Comparison of kinetic and equilibrium reaction models insimulating the behavior of porous media Page: 4 of 9
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The periodic nature of QR in the equilibrium case (Fig. 3a) is related to the spatial discretization of the domain. As
the temperature front propagates through the system, individual grid blocks begin to warm sequentially.
Dissociation in a given grid block begins when T increases above Te at the prevailing pressure P. QR initially
increases with time as the grid block warms, and continues increasing until hydrate dissociation has reduced Sh to a
point at which an increasing fraction of the incoming heat is expended in increasing the temperature of the porous
medium rather than fueling dissociation. QR begins to decrease past that point. Dissociation does not progress
significantly into the next grid block because of the steepness of the dissociation front (see Fig. 2). Thus, the hydrate
dissociation pattern exhibits the periodic pattern observed in Fig. 3a and b, coinciding with the time for dissociation
of individual grid blocks in the ID radial system.
Note that QR becomes negative at some times (Fig. 3a). This phenomenon results from the fact that the pressure
increase caused by dissociation in a grid block causes gas to migrate into the adjacent grid block beyond the
dissociation front, where the temperature is still relatively low, causing hydrate formation due to the increased
pressure. This explains why Sh increases to nearly 0.8 near the dissociation front in Fig. 2b. The rate at which CH4
is produced at the well (QP) is expected to be lower than QR since what is released to the formation does not reach
the production well instantaneously, if at all. Fig. 3b shows that for both the kinetic and equilibrium cases, the
production rates are very similar.
Similarly, the total volumes released from the formation and produced at the well (VR and VP, respectively) are
found to be nearly identical for the kinetic and equilibrium models (Fig. 3c). Similar to the discussion above, VP
comprises the volume of gas that reached the well by a given time, and is therefore less than what is released to the
entire system by that time.
2.3. Sensitivity to initial hydrate saturation, spatial discretization and reaction area
In addition to the reference case with Sh = 0.5, we considered two additional values in order to determine the effect
of hydrate saturation on the system response using the equilibrium and kinetic models. The VR and VP predictions
made using the equilibrium and the kinetic models follow the same pattern as those discussed above for the reference
case (Fig. 4). The predictions made when employing the equilibrium model are practically identical to those from
the kinetic model for Sh = 0.75, while the two predictions exhibit only very minor differences for an initial Sh =
In order to examine the sensitivity of the results to spatial discretization, we performed a simulation with coarser
near-well discretization (0.10 m). In this case the QR and QP rates and the VR and VP volumes are similar for both
dissociation models (Fig. 3d-f). Compared to the simulation performed using finer discretization, the periodicity of
QR approximately doubled (mirroring the increase in Dr) because of the longer time needed for the dissociation front
to propagate through the length of individual grid blocks. However, the total volumes released to the system and
produced at the well are similar to the finer discretization case.
Since the area available for heat transfer in the hydration reaction could conceivably cause differences between
predictions made using the kinetic and equilibrium reaction models, we conducted a series of simulations with
decreasing values of the area adjustment factor FA (varying from the reference value of 1-0.001) to investigate the
issue. The results in Fig. 5a indicate that a kinetic model with decreasing FA results in correspondingly lower
production rates QP than those predicted in the equilibrium case. However, the QP predictions differ substantially
only at very early times, and appear to converge for times greater than 1 day. Thus, with the exception of at early
times or for very short study periods (e.g., which might apply to laboratory studies), QP appears to be independent
of FA (Fig. 5a) in this scenario of thermally induced dissociation. Note that the early QP differences observed for
different FA values appear inconsequential in the prediction of the overall production volume VP in Fig. 5b, which
shows almost complete insensitivity to FA. This is because the early QP differences persist for a very short time and
involve very small volumes.
Predictions of thermally induced gas dissociation and production are practically indistinguishable when using either
the kinetic or the equilibrium model (including for varied levels of initial hydrate saturation, near-well discretization,
and reaction area in the kinetic model), implying that there is no kinetic limitation to gas production from HBL by
means of thermal stimulation.
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Kowalsky, Michael B. & Moridis, George J. Comparison of kinetic and equilibrium reaction models insimulating the behavior of porous media, article, November 29, 2006; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc902720/m1/4/: accessed October 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.