Derivation of Pressure Distribution Models for Horizontal Well Using Source Function

In oil and gas operation, horizontal well technology has become an important technique because of its numerous advantages. Despite these advantages, determination of pressure distribution expression is a problem because it involve 3D transient-flow that need to be solved. In this work, ten (10) models for pressure distribution for horizontal well under different boundary variation were derived following these steps for each of the models:(i) choosing a boundary condition for each axis(ii)selecting the appropriate source function for each axis and (iii)applying Newman product rule to arrive at the pressure expression. In conclusion, the following were observed.(a) along the xaxis, seven of the models have infinite-slab sources in infinite-slab sources(b) five of the models derived, along the yaxis they have infinite-plane sources in infinite-slab sources while for the remaining five along the y- axis they have infinite sources(c) along z-axis, six of the models have infinite-plane sources in infinite-slab sources while four of the remaining one have infinite sources(d) Three types of boundaries are observed:(i) Completely bounded boundaries (ii) Mixed boundaries (iii) infinite-acting boundaries(e)Three instantaneous source functions are involved in the pressure distribution expression.