Fractured Horizontal Well and Completion Nodal Analysis Simulator
Authors: Ochs D.E. , Hareland G. , Rampersad P. 
Published: December 2007

Abstract
HoSim is a flow network solver which can determine rate and pressure at a given point in a flow system based on terminal and inflow relationships.
An analytic model for fractured horizontal wells has been integrated in conjunction with inflow through perforations and different geometries in the horizontal completion. The fractured well model used is based on the premise that a boundary value problem may be conformally mapped onto a complex plane. The model divides each fracture and the wellbore into a number of flow divisions. Flow into a section is based on the length of each section and the associated pressure distribution. The model is pseudo steady state, but has the capability of being integrated with a gridded reservoir simulator the see the reservoir behavior which may include water or gas coning over time.
This paper gives the theoretical development as well as a North Sea field case simulation and results. The simulator is a new tool that gives the completion/reservoir engineer a way to better optimize single or multiple fractured horizontal well designs for maximum recovery.

Introduction
Evaluation of multiple completion and stimulation alternatives has become more difficult in recent years due to the many options available on the market today. One of the most challenging scenarios for simulation is the multiple fractured horizontal well. The potential for enhanced recovery coupled with large completion and stimulation expenditures creates a need for better understanding of these complex flow environments. The model presented here attempts to model a system composed of a reservoir drainage block, multiple orthogonal fractures intercepting a horizontal wellbore, and a completion within that horizontal wellbore. This model is constructed using the concept of a flow network, where each component of the system is further subdivided into multiple flow divisions.

Description of the System
A horizontal wellbore is exists within a rectangular drainage block which has dimensions of axbxh. The wellbore azimuth is coincident with the local least principal stress direction within the drainage block. Hydraulic fractures which are introduced in this well will therefore lie in a plane orthogonal to the wellbore. It is assumed that induced fractures are spaced evenly along the length of the wellbore, making it possible to divide the drainage block into subsections, with one fracture lying within each block. These subsections are indexed as b1,b2,…,bn. Each fracture is assumed to be rectangular, having dimensions ci, Lfi, hfi. A diagram of this system is shown in Figure 1. This subdivision of the problem into multiple subproblems assumes that there is no flow between adjacent subdivisions. The size of the end blocks is adjusted to account for the effect of the 'greedy' end fractures, but this assumption requires that each fracture under consideration be given the same conductivity profile when discretized in the network model.

Theoretical Development
The lengths of the subdivisions of the drainage block can be derived based on the geometry of the system described above by assuming that each equally spaced fracture is geometrically centered in its drainage block, with the exception of the first and last fracture. It can then be stated that the length of the first and last block is given by,
(1)
P. 25