Knowledge about the reservoir temperature is important for reservoir modeling and field development, but the temperature measured in exploration wells is seldom representative for the reservoir temperature. In a paper presented at SPE ATCE in Dubai in September 2016, Meisingset (Statoil) and Pedersen (Calsep) outline a procedure for determining the reservoir temperature from well test data.

Figure 1 is a sketch of the near well bore area in a reservoir during well test. The pressure decreases from reservoir to bottom-hole (drainage). This pressure drop will have some impact on the temperature of the flowing fluid and the temperature effect may be quantified by carrying out an energy balance.

**Figure 1 **The left hand sketch illustrates the pressure drainage in the near well bore area. The right hand sketch shows a scenario with a considerable height difference between the bottom-hole gauge where temperature and pressure are measured and the perforation interval.

The term Δ in the following is used to express differences between properties in the reservoir and in the well at bottom-hole gauge depth (BH in Figure 1). If it is assumed that no work is extracted, the energy balance can be expressed as

(1)

U is internal energy, E_{k} kinetic energy, E_{p }potential energy (for vertical lift of fluid), Q the heat added, P pressure, and V molar volume. Enthalpy is defined as

(2)

The fluid flowing will initially exchange heat with the surroundings, but after some time of flow, the heat exchange with the surroundings will become negligible. By also assuming the change in kinetic energy is negligible, Equation (1) can be rewritten to

(3)

With a height difference of Δh as shown in the right hand sketch of Figure 1 the difference in potential energy of one unit mass of fluid flowing at BH and at perforation heights equals

(4)

If this equation g is gravitational acceleration. If the height difference is zero, the fluid will have the same enthalpy in the reservoir as at bottom hole conditions and the temperature difference will be determined by a Joule-Thomson cooling or heating. The Joule-Thomson (JT) coefficient is defined as the pressure derivative of the temperature at constant enthalpy for a single phase fluid:

(5)

Figure 2 shows the variation in bottom-hole pressure and temperature during five well test periods for a gas condensate fluid. The flow periods are marked by 1-5 in Figure 1. The bottom-hole pressure and temperature gauge was placed 32 m above the top of the perforation interval. The temperature before start of flow was lower than the original reservoir temperature, because the well had been cooled by circulation of drilling mud and other well fluids. At the start of the first flow period, the gas coming from the reservoir has a higher temperature than the surroundings and there is a net heat flow from the gas to the surroundings, which in Figure 1 is seen as a steep increase in bottom hole temperature. After 5 hours of flow the temperature has stabilized telling that the heat exchange with the surroundings has become negligible and Equation (3) will hold. The enthalpy (H) at bottom hole conditions can be derived from a PT flash calculation. The enthalpy at reservoir conditions will be the same corrected for a possible height difference (Equation (4)) and the reservoir temperature can be determined from a PH flash at reservoir pressure. The simulations are carried out using the SRK-Peneloux equation of state.

The flow rate is increased at the transition from one flow period to the next one. With a higher flow rate the pressure drop in the near well bore area increases and the bottom hole pressure decreases. As can be seen from the temperature curve in Figure 2, this causes an increased JT cooling.

To validate the reservoir temperature determined from data for the first flow period, the reservoir temperature is determined for each of the five flow periods by carrying out a PT flash calculation at bottom hole conditions followed by a PH flash at reservoir pressure. Only if the assumption of a negligible heat exchange with the surroundings and the fluid description are correct will the reservoir temperature simulated for each flow period be the same. It is show by the green line in Figure 2 that the reservoir temperature independent of flow period is simulated to be 68.2 ^{o}C.

For the considered gas condensate fluid the reservoir pressure is almost coinciding with the saturation pressure and the flow is at two-phase conditions. This shows that not only the JT coefficient, but also the heat of condensation is simulated well. The potential energy required to lift the reservoir fluid to the bottom-hole temperature gauge depth corresponds to a temperature effect of around 0.1^{o}C.

**Figure 2** Variation in bottom-hole pressure and temperature during well test of Fluid No. 1 (green line also adjusted for potential energy).

The SPE paper presents similar data for three reservoir oils. While the pressure decrease from reservoir to bottom hole conditions resulted in a cooling for the gas condensate mixture, a heating was seen for the three reservoir oil mixtures. This heating could also be quantified using the procedure outlined above.

A copy of the paper may be obtained from Calsep.

### Reference

Meisingset, K.K. and Pedersen, K. S., “Joule-Thomson Coefficients from Well Test Analysis Data”, presented at SPE ATCE Dubai, UAE, September 26-28, 2016.

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