoir acidization models are coupled. The main parameter tying the two models together is the flux distribution along the length of the wellbore, which varies with time. The reservoir acidization model supplies the flux distribution (flow rate into the formation) to the fluid placement model, which requires the parameter as an initial condition. The resulting fluid distribution of injected fluids into the formation generated by the fluid placement model in turn becomes a boundary condition for the reservoir acidization model. The following are two methods of analyzing the interface movement within the wellbore. The analytical solution is supplied to illustrate the behavior of interface movement, while the discretized solution is required for integration with the reservoir simulation model.