Summary
A method is presented for estimating the distribution of a parameter related to the productivity index along the length of a liner-completed horizontal well, using measurements of well flowing pressure at multiple points along the path of flow in the wellbore. This is the concept of near-wellbore diagnosis with multipoint pressure measurements, which in principle can be made with fiber-optic sensors. The deployment mechanism of the sensors is not modeled in this study, although the temperature version of such sensors has been deployed in horizontal wells on an extended-tail-pipe or stinger completion. (The temperature sensors also have been deployed in horizontal wells with sand-screen completions, in direct contact with the formation, but that configuration is not investigated in this study.)
The parameter that is estimated is known in reservoir-simulation terminology as the connection factor (CF), which represents the hydraulic coupling or connectivity between the reservoir and the wellbore (between formation gridblocks and well segments). Parameter CF has units of md-ft, similar to flow capacity, or productivity index multiplied by viscosity. Specifically, the parameter is directly proportional to the geometric mean of the permeability perpendicular to the horizontal axis of the well and is inversely related to skin. No attempts are made in this study to estimate these parameters individually, which may require recourse to other methods of well diagnosis(e.g., dynamic formation testing, transient analysis, and production logging).
The method applies to flow under constant-rate conditions and yields estimates of the CF, which represents the quality of the formation in the vicinity of the well and the integrity of the completion along the well trajectory.
The quality of the inversion is determined by the spatial density and accuracy of the multipoint measurements. Inversion quality also depends on knowledge of the wellbore hydraulic characteristics and the relative permeability characteristics of the formation. The basic configuration investigated in this study consists of a five-node pressure array in a 2,000-fthorizontal well experiencing a total pressure drop of approximately 60 psi when produced at 10,000 STB/D. A reasonable estimate of the distribution of the parametric group CF is obtained even when allowing for measurement drift and errors in liner roughness and relative permeability exponent. Also, the inversion can be rendered insensitive to knowledge of the far-field permeability through a scaling technique. Therefore, good estimates of the near-wellbore CF profile can be obtained with uncertain knowledge of the reservoir permeability field. This is important because the technique can be applied not only to early-time but also to late-time data. The application of the multipoint pressure method is illustrated through a series of examples, and its potential for near-wellbore formation evaluation for horizontal wells is described.
Introduction
Horizontal wells can be diagnosed on the basis of information derived from openhole and cased-hole surveys. These include petrophysical logs, dynamic formation testers, production logging, and pressure-transient testing. With the advent of permanent sensing technologies and the development of methods of production-data inversion or history matching, a new form of cased-hole diagnosis can be envisaged, with improved spatial and temporal coverage and without the need for in-well intervention and interruption of production. The impact of such methods on reservoir-scale characterization can also be significant.
There are two main preconditions for the development of such a methodology, one concerning sensing technology and the other concerning interpretation methodology. Permanent sensing technology has made great progress during the last decade, with the development of single-point and distributed measurements that can be deployed with the completion (pressure, flow rate, and distributed temperature). However, these systems are typically developed as stand alone measurement units and do not enjoy the required degree of integration. Current modeling methods, however, can be used to provide an incentive for such integration.
The well-diagnosis problem is decoupled in our investigation into diagnosis of flow condition in the wellbore and diagnosis of near-wellbore formation characteristics. (By "near-wellbore," we mean the wellbore gridblock scale.)This is partly to adhere to the conventional demarcation between production logging and dynamic formation evaluation and partly to show the natural consequence of the mathematical problem. Basically, the wellbore-diagnosis problem (determination of flux distribution, as in production logging) can treat the formation simply as a boundary condition, but the formation-evaluation problem cannot do the same (i.e., treat the wellbore interface as a boundary condition) because evaluation is based on measurements made inside the wellbore. Thus, both the wellbore and the formation have to betaken into account. (Sensors that are in direct contact with the formation, as mentioned in the Summary, are emerging.8 Therefore, the evolution of this problem is to be expected.) In this study, the permanent or in-situ analog of dynamic formation evaluation is investigated. The in-situ analog of production logging is investigated in a parallel study.