ABSTRACT
Based on the in-depth study of similar structure [13-14] of a variety of reservoir solutions, this paper firstly by proofing the expression of the general boundary value problem (the boundary value problem of zero-order modified Bessel equations) has a similar structural form and then exploring the relation between similar kernel functions and boundary condition, and summarizing the new method for solving such boundary value problems-Similar Structuring Method and the detailed structural steps are listed out, then
1 INTRODUCTION
In the develop process of actual reservoirs, multilayered reservoirs gained much attention [1-14] from researchers around the world. Kuchuk [1] put forward a connect-multilayer reservoir with each layer isotropic, infinite and has equal thick horizontally as well as a same initial pressure. Derive the analytic solutions in Laplace space by using superposition principle; Raghavan [2] et al. compute the layered reservoirs, based on each layer has a constant pressure, and determine the flow of each layer by using the relation between the flow and pressure under the constant pressure, thus the wellhole pressure is obtained; Chen [3] et al. derive the general mathematical model for describing pressure behavior of commingled multilayered reservoirs, arbitrary well pattern and outer boundary can combine into each single layer, physical property and material type may not be the same, and then they combine the multilayered system by using the equation of the single-layer system directly, and then establish a superimposition principle of variable-flow rate; Yao [4] et al. build the triple single-phase reservoir that considering well seepage-transit model of inflow performance relationship for commingling in straight wells,
establishing the mathematical seepage model of layered reservoirs under the condition of three outer boundaries (infinite, closed and constant value). Through the Laplace transform method, similar kernel functions is structured by using the similar structuring method, and the similar structural equation of the solution to the distribution of reservoir pressure is obtained by assembling the similar constructive method. The similar structural equation of the solution to reservoir model obtained by similar structuring method is not only convenient for well test engineer to program the corresponding software for well test analysis but also has an important meaning to the theoretical analysis of the seepage regularity of reservoir.
