ESP design – Step 2: Production Capacity

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Once the first step “Collect basic data” is performed, we pass to the ” step 2: Production Capacity “ of the ESP Nine Step Design Procedure. It consists on predicting the well inflow performance which represents the relationship between pressure and flow rate at the well face of an individual well and it is physically defined as the well flowing bottom-hole pressure (Pwf) as a function of production rate. It describes the flow in the reservoir.

Many inflow performance relationships (IPR’s) are described in the literature. In this article, we will briefly present three of the most widely used IPR’s to describe the well performance:

 

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The Composite Inflow Performance Relationship

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The Composite Inflow Performance Relationship is based on the combination of PI model, presented in the previous articles “Well Inflow Performance”, and “Vogel’s inflow performance relationship”. As per the aforementioned articles, PI model could be used if the well producing a single phase flow with no gas in the solution (Pwf > Pb). In the other hand, Vogel’s IPR could be used when the well’s flowing bottomhole pressure (Pwf) is below the bubble point pressure (Pb) and if the produced fluid is pure oil.

If the Pwf is below Pb and well’s produced fluids is a mixture of oil, water, and gas, the inflow performance could be described by the Composite IPR. In this case, IPR curves are somewhere between the curves valid for pure oil (Vogel model) and the one valid for Pwf > Pb (PI model).

The following graph shows the differences between these methods in graphical form:

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Vogel’s inflow performance relationship

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In 1968, Vogel established an empirical relationship ( Vogel’s inflow performance relationship )for flowrate prediction of a solution gas-drive reservoir in terms of the wellbore pressure based on reservoir simulation results.

Vogel’s Model compared to PI Model…

The PI model works very well for single phase fluid (water, oil, or water/oil) flowing into a wellbore, even though water and oil are two separate phases, they are considered as a single phase since they are both liquid.

But what happens when gas comes out of solution?

” The flow velocity of a fluid in a porous medium is inversely proportional to the fluid viscosity. Typically, gas viscosity in the reservoir is about fifty times smaller than for liquid oil and consequently, the gas flow velocity is much greater. As a result, it is normal, when producing from a reservoir in which there is a free gas saturation, that gas will be produced in disproportionate amounts in comparison to the oil “. (Dake, fundamentals of reservoir engineering).

Compared to liquid, gas has much higher permeability and much lower viscosity. These two factors will give the gas a much higher flow rate than liquid inside the reservoir, so that:

QG >> QL

Below the bubble point pressure, the solution gas escapes from the oil and become free gas. The free gas occupies some portion of pore space and reduces flow of oil. This effect is quantified by:

  • A decrease of oil Relative permeability
  • An increase of oil viscosity (as its solution gas content drops)

Therefore, the combination of the relative permeability effect and the viscosity effect results in lower oil production rate at a given bottom-hole pressure.

Graphically, it would looks like this:

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Introduction to IPR and VLP

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The productivity of the well depends on an efficient use of the compressional energy available in the reservoir allowing the reservoir fluids to flow toward the production separator. As an introduction to IPR and VLP, this article will introduce two key relationships (IPR and VLP) used in the design of the production system.

Introduction to IPR and VLP:

  • Inflow Performance Relationship (IPR) is defined as the well flowing bottom-hole pressure (Pwf) as a function of production rate. It describes the flow in the reservoir. The Pwf is defined in the pressure range between the average reservoir pressure and atmospheric pressure. A typical inflow performance relationship is presented in the following graph:

The intersection of the PI plot with the x-axis is the flow rate corresponding to a Pwf equal to zero. This point in the IPR plot is known as the Absolute Open Flow (AOF) potential of the well.

The following video shows more details about reservoir inflow performance:

 

  • Vertical Lift Performance Relationship (VLP), named also Outflow, describes the bottom-hole pressure as a function of flow rate. The VLP depends on many factors including fluid PVT properties, well depth, tubing size, surface pressure, water cut and GOR. It describes the flow from the bottom-hole of the well to the wellhead.

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Well Inflow Performance

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Well Inflow Performance represents the relationship between pressure and flow rate at the well face of an individual well. The scientist Darcy was the first studied extensively the relationship between pressure and flow rate. His experimental studies consist on creating a pressure differential across a porous media and measured the resulting flow rate.

Darcy’s experiments result in what is known as “Darcy’s law”. For general flow through a porous media:

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