Horizontal Well
Before we start discussing the response of a horizontal well, let’s have a quick look at the golden rules on the derivative.
The Golden Rules

A stabilization on the derivative plot could be indicative of radial flow regime (circular flow towards the well). The level of this stabilization is inversely proportional to the mobility KH/u. So a lower stabilization will mean a higher KH/u. (K:permeability, H: net thickness, u:viscosity)

The vertical separation between the two plots is indicative of skin: a higher separation would mean a higher skin

The Xaxis (called DeltaT) represents the shutin duration (or flow period duration). This could be “replaced” by the radius from the well. For small DeltaT, we are looking near wellbore, at large DeltaT, we are looking further away from the well.
The graph above could be applied to a simple oil and gas vertical well with radial flow regime from 3 to 10 hours. The increase in the derivative plot at late times, from 10 hours onwards, could represent the presence of boundaries.
The radial flow regime towards the vertical well is represented here:
Basic Horizontal Well Response
Now, let’s assume a horizontal well of perforated length L in a homogeneous reservoir of infinite extent, bounded above and below by impermeable planes.
Intuitively, we could imagine that near the wellbore (i.e. at small DeltaT values on the derivative plot) we would have a flow in the plane perpendicular to the well direction.

Vertical radial flow regime at early times
Near wellbore (at small DeltaT values), an initial radial flow regime develops in the vertical plane, along the flowing interval. The derivative plot then shows a stabilization, which is indicative of
with Kv: vertical permeability, Kh: horizontal permeability and L: contributing well length.
This is generally called the “vertical radial flow regime”.
When one of the reservoir upper or lower barrier is reached, this initial flow regime will end. If the horizontal well is not centered in the reservoir, the derivative will follow a new stabilization at a higher level, until both vertical limits are reached.
When the upper and lower impermeable limits are reached, an intermediate flow regime will develop, probably a linear flow regime with:
At late times, a horizontal radial flow regime develops, with a derivative stabilization indicative of K_{H} H.

Horizontal radial flow regime
After an intermediate flow regime, the well acts as a sink point at large distances in the reservoir (i.e. at large DeltaT values in the derivative plot). The flow will converge towards the well with a circular radial flow regime in the bedding plane. This is described by the figure below:
The derivative plot will therefore present a horizontal stabilization indicative of k_{H}H, with H the stratigraphic reservoir thickness and K_{H} the permeability in the bedding plane. At that stage, the horizontal well is similar to a vertical well in the formation.
A basic oil and gas horizontal well response would then have the response below on the derivative plot:
Watch the video
Pressure transient analysis response for a horizontal well showing the matching process and source of uncertainty. Two examples of horizontal well responses are presented.